Composite ML-DSA for use in X.509 Public Key Infrastructure
draft-ietf-lamps-pq-composite-sigs-11
The information below is for an old version of the document.
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| Authors | Mike Ounsworth , John Gray , Massimiliano Pala , Jan Klaußner , Scott Fluhrer | ||
| Last updated | 2025-10-09 (Latest revision 2025-10-05) | ||
| Replaces | draft-ounsworth-pq-composite-sigs | ||
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draft-ietf-lamps-pq-composite-sigs-11
LAMPS M. Ounsworth
Internet-Draft J. Gray
Intended status: Standards Track Entrust
Expires: 13 April 2026 M. Pala
OpenCA Labs
J. Klaussner
Bundesdruckerei GmbH
S. Fluhrer
Cisco Systems
10 October 2025
Composite ML-DSA for use in X.509 Public Key Infrastructure
draft-ietf-lamps-pq-composite-sigs-11
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 since -07 (WGLC) . . . . . . . . . . . . . . . . . . 3
2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1. Conventions and Terminology . . . . . . . . . . . . . . . 7
2.2. Composite Design Philosophy . . . . . . . . . . . . . . . 8
3. Overview of the Composite ML-DSA Signature Scheme . . . . . . 9
3.1. Pre-hashing . . . . . . . . . . . . . . . . . . . . . . . 10
3.2. Prefix, Label and CTX . . . . . . . . . . . . . . . . . . 11
4. Composite ML-DSA Functions . . . . . . . . . . . . . . . . . 12
4.1. Key Generation . . . . . . . . . . . . . . . . . . . . . 12
4.2. Sign . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.3. Verify . . . . . . . . . . . . . . . . . . . . . . . . . 16
5. Serialization . . . . . . . . . . . . . . . . . . . . . . . . 19
5.1. SerializePublicKey and DeserializePublicKey . . . . . . . 20
5.2. SerializePrivateKey and DeserializePrivateKey . . . . . . 23
5.3. SerializeSignatureValue and DeserializeSignatureValue . . 24
6. Use within X.509 and PKIX . . . . . . . . . . . . . . . . . . 27
6.1. Encoding to DER . . . . . . . . . . . . . . . . . . . . . 27
6.2. Key Usage Bits . . . . . . . . . . . . . . . . . . . . . 27
6.3. ASN.1 Definitions . . . . . . . . . . . . . . . . . . . . 28
7. Algorithm Identifiers and Parameters . . . . . . . . . . . . 30
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7.1. RSASSA-PSS Parameters . . . . . . . . . . . . . . . . . . 37
7.2. Rationale for choices . . . . . . . . . . . . . . . . . . 38
8. ASN.1 Module . . . . . . . . . . . . . . . . . . . . . . . . 39
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 46
9.1. Object Identifier Allocations . . . . . . . . . . . . . . 46
9.1.1. Module Registration . . . . . . . . . . . . . . . . . 46
9.1.2. Object Identifier Registrations . . . . . . . . . . . 46
10. Security Considerations . . . . . . . . . . . . . . . . . . . 49
10.1. Why Hybrids? . . . . . . . . . . . . . . . . . . . . . . 50
10.2. EUF-CMA, SUF-CMA and non-separability . . . . . . . . . 50
10.2.1. EUF-CMA . . . . . . . . . . . . . . . . . . . . . . 51
10.2.2. SUF-CMA . . . . . . . . . . . . . . . . . . . . . . 52
10.2.3. Non-separability . . . . . . . . . . . . . . . . . . 52
10.3. Key Reuse . . . . . . . . . . . . . . . . . . . . . . . 53
10.4. Use of Prefix for attack mitigation . . . . . . . . . . 54
10.5. Policy for Deprecated and Acceptable Algorithms . . . . 55
11. Implementation Considerations . . . . . . . . . . . . . . . . 55
11.1. FIPS certification . . . . . . . . . . . . . . . . . . . 55
11.2. Backwards Compatibility . . . . . . . . . . . . . . . . 56
11.3. Profiling down the number of options . . . . . . . . . . 57
11.4. External Pre-hashing . . . . . . . . . . . . . . . . . . 58
12. References . . . . . . . . . . . . . . . . . . . . . . . . . 59
12.1. Normative References . . . . . . . . . . . . . . . . . . 59
12.2. Informative References . . . . . . . . . . . . . . . . . 62
Appendix A. Maximum Key and Signature Sizes . . . . . . . . . . 64
Appendix B. Component Algorithm Reference . . . . . . . . . . . 66
Appendix C. Component AlgorithmIdentifiers for Public Keys and
Signatures . . . . . . . . . . . . . . . . . . . . . . . 68
Appendix D. Message Representative Examples . . . . . . . . . . 76
Appendix E. Test Vectors . . . . . . . . . . . . . . . . . . . . 78
Appendix F. Intellectual Property Considerations . . . . . . . . 201
Appendix G. Contributors and Acknowledgements . . . . . . . . . 201
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 202
1. Changes since -07 (WGLC)
Interop-affecting changes:
* Removed the randomizer, reverting the signature combiner
construction to be similar to the HashComposite construction from
-05.
* Fixed the ASN.1 module for the pk-CompositeSignature and sa-
CompositeSignature to indicate no ASN.1 wrapping is used. This
simply clarifies the intended encoding but could be an interop-
affecting change for implementations that built encoders /
decoders from the ASN.1 and ended up with a non-intended encoding.
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* Aligned the hash function used for the RSA component to the RSA
key size (Thanks Dan!).
* Changed the OID-based Domain Separators into HPKE-style signature
label strings to match draft-irtf-cfrg-concrete-hybrid-kems-00.
* Updated to new prototype OIDs since it is not binary compatible
with the previous release.
* Dan Van Geest correctly pointed out that in ECPrivateKey
(RFC5915), the parameters are not optional. They have been added
to the private keys in the test vectors.
* The Ed25519 and Ed448 private keys had been wrapped in OCTET
STRING to match CurvePrivateKey (RFC8410). This has been changed
to 32/57 byte raw.
Editorial changes:
* Incorporated the feedback from IETF 123, clarifying the pubic,
private key and signature encodings.
* Many minor editorial fixes based on comments from the working
group.
* Adjusted the Security Considerations about EUF-CMA and Non-
Separability to match the removal of the randomizer.
* Clarified that the ECDSA public key is raw X9.62 with no OCTET
STRING wrapping. Test vectors were already correct.
A full review was performed of the encoding of each component:
* ML-DSA:
- pub key, priv key, sig value: Raw, according to FIPS 204. Test
vectors appear to match.
* RSA:
- pub key: ASN.1 RSAPublicKey. Test vectors appear to match
(manually inspected "id-MLDSA44-RSA2048-PSS-SHA256").
- priv key: RSAPrivateKey (CRT). Test vectors appear to match
(manually inspected "id-MLDSA44-RSA2048-PSS-SHA256").
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- sig value: length of sig for "id-MLDSA44-RSA2048-PSS-SHA256"
and "id-MLDSA44-RSA2048-PKCS15-SHA256" verified to be 256
bytes, format hard to manually inspect.
* ECDSA: Inspecting test vectors for "id-MLDSA44-ECDSA-P256-SHA256"
- pub key: The wording of the pub key format in Section 2.2 of
RFC5480 is extremely confusing in how it would apply outside of
a SubjectPublicKeyInfo. The Composite author's interpretation
was for it to be raw X9.62, which is what is already in the
test vectors: verified to be raw X9.62 with a leading byte of
0x04 (uncompressed). Normative text in Section 5 is incorrect
and has been changed.
- priv key: This is the ASN.1 structure ECPrivateKey [RFC5915] as
intended, however, as Dan Van Geest points out, the parameters
field, while marked OPTIONAL is actually required by Section 3
of RFC5915. That means the private keys here are invalid.
This has been corrected in the test vectors.
- sig value: This is an ASN.1 Ecdsa-Sig-Value [RFC3279] as
intended.
* EdDSA:
- pub key: 32 byte raw.
- priv key: Had been wrapped in OCTET STRING to match
CurvePrivateKey (RFC8410). This has been changed to 32/57 byte
raw.
- sig value: 64 byte raw.
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, this
migration gives us the foresight that Traditional cryptographic
algorithms will be broken in the future, with the Traditional
algorithms remaining strong in the interim, the only uncertainty is
around the timing. But there are also some novel challenges. 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 adversary 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 [RFC9794].
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].
Another motivation for using PQ/T Hybrids is regulatory compliance;
for example, in some situations it might be possible to add Post-
Quantum, via a PQ/T Hybrid, to an already audited and compliant
solution without invalidating the existing certification, whereas a
full replacement of the Traditional cryptography would almost
certainly incur regulatory and compliance delays. In other words,
PQ/T Hybrids can allow for deploying Post-Quantum before the PQ
modules and operational procedures are fully audited and certified.
This, more than any other requirement, is what motivates the large
number of algorithm combinations in this specification: the intention
is to provide a stepping-stone off of which ever cryptographic
algorithm(s) an organization might have deployed today.
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
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systems is not directly covered in this specification, but is the
subject of Section 11.2. The idea of a composite was first presented
in [Bindel2017].
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
meanings.
This specification is consistent with the terminology defined in
[RFC9794]. 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
[RFC9794].
*COMPONENT / PRIMITIVE*: The words "component" or "primitive" are
used interchangeably to refer to an asymmetric 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".
*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.
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* (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 parameterized 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.
2.2. Composite Design Philosophy
[RFC9794] 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.
In terms of security properties, Composite ML-DSA will be EUF-CMA
secure if at least one of its component algorithms is EUF-CMA secure
and the message hash PH is collision resistant. SUF-CMA security of
Composite ML-DSA is more complicated. While some of the algorithm
combinations defined in this specification are likely to be SUF-CMA
secure against classical adversaries, none are SUF-CMA secure against
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a quantum adversary. This means that replacing an ML-DSA signature
with a Composite ML-DSA signature could be considered a reduction in
security if your application is sensitive to the difference between
SUF-CMA and EUF-CMA security. Composite ML-DSA is NOT RECOMMENDED
for use in applications requiring SUF-CMA security. Further
discussion can be found in Section 10.2.
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 pre-hashing and prepends
several signature label 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 match the API of a generic signature scheme, which consists of
three algorithms:
* 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 and are provided as internal functions
for use by the public functions KeyGen(), Sign(), and Verify().
These algorithms are inspired by similar algorithms in [RFC9180].
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* 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) -> (mldsaSeed, tradSK): Parse a byte
string to recover the component private keys.
* SerializeSignatureValue(mldsaSig, tradSig) -> bytes: Produce a
byte string encoding of the component signature values.
* DeserializeSignatureValue(bytes) -> (mldsaSig, tradSig): Parse a
byte string to recover the component signature values.
Full definitions of serialization and deserialization algorithms can
be found in Section 5.
3.1. Pre-hashing
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. 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 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.
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See Section 11.4 for a discussion of externalizing the pre-hashing
step.
3.2. Prefix, Label and CTX
The to-be-signed message representative M' is created by
concatenating several values, including the pre-hashed message.
M' := Prefix || Label || len(ctx) || ctx || PH( M )
Prefix: A fixed octet string which is the byte encoding of the ASCII
string "CompositeAlgorithmSignatures2025" which in hex is:
436F6D706F73697465416C676F726974686D5369676E61747572657332303235
See Section 10.4 for more information on the prefix.
Label: A signature label which is specific to each composite
algorithm. The signature label binds the signature to the
specific composite algorithm. Signature label values for each
algorithm are listed in Section 7.
len(ctx): A single unsigned byte encoding the length of the context.
ctx: The context bytes, which allows for applications to bind the
signature to an application context.
PH( M ): The hash of the message to be signed.
Each Composite ML-DSA algorithm has a unique signature label 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 of X.509, or
if the prohibition on reusing key material between a composite and a
non-composite, or between two composites is not adhered to.
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 per-algorithm Label is used as the ctx for the underlying ML-DSA
primitive. The EdDSA component primitive can also expose a ctx
parameter, but this is not used by Composite ML-DSA.
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Within Composite ML-DSA, values of Label are fully specified, and
runtime-variable Label values are not allowed. For authors of
follow-on specifications that allow Label to be runtime-variable, it
should be pre-fixed with the length, len(Label) || Label to prevent
using this as an injection site that could enable various
cryptographic attacks.
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-threaded, multi-process, or multi-module applications might
choose to execute the key generation functions in parallel for better
key generation performance or architectural modularity.
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 "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, mldsaSK) = ML-DSA.KeyGen_internal(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)
This keygen routine make use of the seed-based ML-
DSA.KeyGen_internal(𝜉), which is defined in Algorithm 6 of
[FIPS.204]. For FIPS-certification implications, see Section 11.1.
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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 10.3.
Note that this keygen routine outputs a serialized composite key,
which contains only the ML-DSA seed. Implementations should feel
free to modify this routine to additionally output the expanded
mldsaSK or to make free use of ML-DSA.KeyGen_internal(mldsaSeed) as
needed to expand the ML-DSA seed into an expanded key prior to
performing a signing operation.
The above algorithm MAY be modified to expose an interface of
Composite-ML-DSA<OID>.KeyGen(seed) if it is desirable to have a
deterministic KeyGen that derives both component keys from a shared
seed. Details of implementing this variation are not included in
this document.
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_internal(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 of 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.
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The following describes how to instantiate a Sign() function for a
given Composite ML-DSA algorithm represented by <OID>. See
Section 3.1 for a discussion of the pre-hash function PH. See
Section 3.2 for a discussion on the signature label Label and
application context ctx. See Section 11.4 for a discussion of
externalizing the pre-hashing step.
Composite-ML-DSA<OID>.Sign(sk, M, ctx) -> s
Explicit inputs:
sk Composite private key consisting of signing private keys
for each component.
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 "ML-DSA-65".
Trad The underlying traditional algorithm and
parameter set, for example "sha256WithRSAEncryption"
or "Ed25519".
Prefix The prefix octet string.
Label A signature label which is specific to each composite
algorithm. Additionally, the composite label is passed
into the underlying ML-DSA primitive as the ctx.
Signature Label values are defined in the "Signature Label Values"
section below.
PH The function used to pre-hash M.
Output:
s The composite signature value.
Signature Generation Process:
1. If len(ctx) > 255:
return error
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2. Compute the Message representative M'.
As in FIPS 204, len(ctx) is encoded as a single unsigned byte.
M' := Prefix || Label || len(ctx) || ctx || PH( M )
3. Separate the private key into component keys
and re-generate the ML-DSA key from seed.
(mldsaSeed, tradSK) = DeserializePrivateKey(sk)
(_, mldsaSK) = ML-DSA.KeyGen_internal(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=Label )
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(mldsaSig, tradSig)
return 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.
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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>. See Section 3.1 for
a discussion of the pre-hash function PH. See Section 3.2 for a
discussion on the signature label Label and application context ctx.
See Section 11.4 for a discussion of externalizing the pre-hashing
step.
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 "ML-DSA-65".
Trad The underlying traditional algorithm and
parameter set, for example "sha256WithRSAEncryption"
or "Ed25519".
Prefix The prefix octet string.
Label A signature label which is specific to each composite
algorithm. Additionally, the composite label is passed
into the underlying ML-DSA primitive as the ctx.
Signature Label values are defined in the "Signature Label Values"
section below.
PH The function used to pre-hash M.
Output:
Validity (bool) "Valid signature" (true) if the composite
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signature is valid, "Invalid signature"
(false) otherwise.
Signature Verification Process:
1. If len(ctx) > 255
return error
2. Separate the keys and signatures
(mldsaPK, tradPK) = DeserializePublicKey(pk)
(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 || Label || len(ctx) || ctx || PH( 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=Label ) then
output "Invalid signature"
if not Trad.Verify( tradPK, M', tradSig ) then
output "Invalid signature"
if all succeeded, then
output "Valid signature"
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.
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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 details 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.
+===========+============+=============+===========+
| 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 Sizes
While ML-DSA has a single fixed-size representation for each of
public key, private key (seed), and signature, a traditional
component algorithm might allow multiple valid encodings. For
example, a stand-alone RSA private key can be encoded in Chinese
Remainder Theorem form. In order to obtain interoperability,
composite algorithms MUST use the following encodings of the
underlying components:
* *ML-DSA*: MUST be encoded as specified in section 7.2 of
[FIPS.204], using a 32-byte seed as the private key. The
signature and public key format are encoded as specified in
section 7.2 of [FIPS.204].
* *RSA*: the public key MUST be encoded as RSAPublicKey with the
(n,e) public key representation as specified in A.1.1 of [RFC8017]
and the private key representation as RSAPrivateKey specified in
A.1.2 of [RFC8017] with version 0 and 'otherPrimeInfos' absent.
An RSA signature MUST be encoded as specified in section 8.1.1
(for RSASSA-PSS-SIGN) or 8.2.1 (for RSASSA-PCKS1-V1_5-SIGN) of
[RFC8017].
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* *ECDSA*: public key MUST be encoded as an uncompressed X9.62
[X9.62_2005], including the leading byte 0x04 indicating
uncompressed. This is consistent with the encoding of ECPoint as
specified in section 2.2 of [RFC5480] when no ASN.1 OCTET STRING
wrapping is present. A signature MUST be encoded as an Ecdsa-Sig-
Value as specified in section 2.2.3 of [RFC3279]. The private key
MUST be encoded as ECPrivateKey specified in [RFC5915] without
'NamedCurve' parameter and without 'publicKey' field.
* *EdDSA*: public key and signature MUST be encoded as per section 3
of [RFC8032] and the private key is a 32 or 57 byte raw value for
Ed25519 and Ed448 respectively, which can be converted to a
CurvePrivateKey specified in [RFC8410] by the addition of an OCTET
STRING wrapper.
All ASN.1 objects SHALL be encoded using DER on serialization. For
all serialization routines below, when their output values are
required to be carried in an ASN.1 structure, they are wrapped as
described in Section 6.1.
Even with fixed encodings for the traditional component, there might
be slight differences in size of the encoded value due to, for
example, encoding rules that drop leading zeroes. See Appendix A for
a table of maximum sizes for each composite algorithm and further
discussion of the reason for variations in these sizes.
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.
5.1. SerializePublicKey and DeserializePublicKey
The serialization routine for keys simply concatenates the public
keys of the component signature algorithms, as defined below:
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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
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 "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)
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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
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
parameterized.
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Composite-ML-DSA.DeserializePrivateKey(bytes) -> (mldsaSeed, tradSK)
Explicit inputs:
bytes An encoded composite private key.
Implicit inputs:
None
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.
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)
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(mldsaSig, tradSig) -> bytes
Explicit inputs:
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 mldsaSig || tradSig
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>.
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Composite-ML-DSA<OID>.DeserializeSignatureValue(bytes)
-> (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,
for example "ML-DSA-65".
Output:
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 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 = bytes[:2420]
tradSig = bytes[2420:]
case ML-DSA-65:
mldsaSig = bytes[:3309]
tradSig = bytes[3309:]
case ML-DSA-87:
mldsaSig = bytes[:4627]
tradSig = bytes[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 (mldsaSig, tradSig)
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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.
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-
encoded message format such as an X.509's subjectPublicKey and
signatureValue BIT STRING [RFC5280] or a OneAsymmetricKey.privateKey
OCTET STRING [RFC5958], then the BIT STRING or OCTET STRING contains
this raw byte string encoding of the public key.
When a Composite ML-DSA public key appears outside of a
SubjectPublicKeyInfo type in an environment that uses ASN.1 encoding,
it could be encoded as an OCTET STRING by using the Composite-ML-DSA-
PublicKey type defined below.
Composite-ML-DSA-PublicKey ::= OCTET STRING
Size constraints MAY be enforced, as appropriate as per Appendix A.
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:
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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:
digitalSignature;
nonRepudiation; and
cRLSign.
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 defined to allow
for compact definitions of each composite algorithm, leading to a
smaller overall ASN.1 module.
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pk-CompositeSignature {OBJECT IDENTIFIER:id}
PUBLIC-KEY ::= {
IDENTIFIER id
-- KEY no ASN.1 wrapping --
PARAMS ARE absent
CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign,
cRLSign}
-- PRIVATE-KEY no ASN.1 wrapping --
}
sa-CompositeSignature{OBJECT IDENTIFIER:id,
PUBLIC-KEY:publicKeyType }
SIGNATURE-ALGORITHM ::= {
IDENTIFIER id
-- VALUE no ASN.1 wrapping --
PARAMS ARE absent
PUBLIC-KEYS {publicKeyType}
}
Figure 1: 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:
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:
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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 2: 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
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 10.3.
7. Algorithm Identifiers and Parameters
This section lists the algorithm identifiers and parameters for all
Composite ML-DSA algorithms.
Full specifications for the referenced algorithms can be found in
Appendix B.
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As the number of algorithms can be daunting, implementers who wish to
implement only a single composite algorithm should see Section 11.3
for a discussion of the best algorithm for the most common use cases.
Labels are represented here as ASCII strings, but implementers MUST
convert them to byte strings using the obvious ASCII conversions
prior to concatenating them with other byte values as described in
Section 3.2.
EDNOTE: the OIDs listed below are prototyping OIDs defined in
Entrust's 2.16.840.1.114027.80.9.1 arc but will be replaced by IANA.
* id-MLDSA44-RSA2048-PSS-SHA256
- OID: 2.16.840.1.114027.80.9.1.20
- Label: COMPSIG-MLDSA44-RSA2048-PSS-SHA256
- Pre-Hash function (PH): SHA256
- ML-DSA variant: ML-DSA-44
- Traditional Algorithm: RSA
o Traditional Signature Algorithm: id-RSASSA-PSS
o RSA size: 2048
o RSASSA-PSS parameters: See Table 2
* id-MLDSA44-RSA2048-PKCS15-SHA256
- OID: 2.16.840.1.114027.80.9.1.21
- Label: COMPSIG-MLDSA44-RSA2048-PKCS15-SHA256
- Pre-Hash function (PH): SHA256
- ML-DSA variant: ML-DSA-44
- Traditional Algorithm: RSA
o Traditional Signature Algorithm: sha256WithRSAEncryption
o RSA size: 2048
* id-MLDSA44-Ed25519-SHA512
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- OID: 2.16.840.1.114027.80.9.1.22
- Label: COMPSIG-MLDSA44-Ed25519-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-44
- Traditional Algorithm: Ed25519
o Traditional Signature Algorithm: id-Ed25519
* id-MLDSA44-ECDSA-P256-SHA256
- OID: 2.16.840.1.114027.80.9.1.23
- Label: COMPSIG-MLDSA44-ECDSA-P256-SHA256
- Pre-Hash function (PH): SHA256
- ML-DSA variant: ML-DSA-44
- Traditional Algorithm: ECDSA
o Traditional Signature Algorithm: ecdsa-with-SHA256
o ECDSA curve: secp256r1
* id-MLDSA65-RSA3072-PSS-SHA512
- OID: 2.16.840.1.114027.80.9.1.24
- Label: COMPSIG-MLDSA65-RSA3072-PSS-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-65
- Traditional Algorithm: RSA
o Traditional Signature Algorithm: id-RSASSA-PSS
o RSA size: 3072
o RSASSA-PSS parameters: See Table 2
* id-MLDSA65-RSA3072-PKCS15-SHA512
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- OID: 2.16.840.1.114027.80.9.1.25
- Label: COMPSIG-MLDSA65-RSA3072-PKCS15-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-65
- Traditional Algorithm: RSA
o Traditional Signature Algorithm: sha256WithRSAEncryption
o RSA size: 3072
* id-MLDSA65-RSA4096-PSS-SHA512
- OID: 2.16.840.1.114027.80.9.1.26
- Label: COMPSIG-MLDSA65-RSA4096-PSS-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-65
- Traditional Algorithm: RSA
o Traditional Signature Algorithm: id-RSASSA-PSS
o RSA size: 4096
o RSASSA-PSS parameters: See Table 3
* id-MLDSA65-RSA4096-PKCS15-SHA512
- OID: 2.16.840.1.114027.80.9.1.27
- Label: COMPSIG-MLDSA65-RSA4096-PKCS15-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-65
- Traditional Algorithm: RSA
o Traditional Signature Algorithm: sha384WithRSAEncryption
o RSA size: 4096
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* id-MLDSA65-ECDSA-P256-SHA512
- OID: 2.16.840.1.114027.80.9.1.28
- Label: COMPSIG-MLDSA65-P256-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-65
- Traditional Algorithm: ECDSA
o Traditional Signature Algorithm: ecdsa-with-SHA256
o ECDSA curve: secp256r1
* id-MLDSA65-ECDSA-P384-SHA512
- OID: 2.16.840.1.114027.80.9.1.29
- Label: COMPSIG-MLDSA65-P384-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-65
- Traditional Algorithm: ECDSA
o Traditional Signature Algorithm: ecdsa-with-SHA384
o ECDSA curve: secp384r1
* id-MLDSA65-ECDSA-brainpoolP256r1-SHA512
- OID: 2.16.840.1.114027.80.9.1.30
- Label: COMPSIG-MLDSA65-BP256-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-65
- Traditional Algorithm: ECDSA
o Traditional Signature Algorithm: ecdsa-with-SHA256
o ECDSA curve: brainpoolP256r1
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* id-MLDSA65-Ed25519-SHA512
- OID: 2.16.840.1.114027.80.9.1.31
- Label: COMPSIG-MLDSA65-Ed25519-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-65
- Traditional Algorithm: Ed25519
o Traditional Signature Algorithm: id-Ed25519
* id-MLDSA87-ECDSA-P384-SHA512
- OID: 2.16.840.1.114027.80.9.1.32
- Label: COMPSIG-MLDSA87-P384-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-87
- Traditional Algorithm: ECDSA
o Traditional Signature Algorithm: ecdsa-with-SHA384
o ECDSA curve: secp384r1
* id-MLDSA87-ECDSA-brainpoolP384r1-SHA512
- OID: 2.16.840.1.114027.80.9.1.33
- Label: COMPSIG-MLDSA87-BP384-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-87
- Traditional Algorithm: ECDSA
o Traditional Signature Algorithm: ecdsa-with-SHA384
o ECDSA curve: brainpoolP384r1
* id-MLDSA87-Ed448-SHAKE256
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- OID: 2.16.840.1.114027.80.9.1.34
- Label: COMPSIG-MLDSA87-Ed448-SHAKE256
- Pre-Hash function (PH): SHAKE256/64**
- ML-DSA variant: ML-DSA-87
- Traditional Algorithm: Ed448
o Traditional Signature Algorithm: id-Ed448
* id-MLDSA87-RSA3072-PSS-SHA512
- OID: 2.16.840.1.114027.80.9.1.35
- Label: COMPSIG-MLDSA87-RSA3072-PSS-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-87
- Traditional Algorithm: RSA
o Traditional Signature Algorithm: id-RSASSA-PSS
o RSA size: 3072
o RSASSA-PSS parameters: See Table 2
* id-MLDSA87-RSA4096-PSS-SHA512
- OID: 2.16.840.1.114027.80.9.1.36
- Label: COMPSIG-MLDSA87-RSA4096-PSS-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-87
- Traditional Algorithm: RSA
o Traditional Signature Algorithm: id-RSASSA-PSS
o RSA size: 4096
o RSASSA-PSS parameters: See Table 3
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* id-MLDSA87-ECDSA-P521-SHA512
- OID: 2.16.840.1.114027.80.9.1.37
- Label: COMPSIG-MLDSA87-P521-SHA512
- Pre-Hash function (PH): SHA512
- ML-DSA variant: ML-DSA-87
- Traditional Algorithm: ECDSA
o Traditional Signature Algorithm: ecdsa-with-SHA512
o ECDSA curve: secp521r1
For all RSA key types and sizes, the exponent is RECOMMENDED to be
65537. Implementations MAY support only 65537 and reject other
exponent values. Legacy RSA implementations that use other values
for the exponent MAY be used within a composite, but need to be
careful when interoperating with other implementations.
**Note: 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.
7.1. RSASSA-PSS Parameters
Use of RSASSA-PSS [RFC8017] requires extra parameters to be
specified.
The RSASSA-PSS-params ASN.1 type defined in [RFC8017] is not used in
Composite ML-DSA encodings since the parameter values are fixed by
this specification. However, below refer to the named fields of the
RSASSA-PSS-params ASN.1 type in order to provide a mapping between
the use of RSASSA-PSS in Composite ML-DSA and [RFC8017]
When RSA-PSS is used at the 2048-bit or 3072-bit security level,
RSASSA-PSS SHALL be instantiated with the following parameters:
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+=============================+===========+
| RSASSA-PSS-params field | Value |
+=============================+===========+
| hashAlgorithm | id-sha256 |
+-----------------------------+-----------+
| maskGenAlgorithm.algorithm | id-mgf1 |
+-----------------------------+-----------+
| maskGenAlgorithm.parameters | id-sha256 |
+-----------------------------+-----------+
| saltLength | 32 |
+-----------------------------+-----------+
| trailerField | 1 |
+-----------------------------+-----------+
Table 2: RSASSA-PSS 2048 and 3072
Parameters
When RSA-PSS is used at the 4096-bit security level, RSASSA-PSS SHALL
be instantiated with the following parameters:
+=============================+===========+
| RSASSA-PSS-params field | Value |
+=============================+===========+
| hashAlgorithm | id-sha384 |
+-----------------------------+-----------+
| maskGenAlgorithm.algorithm | id-mgf1 |
+-----------------------------+-----------+
| maskGenAlgorithm.parameters | id-sha384 |
+-----------------------------+-----------+
| saltLength | 48 |
+-----------------------------+-----------+
| trailerField | 1 |
+-----------------------------+-----------+
Table 3: RSASSA-PSS 4096 Parameters
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
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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 adversaries and "qubits of security"
against quantum adversaries.
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.
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;
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) }
;
--
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-- Object Identifiers
--
--
-- Information Object Classes
--
pk-CompositeSignature {OBJECT IDENTIFIER:id}
PUBLIC-KEY ::= {
IDENTIFIER id
-- KEY no ASN.1 wrapping --
PARAMS ARE absent
CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign,
cRLSign}
-- PRIVATE-KEY no ASN.1 wrapping --
}
sa-CompositeSignature{OBJECT IDENTIFIER:id,
PUBLIC-KEY:publicKeyType }
SIGNATURE-ALGORITHM ::= {
IDENTIFIER id
-- VALUE no ASN.1 wrapping --
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-mldsa(9) signature(1) 20 }
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,
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-mldsa(9) signature(1) 21 }
pk-MLDSA44-RSA2048-PKCS15-SHA256 PUBLIC-KEY ::=
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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-mldsa(9) signature(1) 22 }
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-mldsa(9) signature(1) 23 }
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-mldsa(9) signature(1) 24 }
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 }
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-- 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-mldsa(9) signature(1) 25 }
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-mldsa(9) signature(1) 26 }
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-mldsa(9) signature(1) 27 }
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 }
-- 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-mldsa(9) signature(1) 28 }
pk-MLDSA65-ECDSA-P256-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA65-ECDSA-P256-SHA512}
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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-mldsa(9) signature(1) 29 }
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-mldsa(9) signature(1) 30 }
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-mldsa(9) signature(1) 31 }
pk-MLDSA65-Ed25519-SHA512 PUBLIC-KEY ::=
pk-CompositeSignature{ id-MLDSA65-Ed25519-SHA512}
sa-MLDSA65-Ed25519-SHA512 SIGNATURE-ALGORITHM ::=
sa-CompositeSignature{
id-MLDSA65-Ed25519-SHA512,
pk-MLDSA65-Ed25519-SHA512 }
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-- 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-mldsa(9) signature(1) 32 }
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-mldsa(9) signature(1) 33 }
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-mldsa(9) signature(1) 34 }
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 }
-- 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-mldsa(9) signature(1) 35 }
pk-MLDSA87-RSA3072-PSS-SHA512 PUBLIC-KEY ::=
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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-mldsa(9) signature(1) 36 }
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-mldsa(9) signature(1) 37 }
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 |
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 |
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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 assign an object identifier (OID) for the module
identifier (TBDMOD) with a Description of "id-mod-composite-mldsa-
2025". The OID for the module should be allocated in the "SMI
Security for PKIX Module Identifier" registry (1.3.6.1.5.5.7.0).
IANA is also requested to allocate values from the "SMI Security for
PKIX Algorithms" registry (1.3.6.1.5.5.7.6) 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 Section 7.
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":
* id-MLDSA44-RSA2048-PSS-SHA256
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- 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
* id-MLDSA65-RSA4096-PSS-SHA512
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- 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
* id-MLDSA87-ECDSA-P384-SHA512
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- 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
10. Security Considerations
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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 adversary 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 adversary 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, and also in the fact that
the composite public key could be trusted by the verifier while the
component keys in isolation are not, thus requiring the adversary to
forge a whole composite signature.
*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. EUF-CMA, SUF-CMA and non-separability
First, a note about the security model under which this analysis is
performed. This specification strictly forbids re-using component
key material between composite and non-composite keys, or between
multiple composite keys. This specification also exists within the
X.509 PKI architecture where trust in a public verification key is
assumed to be established either directly via a trust store or via a
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certificate chain. That said, these are both policy mechanisms that
are outside the formal definitions of EUF-CMA and SUF-CMA under which
a signature primitive must be analysed, therefore this section
considers attacks that may be mitigated partially or completely
within a strictly-implemented PKI setting, but which need to be
considered when considering Composite ML-DSA as a general-purpose
signature primitive that could be used outside of the X.509 setting.
The second securtiy model considiration is that composites are
designed to provide value even if one algorithm is broken, even if
you do not know which. However, the security properties offered by
the composite signature can differ based on which algorithm you
consider to be broken.
10.2.1. EUF-CMA
A signature algorithm is Existentially Unforgeable under Chosen-
Message Attack (EUF-CMA) if an adversary that has access to a signing
oracle cannot create a message-signature pair (M, Sig) that would be
accepted by the verifier for any message M that was not an input to a
signing oracle query.
In general, Composite ML-DSA will be EUF-CMA secure if at least one
of the component algorithms is EUF-CMA secure and PH is collision
resistant. Any algorithm that creates an existential forgery (M,
(mldsaSig, tradSig)) for Composite ML-DSA can be converted into a
pair of algorithms that will either create existential forgeries (M',
mldsaSig) and (M', tradSig) for the component algorithms or a
collision in PH.
However, the nature of the EUF-CMA security guarantee can still
change if one of the component algorithms is broken:
* If the traditional component is broken, then Composite ML-DSA will
remain EUF-CMA secure against quantum adversaries.
* If ML-DSA is broken, then Composite ML-DSA will only be EUF-CMA
secure against classical adversaries.
The same properties will hold for X.509 certificates that use
Composite ML-DSA: a classical adversary cannot forge a Composite ML-
DSA signed certificate if at least one component algorithm is
classically EUF-CMA secure, and a quantum adversary cannot forge a
Composite ML-DSA signed certificate if ML-DSA remains quantumly EUF-
CMA secure.
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10.2.2. SUF-CMA
A signature algorithm is Strongly Unforgeable under Chosen-Message
Attack (SUF-CMA) if an adversary that has access to a signing oracle
cannot create a message-signature pair (M, Sig) that was not an
output of a signing oracle query. This is a stronger property than
EUF-CMA since the message M does not need to be different. SUF-CMA
security is also more complicated for Composite ML-DSA than EUF-CMA.
A SUF-CMA failure in one component algorithm can lead to a SUF-CMA
failure in the composite. For example, an ECDSA signature can be
trivially modified to produce a different signature that is still
valid for the same message and this property passes directly through
to Composite ML-DSA with ECDSA.
Unfortunately, it is not generally sufficient for both component
algorithms to be SUF-CMA secure. If repeated calls to the signing
oracle produce two valid message-signature pairs (M, (mldsaSig1,
tradSig1)) and (M, (mldsaSig2, tradSig2)) for the same message M, but
where mldsaSig1 =/= mldsaSig2 and tradSig1 =/= tradSig2, then the
adversary can construct a third pair (M, (mldsaSig1, tradSig2)) that
will also be valid.
Note that this SUF-CMA failure does not apply to the situation where
Composite ML-DSA is used to sign X.509 certificates. Repeated calls
to a certificate signing oracle will produce certificates with
different serial numbers and so mixing the component signatures does
not give a valid composite signature in the same way.
Nevertheless, Composite ML-DSA will not be SUF-CMA secure, and
Composite ML-DSA signed X.509 certificates will not be strongly
unforgeable, against quantum adversaries since a quantum adversary
will be able to break the SUF-CMA security of the traditional
component.
Consequently, applications where SUF-CMA security is critical SHOULD
NOT use Composite ML-DSA.
10.2.3. Non-separability
Weak Non-Separability (WNS) of a hybrid signature is defined in
[I-D.ietf-pquip-hybrid-signature-spectrums] as the guarantee that an
adversary cannot simply "remove" one of the component signatures
without evidence left behind.
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Strong Non-Separability (SNS) is the stronger notion that an
adversary cannot take a hybrid signature and produce a component
signature, with a potentially different message, that will be
accepted by the component verifier.
Composite ML-DSA signs a message M by passing M' as defined in
Section 3.2 to the component signature primitives. Consider an
adversary that takes a composite signature (M, (mldsaSig, tradSig))
and splits it into the component signatures (M', mldsaSig) and (M',
tradSig). On the traditional side, (M', tradSig) will verify
correctly, but the static Prefix defined in Section 3.2 remains as
evidence of the original composite. On the ML-DSA side, (M',
mldsaSig) is signed with ML-DSA's context value equal to the
composite algorithm's Label so will fail to verify under ML-
DSA.Verify(M', ctx=""). Consequently, Composite ML-DSA will provide
WNS for both components and a limited form of SNS for the ML-DSA
component. It can achieve stronger non-separability in practice for
both components if the prefix-based mitigation described in
Section 10.4 is applied.
When used within X.509, the OID of the signature algorithm is
included in the signed object so if one of the component signatures
is removed from the Composite ML-DSA signature then the signed-over
OID will still indicate the composite algorithm, and this will fail
at the X.509 processing layer. Composite ML-DSA therefore provides a
version of SNS for X.509. The prohibition on key reuse between
composite and single-algorithm contexts discussed in Section 10.3
further strengthens the non-separability in practice.
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.
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
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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.
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.
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10.5. 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.
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_internal(seed) which
might not be available in a cryptographic module running in FIPS-
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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. However, using an interface which
doesn't support a seed will prevent the implementation from encoding
the private key according to Section 5.2. Another example is pre-
hashing; a pre-hash is inherent to RSA, ECDSA, and ML-DSA (μ), 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.
Note also that also that Section 4.1 depicts the generation of the
seed as mldsaSeed = Random(), when implementing this for FIPS
certification, this MUST be the direct output of a FIPS-approved
DRBG.
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 document explicitly does not provide
backwards compatibility, only upgraded systems will understand the
OIDs defined in this specification.
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.
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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 as it provides the best overall balance of
performance and security.
id-MLDSA65-ECDSA-P256-SHA512
Below we list a few other recommendations for specific scenarios.
In applications that require RSA, it is RECOMMENDED to focus
implementation effort on:
id-MLDSA65-RSA3072-PSS-SHA512
In applications that are performance and bandwidth-sensitive, it is
RECOMMENDED to focus implementation effort on:
id-MLDSA44-ECDSA-P256-SHA256
or
id-MLDSA44-Ed25519-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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In applications that require the signature primitive to provide SUF-
CMA, it is RECOMMENDED to focus implementation effort on:
id-MLDSA65-Ed25519-SHA512
11.4. External Pre-hashing
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>.Prehash(M) -> ph
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:
ph The pre-hash which equals PH ( M )
Process:
1. Compute the Prehash of the message using the Hash function
defined by PH
ph = PH ( M )
2. Output ph
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Composite-ML-DSA<OID>.Sign_ph(sk, ph, ctx) -> s
Explicit inputs:
sk Composite private key consisting of signing private keys
for each component.
ph The pre-hash digest over 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 "ML-DSA-65".
Trad The underlying traditional algorithm and
parameter set, for example "sha256WithRSAEncryption"
or "Ed25519".
Prefix The prefix octet string.
Label A signature label which is specific to each composite
algorithm. Additionally, the composite label is passed
into the underlying ML-DSA primitive as the ctx.
Signature Label values are defined in the "Signature Label Values"
section below.
Process:
1. Identical to Composite-ML-DSA<OID>.Sign (sk, M, ctx) but
replace the internally generated PH( M ) from step 2 of
Composite-ML-DSA<OID>.Sign (sk, M, ctx) with ph which is
input into this function.
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>.
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[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>.
[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>.
[RFC3279] Bassham, L., Polk, W., and R. Housley, "Algorithms and
Identifiers for the Internet X.509 Public Key
Infrastructure Certificate and Certificate Revocation List
(CRL) Profile", RFC 3279, DOI 10.17487/RFC3279, April
2002, <https://www.rfc-editor.org/info/rfc3279>.
[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>.
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[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>.
[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>.
[RFC5915] Turner, S. and D. Brown, "Elliptic Curve Private Key
Structure", RFC 5915, DOI 10.17487/RFC5915, June 2010,
<https://www.rfc-editor.org/info/rfc5915>.
[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>.
[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>.
[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>.
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[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.
[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>.
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[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>.
[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>.
[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>.
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[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>.
[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>.
[RFC9794] Driscoll, F., Parsons, M., and B. Hale, "Terminology for
Post-Quantum Traditional Hybrid Schemes", RFC 9794,
DOI 10.17487/RFC9794, June 2025,
<https://www.rfc-editor.org/info/rfc9794>.
Appendix A. Maximum Key and Signature Sizes
The sizes listed below are maximas. 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 is size between 3 and n
- 1 [RFC8017]. Note that the size table below assumes the
recommended value of e = 65537, so for RSA combinations it is in
fact not a true maximum.
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* 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.
Size values marked with an asterisk (*) in the table are not fixed
but maximum possible values for the composite key or ciphertext.
Implementations should be careful when performing length checking
based on such values.
Non-hybrid ML-DSA is included for reference.
+=========================================+======+=======+=========+
| 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* |1226* |2676 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA44-RSA2048-PKCS15-SHA256 |1582* |1226* |2676 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA44-Ed25519-SHA512 |1344 |64 |2484 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA44-ECDSA-P256-SHA256 |1377 |81 |2492* |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-RSA3072-PSS-SHA512 |2350* |1802* |3693 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-RSA3072-PKCS15-SHA512 |2350* |1802* |3693 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-RSA4096-PSS-SHA512 |2478* |2383* |3821 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-RSA4096-PKCS15-SHA512 |2478* |2383* |3821 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-ECDSA-P256-SHA512 |2017 |81 |3381* |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-ECDSA-P384-SHA512 |2049 |94 |3413* |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 |2017 |82 |3381* |
+-----------------------------------------+------+-------+---------+
| id-MLDSA65-Ed25519-SHA512 |1984 |64 |3373 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA87-ECDSA-P384-SHA512 |2689 |94 |4731* |
+-----------------------------------------+------+-------+---------+
| id-MLDSA87-ECDSA-brainpoolP384r1-SHA512 |2689 |98 |4731* |
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+-----------------------------------------+------+-------+---------+
| id-MLDSA87-Ed448-SHAKE256 |2649 |89 |4741 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA87-RSA3072-PSS-SHA512 |2990* |1802* |5011 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA87-RSA4096-PSS-SHA512 |3118* |2383* |5139 |
+-----------------------------------------+------+-------+---------+
| id-MLDSA87-ECDSA-P521-SHA512 |2725 |112 |4766* |
+-----------------------------------------+------+-------+---------+
Table 4: Maximum size values of composite ML-DSA
Appendix B. Component Algorithm Reference
This section provides references to the full specification of the
algorithms used in the composite constructions.
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+=========================+=========================+=============+
| 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 |[RFC3279], |
| | |[RFC5915], |
| | |[RFC5758], |
| | |[RFC5480], |
| | |[SEC1], |
| | |[X9.62_2005] |
+-------------------------+-------------------------+-------------+
| ecdsa-with-SHA384 | 1.2.840.10045.4.3.3 |[RFC3279], |
| | |[RFC5915], |
| | |[RFC5758], |
| | |[RFC5480], |
| | |[SEC1], |
| | |[X9.62_2005] |
+-------------------------+-------------------------+-------------+
| ecdsa-with-SHA512 | 1.2.840.10045.4.3.4 |[RFC3279], |
| | |[RFC5915], |
| | |[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 5: 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 6: Elliptic Curves used in Composite Constructions
+=============+=========================+===============+
| HashID | OID | Specification |
+=============+=========================+===============+
| id-sha256 | 2.16.840.1.101.3.4.2.1 | [RFC6234] |
+-------------+-------------------------+---------------+
| id-sha384 | 2.16.840.1.101.3.4.2.2 | [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 7: Hash algorithms used in pre-hashed Composite
Constructions to build PH element
Appendix C. Component AlgorithmIdentifiers for Public Keys and
Signatures
Many cryptographic libraries are X.509-focused and do not expose
interfaces to instantiate a public key from raw bytes, but only from
a SubjectPublicKeyInfo structure as you would find in an X.509
certificate, therefore implementing composite in those libraries
requires reconstructing the SPKI for each component algorithm. In
order to aid implementers and reduce interoperability issues, this
section lists out the full public key and signature
AlgorithmIdentifiers for each component algorithm.
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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 & 3072*
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 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-sha384, -- (2.16.840.1.101.3.4.2.2)
parameters NULL
},
AlgorithmIdentifier ::= {
algorithm id-mgf1, -- (1.2.840.113549.1.1.8)
parameters AlgorithmIdentifier ::= {
algorithm id-sha384, -- (2.16.840.1.101.3.4.2.2)
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 02 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 02 05 00 A2 03
02 01 40
*RSASSA-PKCS1-v1_5 2048 & 3072*
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
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AlgorithmIdentifier of Signature
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 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 sha384WithRSAEncryption, -- (1.2.840.113549.1.1.12)
parameters NULL
}
DER:
30 0D 06 09 2A 86 48 86 F7 0D 01 01 0C 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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* Label is the specific signature label for this composite
algorithm, as defined in Section 7.
* 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.
* PH(M) is the output of hashing 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.
Example of id-MLDSA65-ECDSA-P256-SHA512 construction of M'.
# Inputs:
M: 00010203040506070809
ctx: <empty>
# Components of M':
Prefix:
436f6d706f73697465416c676f726974686d5369676e61747572657332303235
Label: COMPSIG-MLDSA65-P256-SHA512
len(ctx): 00
ctx: <empty>
PH(M): 0f89ee1fcb7b0a4f7809d1267a029719004c5a5e5ec323a7c3523a20974f
9a3f202f56fadba4cd9e8d654ab9f2e96dc5c795ea176fa20ede8d854c342f90353
3
# Outputs:
# M' = Prefix || Label || len(ctx) || ctx || PH(M)
M': 436f6d706f73697465416c676f726974686d5369676e6174757265733230323
5434f4d505349472d4d4c44534136352d503235362d534841353132000f89ee1fcb
7b0a4f7809d1267a029719004c5a5e5ec323a7c3523a20974f9a3f202f56fadba4c
d9e8d654ab9f2e96dc5c795ea176fa20ede8d854c342f903533
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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'.
Example of id-MLDSA65-ECDSA-P256-SHA512 construction of M'.
# Inputs:
M: 00010203040506070809
ctx: 0813061205162623
# Components of M':
Prefix:
436f6d706f73697465416c676f726974686d5369676e61747572657332303235
Label: COMPSIG-MLDSA65-P256-SHA512
len(ctx): 08
ctx: 0813061205162623
PH(M): 0f89ee1fcb7b0a4f7809d1267a029719004c5a5e5ec323a7c3523a20974f
9a3f202f56fadba4cd9e8d654ab9f2e96dc5c795ea176fa20ede8d854c342f90353
3
# Outputs:
# M' = Prefix || Label || len(ctx) || ctx || PH(M)
M': 436f6d706f73697465416c676f726974686d5369676e6174757265733230323
5434f4d505349472d4d4c44534136352d503235362d534841353132080813061205
1626230f89ee1fcb7b0a4f7809d1267a029719004c5a5e5ec323a7c3523a20974f9
a3f202f56fadba4cd9e8d654ab9f2e96dc5c795ea176fa20ede8d854c342f903533
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:
Ounsworth, et al. Expires 13 April 2026 [Page 78]
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* tcId the name of the algorithm.
* pk the verification public key.
* x5c a self-signed X.509 certificate of the public key.
* 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
{
"m":
"VGhlIHF1aWNrIGJyb3duIGZveCBqdW1wcyBvdmVyIHRoZSBsYXp5IGRvZy4=",
"tests": [
{
"tcId": "id-ML-DSA-44",
"pk": "Pt0xq/YgSq0cwBnJoO+rB4tu
6rQwUSNeXgM8WAKRacRSBfCzlazV6YWykOdYA8Ct1/Ox7jWe3/aSLcXcWJv2Cne25xY/
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JvVhbzoNKUBimTRT3g7z+jWe1AHcBsIRMeRcZVXOOIjISO1XWXwi9FiRXZM0z+FpwKIp
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"x5c": "MIIPjDCCBgKgAwIBAgIUTi0g/HXrJ
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"sk":
"pi0x7ByDQmmJ/9gIwrsEoUGNLN3HKLplrp0e8Ee95j0=",
"sk_pkcs8": "MDQCAQA
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Ounsworth, et al. Expires 13 April 2026 [Page 82]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 83]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 84]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 85]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 86]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 87]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 88]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 89]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 90]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 91]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 92]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 93]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 94]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 95]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 96]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 97]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 98]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 99]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 100]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 101]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 102]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 103]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 104]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 105]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 106]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 107]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 108]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 109]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 110]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 111]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 112]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 113]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 114]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 115]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 116]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 117]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 118]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 119]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 120]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 121]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 122]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 123]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 124]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 125]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 126]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 127]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 128]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 129]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 130]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 131]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 132]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 133]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 134]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 135]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 136]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 137]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 138]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 139]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 140]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 141]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 142]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 143]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 144]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 145]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 146]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 147]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 148]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 149]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 150]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 151]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 152]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 153]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 154]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 155]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 156]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 157]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 158]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 159]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 160]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 161]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 162]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 163]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 164]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 165]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 166]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 167]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 168]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 169]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 170]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 171]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 172]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 173]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 174]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 175]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 176]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 177]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 178]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 179]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 180]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 181]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 182]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 183]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 184]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 185]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 186]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 187]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 188]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 189]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 190]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 191]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 192]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 193]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 194]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 195]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 196]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 197]
Internet-Draft Composite ML-DSA October 2025
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Ounsworth, et al. Expires 13 April 2026 [Page 198]
Internet-Draft Composite ML-DSA October 2025
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]
}
Appendix F. Intellectual Property Considerations
The following IPR Disclosure relates to this document:
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:
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Serge Mister (Entrust), Felipe Ventura (Entrust), Richard Kettlewell
(Entrust), Ali Noman (Entrust), 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 (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 to Dr. Hale along with Peter C and John Mattsson
with analyzing the scheme with respect to EUF-CMA, SUF-CMA and Non-
Separability properties.
We wish to acknowledge particular effort from Carl Wallace and Daniel
Van Geest (CryptoNext Security), who have put in sustained effort
over multiple years both reviewing and implementing at the hackathon
each iteration of this document.
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
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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
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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