Composite ML-DSA for use in X.509 Public Key Infrastructure
draft-ietf-lamps-pq-composite-sigs-05
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draft-ietf-lamps-pq-composite-sigs-05
LAMPS M. Ounsworth
Internet-Draft J. Gray
Intended status: Standards Track Entrust
Expires: 18 December 2025 M. Pala
OpenCA Labs
J. Klaussner
Bundesdruckerei GmbH
S. Fluhrer
Cisco Systems
16 June 2025
Composite ML-DSA for use in X.509 Public Key Infrastructure
draft-ietf-lamps-pq-composite-sigs-05
Abstract
This document defines combinations of ML-DSA [FIPS.204] in hybrid
with traditional algorithms RSASSA-PKCS1-v1_5, RSASSA-PSS, ECDSA,
Ed25519, and Ed448. These combinations are tailored to meet security
best practices and regulatory guidelines. Composite ML-DSA is
applicable in any application that uses X.509 or PKIX data structures
that accept ML-DSA, but where the operator wants extra protection
against breaks or catastrophic bugs in ML-DSA.
About This Document
This note is to be removed before publishing as an RFC.
The latest revision of this draft can be found at https://lamps-
wg.github.io/draft-composite-sigs/draft-ietf-lamps-pq-composite-
sigs.html. Status information for this document may be found at
https://datatracker.ietf.org/doc/draft-ietf-lamps-pq-composite-sigs/.
Discussion of this document takes place on the LAMPS Working Group
mailing list (mailto:spams@ietf.org), which is archived at
https://datatracker.ietf.org/wg/lamps/about/. Subscribe at
https://www.ietf.org/mailman/listinfo/spams/.
Source for this draft and an issue tracker can be found at
https://github.com/lamps-wg/draft-composite-sigs.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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document authors. All rights reserved.
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Table of Contents
1. Changes in -05 . . . . . . . . . . . . . . . . . . . . . . . 3
2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1. Conventions and Terminology . . . . . . . . . . . . . . . 5
2.2. Composite Design Philosophy . . . . . . . . . . . . . . . 7
3. Overview of the Composite ML-DSA Signature Scheme . . . . . . 7
3.1. Pre-hashing and Randomizer . . . . . . . . . . . . . . . 9
3.2. Prefix, Domain Separators and CTX . . . . . . . . . . . . 9
4. Composite ML-DSA Functions . . . . . . . . . . . . . . . . . 10
4.1. Key Generation . . . . . . . . . . . . . . . . . . . . . 10
4.2. Sign . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.3. Verify . . . . . . . . . . . . . . . . . . . . . . . . . 14
5. Serialization . . . . . . . . . . . . . . . . . . . . . . . . 16
5.1. SerializePublicKey and DeserializePublicKey . . . . . . . 18
5.2. SerializePrivateKey and DeserializePrivateKey . . . . . . 20
5.3. SerializeSignatureValue and DeserializeSignatureValue . . 21
6. Use within X.509 and PKIX . . . . . . . . . . . . . . . . . . 23
6.1. Encoding to DER . . . . . . . . . . . . . . . . . . . . . 24
6.2. Key Usage Bits . . . . . . . . . . . . . . . . . . . . . 24
6.3. ASN.1 Definitions . . . . . . . . . . . . . . . . . . . . 25
7. Algorithm Identifiers . . . . . . . . . . . . . . . . . . . . 27
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7.1. Domain Separator Values . . . . . . . . . . . . . . . . . 29
7.2. Rationale for choices . . . . . . . . . . . . . . . . . . 31
7.3. RSASSA-PSS Parameters . . . . . . . . . . . . . . . . . . 31
8. ASN.1 Module . . . . . . . . . . . . . . . . . . . . . . . . 32
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 39
9.1. Object Identifier Allocations . . . . . . . . . . . . . . 39
9.1.1. Module Registration . . . . . . . . . . . . . . . . . 39
9.1.2. Object Identifier Registrations . . . . . . . . . . . 39
10. Security Considerations . . . . . . . . . . . . . . . . . . . 43
10.1. Why Hybrids? . . . . . . . . . . . . . . . . . . . . . . 43
10.2. Non-separability, EUF-CMA and SUF . . . . . . . . . . . 43
10.2.1. Implications of multiple encodings . . . . . . . . . 45
10.3. Key Reuse . . . . . . . . . . . . . . . . . . . . . . . 45
10.4. Use of Prefix for attack mitigation . . . . . . . . . . 47
10.5. Implications of pre-hash randomizer . . . . . . . . . . 47
10.6. Policy for Deprecated and Acceptable Algorithms . . . . 49
11. Implementation Considerations . . . . . . . . . . . . . . . . 49
11.1. FIPS certification . . . . . . . . . . . . . . . . . . . 49
11.2. Backwards Compatibility . . . . . . . . . . . . . . . . 50
11.3. Profiling down the number of options . . . . . . . . . . 51
11.4. External Pre-hashing . . . . . . . . . . . . . . . . . . 52
11.4.1. Serialization and Deserialization of the
PreHashToken . . . . . . . . . . . . . . . . . . . . 53
12. References . . . . . . . . . . . . . . . . . . . . . . . . . 55
12.1. Normative References . . . . . . . . . . . . . . . . . . 55
12.2. Informative References . . . . . . . . . . . . . . . . . 58
Appendix A. Approximate Key and Signature Sizes . . . . . . . . 60
Appendix B. Component Algorithm Reference . . . . . . . . . . . 62
Appendix C. Component AlgorithmIdentifiers for Public Keys and
Signatures . . . . . . . . . . . . . . . . . . . . . . . 63
Appendix D. Message Representative Examples . . . . . . . . . . 71
Appendix E. Test Vectors . . . . . . . . . . . . . . . . . . . . 74
Appendix F. Intellectual Property Considerations . . . . . . . . 199
Appendix G. Contributors and Acknowledgements . . . . . . . . . 199
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 200
1. Changes in -05
Interop-affecting changes:
* MAJOR CHANGE: Authors decided to remove all "pure" composites and
leave only the pre-hashed variants (which were renamed to simply
be "Composite" instead of "HashComposite"). The core construction
of M' was not modified, simply re-named. This results in a ~50%
reduction in the length of the draft since we removed ~50% of the
content. This is the result of long design discussions, some of
which is captured in https://github.com/lamps-wg/draft-composite-
sigs/issues/131
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* The construction has been enhanced by adding a pre-hash randomizer
PH( r || M ) to help mitigate the generation of message pairs M1,
M2 such that PH(M1) = PH(M2) before committing to the signature,
as well as to prevent mixed-key forgeries. This construction is
taken directly from [BonehShoup] section 13.2.1.
* Adjusted the choice of pre-hash function for Ed448 to SHAKE256/64
to match the hash functions used in ED448ph in RFC8032.
* ML-DSA secret keys are now only seeds.
* Since all ML-DSA keys and signatures are now fixed-length, dropped
the length-tagged encoding.
* Added id-MLDSA87-RSA3072-PSS-SHA512 as a more performant
alternative to id-MLDSA87-RSA4096-PSS-SHA512.
* Added new prototype OIDs to avoid interoperability issues with
previous versions
* Added complete test vectors.
* Removed the "Use in CMS" section so that we can get this document
across the finish line, and defer CMS-related debates to a
separate document.
Editorial changes:
* Since the serialization is now non-DER, drastically reduced the
ASN.1-based text.
Still to do in a future version:
* Nothing. Authors believe this version to be complete.
2. Introduction
The advent of quantum computing poses a significant threat to current
cryptographic systems. Traditional cryptographic signature
algorithms such as RSA, DSA and its elliptic curve variants are
vulnerable to quantum attacks. During the transition to post-quantum
cryptography (PQC), there is considerable uncertainty regarding the
robustness of both existing and new cryptographic algorithms. While
we can no longer fully trust traditional cryptography, we also cannot
immediately place complete trust in post-quantum replacements until
they have undergone extensive scrutiny and real-world testing to
uncover and rectify both algorithmic weaknesses as well as
implementation flaws across all the new implementations.
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Unlike previous migrations between cryptographic algorithms, the
decision of when to migrate and which algorithms to adopt is far from
straightforward. For instance, the aggressive migration timelines
may require deploying PQC algorithms before their implementations
have been fully hardened or certified, and dual-algorithm data
protection may be desirable over a longer time period to hedge
against CVEs and other implementation flaws in the new
implementations.
Cautious implementers may opt to combine cryptographic algorithms in
such a way that an attacker would need to break all of them
simultaneously to compromise the protected data. These mechanisms
are referred to as Post-Quantum/Traditional (PQ/T) Hybrids
[I-D.ietf-pquip-pqt-hybrid-terminology].
Certain jurisdictions are already recommending or mandating that PQC
lattice schemes be used exclusively within a PQ/T hybrid framework.
The use of a composite scheme provides a straightforward
implementation of hybrid solutions compatible with (and advocated by)
some governments and cybersecurity agencies [BSI2021], [ANSSI2024].
This specification defines a specific instantiation of the PQ/T
Hybrid paradigm called "composite" where multiple cryptographic
algorithms are combined to form a single signature algorithm
presenting a single public key and signature value such that it can
be treated as a single atomic algorithm at the protocol level; a
property referred to as "protocol backwards compatibility" since it
can be applied to protocols that are not explicitly hybrid-aware.
Composite algorithms address algorithm strength uncertainty because
the composite algorithm remains strong so long as one of its
components remains strong. Concrete instantiations of composite ML-
DSA algorithms are provided based on ML-DSA, RSASSA-PKCS1-v1_5,
RSASSA-PSS, ECDSA, Ed25519, and Ed448. Backwards compatibility in
the sense of upgraded systems continuing to inter-operate with legacy
systems is not directly covered in this specification, but is the
subject of Section 11.2.
Composite ML-DSA is applicable in any PKIX-related application that
would otherwise use ML-DSA.
2.1. Conventions and Terminology
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in
BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here. These words may also appear in this
document in lower case as plain English words, absent their normative
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meanings.
This specification is consistent with the terminology defined in
[I-D.ietf-pquip-pqt-hybrid-terminology]. In addition, the following
terminology is used throughout this specification:
*ALGORITHM*: The usage of the term "algorithm" within this
specification generally refers to any function which has a registered
Object Identifier (OID) for use within an ASN.1 AlgorithmIdentifier.
This loosely, but not precisely, aligns with the definitions of
"cryptographic algorithm" and "cryptographic scheme" given in
[I-D.ietf-pquip-pqt-hybrid-terminology].
*COMPONENT / PRIMITIVE*: The words "component" or "primitive" are
used interchangeably to refer to a cryptographic algorithm that is
used internally within a composite algorithm. For example this could
be an asymmetric algorithm such as "ML-DSA-65" or "RSASSA-PSS", or a
Hash such as "SHA256".
*DER*: Distinguished Encoding Rules as defined in [X.690].
*PKI*: Public Key Infrastructure, as defined in [RFC5280].
*SIGNATURE*: A digital cryptographic signature, making no assumptions
about which algorithm.
Notation: The algorithm descriptions use python-like syntax. The
following symbols deserve special mention:
* || represents concatenation of two byte arrays.
* [:] represents byte array slicing.
* (a, b) represents a pair of values a and b. Typically this
indicates that a function returns multiple values; the exact
conveyance mechanism -- tuple, struct, output parameters, etc --
is left to the implementer.
* (a, _): represents a pair of values where one -- the second one in
this case -- is ignored.
* Func<TYPE>(): represents a function that is parametrized by <TYPE>
meaning that the function's implementation will have minor
differences depending on the underlying TYPE. Typically this
means that a function will need to look up different constants or
use different underlying cryptographic primitives depending on
which composite algorithm it is implementing.
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2.2. Composite Design Philosophy
[I-D.ietf-pquip-pqt-hybrid-terminology] defines composites as:
_Composite Cryptographic Element_: A cryptographic element that
incorporates multiple component cryptographic elements of the same
type in a multi-algorithm scheme.
Composite algorithms, as defined in this specification, follow this
definition and should be regarded as a single key that performs a
single cryptographic operation typical of a digital signature
algorithm, such as key generation, signing, or verifying -- using its
internal sequence of component keys as if they form a single key.
This generally means that the complexity of combining algorithms can
and should be handled by the cryptographic library or cryptographic
module, and the single composite public key, private key, and
signature value can be carried in existing fields in protocols such
as PKCS#10 [RFC2986], CMP [RFC4210], X.509 [RFC5280], the CMS
[RFC5652], and the Trust Anchor Format [RFC5914]. In this way,
composites achieve "protocol backwards-compatibility" in that they
will drop cleanly into any protocol that accepts an analogous single-
algorithm cryptographic scheme without requiring any modification of
the protocol to handle multiple algorithms.
Discussion of the specific choices of algorithm pairings can be found
in Section 7.2.
3. Overview of the Composite ML-DSA Signature Scheme
Composite ML-DSA is a Post-Quantum / Traditional hybrid signature
scheme which combines ML-DSA as specified in [FIPS.204] and
[I-D.ietf-lamps-dilithium-certificates] with one of RSASSA-PKCS1-v1_5
or RSASSA-PSS algorithms defined in [RFC8017], the Elliptic Curve
Digital Signature Algorithm ECDSA scheme defined in section 6 of
[FIPS.186-5], or Ed25519 / Ed448 defined in [RFC8410]. The two
component signatures are combined into a composite algorithm via a
"signature combiner" function which performs randomized pre-hashing
and prepends several domain separator values to the message prior to
passing it to the component algorithms. Composite ML-DSA achieves
weak non-separability as well as several other security properties
which are described in the Security Considerations in Section 10.
Composite signature schemes are defined as cryptographic primitives
that consist of three algorithms:
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* KeyGen() -> (pk, sk): A probabilistic key generation algorithm
which generates a public key pk and a secret key sk. Some
cryptographic modules may also expose a KeyGen(seed) -> (pk, sk),
which generates pk and sk deterministically from a seed. This
specification assumes a seed-based keygen for ML-DSA.
* Sign(sk, M) -> s: A signing algorithm which takes as input a
secret key sk and a message M, and outputs a signature s. Signing
routines may take additional parameters such as a context string
or a hash function to use for pre-hashing the message.
* Verify(pk, M, s) -> true or false: A verification algorithm which
takes as input a public key pk, a message M and a signature s, and
outputs true if the signature verifies correctly and false or an
error otherwise. Verification routines may take additional
parameters such as a context string or a hash function to use for
pre-hashing the message.
The following algorithms are defined for serializing and
deserializing component values. These algorithms are inspired by
similar algorithms in [RFC9180].
* SerializePublicKey(mlkdsaPK, tradPK) -> bytes: Produce a byte
string encoding of the component public keys.
* DeserializePublicKey(bytes) -> (mldsaPK, tradPK): Parse a byte
string to recover the component public keys.
* SerializePrivateKey(mldsaSeed, tradSK) -> bytes: Produce a byte
string encoding of the component private keys. Note that the
keygen seed is used as the interoperable private key format for
ML-DSA.
* DeserializePrivateKey(bytes) -> (mlkemSeed, tradSK): Parse a byte
string to recover the component private keys.
* SerializeSignatureValue(r, mldsaSig, tradSig) -> bytes: Produce a
byte string encoding of the component signature values. The
randomizer r is explained in Section 3.1.
* DeserializeSignatureValue(bytes) -> (r, mldsaSig, tradSig): Parse
a byte string to recover the randomizer and the component
signature values.
Full definitions of serialization and deserialization algorithms can
be found in Section 5.
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3.1. Pre-hashing and Randomizer
In [FIPS.204] NIST defines separate algorithms for pure and pre-
hashed modes of ML-DSA, referred to as "ML-DSA" and "HashML-DSA"
respectively. This specification defines a single mode which is
similar in construction to HashML-DSA with the addition of a pre-hash
randomizer inspired by [BonehShoup]. See Section 10.5 for detailed
discussion of the security properties of the randomized pre-hash.
This design provides a compromised balance between performance and
security. Since pre-hashing is done at the composite level, "pure"
ML-DSA is used as the underlying ML-DSA primitive.
The primary design motivation behind pre-hashing is to perform only a
single pass over the potentially large input message M, compared to
passing the full message to both component primitives, and to allow
for optimizations in cases such as signing the same message digest
with multiple different keys. The actual length of the to-be-signed
message M' depends on the application context ctx provided at runtime
but since ctx has a maximum length of 255 bytes, M' has a fixed
maximum length which depends on the output size of the hash function
chosen as PH, but can be computed per composite algorithm.
This simplification into a single strongly-pre-hashed algorithm
avoids the need for duplicate sets of "Composite-ML-DSA" and "Hash-
Composite-ML-DSA" algorithms.
See Section 10.5 for a discussion of security implications of the
randomized pre-hash.
See Section 11.4 for a discussion of externalizing the pre-hashing
step.
3.2. Prefix, Domain Separators and CTX
When constructing the to-be-signed message representative M', several
domain separator values are pre-pended to the message pre-hash prior
to signing.
First a fixed prefix string is pre-pended which is the byte encoding
of the ASCII string "CompositeAlgorithmSignatures2025" which in hex
is:
436F6D706F73697465416C676F726974686D5369676E61747572657332303235
Additional discussion of the prefix can be found in Section 10.4.
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Next, the Domain separator defined in Section 7.1 which is the DER
encoding of the OID of the specific composite algorithm is
concatenated with the length of the context in bytes, the context,
the randomizer r, an additional DER encoded value that represents the
OID of the hash function PH, and finally the hash of the message to
be signed. The Domain separator serves to bind the signature to the
specific composite algorithm used. The context string allows for
applications to bind the signature to some application context. The
randomizer is described in detail in Section 3.1. And finally the
OID of the hash function PH protects against substituting for a
weaker hash function, although in practice each composite algorithm
specifies only one allowed hash function.
Note that there are two different context strings ctx at play: the
first is the application context that is passed in to Composite-ML-
DSA.Sign and bound to the to-be-signed message M'. The second is the
ctx that is passed down into the underlying ML-DSA.Sign and here
Composite ML-DSA itself is the application that we wish to bind and
so the DER-encoded OID of the composite algorithm, called Domain, is
used as the ctx for the underlying ML-DSA primitive.
4. Composite ML-DSA Functions
This section describes the composite ML-DSA functions needed to
instantiate the public API of a digital signature scheme as defined
in Section 3.
4.1. Key Generation
In order to maintain security properties of the composite,
applications that use composite keys MUST always perform fresh key
generations of both component keys and MUST NOT reuse existing key
material. See Section 10.3 for a discussion.
To generate a new key pair for composite schemes, the KeyGen() ->
(pk, sk) function is used. The KeyGen() function calls the two key
generation functions of the component algorithms independently.
Multi-process or multi-threaded applications might choose to execute
the key generation functions in parallel for better key generation
performance.
The following describes how to instantiate a KeyGen() function for a
given composite algorithm represented by <OID>.
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Composite-ML-DSA<OID>.KeyGen() -> (pk, sk)
Explicit inputs:
None
Implicit inputs mapped from <OID>:
ML-DSA The underlying ML-DSA algorithm and
parameter set, for example, could be "ML-DSA-65".
Trad The underlying traditional algorithm and
parameter set, for example "RSASSA-PSS"
or "Ed25519".
Output:
(pk, sk) The composite key pair.
Key Generation Process:
1. Generate component keys
mldsaSeed = Random(32)
(mldsaPK, _) = ML-DSA.KeyGen(mldsaSeed)
(tradPK, tradSK) = Trad.KeyGen()
2. Check for component key gen failure
if NOT (mldsaPK, mldsaSK) or NOT (tradPK, tradSK):
output "Key generation error"
3. Output the composite public and private keys
pk = SerializePublicKey(mldsaPK, tradPK)
sk = SerializePrivateKey(mldsaSeed, tradSK)
return (pk, sk)
Figure 1: Composite-ML-DSA<OID>.KeyGen() -> (pk, sk)
In order to ensure fresh keys, the key generation functions MUST be
executed for both component algorithms. Compliant parties MUST NOT
use, import or export component keys that are used in other contexts,
combinations, or by themselves as keys for standalone algorithm use.
For more details on the security considerations around key reuse, see
section Section 10.3.
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Note that in step 2 above, both component key generation processes
are invoked, and no indication is given about which one failed. This
SHOULD be done in a timing-invariant way to prevent side-channel
attackers from learning which component algorithm failed.
Variations in the keygen process above and signature processes below
to accommodate particular private key storage mechanisms or alternate
interfaces to the underlying cryptographic modules are considered to
be conformant to this specification so long as they produce the same
output and error handling. For example, component private keys
stored in separate software or hardware modules where it is not
possible to do a joint simultaneous keygen would be considered
compliant so long as both keys are freshly generated. It is also
possible that the underlying cryptographic module does not expose a
ML-DSA.KeyGen(seed) that accepts an externally-generated seed, and
instead an alternate keygen interface must be used. Note however
that cryptographic modules that do not support seed-based ML-DSA key
generation will be incapable of importing or exporting composite keys
in the standard format since the private key serialization routines
defined in Section 5.2 only support ML-DSA keys as seeds.
4.2. Sign
The Sign() algorithm of Composite ML-DSA mirrors the construction of
ML-DSA.Sign(sk, M, ctx) defined in Algorithm 3 Section 5.2 of
[FIPS.204]. Composite ML-DSA exposes an API similar to that of ML-
DSA, despite the fact that it includes pre-hashing in a similar way
to HashML-DSA. Internally it uses pure ML-DSA as the component
algorithm since there is no advantage to pre-hashing twice.
See Section 3.1 for a discussion of the pre-hashed design and
randomizer r.
See Section 3.2 for a discussion on the domain separator and context
values.
See Section 11.4 for a discussion of externalizing the pre-hashing
step.
The following describes how to instantiate a Sign() function for a
given Composite ML-DSA algorithm represented by <OID>.
Composite-ML-DSA<OID>.Sign(sk, M, ctx) -> s
Explicit inputs:
sk Composite private key consisting of signing private keys for
each component.
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M The message to be signed, an octet string.
ctx The application context string used in the composite
signature combiner, which defaults to the empty string.
Implicit inputs mapped from <OID>:
ML-DSA The underlying ML-DSA algorithm and
parameter set, for example, could be "ML-DSA-65".
Trad The underlying traditional algorithm and
parameter set, for example "RSASSA-PSS with id-sha256"
or "Ed25519".
Prefix The prefix String which is the byte encoding of the String
"CompositeAlgorithmSignatures2025" which in hex is
436F6D706F73697465416C676F726974686D5369676E61747572657332303235
Domain Domain separator value for binding the signature to the
Composite ML-DSA OID. Additionally, the composite Domain
is passed into the underlying ML-DSA primitive as the ctx.
Domain values are defined in the "Domain Separator Values"
section below.
PH The hash function to use for pre-hashing.
Output:
s The composite signature value.
Signature Generation Process:
1. If len(ctx) > 255:
return error
2. Compute the Message representative M'.
As in FIPS 204, len(ctx) is encoded as a single unsigned byte.
Randomize the pre-hash.
r = Random(32)
M' := Prefix || Domain || len(ctx) || ctx || r
|| PH( r || M )
3. Separate the private key into component keys
and re-generate the ML-DSA key from seed.
(mldsaSeed, tradSK) = DeserializePrivateKey(sk)
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(_, mldsaSK) = ML-DSA.KeyGen(mldsaSeed)
4. Generate the two component signatures independently by calculating
the signature over M' according to their algorithm specifications.
mldsaSig = ML-DSA.Sign( mldsaSK, M', ctx=Domain )
tradSig = Trad.Sign( tradSK, M' )
5. If either ML-DSA.Sign() or Trad.Sign() return an error, then this
process MUST return an error.
if NOT mldsaSig or NOT tradSig:
output "Signature generation error"
6. Output the encoded composite signature value.
s = SerializeSignatureValue(r, mldsaSig, tradSig)
return s
Figure 2: Composite-ML-DSA<OID>.Sign(sk, M, ctx) -> s
Note that in step 4 above, both component signature processes are
invoked, and no indication is given about which one failed. This
SHOULD be done in a timing-invariant way to prevent side-channel
attackers from learning which component algorithm failed.
It is possible to use component private keys stored in separate
software or hardware keystores. Variations in the process to
accommodate particular private key storage mechanisms are considered
to be conformant to this specification so long as it produces the
same output and error handling as the process sketched above.
4.3. Verify
The Verify() algorithm of Composite ML-DSA mirrors the construction
of ML-DSA.Verify(pk, M, s, ctx) defined in Algorithm 3 Section 5.3 of
[FIPS.204]. Composite ML-DSA exposes an API similar to that of ML-
DSA, despite the fact that it includes pre-hashing in a similar way
to HashML-DSA. Internally it uses pure ML-DSA as the component
algorithm since there is no advantage to pre-hashing twice.
Compliant applications MUST output "Valid signature" (true) if and
only if all component signatures were successfully validated, and
"Invalid signature" (false) otherwise.
The following describes how to instantiate a Verify() function for a
given composite algorithm represented by <OID>.
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Composite-ML-DSA<OID>.Verify(pk, M, s, ctx) -> true or false
Explicit inputs:
pk Composite public key consisting of verification public
keys for each component.
M Message whose signature is to be verified, an octet
string.
s A composite signature value to be verified.
ctx The application context string used in the composite
signature combiner, which defaults to the empty string.
Implicit inputs mapped from <OID>:
ML-DSA The underlying ML-DSA algorithm and
parameter set, for example, could be "ML-DSA-65".
Trad The underlying traditional algorithm and
parameter set, for example "RSASSA-PSS with id-sha256"
or "Ed25519".
Prefix The prefix String which is the byte encoding of the String
"CompositeAlgorithmSignatures2025" which in hex is
436F6D706F73697465416C676F726974686D5369676E61747572657332303235
Domain Domain separator value for binding the signature to the
Composite ML-DSA OID. Additionally, the composite Domain
is passed into the underlying ML-DSA primitive as the ctx.
Domain values are defined in the "Domain Separators"
section below.
PH The Message Digest Algorithm for pre-hashing. See
section on pre-hashing the message below.
Output:
Validity (bool) "Valid signature" (true) if the composite
signature is valid, "Invalid signature"
(false) otherwise.
Signature Verification Process:
1. If len(ctx) > 255
return error
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2. Separate the keys and signatures
(mldsaPK, tradPK) = DeserializePublicKey(pk)
(r, mldsaSig, tradSig) = DeserializeSignatureValue(s)
If Error during deserialization, or if any of the component
keys or signature values are not of the correct type or
length for the given component algorithm then output
"Invalid signature" and stop.
3. Compute a Hash of the Message.
As in FIPS 204, len(ctx) is encoded as a single unsigned byte.
M' = Prefix || Domain || len(ctx) || ctx || r
|| PH( r || M )
4. Check each component signature individually, according to its
algorithm specification.
If any fail, then the entire signature validation fails.
if not ML-DSA.Verify( mldsaPK, M', mldsaSig, ctx=Domain ) then
output "Invalid signature"
if not Trad.Verify( tradPK, M', tradSig ) then
output "Invalid signature"
if all succeeded, then
output "Valid signature"
Figure 3: Composite-ML-DSA<OID>.Verify(pk, M, signature, ctx)
Note that in step 4 above, the function fails early if the first
component fails to verify. Since no private keys are involved in a
signature verification, there are no timing attacks to consider, so
this is ok.
5. Serialization
This section presents routines for serializing and deserializing
composite public keys, private keys, and signature values to bytes
via simple concatenation of the underlying encodings of the component
algorithms. The functions defined in this section are considered
internal implementation detail and are referenced from within the
public API definitions in Section 4.
Deserialization is possible because ML-DSA has fixed-length public
keys, private keys (seeds), and signature values as shown in the
following table.
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+===========+============+=============+===========+
| Algorithm | Public key | Private key | Signature |
+===========+============+=============+===========+
| ML-DSA-44 | 1312 | 32 | 2420 |
+-----------+------------+-------------+-----------+
| ML-DSA-65 | 1952 | 32 | 3309 |
+-----------+------------+-------------+-----------+
| ML-DSA-87 | 2592 | 32 | 4627 |
+-----------+------------+-------------+-----------+
Table 1: ML-DSA Key and Signature Sizes in bytes
For all serialization routines below, when these values are required
to be carried in an ASN.1 structure, they are wrapped as described in
Section 6.1.
While ML-DSA has a single fixed-size representation for each of
public key, private key (seed), and signature, the traditional
component might allow multiple valid encodings; for example an
elliptic curve public key might be validly encoded as either
compressed or uncompressed [SEC1], or an RSA private key could be
encoded in Chinese Remainder Theorem form [RFC8017]. In order to
obtain interoperability, composite algorithms MUST use the following
encodings of the underlying components:
* *ML-DSA*: MUST be encoded as specified in [FIPS.204], using a
32-byte seed as the private key.
* *RSA*: MUST be encoded with the (n,e) public key representation as
specified in A.1.1 of [RFC8017] and the private key representation
as specified in A.1.2 of [RFC8017].
* *ECDSA*: public key MUST be encoded as an ECPoint as specified in
section 2.2 of [RFC5480], with both compressed and uncompressed
keys supported. For maximum interoperability, it is RECOMMENEDED
to use uncompressed points.
* *EdDSA*: MUST be encoded as per section 3 of [RFC8032].
Even with fixed encodings for the traditional component, there may be
slight differences in size of the encoded value due to, for example,
encoding rules that drop leading zeroes. See Appendix A for further
discussion of encoded size of each composite algorithm.
The deserialization routines described below do not check for well-
formedness of the cryptographic material they are recovering. It is
assumed that underlying cryptographic primitives will catch malformed
values and raise an appropriate error.
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5.1. SerializePublicKey and DeserializePublicKey
The serialization routine for keys simply concatenates the public
keys of the component signature algorithms, as defined below:
Composite-ML-DSA.SerializePublicKey(mldsaPK, tradPK) -> bytes
Explicit inputs:
mldsaPK The ML-DSA public key, which is bytes.
tradPK The traditional public key in the appropriate
encoding for the underlying component algorithm.
Implicit inputs:
None
Output:
bytes The encoded composite public key.
Serialization Process:
1. Combine and output the encoded public key
output mldsaPK || tradPK
Figure 4: Composite-ML-DSA.SerializePublicKey(mldsaPK, tradPK) ->
bytes
Deserialization reverses this process. Each component key is
deserialized according to their respective specification as shown in
Appendix B.
The following describes how to instantiate a
DeserializePublicKey(bytes) function for a given composite algorithm
represented by <OID>.
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Composite-ML-DSA<OID>.DeserializePublicKey(bytes) -> (mldsaPK, tradPK)
Explicit inputs:
bytes An encoded composite public key.
Implicit inputs mapped from <OID>:
ML-DSA The underlying ML-DSA algorithm and
parameter set to use, for example, could be "ML-DSA-65".
Output:
mldsaPK The ML-DSA public key, which is bytes.
tradPK The traditional public key in the appropriate
encoding for the underlying component algorithm.
Deserialization Process:
1. Parse each constituent encoded public key.
The length of the mldsaKey is known based on the size of
the ML-DSA component key length specified by the Object ID.
switch ML-DSA do
case ML-DSA-44:
mldsaPK = bytes[:1312]
tradPK = bytes[1312:]
case ML-DSA-65:
mldsaPK = bytes[:1952]
tradPK = bytes[1952:]
case ML-DSA-87:
mldsaPK = bytes[:2592]
tradPK = bytes[2592:]
Note that while ML-DSA has fixed-length keys, RSA and ECDSA
may not, depending on encoding, so rigorous length-checking
of the overall composite key is not always possible.
2. Output the component public keys
output (mldsaPK, tradPK)
Figure 5: Composite-ML-DSA<OID>.DeserializePublicKey(bytes) ->
(mldsaPK, tradPK)
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5.2. SerializePrivateKey and DeserializePrivateKey
The serialization routine for keys simply concatenates the private
keys of the component signature algorithms, as defined below:
Composite-ML-DSA.SerializePrivateKey(mldsaSeed, tradSK) -> bytes
Explicit inputs:
mldsaSeed The ML-DSA private key, which is the bytes of the seed.
tradSK The traditional private key in the appropriate
encoding for the underlying component algorithm.
Implicit inputs:
None
Output:
bytes The encoded composite private key.
Serialization Process:
1. Combine and output the encoded private key.
output mldsaSeed || tradSK
Figure 6: Composite-ML-DSA.SerializePrivateKey(mldsaSeed, tradSK)
-> bytes
Deserialization reverses this process. Each component key is
deserialized according to their respective specification as shown in
Appendix B.
The following describes how to instantiate a
DeserializePrivateKey(bytes) function. Since ML-DSA private keys are
32 bytes for all parameter sets, this function does not need to be
parametrized.
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Composite-ML-DSA.DeserializePrivateKey(bytes) -> (mldsaSeed, tradSK)
Explicit inputs:
bytes An encoded composite private key.
Implicit inputs:
That an ML-DSA private key is 32 bytes for all parameter sets.
Output:
mldsaSeed The ML-DSA private key, which is the bytes of the seed.
tradSK The traditional private key in the appropriate
encoding for the underlying component algorithm.
Deserialization Process:
1. Parse each constituent encoded key.
The length of an ML-DSA private key is always a 32 byte seed
for all parameter sets.
mldsaSeed = bytes[:32]
tradSK = bytes[32:]
Note that while ML-DSA has fixed-length keys, RSA and ECDSA
may not, depending on encoding, so rigorous length-checking
of the overall composite key is not always possible.
2. Output the component private keys
output (mldsaSeed, tradSK)
Figure 7: Composite-ML-DSA.DeserializePrivateKey(bytes) ->
(mldsaSeed, tradSK)
5.3. SerializeSignatureValue and DeserializeSignatureValue
The serialization routine for the composite signature value simply
concatenates the fixed-length ML-DSA signature value with the
signature value from the traditional algorithm, as defined below:
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Composite-ML-DSA.SerializeSignatureValue(r, mldsaSig, tradSig) -> bytes
Explicit inputs:
r The 32 byte signature randomizer.
mldsaSig The ML-DSA signature value, which is bytes.
tradSig The traditional signature value in the appropriate
encoding for the underlying component algorithm.
Implicit inputs:
None
Output:
bytes The encoded composite signature value.
Serialization Process:
1. Combine and output the encoded composite signature
output r || mldsaSig || tradSig
Figure 8: Composite-ML-DSA.SerializeSignatureValue(r, mldsaSig,
tradSig) -> bytes
Deserialization reverses this process, raising an error in the event
that the input is malformed. Each component signature is
deserialized according to their respective specification as shown in
Appendix B.
The following describes how to instantiate a
DeserializeSignatureValue(bytes) function for a given composite
algorithm represented by <OID>.
Composite-ML-DSA<OID>.DeserializeSignatureValue(bytes)
-> (r, mldsaSig, tradSig)
Explicit inputs:
bytes An encoded composite signature value.
Implicit inputs mapped from <OID>:
ML-DSA The underlying ML-DSA algorithm and
parameter set to use, for example, could be "ML-DSA-65".
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Output:
r The 32 byte signature randomizer.
mldsaSig The ML-DSA signature value, which is bytes.
tradSig The traditional signature value in the appropriate
encoding for the underlying component algorithm.
Deserialization Process:
1. Parse the randomizer r.
r = bytes[:32]
sigs = bytes[32:] # truncate off the randomizer
2. Parse each constituent encoded signature.
The length of the mldsaSig is known based on the size of
the ML-DSA component signature length specified by the Object ID.
switch ML-DSA do
case ML-DSA-44:
mldsaSig = sigs[:2420]
tradSig = sigs[2420:]
case ML-DSA-65:
mldsaSig = sigs[:3309]
tradSig = sigs[3309:]
case ML-DSA-87:
mldsaSig = sigs[:4627]
tradSig = sigs[4627:]
Note that while ML-DSA has fixed-length signatures, RSA and ECDSA
may not, depending on encoding, so rigorous length-checking is
not always possible here.
3. Output the component signature values
output (r, mldsaSig, tradSig)
Figure 9: Composite-ML-DSA<OID>.DeserializeSignatureValue(bytes)
-> (r, mldsaSig, tradSig)
6. Use within X.509 and PKIX
The following sections provide processing logic and the ASN.1 modules
necessary to use composite ML-DSA within X.509 and PKIX protocols.
Use within the Cryptographic Message Syntax (CMS) will be covered in
a separate specification.
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While composite ML-DSA keys and signature values MAY be used raw, the
following sections provide conventions for using them within X.509
and other PKIX protocols such that Composite ML-DSA can be used as a
drop-in replacement for existing digital signature algorithms in
PKCS#10 [RFC2986], CMP [RFC4210], X.509 [RFC5280], and related
protocols.
6.1. Encoding to DER
The serialization routines presented in Section 5 produce raw binary
values. When these values are required to be carried within a DER-
endeded message format such as an X.509's subjectPublicKey and
signatureValue BIT STRING [RFC5280] or a CMS SignerInfo.signature
OCTET STRING [RFC5652], then the composite value MUST be wrapped into
a DER BIT STRING or OCTET STRING in the obvious ways.
When a BIT STRING is required, the octets of the composite data value
SHALL be used as the bits of the bit string, with the most
significant bit of the first octet becoming the first bit, and so on,
ending with the least significant bit of the last octet becoming the
last bit of the bit string.
When an OCTET STRING is required, the DER encoding of the composite
data value SHALL be used directly.
6.2. Key Usage Bits
When any Composite ML-DSA Object Identifier appears within the
SubjectPublicKeyInfo.AlgorithmIdentifier field of an X.509
certificate [RFC5280], the key usage certificate extension MUST only
contain signing-type key usages.
The normal keyUsage rules for signing-type keys from [RFC5280] apply,
and are reproduced here for completeness.
For Certification Authority (CA) certificates that carry a Composite
ML-DSA public key, any combination of the following values MAY be
present and any other values MUST NOT be present:
digitalSignature;
nonRepudiation;
keyCertSign; and
cRLSign.
For End Entity certificates, any combination of the following values
MAY be present and any other values MUST NOT be present:
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digitalSignature; and
nonRepudiation;
Composite ML-DSA keys MUST NOT be used in a "dual usage" mode because
even if the traditional component key supports both signing and
encryption, the post-quantum algorithms do not and therefore the
overall composite algorithm does not. Implementations MUST NOT use
one component of the composite for the purposes of digital signature
and the other component for the purposes of encryption or key
establishment.
6.3. ASN.1 Definitions
Composite ML-DSA uses a substantially non-ASN.1 based encoding, as
specified in Section 5. However, as composite algorithms will be
used within ASN.1-based X.509 and PKIX protocols, some conventions
for ASN.1 wrapping are necessary.
The following ASN.1 Information Object Classes are are defined to
allow for compact definitions of each composite algorithm, leading to
a smaller overall ASN.1 module.
pk-CompositeSignature {OBJECT IDENTIFIER:id, PublicKeyType}
PUBLIC-KEY ::= {
IDENTIFIER id
KEY BIT STRING
PARAMS ARE absent
CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign,
cRLSign}
}
sa-CompositeSignature{OBJECT IDENTIFIER:id,
PUBLIC-KEY:publicKeyType }
SIGNATURE-ALGORITHM ::= {
IDENTIFIER id
VALUE BIT STRING
PARAMS ARE absent
PUBLIC-KEYS {publicKeyType}
}
Figure 10: ASN.1 Object Information Classes for Composite ML-DSA
As an example, the public key and signature algorithm types
associated with id-MLDSA44-ECDSA-P256-SHA256 are defined as:
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pk-MLDSA44-ECDSA-P256-SHA256 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA44-ECDSA-P256-SHA256}
sa-MLDSA44-ECDSA-P256-SHA256 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA44-ECDSA-P256-SHA256,
pk-MLDSA44-ECDSA-P256-SHA256 }
The full set of key types defined by this specification can be found
in the ASN.1 Module in Section 8.
Use cases that require an interoperable encoding for composite
private keys will often need to place a composite private key inside
a OneAsymmetricKey structure defined in [RFC5958], such as when
private keys are carried in PKCS #12 [RFC7292], CMP [RFC4210] or CRMF
[RFC4211]. The definition of OneAsymmetricKey is copied here for
convenience:
OneAsymmetricKey ::= SEQUENCE {
version Version,
privateKeyAlgorithm PrivateKeyAlgorithmIdentifier,
privateKey PrivateKey,
attributes [0] Attributes OPTIONAL,
...,
[[2: publicKey [1] PublicKey OPTIONAL ]],
...
}
...
PrivateKey ::= OCTET STRING
-- Content varies based on type of key. The
-- algorithm identifier dictates the format of
-- the key.
Figure 11: OneAsymmetricKey as defined in [RFC5958]
When a composite private key is conveyed inside a OneAsymmetricKey
structure (version 1 of which is also known as PrivateKeyInfo)
[RFC5958], the privateKeyAlgorithm field SHALL be set to the
corresponding composite algorithm identifier defined according to
Section 7 and its parameters field MUST be absent. The privateKey
field SHALL contain the OCTET STRING representation of the serialized
composite private key as per Section 5.2. The publicKey field
remains OPTIONAL. If the publicKey field is present, it MUST be a
composite public key as per Section 5.1.
Some applications might need to reconstruct the SubjectPublicKeyInfo
or OneAsymmetricKey objects corresponding to each component key
individually, for example if this is required for invoking the
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underlying primitive. Section 7 provides the necessary mapping
between composite and their component algorithms for doing this
reconstruction.
Component keys of a composite MUST NOT be used in any other type of
key or as a standalone key. For more details on the security
considerations around key reuse, see section Section 10.3.
7. Algorithm Identifiers
This table summarizes the OID and the component algorithms for each
Composite ML-DSA algorithm.
EDNOTE: these are prototyping OIDs to be replaced by IANA.
<CompSig> is equal to 2.16.840.1.114027.80.8.1
+=============================+=============+====+=======================+============+
|Composite Signature Algorithm|OID |ML- |Trad |Pre-Hash |
| | |DSA | | |
+=============================+=============+====+=======================+============+
|id-MLDSA44-RSA2048-PSS-SHA256|<CompSig>.100|ML-D|RSASSA-PSS with SHA256 |SHA256 |
| | |SA-4| | |
| | |4 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id- |<CompSig>.101|ML-D|sha256WithRSAEncryption|SHA256 |
|MLDSA44-RSA2048-PKCS15-SHA256| |SA-4| | |
| | |4 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA44-Ed25519-SHA512 |<CompSig>.102|ML-D|Ed25519 |SHA512 |
| | |SA-4| | |
| | |4 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA44-ECDSA-P256-SHA256 |<CompSig>.103|ML-D|ecdsa-with-SHA256 with |SHA256 |
| | |SA-4|secp256r1 | |
| | |4 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA65-RSA3072-PSS-SHA512|<CompSig>.104|ML-D|RSASSA-PSS with SHA256 |SHA512 |
| | |SA-6| | |
| | |5 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id- |<CompSig>.105|ML-D|sha256WithRSAEncryption|SHA512 |
|MLDSA65-RSA3072-PKCS15-SHA512| |SA-6| | |
| | |5 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA65-RSA4096-PSS-SHA512|<CompSig>.106|ML-D|RSASSA-PSS with SHA384 |SHA512 |
| | |SA-6| | |
| | |5 | | |
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+-----------------------------+-------------+----+-----------------------+------------+
|id- |<CompSig>.107|ML-D|sha384WithRSAEncryption|SHA512 |
|MLDSA65-RSA4096-PKCS15-SHA512| |SA-6| | |
| | |5 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA65-ECDSA-P256-SHA512 |<CompSig>.108|ML-D|ecdsa-with-SHA256 with |SHA512 |
| | |SA-6|secp256r1 | |
| | |5 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA65-ECDSA-P384-SHA512 |<CompSig>.109|ML-D|ecdsa-with-SHA384 with |SHA512 |
| | |SA-6|secp384r1 | |
| | |5 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA65-ECDSA- |<CompSig>.110|ML-D|ecdsa-with-SHA256 with |SHA512 |
|brainpoolP256r1-SHA512 | |SA-6|brainpoolP256r1 | |
| | |5 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA65-Ed25519-SHA512 |<CompSig>.111|ML-D|Ed25519 |SHA512 |
| | |SA-6| | |
| | |5 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA87-ECDSA-P384-SHA512 |<CompSig>.112|ML-D|ecdsa-with-SHA384 with |SHA512 |
| | |SA-8|secp384r1 | |
| | |7 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA87-ECDSA- |<CompSig>.113|ML-D|ecdsa-with-SHA384 with |SHA512 |
|brainpoolP384r1-SHA512 | |SA-8|brainpoolP384r1 | |
| | |7 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA87-Ed448-SHAKE256 |<CompSig>.114|ML-D|Ed448 |SHAKE256/512|
| | |SA-8| | |
| | |7 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA87-RSA3072-PSS-SHA512|<CompSig>.117|ML-D|RSASSA-PSS with SHA384 |SHA512 |
| | |SA-8| | |
| | |7 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA87-RSA4096-PSS-SHA512|<CompSig>.115|ML-D|RSASSA-PSS with SHA384 |SHA512 |
| | |SA-8| | |
| | |7 | | |
+-----------------------------+-------------+----+-----------------------+------------+
|id-MLDSA87-ECDSA-P521-SHA512 |<CompSig>.116|ML-D|ecdsa-with-SHA512 with |SHA512 |
| | |SA-8|secp521r1 | |
| | |7 | | |
+-----------------------------+-------------+----+-----------------------+------------+
Table 2: ML-DSA Composite Signature Algorithms
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The pre-hash functions were chosen to roughly match the security
level of the stronger component. In the case of Ed25519 and Ed448
they match the hash function defined in [RFC8032]; SHA512 for
Ed25519ph and SHAKE256(x, 64), which is SHAKE256 producing 64 bytes
(512 bits) of output, for Ed448ph.
Full specifications for the referenced algorithms can be found in
Appendix B.
As the number of algorithms can be daunting to implementers, see
Section 11.3 for a discussion of choosing a subset to support.
7.1. Domain Separator Values
Each Composite ML-DSA algorithm has a unique domain separator value
which is used in constructing the message representative M' in the
Composite-ML-DSA.Sign() (Section 4.2) and Composite-ML-DSA.Verify()
(Section 4.3). This helps protect against component signature values
being removed from the composite and used out of context.
The domain separator is simply the DER encoding of the OID. The
following table shows the HEX-encoded domain separator value for each
Composite ML-DSA algorithm.
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+=======================================+==========================+
|Composite Signature Algorithm |Domain Separator (in Hex |
| |encoding) |
+=======================================+==========================+
|id-MLDSA44-RSA2048-PSS-SHA256 |060B6086480186FA6B50080164|
+---------------------------------------+--------------------------+
|id-MLDSA44-RSA2048-PKCS15-SHA256 |060B6086480186FA6B50080165|
+---------------------------------------+--------------------------+
|id-MLDSA44-Ed25519-SHA512 |060B6086480186FA6B50080166|
+---------------------------------------+--------------------------+
|id-MLDSA44-ECDSA-P256-SHA256 |060B6086480186FA6B50080167|
+---------------------------------------+--------------------------+
|id-MLDSA65-RSA3072-PSS-SHA512 |060B6086480186FA6B50080169|
+---------------------------------------+--------------------------+
|id-MLDSA65-RSA4096-PSS-SHA512 |060B6086480186FA6B5008016A|
+---------------------------------------+--------------------------+
|id-MLDSA65-RSA4096-PKCS15-SHA512 |060B6086480186FA6B5008016B|
+---------------------------------------+--------------------------+
|id-MLDSA65-ECDSA-P256-SHA512 |060B6086480186FA6B5008016C|
+---------------------------------------+--------------------------+
|id-MLDSA65-ECDSA-P384-SHA512 |060B6086480186FA6B5008016D|
+---------------------------------------+--------------------------+
|id-MLDSA65-ECDSA-brainpoolP256r1-SHA512|060B6086480186FA6B5008016E|
+---------------------------------------+--------------------------+
|id-MLDSA65-Ed25519-SHA512 |060B6086480186FA6B5008016F|
+---------------------------------------+--------------------------+
|id-MLDSA87-ECDSA-P384-SHA512 |060B6086480186FA6B50080170|
+---------------------------------------+--------------------------+
|id-MLDSA87-ECDSA-brainpoolP384r1-SHA512|060B6086480186FA6B50080171|
+---------------------------------------+--------------------------+
|id-MLDSA87-Ed448-SHAKE256 |060B6086480186FA6B50080172|
+---------------------------------------+--------------------------+
|id-MLDSA87-RSA3072-PSS-SHA512 |060B6086480186FA6B50080175|
+---------------------------------------+--------------------------+
|id-MLDSA87-RSA4096-PSS-SHA512 |060B6086480186FA6B50080173|
+---------------------------------------+--------------------------+
|id-MLDSA87-ECDSA-P521-SHA512 |060B6086480186FA6B50080174|
+---------------------------------------+--------------------------+
Table 3: ML-DSA Composite Signature Domain Separators
EDNOTE: these domain separators are based on the prototyping OIDs
assigned on the Entrust arc. We will need to ask for IANA early
assignment of these OIDs so that we can re-compute the domain
separators over the final OIDs.
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7.2. Rationale for choices
In generating the list of composite algorithms, the idea was to
provide composite algorithms at various security levels with varying
performance characteristics.
The main design consideration in choosing pairings is to prioritize
providing pairings of each ML-DSA security level with commonly-
deployed traditional algorithms. This supports the design goal of
using composites as a stepping stone to efficiently deploy post-
quantum on top of existing hardened and certified traditional
algorithm implementations. This was prioritized rather than
attempting to exactly match the security level of the post-quantum
and traditional components -- which in general is difficult to do
since there is no academic consensus on how to compare the "bits of
security" against classical attackers and "qubits of security"
against quantum attackers.
SHA2 is prioritized over SHA3 in order to facilitate implementations
that do not have easy access to SHA3 outside of the ML-DSA module.
However SHAKE256 is used with Ed448 since this is already the
recommended hash functions chosen for ED448ph in [RFC8032].
In some cases, multiple hash functions are used within the same
composite algorithm. Consider for example id-MLDSA65-ECDSA-
P256-SHA512 which requires SHA512 as the overall composite pre-hash
in order to maintain the security level of ML-DSA-65, but uses SHA256
within the ecdsa-with-SHA256 with secp256r1 traditional component.
While this increases the implementation burden of needing to carry
multiple hash functions for a single composite algorithm, this aligns
with the design goal of choosing commonly-implemented traditional
algorithms since ecdsa-with-SHA256 with secp256r1 is far more common
than, for example, ecdsa-with-SHA512 with secp256r1.
7.3. RSASSA-PSS Parameters
Use of RSASSA-PSS [RFC8017] requires extra parameters to be
specified.
As with the other composite signature algorithms, when a composite
algorithm OID involving RSA-PSS is used in an AlgorithmIdentifier,
the parameters MUST be absent.
When RSA-PSS is used at the 2048-bit security level, RSASSA-PSS SHALL
be instantiated with the following parameters:
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+=============================+===========+
| RSASSA-PSS Parameter | Value |
+=============================+===========+
| MaskGenAlgorithm.algorithm | id-mgf1 |
+-----------------------------+-----------+
| maskGenAlgorithm.parameters | id-sha256 |
+-----------------------------+-----------+
| Message Digest Algorithm | id-sha256 |
+-----------------------------+-----------+
| Salt Length in bits | 256 |
+-----------------------------+-----------+
Table 4: RSASSA-PSS 2048 Parameters
When RSA-PSS is used at the 3072-bit or 4096-bit security level,
RSASSA-PSS SHALL be instantiated with the following parameters:
+=============================+===========+
| RSASSA-PSS Parameter | Value |
+=============================+===========+
| MaskGenAlgorithm.algorithm | id-mgf1 |
+-----------------------------+-----------+
| maskGenAlgorithm.parameters | id-sha512 |
+-----------------------------+-----------+
| Message Digest Algorithm | id-sha512 |
+-----------------------------+-----------+
| Salt Length in bits | 512 |
+-----------------------------+-----------+
Table 5: RSASSA-PSS 3072 and 4096
Parameters
Full specifications for the referenced algorithms can be found in
Appendix B.
8. ASN.1 Module
<CODE STARTS>
Composite-MLDSA-2025
{ iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-composite-mldsa-2025(TBDMOD) }
DEFINITIONS IMPLICIT TAGS ::= BEGIN
EXPORTS ALL;
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IMPORTS
PUBLIC-KEY, SIGNATURE-ALGORITHM, SMIME-CAPS, AlgorithmIdentifier{}
FROM AlgorithmInformation-2009 -- RFC 5912 [X509ASN1]
{ iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-algorithmInformation-02(58) }
;
--
-- Object Identifiers
--
--
-- Information Object Classes
--
pk-CompositeSignature {OBJECT IDENTIFIER:id}
PUBLIC-KEY ::= {
IDENTIFIER id
KEY BIT STRING
PARAMS ARE absent
CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign,
cRLSign}
}
sa-CompositeSignature{OBJECT IDENTIFIER:id,
PUBLIC-KEY:publicKeyType }
SIGNATURE-ALGORITHM ::= {
IDENTIFIER id
VALUE OCTET STRING
PARAMS ARE absent
PUBLIC-KEYS {publicKeyType}
}
-- Composite ML-DSA which uses a PreHash Message
-- TODO: OID to be replaced by IANA
id-MLDSA44-RSA2048-PSS-SHA256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 100 }
pk-MLDSA44-RSA2048-PSS-SHA256 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA44-RSA2048-PSS-SHA256}
sa-MLDSA44-RSA2048-PSS-SHA256 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA44-RSA2048-PSS-SHA256,
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pk-MLDSA44-RSA2048-PSS-SHA256 }
-- TODO: OID to be replaced by IANA
id-MLDSA44-RSA2048-PKCS15-SHA256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 101 }
pk-MLDSA44-RSA2048-PKCS15-SHA256 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA44-RSA2048-PKCS15-SHA256}
sa-MLDSA44-RSA2048-PKCS15-SHA256 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA44-RSA2048-PKCS15-SHA256,
pk-MLDSA44-RSA2048-PKCS15-SHA256 }
-- TODO: OID to be replaced by IANA
id-MLDSA44-Ed25519-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 102 }
pk-MLDSA44-Ed25519-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA44-Ed25519-SHA512}
sa-MLDSA44-Ed25519-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA44-Ed25519-SHA512,
pk-MLDSA44-Ed25519-SHA512 }
-- TODO: OID to be replaced by IANA
id-MLDSA44-ECDSA-P256-SHA256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 103 }
pk-MLDSA44-ECDSA-P256-SHA256 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA44-ECDSA-P256-SHA256}
sa-MLDSA44-ECDSA-P256-SHA256 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA44-ECDSA-P256-SHA256,
pk-MLDSA44-ECDSA-P256-SHA256 }
-- TODO: OID to be replaced by IANA
id-MLDSA65-RSA3072-PSS-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 104 }
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pk-MLDSA65-RSA3072-PSS-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA65-RSA3072-PSS-SHA512}
sa-MLDSA65-RSA3072-PSS-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA65-RSA3072-PSS-SHA512,
pk-MLDSA65-RSA3072-PSS-SHA512 }
-- TODO: OID to be replaced by IANA
id-MLDSA65-RSA3072-PKCS15-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 105 }
pk-MLDSA65-RSA3072-PKCS15-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA65-RSA3072-PKCS15-SHA512}
sa-MLDSA65-RSA3072-PKCS15-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA65-RSA3072-PKCS15-SHA512,
pk-MLDSA65-RSA3072-PKCS15-SHA512 }
-- TODO: OID to be replaced by IANA
id-MLDSA65-RSA4096-PSS-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 106 }
pk-MLDSA65-RSA4096-PSS-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA65-RSA4096-PSS-SHA512}
sa-MLDSA65-RSA4096-PSS-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA65-RSA4096-PSS-SHA512,
pk-MLDSA65-RSA4096-PSS-SHA512 }
-- TODO: OID to be replaced by IANA
id-MLDSA65-RSA4096-PKCS15-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 107 }
pk-MLDSA65-RSA4096-PKCS15-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA65-RSA4096-PKCS15-SHA512}
sa-MLDSA65-RSA4096-PKCS15-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA65-RSA4096-PKCS15-SHA512,
pk-MLDSA65-RSA4096-PKCS15-SHA512 }
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-- TODO: OID to be replaced by IANA
id-MLDSA65-ECDSA-P256-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 108 }
pk-MLDSA65-ECDSA-P256-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA65-ECDSA-P256-SHA512}
sa-MLDSA65-ECDSA-P256-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA65-ECDSA-P256-SHA512,
pk-MLDSA65-ECDSA-P256-SHA512 }
-- TODO: OID to be replaced by IANA
id-MLDSA65-ECDSA-P384-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 109 }
pk-MLDSA65-ECDSA-P384-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA65-ECDSA-P384-SHA512}
sa-MLDSA65-ECDSA-P384-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA65-ECDSA-P384-SHA512,
pk-MLDSA65-ECDSA-P384-SHA512 }
-- TODO: OID to be replaced by IANA
id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 110 }
pk-MLDSA65-ECDSA-brainpoolP256r1-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA65-ECDSA-brainpoolP256r1-SHA512}
sa-MLDSA65-ECDSA-brainpoolP256r1-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA65-ECDSA-brainpoolP256r1-SHA512,
pk-MLDSA65-ECDSA-brainpoolP256r1-SHA512 }
-- TODO: OID to be replaced by IANA
id-MLDSA65-Ed25519-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 111 }
pk-MLDSA65-Ed25519-SHA512 PUBLIC-KEY ::=
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pk-CompositeSignature{ id-MLDSA65-Ed25519-SHA512}
sa-MLDSA65-Ed25519-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA65-Ed25519-SHA512,
pk-MLDSA65-Ed25519-SHA512 }
-- TODO: OID to be replaced by IANA
id-MLDSA87-ECDSA-P384-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 112 }
pk-MLDSA87-ECDSA-P384-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA87-ECDSA-P384-SHA512}
sa-MLDSA87-ECDSA-P384-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA87-ECDSA-P384-SHA512,
pk-MLDSA87-ECDSA-P384-SHA512 }
-- TODO: OID to be replaced by IANA
id-MLDSA87-ECDSA-brainpoolP384r1-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 113 }
pk-MLDSA87-ECDSA-brainpoolP384r1-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA87-ECDSA-brainpoolP384r1-SHA512}
sa-MLDSA87-ECDSA-brainpoolP384r1-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA87-ECDSA-brainpoolP384r1-SHA512,
pk-MLDSA87-ECDSA-brainpoolP384r1-SHA512 }
-- TODO: OID to be replaced by IANA
id-MLDSA87-Ed448-SHAKE256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 114 }
pk-MLDSA87-Ed448-SHAKE256 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA87-Ed448-SHAKE256}
sa-MLDSA87-Ed448-SHAKE256 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA87-Ed448-SHAKE256,
pk-MLDSA87-Ed448-SHAKE256 }
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-- TODO: OID to be replaced by IANA
id-MLDSA87-RSA3072-PSS-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 117 }
pk-MLDSA87-RSA3072-PSS-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA87-RSA3072-PSS-SHA512}
sa-MLDSA87-RSA3072-PSS-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA87-RSA3072-PSS-SHA512,
pk-MLDSA87-RSA3072-PSS-SHA512 }
-- TODO: OID to be replaced by IANA
id-MLDSA87-RSA4096-PSS-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 115 }
pk-MLDSA87-RSA4096-PSS-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA87-RSA4096-PSS-SHA512}
sa-MLDSA87-RSA4096-PSS-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA87-RSA4096-PSS-SHA512,
pk-MLDSA87-RSA4096-PSS-SHA512 }
-- TODO: OID to be replaced by IANA
id-MLDSA87-ECDSA-P521-SHA512 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1)
entrust(114027) algorithm(80) composite(8) signature(1) 116 }
pk-MLDSA87-ECDSA-P521-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA87-ECDSA-P521-SHA512}
sa-MLDSA87-ECDSA-P521-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA87-ECDSA-P521-SHA512,
pk-MLDSA87-ECDSA-P521-SHA512 }
SignatureAlgorithmSet SIGNATURE-ALGORITHM ::= {
sa-MLDSA44-RSA2048-PSS-SHA256 |
sa-MLDSA44-RSA2048-PKCS15-SHA256 |
sa-MLDSA44-Ed25519-SHA512 |
sa-MLDSA44-ECDSA-P256-SHA256 |
sa-MLDSA65-RSA3072-PSS-SHA512 |
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sa-MLDSA65-RSA3072-PKCS15-SHA512 |
sa-MLDSA65-RSA4096-PSS-SHA512 |
sa-MLDSA65-RSA4096-PKCS15-SHA512 |
sa-MLDSA65-ECDSA-P256-SHA512 |
sa-MLDSA65-ECDSA-P384-SHA512 |
sa-MLDSA65-ECDSA-brainpoolP256r1-SHA512 |
sa-MLDSA65-Ed25519-SHA512 |
sa-MLDSA87-ECDSA-P384-SHA512 |
sa-MLDSA87-ECDSA-brainpoolP384r1-SHA512 |
sa-MLDSA87-Ed448-SHAKE256 |
sa-MLDSA87-RSA3072-PSS-SHA512 |
sa-MLDSA87-RSA4096-PSS-SHA512 |
sa-MLDSA87-ECDSA-P521-SHA512,
... }
END
<CODE ENDS>
9. IANA Considerations
IANA is requested to allocate a value from the "SMI Security for PKIX
Module Identifier" registry [RFC7299] for the included ASN.1 module,
and allocate values from "SMI Security for PKIX Algorithms" to
identify the eighteen algorithms defined within.
9.1. Object Identifier Allocations
EDNOTE to IANA: OIDs will need to be replaced in both the ASN.1
module and in Table 2.
9.1.1. Module Registration
The following is to be registered in "SMI Security for PKIX Module
Identifier":
* Decimal: IANA Assigned - *Replace TBDMOD*
* Description: Composite-Signatures-2025 - id-mod-composite-
signatures
* References: This Document
9.1.2. Object Identifier Registrations
The following are to be registered in "SMI Security for PKIX
Algorithms":
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* id-MLDSA44-RSA2048-PSS-SHA256
- Decimal: IANA Assigned
- Description: id-MLDSA44-RSA2048-PSS-SHA256
- References: This Document
* id-MLDSA44-RSA2048-PKCS15-SHA256
- Decimal: IANA Assigned
- Description: id-MLDSA44-RSA2048-PKCS15-SHA256
- References: This Document
* id-MLDSA44-Ed25519-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA44-Ed25519-SHA512
- References: This Document
* id-MLDSA44-ECDSA-P256-SHA256
- Decimal: IANA Assigned
- Description: id-MLDSA44-ECDSA-P256-SHA256
- References: This Document
* id-MLDSA65-RSA3072-PSS-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA65-RSA3072-PSS-SHA512
- References: This Document
* id-MLDSA65-RSA3072-PKCS15-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA65-RSA3072-PKCS15-SHA512
- References: This Document
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* id-MLDSA65-RSA4096-PSS-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA65-RSA4096-PSS-SHA512
- References: This Document
* id-MLDSA65-RSA4096-PKCS15-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA65-RSA4096-PKCS15-SHA512
- References: This Document
* id-MLDSA65-ECDSA-P256-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA65-ECDSA-P256-SHA512
- References: This Document
* id-MLDSA65-ECDSA-P384-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA65-ECDSA-P384-SHA512
- References: This Document
* id-MLDSA65-ECDSA-brainpoolP256r1-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA65-ECDSA-brainpoolP256r1-SHA512
- References: This Document
* id-MLDSA65-Ed25519-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA65-Ed25519-SHA512
- References: This Document
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* id-MLDSA87-ECDSA-P384-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA87-ECDSA-P384-SHA512
- References: This Document
* id-MLDSA87-ECDSA-brainpoolP384r1-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA87-ECDSA-brainpoolP384r1-SHA512
- References: This Document
* id-MLDSA87-Ed448-SHAKE256
- Decimal: IANA Assigned
- Description: id-MLDSA87-Ed448-SHAKE256
- References: This Document
* id-MLDSA87-RSA3072-PSS-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA87-RSA3072-PSS-SHA512
- References: This Document
* id-MLDSA87-RSA4096-PSS-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA87-RSA4096-PSS-SHA512
- References: This Document
* id-MLDSA87-ECDSA-P521-SHA512
- Decimal: IANA Assigned
- Description: id-MLDSA87-ECDSA-P521-SHA512
- References: This Document
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10. Security Considerations
10.1. Why Hybrids?
In broad terms, a PQ/T Hybrid can be used either to provide dual-
algorithm security or to provide migration flexibility. Let's
quickly explore both.
Dual-algorithm security. The general idea is that the data is
protected by two algorithms such that an attacker would need to break
both in order to compromise the data. As with most of cryptography,
this property is easy to state in general terms, but becomes more
complicated when expressed in formalisms. Section 10.2 goes into
more detail here. One common counter-argument against PQ/T hybrid
signatures is that if an attacker can forge one of the component
algorithms, then why attack the hybrid-signed message at all when
they could simply forge a completely new message? The answer to this
question must be found outside the cryptographic primitives
themselves, and instead in policy; once an algorithm is known to be
broken it ought to be disallowed for single-algorithm use by
cryptographic policy, while hybrids involving that algorithm may
continue to be used and to provide value.
Migration flexibility. Some PQ/T hybrids exist to provide a sort of
"OR" mode where the application can choose to use one algorithm or
the other or both. The intention is that the PQ/T hybrid mechanism
builds in backwards compatibility to allow legacy and upgraded
applications to co-exist and communicate. The composites presented
in this specification do not provide this since they operate in a
strict "AND" mode. They do, however, provide codebase migration
flexibility. Consider that an organization has today a mature,
validated, certified, hardened implementation of RSA or ECC;
composites allow them to add an ML-DSA implementation which
immediately starts providing benefits against long-term document
integrity attacks even if that ML-DSA implementation is still an
experimental, non-validated, non-certified, non-hardened
implementation. More details of obtaining FIPS certification of a
composite algorithm can be found in Section 11.1.
10.2. Non-separability, EUF-CMA and SUF
The signature combiner defined in this specification is Weakly Non-
Separable (WNS), as defined in
[I-D.ietf-pquip-hybrid-signature-spectrums], since the forged message
M’ will include the composite domain separator as evidence. The
prohibition on key reuse between composite and single-algorithm
contexts discussed in Section 10.3 further strengthens the non-
separability in practice, but does not achieve Strong Non-
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Separability (SNS) since policy mechanisms such as this are outside
the definition of SNS.
Unforgeability properties are somewhat more nuanced. We recall first
the definitions of Existential Unforgeability under Chosen Message
Attack (EUF-CMA) and Strong Unforgeability (SUF). The classic EUF-
CMA game is in reference to a pair of algorithms ( Sign(), Verify() )
where the attacker has access to a signing oracle using the Sign()
and must produce a message-signature pair (m', s') that is accepted
by the verifier using Verify() and where m' was never signed by the
oracle. SUF is similar but requires only that (m', s') != (m, s) for
any honestly-generated (m, s), i.e. that the attacker cannot
construct a new signature to an already-signed message.
The pair ( CompositeML-DSA.Sign(), CompositeML-DSA.Verify() ) is EUF-
CMA secure so long as at least one component algorithm is EUF-CMA
secure since any attempt to modify the message would cause the EUF-
CMA secure component to fail its Verify() which in turn will cause
CompositeML-DSA.Verify() to fail.
Composite ML-DSA only achieves SUF security if both components are
SUF secure, which is not a useful property; the argument is that if
the first component algorithm is not SUF secure then by definition it
admits at least one (m, s1') pair where s1' was not produced by the
honest signer, and the attacker can then combine it with an honestly-
signed (m, s2) signature produced by the second algorithm over the
same message m to create (m, (s1', s2)) which violates SUF for the
composite algorithm. Of the traditional signature component
algorithms used in this specification, only Ed25519 and Ed448 are SUF
secure and therefore applications that require SUF security to be
maintained even in the event that ML-DSA is broken SHOULD use it in
composite with Ed25519 or Ed448.
In addition to the classic EUF-CMA game, we also consider a “cross-
protocol” version of the EUF-CMA game that is relevant to hybrids.
Specifically, we want to consider a modified version of the EUF-CMA
game where the attacker has access to either a signing oracle over
the two component algorithms in isolation, Trad.Sign() and ML-
DSA.Sign(), and attempts to fraudulently present them as a composite,
or where the attacker has access to a composite signing oracle and
then attempts to split the signature back into components and present
them to either ML-DSA.Verify() or Trad.Verify().
In the case of Composite ML-DSA, a specific message forgery exists
for a cross-protocol EUF-CMA attack, namely introduced by the prefix
construction used to construct the to-be-signed message
representative M'. This applies to use of individual component
signing oracles with fraudulent presentation of the signature to a
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composite verification oracle, and use of a composite signing oracle
with fraudulent splitting of the signature for presentation to
component verification oracle(s) of either ML-DSA.Verify() or
Trad.Verify(). In the first case, an attacker with access to signing
oracles for the two component algorithms can sign M’ and then
trivially assemble a composite. In the second case, the message M’
(containing the composite domain separator) can be presented as
having been signed by a standalone component algorithm. However, use
of the context string for domain separation enables Weak Non-
Separability and auditable checks on hybrid use, which is deemed a
reasonable trade-off. Moreover and very importantly, the cross-
protocol EUF-CMA attack in either direction is foiled if implementers
strictly follow the prohibition on key reuse presented in
Section 10.3 since there cannot exist simultaneously composite and
non-composite signers and verifiers for the same keys.
10.2.1. Implications of multiple encodings
As noted in Section 5, this specification leaves some flexibility the
choice of encoding of the traditional component. As such it is
possible for the same composite public key to carry multiple valid
representations (mldsaPK, tradPK1) and (mldsaPK, tradPK2) where
tradPK1 and tradPK2 are alternate encodings of the same key, for
example compressed vs uncompressed EC points. In theory alternate
encodings of the traditional signature value are also possible,
although the authors are not aware of any.
In theory this introduces complications for EUF-CMA and SUF-CMA
security proofs. Implementers who are concerned with this SHOULD
choose implementations of the traditional component that only accept
a single encoding and performs appropriate length-checking, and
reject composites which contain any other encodings. This would
reduce interoperability with other Composite ML-DSA implementations,
but it is permitted by this specification.
10.3. Key Reuse
While conformance with this specification requires that both
components of a composite key MUST be freshly generated, the
designers are aware that some implementers may be forced to break
this rule due to operational constraints. This section documents the
implications of doing so.
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When using single-algorithm cryptography, the best practice is to
always generate fresh key material for each purpose, for example when
renewing a certificate, or obtaining both a TLS and S/MIME
certificate for the same device. However, in practice key reuse in
such scenarios is not always catastrophic to security and therefore
often tolerated. However this reasoning does not hold in the PQ/T
hybrid setting.
Within the broader context of PQ/T hybrids, we need to consider new
attack surfaces that arise due to the hybrid constructions that did
not exist in single-algorithm contexts. One of these is key reuse
where the component keys within a hybrid are also used by themselves
within a single-algorithm context. For example, it might be tempting
for an operator to take an already-deployed RSA key pair and combine
it with an ML-DSA key pair to form a hybrid key pair for use in a
hybrid algorithm. Within a hybrid signature context this leads to a
class of attacks referred to as "stripping attacks" discussed in
Section 10.2 and may also open up risks from further cross-protocol
attacks. Despite the weak non-separability property offered by the
composite signature combiner, key reuse MUST be avoided to prevent
the introduction of EUF-CMA vulnerabilities.
In addition, there is a further implication to key reuse regarding
certificate revocation. Upon receiving a new certificate enrolment
request, many certification authorities will check if the requested
public key has been previously revoked due to key compromise. Often
a CA will perform this check by using the public key hash.
Therefore, if one, or even both, components of a composite have been
previously revoked, the CA may only check the hash of the combined
composite key and not find the revocations. Therefore, because the
possibility of key reuse exists even though forbidden in this
specification, CAs performing revocation checks on a composite key
SHOULD also check both component keys independently to verify that
the component keys have not been revoked.
Some application might disregard the requirements of this
specification to not reuse key material between single-algorithm and
composite contexts. While doing so is still a violation of this
specification, the weakening of security from doing so can be
mitigated by using an appropriate ctx value, such as ctx=Foobar-dual-
cert-sig to indicate that this signature belongs to the Foobar
protocol where two certificates were used to create a single
composite signature. This specification does not endorse such uses,
and per-application security analysis is needed.
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10.4. Use of Prefix for attack mitigation
The Prefix value specified in Section 3.2 allows for cautious
implementers to wrap their existing Traditional Verify()
implementations with a guard that looks for messages starting with
this string and fail with an error -- i.e. this can act as an extra
protection against taking a composite signature and splitting it back
into components. However, an implementation that does this will be
unable to perform a Traditional signature and verification on a
message which happens to start with this string. The designers
accepted this trade-off.
10.5. Implications of pre-hash randomizer
The primary design motivation behind pre-hashing is to perform only a
single pass over the potentially large input message M and to allow
for optimizations in cases such as signing the same message digest
with multiple different keys.
To combat potential collision weaknesses introduced by the pre-hash,
Composite ML-DSA introduces a 32-byte randomizer into the pre-hash:
PH( r || M )
as part of the overall construction of the to-be-signed message:
r = Random(32)
M' := Prefix || Domain || len(ctx) || ctx || r
|| PH( r || M )
...
output (r, mldsaSig, tradSig)
This follows closely the construction given in section 13.2.1 of
[BonehShoup] which is also referred to as a "keyed pre-hash" and is
given as:
S'(sk, m) :=
r <-R- K_h
h <- H(r, m)
s <- S(sk, (r,h))
output (s, r)
Figure 12: Listing 13.2 from Boneh-Shoup showing how to extend a
signature scheme with a Target Collision Resistant hash
Randomizing the pre-hash strongly protects against pre-computed
collision attacks where an attacker pre-computes a message pair M1,
M2 such that PH(M1) = PH(M2) and submits one to the signing oracle,
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thus obtaining a valid signature for both. However, collision-
finding pre-computation cannot be performed against PH(r || M1) =
PH(r || M2) when r is unknown to the attacker in advance. We also
consider signature forgeries via finding a second pre-image after the
signature has been created honestly. In this case, the attack is
only possible if the attacker can perform what [BonehShoup] calls a
target collision attack where the attacker takes the honestly-
produced signature s = (r, mldsaSig, tradSig) over the message M and
finds a second message M2 such that PH(r || M) = PH(r || M2) for the
same randomizer r.
[BonehShoup] defines Target Collision Resistance (TCR) as a security
notion that applies to keyed hash functions and notes in section
13.2.1:
The benefit of the TCR construction is that security only relies
on H being TCR, which is a much weaker property than collision
resistance and hence more likely to hold for H. For example, the
function SHA256 may eventually be broken as a collision-resistant
hash, but the function
H(r, m) := SHA256(r || m) may still be secure as a TCR.
Note that, with this construction, H is TCR if the hash function
(SHA256 in this example) is second preimage resistant.
To this goal, it is sufficient that the randomizer be un-predictable
from outside the signing oracle -- i.e. the caller of Composite-ML-
DSA<OID>.Sign(sk, M, ctx) cannot predict the randomizer value that
will be used. In some contexts it MAY be acceptable to use a
randomizer which is not truly random without compromising the stated
security properties; for example if performing batch signatures where
the same message is signed with multiple keys, it MAY be acceptable
to pre-hash the message once and then sign that digest multiple times
-- i.e. using the same randomizer across multiple signatures.
Provided that the batch signature is performed as an atomic signing
oracle and an attacker is never able to see the randomizer that will
be used in a future signature then this ought to satisfy the stated
security requirements, but detailed security analysis of such a
modification of the Composite ML-DSA signing routine MUST be
performed on a per-application basis.
Another benefit to the randomizer is to prevent a class of attacks
unique to composites, which we define as a "mixed-key forgery
attack": Take two composite keys (mldsaPK1, tradPK1) and (mldsaPK2,
tradPK2) which do not share any key material and have them produce
signatures (r1, mldsaSig1, tradSig1) and (r2, mldsaSig2, tradSig2)
respectively over the same message M. Consider whether it is
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possible to construct a forgery by swapping components and presenting
(r, mldsaSig1, tradSig2) that verifies under a forged public key
(mldsaPK1, tradPK2). This forgery attack is blocked by the
randomizer r so long as r1 != r2.
A failure of randomness, for example r = 0, reverts the overall
collision and second pre-image resistance of Composite ML-DSA to that
of the hash function used as PH, which is no worse than the security
properties that Composite ML-DSA would have had without a randomizer,
which is the same collision and second pre-image resistance
properties that RSA, ECDSA, and ML-DSA have.
Introduction of the randomizer might introduce other beneficial
security properties, but these are outside the scope of design
consideration.
10.6. Policy for Deprecated and Acceptable Algorithms
Traditionally, a public key or certificate contains a single
cryptographic algorithm. If and when an algorithm becomes deprecated
(for example, RSA-512, or SHA1), the path to deprecating it through
policy and removing it from operational environments is, at least is
principle, straightforward.
In the composite model this is less obvious since a PQ/T hybrid is
expected to still be considered valid after the traditional component
is deprecated for individual use. As such, a single composite public
key or certificate may contain a mixture of deprecated and non-
deprecated algorithms. In general this should be manageable through
policy by removing OIDs for the standalone component algorithms while
still allowing OIDs for composite algorithms. However, complications
may arise when the composite implementation needs to invoke the
cryptographic module for a deprecated component algorithm. In
particular, this could lead to complex Cryptographic Bills of
Materials that show implementations of deprecated algorithms still
present and being used.
11. Implementation Considerations
11.1. FIPS certification
The following sections give guidance to implementers wishing to FIPS-
certify a composite implementation.
This guidance is not authoritative and has not been endorsed by NIST.
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One of the primary design goals of this specification is for the
overall composite algorithm to be able to be considered FIPS-approved
even when one of the component algorithms is not.
Implementers seeking FIPS certification of a composite signature
algorithm where only one of the component algorithms has been FIPS-
validated or FIPS-approved should credit the FIPS-validated component
algorithm with full security strength, the non-FIPS-validated
component algorithm with zero security, and the overall composite
should be considered at least as strong and thus FIPS-approved.
The composite algorithm has been designed to treat the underlying
primitives as "black-box implementations" and not impose any
additional requirements on them that could require an existing
implementation of an underlying primitive to run in a mode different
from the one under which it was certified. For example, the KeyGen
defined in Section 4.1 invokes ML-DSA.KeyGen(seed) which might not be
available in a cryptographic module running in FIPS-mode, but
Section 4.1 is only a suggested implementation and the composite
KeyGen MAY be implemented using a different available interface for
ML-DSA.KeyGen. Another example is pre-hashing; a pre-hash is
inherent to RSA, ECDSA, and ML-DSA (mu), and composite makes no
assumptions or requirements about whether component-specific pre-
hashing is done locally as part of the composite, or remotely as part
of the component primitive.
The pre-hash randomizer r requires the composite implementation to
have access to a cryptographic random number generator. However, as
noted in Section 10.5, this provides additional security properties
on top of those provided by ML-DSA, RSA, ECDSA, and EdDSA, and
failure of randomness does not compromise the Composite ML-DSA
algorithm or the underlying primitives. Therefore it should be
possible to exclude this RNG invocation from the FIPS boundary if an
implementation is not able to guarantee use of a FIPS-approved RNG.
The authors wish to note that composite algorithms provide a design
pattern to provide utility in future situations that require care to
remain FIPS-compliant, such as future cryptographic migrations as
well as bridging across jurisdictions with non-intersecting
cryptographic requirements.
11.2. Backwards Compatibility
The term "backwards compatibility" is used here to mean that existing
systems as they are deployed today can interoperate with the upgraded
systems of the future. This draft explicitly does not provide
backwards compatibility, only upgraded systems will understand the
OIDs defined in this specification.
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If backwards compatibility is required, then additional mechanisms
will be needed. Migration and interoperability concerns need to be
thought about in the context of various types of protocols that make
use of X.509 and PKIX with relation to digital signature objects,
from online negotiated protocols such as TLS 1.3 [RFC8446] and IKEv2
[RFC7296], to non-negotiated asynchronous protocols such as S/MIME
signed email [RFC8551], document signing such as in the context of
the European eIDAS regulations [eIDAS2014], and publicly trusted code
signing [codesigningbrsv3.8], as well as myriad other standardized
and proprietary protocols and applications that leverage CMS
[RFC5652] signed structures. Composite simplifies the protocol
design work because it can be implemented as a signature algorithm
that fits into existing systems.
11.3. Profiling down the number of options
One daunting aspect of this specification is the number of composite
algorithm combinations. Each option has been specified because there
is a community that has a direct application for it; typically
because the traditional component is already deployed in a change-
managed environment, or because that specific traditional component
is required for regulatory reasons.
However, this large number of combinations leads either to fracturing
of the ecosystem into non-interoperable sub-groups when different
communities choose non-overlapping subsets to support, or on the
other hand it leads to spreading development resources too thin when
trying to support all options.
This specification does not list any particular composite algorithm
as mandatory-to-implement, however organizations that operate within
specific application domains are encouraged to define profiles that
select a small number of composites appropriate for that application
domain. For applications that do not have any regulatory
requirements or legacy implementations to consider, it is RECOMMENDED
to focus implementation effort on:
id-MLDSA65-ECDSA-P256-SHA512
In applications that require RSA, it is RECOMMENDED to focus
implementation effort on:
id-MLDSA65-RSA3072-PSS-SHA512
In applications that only allow NIST PQC Level 5, it is RECOMMENDED
to focus implementation effort on:
id-MLDSA87-ECDSA-P384-SHA512
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11.4. External Pre-hashing
Composite ML-DSA uses a randomized pre-hash PH( r || m ) to construct
the to-be-signed message representative M'. Implementers MAY
externalize the pre-hash computation outside the module that computes
Composite-ML-DSA.Sign() in an analogous way to how pre-hash signing
is used for RSA, ECDSA or HashML-DSA. Such a modification to the
Composite-ML-DSA.Sign() algorithm is considered compliant to this
specification so long as it produces the same output and error
conditions.
Below is a suggested implementation for splitting the pre-hashing and
signing between two parties.
Composite-ML-DSA<OID>.PrehashToken(M) -> T
Explicit inputs:
M The message to be signed, an octet string.
Implicit inputs mapped from <OID>:
PH The hash function to use for pre-hashing.
Output:
T The pre-hash token which equals r || PH (r || M)
Process:
1. Compute the random 32-byte value r:
r = Random(32)
2. Compute the Prehash of the message using the Hash function
defined by PH
ph = PH (r || M)
3. Generate the pre-hash token T:
T = SerializePrehashToken(r,ph)
4. Output T
Figure 13: Generation of the external pre-hash token
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Composite-ML-DSA<OID>.Sign_ph(sk, T, ctx) -> s
Explicit inputs:
sk Composite private key consisting of signing private keys for
each component.
T The pre-hash token used to sign the message
ctx The Message context string used in the composite signature
combiner, which defaults to the empty string.
Implicit inputs mapped from <OID>:
ML-DSA The underlying ML-DSA algorithm and
parameter set, for example, could be "ML-DSA-65".
Trad The underlying traditional algorithm and
parameter set, for example "RSASSA-PSS with id-sha256"
or "Ed25519".
Prefix The prefix String which is the byte encoding of the String
"CompositeAlgorithmSignatures2025" which in hex is
436F6D706F73697465416C676F726974686D5369676E61747572657332303235
Domain Domain separator value for binding the signature to the
Composite OID. Additionally, the composite Domain is passed into
the underlying ML-DSA primitive as the ctx.
Domain values are defined in the "Domain Separators" section below.
Process:
1. separate r and ph from T:
(r, ph) = DeserializePrehashToken(T)
2. Identical to Composite-ML-DSA<OID>.Sign (sk, M, ctx) but replace the internally
generated r and PH(r || M) from step 2 of Composite-ML-DSA<OID>.Sign (sk, M, ctx)
with r and ph from step 1 of this function.
Figure 14: Suggested implementation of external pre-hashing
11.4.1. Serialization and Deserialization of the PreHashToken
Serialization simply concatenates the two PreHashToken values r and
ph together.
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SerializePrehashToken(r, ph) -> bytes
Explicit Inputs:
r 32-bytes of externally generated random data
ph The result of computing PH(r || M)
Implicit inputs:
None
Output:
bytes The encoded pre-hash Token T
Serialization Process:
1. Combine r with ph
output r || ph
Figure 15: SerializePreHashToken(r, ph) -> bytes
Deserialization reverses this process, separating r from ph, raising
an error in the event that the input is malformed. The following
describes how to instantiate a DeserializePreHashToken(bytes)
function.
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DeserializePreHashToken(bytes) -> (r, ph)
Explicit inputs:
bytes An encoded prehash token
Implicit inputs:
None
Output:
r The 32 byte signature randomizer.
ph The pre-hashed value representating the has of the randomizer
concatenated with the Message which is 'PH(r || M)'.
Deserialization Process:
1. Parse the randomizer r which is the first 32 bytes.
r = bytes[:32]
2. Parse the Prehash. The length of the Prehash is based on the size of the
pre-hash algorithm for the specificed composite algorithm.
ph = bytes[32:]
3. Output (r, ph)
Figure 16: DeserializePreHashToken(bytes) -> (r, ph)
12. References
12.1. Normative References
[FIPS.186-5]
National Institute of Standards and Technology (NIST),
"Digital Signature Standard (DSS)", February 2023,
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.186-5.pdf>.
[FIPS.202] National Institute of Standards and Technology (NIST),
"SHA-3 Standard: Permutation-Based Hash and Extendable-
Output Functions", August 2015,
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.202.pdf>.
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[FIPS.204] National Institute of Standards and Technology (NIST),
"Module-Lattice-Based Digital Signature Standard", FIPS
PUB 204, August 2024,
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.204.pdf>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/info/rfc2119>.
[RFC2986] Nystrom, M. and B. Kaliski, "PKCS #10: Certification
Request Syntax Specification Version 1.7", RFC 2986,
DOI 10.17487/RFC2986, November 2000,
<https://www.rfc-editor.org/info/rfc2986>.
[RFC4210] Adams, C., Farrell, S., Kause, T., and T. Mononen,
"Internet X.509 Public Key Infrastructure Certificate
Management Protocol (CMP)", RFC 4210,
DOI 10.17487/RFC4210, September 2005,
<https://www.rfc-editor.org/info/rfc4210>.
[RFC4211] Schaad, J., "Internet X.509 Public Key Infrastructure
Certificate Request Message Format (CRMF)", RFC 4211,
DOI 10.17487/RFC4211, September 2005,
<https://www.rfc-editor.org/info/rfc4211>.
[RFC5280] Cooper, D., Santesson, S., Farrell, S., Boeyen, S.,
Housley, R., and W. Polk, "Internet X.509 Public Key
Infrastructure Certificate and Certificate Revocation List
(CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, May 2008,
<https://www.rfc-editor.org/info/rfc5280>.
[RFC5480] Turner, S., Brown, D., Yiu, K., Housley, R., and T. Polk,
"Elliptic Curve Cryptography Subject Public Key
Information", RFC 5480, DOI 10.17487/RFC5480, March 2009,
<https://www.rfc-editor.org/info/rfc5480>.
[RFC5639] Lochter, M. and J. Merkle, "Elliptic Curve Cryptography
(ECC) Brainpool Standard Curves and Curve Generation",
RFC 5639, DOI 10.17487/RFC5639, March 2010,
<https://www.rfc-editor.org/info/rfc5639>.
[RFC5652] Housley, R., "Cryptographic Message Syntax (CMS)", STD 70,
RFC 5652, DOI 10.17487/RFC5652, September 2009,
<https://www.rfc-editor.org/info/rfc5652>.
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[RFC5758] Dang, Q., Santesson, S., Moriarty, K., Brown, D., and T.
Polk, "Internet X.509 Public Key Infrastructure:
Additional Algorithms and Identifiers for DSA and ECDSA",
RFC 5758, DOI 10.17487/RFC5758, January 2010,
<https://www.rfc-editor.org/info/rfc5758>.
[RFC5958] Turner, S., "Asymmetric Key Packages", RFC 5958,
DOI 10.17487/RFC5958, August 2010,
<https://www.rfc-editor.org/info/rfc5958>.
[RFC6090] McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic
Curve Cryptography Algorithms", RFC 6090,
DOI 10.17487/RFC6090, February 2011,
<https://www.rfc-editor.org/info/rfc6090>.
[RFC6234] Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms
(SHA and SHA-based HMAC and HKDF)", RFC 6234,
DOI 10.17487/RFC6234, May 2011,
<https://www.rfc-editor.org/info/rfc6234>.
[RFC8032] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital
Signature Algorithm (EdDSA)", RFC 8032,
DOI 10.17487/RFC8032, January 2017,
<https://www.rfc-editor.org/info/rfc8032>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/info/rfc8174>.
[RFC8410] Josefsson, S. and J. Schaad, "Algorithm Identifiers for
Ed25519, Ed448, X25519, and X448 for Use in the Internet
X.509 Public Key Infrastructure", RFC 8410,
DOI 10.17487/RFC8410, August 2018,
<https://www.rfc-editor.org/info/rfc8410>.
[SEC1] Certicom Research, "SEC 1: Elliptic Curve Cryptography",
May 2009, <https://www.secg.org/sec1-v2.pdf>.
[SEC2] Certicom Research, "SEC 2: Recommended Elliptic Curve
Domain Parameters", January 2010,
<https://www.secg.org/sec2-v2.pdf>.
[X.690] ITU-T, "Information technology - ASN.1 encoding Rules:
Specification of Basic Encoding Rules (BER), Canonical
Encoding Rules (CER) and Distinguished Encoding Rules
(DER)", ISO/IEC 8825-1:2015, November 2015.
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[X9.62_2005]
American National Standards Institute, "Public Key
Cryptography for the Financial Services Industry The
Elliptic Curve Digital Signature Algorithm (ECDSA)",
November 2005.
12.2. Informative References
[ANSSI2024]
French Cybersecurity Agency (ANSSI), Federal Office for
Information Security (BSI), Netherlands National
Communications Security Agency (NLNCSA), and Swedish
National Communications Security Authority, Swedish Armed
Forces, "Position Paper on Quantum Key Distribution",
n.d., <https://cyber.gouv.fr/sites/default/files/document/
Quantum_Key_Distribution_Position_Paper.pdf>.
[Bindel2017]
Bindel, N., Herath, U., McKague, M., and D. Stebila,
"Transitioning to a quantum-resistant public key
infrastructure", 2017, <https://link.springer.com/
chapter/10.1007/978-3-319-59879-6_22>.
[BonehShoup]
Boneh, D. and V. Shoup, "A Graduate Course in Applied
Cryptography v0.6", January 2023,
<https://crypto.stanford.edu/~dabo/cryptobook/
BonehShoup_0_6.pdf>.
[BSI2021] Federal Office for Information Security (BSI), "Quantum-
safe cryptography - fundamentals, current developments and
recommendations", October 2021,
<https://www.bsi.bund.de/SharedDocs/Downloads/EN/BSI/
Publications/Brochure/quantum-safe-cryptography.pdf>.
[codesigningbrsv3.8]
CA/Browser Forum, "Baseline Requirements for the Issuance
and Management of Publicly‐Trusted Code Signing
Certificates Version 3.8.0", n.d., <https://cabforum.org/
working-groups/code-signing/documents/>.
[eIDAS2014]
European Parliament and Council, "Regulation (EU) No
910/2014 of the European Parliament and of the Council of
23 July 2014 on electronic identification and trust
services for electronic transactions in the internal
market and repealing Directive 1999/93/EC", n.d.,
<https://eur-lex.europa.eu/eli/reg/2014/910/oj/eng>.
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[I-D.ietf-lamps-dilithium-certificates]
Massimo, J., Kampanakis, P., Turner, S., and B.
Westerbaan, "Internet X.509 Public Key Infrastructure -
Algorithm Identifiers for the Module-Lattice-Based Digital
Signature Algorithm (ML-DSA)", Work in Progress, Internet-
Draft, draft-ietf-lamps-dilithium-certificates-11, 22 May
2025, <https://datatracker.ietf.org/doc/html/draft-ietf-
lamps-dilithium-certificates-11>.
[I-D.ietf-pquip-hybrid-signature-spectrums]
Bindel, N., Hale, B., Connolly, D., and F. D, "Hybrid
signature spectrums", Work in Progress, Internet-Draft,
draft-ietf-pquip-hybrid-signature-spectrums-06, 9 January
2025, <https://datatracker.ietf.org/doc/html/draft-ietf-
pquip-hybrid-signature-spectrums-06>.
[I-D.ietf-pquip-pqt-hybrid-terminology]
D, F., P, M., and B. Hale, "Terminology for Post-Quantum
Traditional Hybrid Schemes", Work in Progress, Internet-
Draft, draft-ietf-pquip-pqt-hybrid-terminology-06, 10
January 2025, <https://datatracker.ietf.org/doc/html/
draft-ietf-pquip-pqt-hybrid-terminology-06>.
[RFC5914] Housley, R., Ashmore, S., and C. Wallace, "Trust Anchor
Format", RFC 5914, DOI 10.17487/RFC5914, June 2010,
<https://www.rfc-editor.org/info/rfc5914>.
[RFC7292] Moriarty, K., Ed., Nystrom, M., Parkinson, S., Rusch, A.,
and M. Scott, "PKCS #12: Personal Information Exchange
Syntax v1.1", RFC 7292, DOI 10.17487/RFC7292, July 2014,
<https://www.rfc-editor.org/info/rfc7292>.
[RFC7296] Kaufman, C., Hoffman, P., Nir, Y., Eronen, P., and T.
Kivinen, "Internet Key Exchange Protocol Version 2
(IKEv2)", STD 79, RFC 7296, DOI 10.17487/RFC7296, October
2014, <https://www.rfc-editor.org/info/rfc7296>.
[RFC7299] Housley, R., "Object Identifier Registry for the PKIX
Working Group", RFC 7299, DOI 10.17487/RFC7299, July 2014,
<https://www.rfc-editor.org/info/rfc7299>.
[RFC8017] Moriarty, K., Ed., Kaliski, B., Jonsson, J., and A. Rusch,
"PKCS #1: RSA Cryptography Specifications Version 2.2",
RFC 8017, DOI 10.17487/RFC8017, November 2016,
<https://www.rfc-editor.org/info/rfc8017>.
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[RFC8411] Schaad, J. and R. Andrews, "IANA Registration for the
Cryptographic Algorithm Object Identifier Range",
RFC 8411, DOI 10.17487/RFC8411, August 2018,
<https://www.rfc-editor.org/info/rfc8411>.
[RFC8446] Rescorla, E., "The Transport Layer Security (TLS) Protocol
Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
<https://www.rfc-editor.org/info/rfc8446>.
[RFC8551] Schaad, J., Ramsdell, B., and S. Turner, "Secure/
Multipurpose Internet Mail Extensions (S/MIME) Version 4.0
Message Specification", RFC 8551, DOI 10.17487/RFC8551,
April 2019, <https://www.rfc-editor.org/info/rfc8551>.
[RFC9180] Barnes, R., Bhargavan, K., Lipp, B., and C. Wood, "Hybrid
Public Key Encryption", RFC 9180, DOI 10.17487/RFC9180,
February 2022, <https://www.rfc-editor.org/info/rfc9180>.
Appendix A. Approximate Key and Signature Sizes
The sizes listed below are approximate: these values are measured
from the test vectors, however, several factors could cause
fluctuations in the size of the traditional component. For example,
this could be due to:
* Compressed vs uncompressed EC point.
* The RSA public key (n, e) allows e to vary in size between 3 and n
- 1 [RFC8017].
* When the underlying RSA or EC value is itself DER-encoded, integer
values could occasionally be shorter than expected due to leading
zeros being dropped from the encoding.
By contrast, ML-DSA values are always fixed size, so composite values
can always be correctly de-serialized based on the size of the ML-DSA
component. It is expected for the size values of RSA and ECDSA
variants to fluctuate by a few bytes even between subsequent runs of
the same composite implementation.
Implementations MUST NOT perform strict length checking based on the
values in this table except for ML-DSA + EdDSA; since these
algorithms produce fixed-size outputs, the values in the table below
for these variants MAY be treated as constants.
Non-hybrid ML-DSA is included for reference.
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+=========================================+======+=======+=========+
| Algorithm |Public|Private|Signature|
| |key |key | |
+=========================================+======+=======+=========+
| id-ML-DSA-44 |1312 |32 |2420 |
+-----------------------------------------+------+-------+---------+
| id-ML-DSA-65 |1952 |32 |3309 |
+-----------------------------------------+------+-------+---------+
| id-ML-DSA-87 |2592 |32 |4627 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA44-RSA2048-PSS-SHA256 |1582 |1248 |2708 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA44-RSA2048-PKCS15-SHA256 |1582 |1250 |2708 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA44-Ed25519-SHA512 |1344 |64 |2516 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA44-ECDSA-P256-SHA256 |1377 |170 |2524 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-RSA3072-PSS-SHA512 |2350 |1826 |3725 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-RSA4096-PSS-SHA512 |2478 |2406 |3853 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-RSA4096-PKCS15-SHA512 |2478 |2407 |3853 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-ECDSA-P256-SHA512 |2017 |170 |3413 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-ECDSA-P384-SHA512 |2049 |217 |3444 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 |2017 |171 |3411 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-Ed25519-SHA512 |1984 |64 |3405 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA87-ECDSA-P384-SHA512 |2689 |217 |4763 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA87-ECDSA-brainpoolP384r1-SHA512 |2689 |221 |4761 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA87-RSA4096-PSS-SHA512 |3118 |2405 |5171 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA87-Ed448-SHAKE256 |2649 |89 |4773 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA87-RSA3072-PSS-SHA512 |2990 |1826 |5043 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA87-ECDSA-P521-SHA512 |2085 |273 |3480 |
+-----------------------------------------+------+-------+---------+
Table 6: Approximate size values of composite ML-DSA
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Appendix B. Component Algorithm Reference
This section provides references to the full specification of the
algorithms used in the composite constructions.
+=========================+=========================+=============+
| Component Signature | OID |Specification|
| Algorithm ID | | |
+=========================+=========================+=============+
| id-ML-DSA-44 | 2.16.840.1.101.3.4.3.17 |[FIPS.204] |
+-------------------------+-------------------------+-------------+
| id-ML-DSA-65 | 2.16.840.1.101.3.4.3.18 |[FIPS.204] |
+-------------------------+-------------------------+-------------+
| id-ML-DSA-87 | 2.16.840.1.101.3.4.3.19 |[FIPS.204] |
+-------------------------+-------------------------+-------------+
| id-Ed25519 | 1.3.101.112 |[RFC8032], |
| | |[RFC8410] |
+-------------------------+-------------------------+-------------+
| id-Ed448 | 1.3.101.113 |[RFC8032], |
| | |[RFC8410] |
+-------------------------+-------------------------+-------------+
| ecdsa-with-SHA256 | 1.2.840.10045.4.3.2 |[RFC5758], |
| | |[RFC5480], |
| | |[SEC1], |
| | |[X9.62_2005] |
+-------------------------+-------------------------+-------------+
| ecdsa-with-SHA384 | 1.2.840.10045.4.3.3 |[RFC5758], |
| | |[RFC5480], |
| | |[SEC1], |
| | |[X9.62_2005] |
+-------------------------+-------------------------+-------------+
| ecdsa-with-SHA512 | 1.2.840.10045.4.3.4 |[RFC5758], |
| | |[RFC5480], |
| | |[SEC1], |
| | |[X9.62_2005] |
+-------------------------+-------------------------+-------------+
| sha256WithRSAEncryption | 1.2.840.113549.1.1.11 |[RFC8017] |
+-------------------------+-------------------------+-------------+
| sha384WithRSAEncryption | 1.2.840.113549.1.1.12 |[RFC8017] |
+-------------------------+-------------------------+-------------+
| id-RSASSA-PSS | 1.2.840.113549.1.1.10 |[RFC8017] |
+-------------------------+-------------------------+-------------+
Table 7: Component Signature Algorithms used in Composite
Constructions
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+==================+=======================+===================+
| Elliptic CurveID | OID | Specification |
+==================+=======================+===================+
| secp256r1 | 1.2.840.10045.3.1.7 | [RFC6090], [SEC2] |
+------------------+-----------------------+-------------------+
| secp384r1 | 1.3.132.0.34 | [RFC5480], |
| | | [RFC6090], [SEC2] |
+------------------+-----------------------+-------------------+
| secp521r1 | 1.3.132.0.35 | [RFC5480], |
| | | [RFC6090], [SEC2] |
+------------------+-----------------------+-------------------+
| brainpoolP256r1 | 1.3.36.3.3.2.8.1.1.7 | [RFC5639] |
+------------------+-----------------------+-------------------+
| brainpoolP384r1 | 1.3.36.3.3.2.8.1.1.11 | [RFC5639] |
+------------------+-----------------------+-------------------+
Table 8: Elliptic Curves used in Composite Constructions
+=============+=========================+===============+
| HashID | OID | Specification |
+=============+=========================+===============+
| id-sha256 | 2.16.840.1.101.3.4.2.1 | [RFC6234] |
+-------------+-------------------------+---------------+
| id-sha512 | 2.16.840.1.101.3.4.2.3 | [RFC6234] |
+-------------+-------------------------+---------------+
| id-shake256 | 2.16.840.1.101.3.4.2.18 | [FIPS.202] |
+-------------+-------------------------+---------------+
| id-mgf1 | 1.2.840.113549.1.1.8 | [RFC8017] |
+-------------+-------------------------+---------------+
Table 9: Hash algorithms used in pre-hashed Composite
Constructions to build PH element
Appendix C. Component AlgorithmIdentifiers for Public Keys and
Signatures
The following sections list explicitly the DER encoded
AlgorithmIdentifier that MUST be used when reconstructing
SubjectPublicKeyInfo and Signature Algorithm objects for each
component algorithm type, which may be required for example if
cryptographic library requires the public key in this form in order
to process each component algorithm. The public key BIT STRING
should be taken directly from the respective component of the
Composite ML-DSA public key.
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For newer Algorithms like Ed25519 or ML-DSA the AlgorithmIdentifiers
are the same for Public Key and Signature. Older Algorithms have
different AlgorithmIdentifiers for keys and signatures and are
specified separately here for each component.
*ML-DSA-44*
AlgorithmIdentifier of Public Key and Signature
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-ML-DSA-44 -- (2 16 840 1 101 3 4 3 17)
}
DER:
30 0B 06 09 60 86 48 01 65 03 04 03 11
*ML-DSA-65*
AlgorithmIdentifier of Public Key and Signature
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-ML-DSA-65 -- (2 16 840 1 101 3 4 3 18)
}
DER:
30 0B 06 09 60 86 48 01 65 03 04 03 12
*ML-DSA-87*
AlgorithmIdentifier of Public Key and Signature
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-ML-DSA-87 -- (2 16 840 1 101 3 4 3 19)
}
DER:
30 0B 06 09 60 86 48 01 65 03 04 03 13
*RSASSA-PSS 2048*
AlgorithmIdentifier of Public Key
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Note that we suggest here to use id-RSASSA-PSS
(1.2.840.113549.1.1.10) as the public key OID for RSA-PSS, although
most implementations also would accept rsaEncryption
(1.2.840.113549.1.1.1), and some might in fact prefer or require it.
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-RSASSA-PSS -- (1.2.840.113549.1.1.10)
}
DER:
30 0B 06 09 2A 86 48 86 F7 0D 01 01 0A
AlgorithmIdentifier of Signature
ASN.1:
signatureAlgorithm AlgorithmIdentifier ::= {
algorithm id-RSASSA-PSS, -- (1.2.840.113549.1.1.10)
parameters ANY ::= {
AlgorithmIdentifier ::= {
algorithm id-sha256, -- (2.16.840.1.101.3.4.2.1)
parameters NULL
},
AlgorithmIdentifier ::= {
algorithm id-mgf1, -- (1.2.840.113549.1.1.8)
parameters AlgorithmIdentifier ::= {
algorithm id-sha256, -- (2.16.840.1.101.3.4.2.1)
parameters NULL
}
},
saltLength 32
}
}
DER:
30 41 06 09 2A 86 48 86 F7 0D 01 01 0A 30 34 A0 0F 30 0D 06 09 60 86
48 01 65 03 04 02 01 05 00 A1 1C 30 1A 06 09 2A 86 48 86 F7 0D 01 01
08 30 0D 06 09 60 86 48 01 65 03 04 02 01 05 00 A2 03 02 01 20
*RSASSA-PSS 3072 & 4096*
AlgorithmIdentifier of Public Key
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ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-RSASSA-PSS -- (1.2.840.113549.1.1.10)
}
DER:
30 0B 06 09 2A 86 48 86 F7 0D 01 01 0A
AlgorithmIdentifier of Signature
ASN.1:
signatureAlgorithm AlgorithmIdentifier ::= {
algorithm id-RSASSA-PSS, -- (1.2.840.113549.1.1.10)
parameters ANY ::= {
AlgorithmIdentifier ::= {
algorithm id-sha512, -- (2.16.840.1.101.3.4.2.3)
parameters NULL
},
AlgorithmIdentifier ::= {
algorithm id-mgf1, -- (1.2.840.113549.1.1.8)
parameters AlgorithmIdentifier ::= {
algorithm id-sha512, -- (2.16.840.1.101.3.4.2.3)
parameters NULL
}
},
saltLength 64
}
}
DER:
30 41 06 09 2A 86 48 86 F7 0D 01 01 0A 30 34 A0 0F 30 0D 06 09 60 86
48 01 65 03 04 02 03 05 00 A1 1C 30 1A 06 09 2A 86 48 86 F7 0D 01 01
08 30 0D 06 09 60 86 48 01 65 03 04 02 03 05 00 A2 03 02 01 40
*RSASSA-PKCS1-v1_5 2048*
AlgorithmIdentifier of Public Key
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm rsaEncryption, -- (1.2.840.113549.1.1.1)
parameters NULL
}
DER:
30 0D 06 09 2A 86 48 86 F7 0D 01 01 01 05 00
AlgorithmIdentifier of Signature
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ASN.1:
signatureAlgorithm AlgorithmIdentifier ::= {
algorithm sha256WithRSAEncryption, -- (1.2.840.113549.1.1.11)
parameters NULL
}
DER:
30 0D 06 09 2A 86 48 86 F7 0D 01 01 0D 05 00
*RSASSA-PKCS1-v1_5 3072 & 4096*
AlgorithmIdentifier of Public Key
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm rsaEncryption, -- (1.2.840.113549.1.1.1)
parameters NULL
}
DER:
30 0D 06 09 2A 86 48 86 F7 0D 01 01 01 05 00
AlgorithmIdentifier of Signature
ASN.1:
signatureAlgorithm AlgorithmIdentifier ::= {
algorithm sha512WithRSAEncryption, -- (1.2.840.113549.1.1.13)
parameters NULL
}
DER:
30 0D 06 09 2A 86 48 86 F7 0D 01 01 0D 05 00
*ECDSA NIST P256*
AlgorithmIdentifier of Public Key
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ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-ecPublicKey -- (1.2.840.10045.2.1)
parameters ANY ::= {
AlgorithmIdentifier ::= {
algorithm secp256r1 -- (1.2.840.10045.3.1.7)
}
}
}
DER:
30 13 06 07 2A 86 48 CE 3D 02 01 06 08 2A 86 48 CE 3D 03 01 07
AlgorithmIdentifier of Signature
ASN.1:
signature AlgorithmIdentifier ::= {
algorithm ecdsa-with-SHA256 -- (1.2.840.10045.4.3.2)
}
DER:
30 0A 06 08 2A 86 48 CE 3D 04 03 02
*ECDSA NIST P384*
AlgorithmIdentifier of Public Key
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-ecPublicKey -- (1.2.840.10045.2.1)
parameters ANY ::= {
AlgorithmIdentifier ::= {
algorithm secp384r1 -- (1.3.132.0.34)
}
}
}
DER:
30 10 06 07 2A 86 48 CE 3D 02 01 06 05 2B 81 04 00 22
AlgorithmIdentifier of Signature
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ASN.1:
signature AlgorithmIdentifier ::= {
algorithm ecdsa-with-SHA384 -- (1.2.840.10045.4.3.3)
}
DER:
30 0A 06 08 2A 86 48 CE 3D 04 03 03
*ECDSA NIST P521*
AlgorithmIdentifier of Public Key
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-ecPublicKey -- (1.2.840.10045.2.1)
parameters ANY ::= {
AlgorithmIdentifier ::= {
algorithm secp521r1 -- (1.3.132.0.35)
}
}
}
DER:
30 10 06 07 2A 86 48 CE 3D 02 01 06 05 2B 81 04 00 23
AlgorithmIdentifier of Signature
ASN.1:
signature AlgorithmIdentifier ::= {
algorithm ecdsa-with-SHA512 -- (1.2.840.10045.4.3.4)
}
DER:
30 0A 06 08 2A 86 48 CE 3D 04 03 04
*ECDSA Brainpool-P256*
AlgorithmIdentifier of Public Key
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ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-ecPublicKey -- (1.2.840.10045.2.1)
parameters ANY ::= {
AlgorithmIdentifier ::= {
algorithm brainpoolP256r1 -- (1.3.36.3.3.2.8.1.1.7)
}
}
}
DER:
30 14 06 07 2A 86 48 CE 3D 02 01 06 09 2B 24 03 03 02 08 01 01 07
AlgorithmIdentifier of Signature
ASN.1:
signature AlgorithmIdentifier ::= {
algorithm ecdsa-with-SHA256 -- (1.2.840.10045.4.3.2)
}
DER:
30 0A 06 08 2A 86 48 CE 3D 04 03 02
*ECDSA Brainpool-P384*
AlgorithmIdentifier of Public Key
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-ecPublicKey -- (1.2.840.10045.2.1)
parameters ANY ::= {
AlgorithmIdentifier ::= {
algorithm brainpoolP384r1 -- (1.3.36.3.3.2.8.1.1.11)
}
}
}
DER:
30 14 06 07 2A 86 48 CE 3D 02 01 06 09 2B 24 03 03 02 08 01 01 0B
AlgorithmIdentifier of Signature
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ASN.1:
signature AlgorithmIdentifier ::= {
algorithm ecdsa-with-SHA384 -- (1.2.840.10045.4.3.3)
}
DER:
30 0A 06 08 2A 86 48 CE 3D 04 03 03
*Ed25519*
AlgorithmIdentifier of Public Key and Signature
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-Ed25519 -- (1.3.101.112)
}
DER:
30 05 06 03 2B 65 70
*Ed448*
AlgorithmIdentifier of Public Key and Signature
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-Ed448 -- (1.3.101.113)
}
DER:
30 05 06 03 2B 65 71
Appendix D. Message Representative Examples
This section provides examples of constructing the message
representative M', showing all intermediate values. This is intended
to be useful for debugging purposes.
The input message for this example is the hex string "00 01 02 03 04
05 06 07 08 09".
Each input component is shown. Note that values are shown hex-
encoded for display purposes only, they are actually raw binary
values.
* Prefix is the fixed constant defined in Section 3.2.
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* Domain is the specific domain separator for this composite
algorithm, as defined in Section 7.1.
* len(ctx) is the length of the Message context String which is 00
when no context is used.
* ctx is the Message context string used in the composite signature
combiner. It is empty in this example.
* r is a random 32-byte value chosen by the signer.
* PH(r||M) is the output of hashing the randomizer together with the
message M.
Finally, the fully assembled M' is given, which is simply the
concatenation of the above values.
First is an example of constructing the message representative M' for
MLDSA65-ECDSA-P256-SHA256 without a context string ctx.
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Example of id-MLDSA65-ECDSA-P256-SHA512 construction of M'.
# Inputs:
M: 00010203040506070809
ctx: <empty>
# Components of M':
Prefix:
436f6d706f73697465416c676f726974686d5369676e61747572657332303235
Domain: 060b6086480186fa6b5008016c
len(ctx): 00
ctx: <empty>
r: eef161e927b34b33f15856e15e71e432672944b6e2b85cb3abdf8ae8488ad8f9
PH(r||M): 686537666b03639323e39ce919ce1d1dfc75324888c899fcc616d3bd008d
ee79368a5fb103390b45f06fe8b798d9ce7eb3130ba6006bf9caf9cd2cd7e415b23c
# Outputs:
# M' = Prefix || Domain || len(ctx) || ctx || r || PH(r||M)
M': 436f6d706f73697465416c676f726974686d5369676e6174757265733230323506
0b6086480186fa6b5008016c00eef161e927b34b33f15856e15e71e432672944b6e2b8
5cb3abdf8ae8488ad8f9686537666b03639323e39ce919ce1d1dfc75324888c899fcc6
16d3bd008dee79368a5fb103390b45f06fe8b798d9ce7eb3130ba6006bf9caf9cd2cd7
e415b23c
Second is an example of constructing the message representative M'
for MLDSA65-ECDSA-P256-SHA256 with a context string ctx.
The inputs are similar to the first example with the exception that
there is an 8 byte context string 'ctx'.
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Example of id-MLDSA65-ECDSA-P256-SHA512 construction of M'.
# Inputs:
M: 00010203040506070809
ctx: 0813061205162623
# Components of M':
Prefix:
436f6d706f73697465416c676f726974686d5369676e61747572657332303235
Domain: 060b6086480186fa6b5008016c
len(ctx): 08
ctx: 0813061205162623
r: 6140a149fd5dc32be662d0b2086181ee2d268e727dbbe8e70866439d734d46c9
PH(r||M): 62a2e4b3feb86fa2b86dcb0f43b6916727202abfa786f04ce615558ae7ba
ee4fdec40cc33a7042024ec334d96729c9a3006676aea5d2787de3c83814c696345b
# Outputs:
# M' = Prefix || Domain || len(ctx) || ctx || r || PH(r||M)
M': 436f6d706f73697465416c676f726974686d5369676e6174757265733230323506
0b6086480186fa6b5008016c0808130612051626236140a149fd5dc32be662d0b20861
81ee2d268e727dbbe8e70866439d734d46c962a2e4b3feb86fa2b86dcb0f43b6916727
202abfa786f04ce615558ae7baee4fdec40cc33a7042024ec334d96729c9a3006676ae
a5d2787de3c83814c696345b
Appendix E. Test Vectors
The following test vectors are provided in a format similar to the
NIST ACVP Known-Answer-Tests (KATs).
The structure is that a global message m is signed over in all test
cases. m is the ASCII string "The quick brown fox jumps over the lazy
dog."
Within each test case there are the following values:
* tcId the name of the algorithm.
* pk the verification public key.
* x5c a self-signed X.509 certificate of the public key.
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* sk the raw signature private key.
* sk_pkcs8 the signature private key in a PKCS#8 object.
* s the signature value.
Implementers should be able to perform the following tests using the
test vectors below:
1. Load the public key pk or certificate x5c and use it to verify
the signature s over the message m.
2. Validate the self-signed certificate x5c.
3. Load the signing private key sk or sk_pkcs8 and use it to produce
a new signature which can be verified using the provided pk or
x5c.
Test vectors are provided for each underlying ML-DSA algorithm in
isolation for the purposes of debugging.
Due to the length of the test vectors, some readers will prefer to
retrieve the non-word-wrapped copy from GitHub. The reference
implementation written in python that generated them is also
available:
https://github.com/lamps-wg/draft-composite-sigs/tree/main/src
TODO: lock this to a specific commit.
{
"m":
"VGhlIHF1aWNrIGJyb3duIGZveCBqdW1wcyBvdmVyIHRoZSBsYXp5IGRvZy4=",
"tests": [
{
"tcId": "id-ML-DSA-44",
"pk": "jYk63+WeFzE2gPn/DhyudpNQ
w7ucn2u3/58efuYvO2BcqbZhBbSO0pimoXNpW5oOgqbtQ1PulPDO+O0Q2pbkzaZNuH3M
8reJTZICcpUejHUP86fNIw2LaTfRZ4mL1Qz6Leh3vfvrNQhS5n3h4so/ZZsvfG1dNIS+
vDKr8Aix16NWNUouzxzwDTAk6cx0VhjjXCkFlsihKYc8sGZVGNQXkL4NrSBwMmWPOhuH
PT6Yij8g292cAfkul32QkdOkrVSZAhUFc4kkRwj0HBHKE4MxQHsPe6aWrrdBxiPMoH6I
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L+ApXaLvB+Ux24ge/9w7vOalGWWH4nDeMo0bCiNdxbErztFVSri1ZqDVkpK6nfuNFU50
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"x5c": "MIIPjDCCBgKgAwIBAgIUebJ7bfAKe
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nh5hYycwMLD1+Ll9vj5+gAAAAAAAAAAAAAAAAAAAAAKHS5A",
"sk":
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"VZRcAfPgouPlrA9MNZYDSdDmsIYj6eLmbEiNI3YxQ04=",
"sk_pkcs8": "MDICAQA
wCwYJYIZIAWUDBAMRBCBVlFwB8+Ci4+WsD0w1lgNJ0OawhiPp4uZsSI0jdjFDTg==",
"s": "Goh63CtXLO55wDcobdCXkjF7ruw9gn8xAyHVOjBeGqODoyrSkeHCWLd6KTJF6+
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Ounsworth, et al. Expires 18 December 2025 [Page 78]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 79]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 80]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 81]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 82]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 83]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 84]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 85]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 86]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 87]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 88]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 89]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 90]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 91]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 92]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 93]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 94]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 95]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 96]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 97]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 98]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 99]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 100]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 101]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 102]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 103]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 104]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 105]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 106]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 107]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 108]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 109]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 110]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 111]
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Ounsworth, et al. Expires 18 December 2025 [Page 112]
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Ounsworth, et al. Expires 18 December 2025 [Page 113]
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Ounsworth, et al. Expires 18 December 2025 [Page 114]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 115]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 116]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 117]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 118]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 119]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 120]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 121]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 122]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 123]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 124]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 125]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 126]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 127]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 128]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 129]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 130]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 131]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 132]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 133]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 134]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 135]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 136]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 137]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 138]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 139]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 140]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 141]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 142]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 143]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 144]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 145]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 146]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 147]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 148]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 149]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 150]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 151]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 152]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 153]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 154]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 155]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 156]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 157]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 158]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 159]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 160]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 161]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 162]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 163]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 164]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 165]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 166]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 167]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 168]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 169]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 170]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 171]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 172]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 173]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 174]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 175]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 176]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 177]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 178]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 179]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 180]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 181]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 182]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 183]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 184]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 185]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 186]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 187]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 188]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 189]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 190]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 191]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 192]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 193]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 194]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 195]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 196]
Internet-Draft Composite ML-DSA June 2025
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Ounsworth, et al. Expires 18 December 2025 [Page 197]
Internet-Draft Composite ML-DSA June 2025
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}
]
}
Appendix F. Intellectual Property Considerations
The following IPR Disclosure relates to this draft:
https://datatracker.ietf.org/ipr/3588/
Appendix G. Contributors and Acknowledgements
This document incorporates contributions and comments from a large
group of experts. The editors would especially like to acknowledge
the expertise and tireless dedication of the following people, who
attended many long meetings and generated millions of bytes of
electronic mail and VOIP traffic over the past six years in pursuit
of this document:
Serge Mister (Entrust), Felipe Ventura (Entrust), Richard Kettlewell
(Entrust), Ali Noman (Entrust), Daniel Van Geest (CryptoNext), Dr.
Britta Hale (Naval Postgraduade School), Tim Hollebeek (Digicert),
Panos Kampanakis (Amazon), Chris A. Wood (Apple), Christopher D.
Wood (Apple), Sophie Schmieg (Google), Bas Westerbaan (Cloudflare),
Deirdre Connolly (SandboxAQ), Richard Kisley (IBM), Piotr Popis
(Enigma), François Rousseau, Falko Strenzke, Alexander Ralien
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(Siemens), José Ignacio Escribano, Jan Oupický, 陳志華 (Abel C. H.
Chen, Chunghwa Telecom), 林邦曄 (Austin Lin, Chunghwa Telecom), Zhao
Peiduo (Seventh Sense AI), Phil Hallin (Microsoft), Samuel Lee
(Microsoft), Alicja Kario (Red Hat), Jean-Pierre Fiset (Crypto4A),
Varun Chatterji (Seventh Sense AI), Mojtaba Bisheh-Niasar and Douglas
Stebila (University of Waterloo).
We especially want to recognize the contributions of Dr. Britta Hale
who has helped immensely with strengthening the signature combiner
construction, and with analyzing the scheme with respect to EUF-CMA
and Non-Separability properties.
Thanks to Giacomo Pope (github.com/GiacomoPope) whose ML-DSA and ML-
KEM implementations were used to generate the test vectors.
We are grateful to all who have given feedback over the years,
formally or informally, on mailing lists or in person, including any
contributors who may have been inadvertently omitted from this list.
Finally, we wish to thank the authors of all the referenced documents
upon which this specification was built. "Copying always makes
things easier and less error prone" - [RFC8411].
Authors' Addresses
Mike Ounsworth
Entrust Limited
2500 Solandt Road – Suite 100
Ottawa, Ontario K2K 3G5
Canada
Email: mike.ounsworth@entrust.com
John Gray
Entrust Limited
2500 Solandt Road – Suite 100
Ottawa, Ontario K2K 3G5
Canada
Email: john.gray@entrust.com
Massimiliano Pala
OpenCA Labs
New York City, New York,
United States of America
Email: director@openca.org
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Jan Klaussner
Bundesdruckerei GmbH
Kommandantenstr. 18
10969 Berlin
Germany
Email: jan.klaussner@bdr.de
Scott Fluhrer
Cisco Systems
Email: sfluhrer@cisco.com
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