Composite ML-KEM for use in X.509 Public Key Infrastructure
draft-ietf-lamps-pq-composite-kem-12
| Document | Type | Active Internet-Draft (lamps WG) | |
|---|---|---|---|
| Authors | Mike Ounsworth , John Gray , Massimiliano Pala , Jan Klaußner , Scott Fluhrer | ||
| Last updated | 2026-01-07 | ||
| Replaces | draft-ounsworth-pq-composite-kem | ||
| RFC stream | Internet Engineering Task Force (IETF) | ||
| Intended RFC status | (None) | ||
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draft-ietf-lamps-pq-composite-kem-12
LAMPS M. Ounsworth
Internet-Draft J. Gray
Intended status: Standards Track Entrust
Expires: 12 July 2026 M. Pala
OpenCA Labs
J. Klaussner
Bundesdruckerei GmbH
S. Fluhrer
Cisco Systems
8 January 2026
Composite ML-KEM for use in X.509 Public Key Infrastructure
draft-ietf-lamps-pq-composite-kem-12
Abstract
This document defines combinations of US NIST ML-KEM [FIPS.203] in
hybrid with traditional algorithms RSA-OAEP, ECDH, X25519, and X448.
These combinations are tailored to meet security best practices and
regulatory guidelines. Composite ML-KEM is applicable in any
application that uses X.509 or PKIX data structures that accept ML-
KEM, but where the operator wants extra protection against breaks or
catastrophic bugs in ML-KEM.
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-kem/draft-ietf-lamps-pq-composite-
kem.html. Status information for this document may be found at
https://datatracker.ietf.org/doc/draft-ietf-lamps-pq-composite-kem/.
Discussion of this document takes place on the LAMPS Working Group
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Source for this draft and an issue tracker can be found at
https://github.com/lamps-wg/draft-composite-kem.
Status of This Memo
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This Internet-Draft will expire on 12 July 2026.
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Table of Contents
1. Introduction
1.1. Conventions and Terminology
1.2. Notation
1.3. Composite Design Philosophy
2. Overview of the Composite ML-KEM Scheme
2.1. Promotion of RSA-OAEP into a KEM
2.2. Promotion of ECDH into a KEM
3. Composite ML-KEM Functions
3.1. Key Generation
3.1.1. Allowed Modifications to the Key Generation Process
3.2. Encapsulation
3.3. Decapsulation
3.4. KEM Combiner Function
3.5. Error Handling and Explicit Rejection
4. Serialization
4.1. SerializePublicKey and DeserializePublicKey
4.2. SerializePrivateKey and DeserializePrivateKey
4.3. SerializeCiphertext and DeserializeCiphertext
5. Use within X.509 and PKIX
5.1. Encoding to DER
5.2. Key Usage Bits
5.3. ASN.1 Definitions
6. Algorithm Identifiers and Parameters
6.1. RSA-OAEP Parameters
6.2. Rationale for choices
7. ASN.1 Module
8. IANA Considerations
8.1. Object Identifier Allocations
8.1.1. Module Registration
8.1.2. Object Identifier Registrations
9. Security Considerations
9.1. Why Hybrids?
9.2. KEM Combiner
9.2.1. IND-CCA2 Security of the hybrid scheme
9.2.2. Second pre-image resistance of component KEMs
9.2.3. Generifying this construction
9.3. Key Reuse
9.4. Policy for Deprecated and Acceptable Algorithms
10. Implementation Considerations
10.1. FIPS Certification
10.1.1. Combiner Function
10.1.2. Order of KDF inputs with Non-Approved Algorithms
10.2. Backwards Compatibility
10.3. Profiling down the number of options
10.4. Decapsulation Requires the Public Key
10.4.1. Extracting RSAPublicKey from RSAPrivateKey
10.4.2. Deriving the public ECPoint from ECPrivateKey
11. References
11.1. Normative References
11.2. Informative References
Appendix A. Maximum Key and Ciphertext Sizes
Appendix B. Component Algorithm Reference
Appendix C. Fixed Component Algorithm Identifiers
Appendix D. Comparison with other Hybrid KEMs
D.1. X-Wing
D.2. ETSI CatKDF
Appendix E. Examples of KEM Combiner Intermediate Values
Appendix F. Test Vectors
Appendix G. Contributors and Acknowledgments
Authors' Addresses
1. Introduction
The advent of quantum computing poses a significant threat to current
cryptographic systems because traditional cryptographic key
establishment algorithms such as RSA-OAEP, Diffie-Hellman and its
elliptic curve variants will become vulnerable to quantum attacks.
Unlike previous migrations between cryptographic algorithms, this
migration gives us the foresight that traditional cryptographic
algorithms will be broken in the future, but will remain 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 security vulnerabilities and other implementation
flaws in the new implementations.
Cautious implementers may opt to combine cryptographic algorithms in
such a way that an attacker would need to break all of them
simultaneously to compromise the protected data. These mechanisms
are referred to as "Post-Quantum / Traditional (PQ/T) Hybrids"
[RFC9794].
This specification defines a specific instantiation of the PQ/T
Hybrid paradigm called "composite" where multiple cryptographic
algorithms are combined to form a single key encapsulation mechanism
(KEM). The composite KEM presents a single public key and ciphertext
such that it can be treated as a single atomic algorithm at the
protocol level. This provides a property referred to as "protocol
backwards compatibility" since it can be applied to protocols that
are not explicitly hybrid-aware. The idea of a composite was first
presented in [Bindel2017]. Composite algorithms retain some security
even if one of their component algorithms is broken, which is
discussed in detail in Section 9. This specification creates PQ/T
Hybrids with ML-KEM, defined in [FIPS.203] as the PQ component.
Instantiations of the composite ML-KEM scheme are provided based on
ML-KEM, RSA-OAEP and ECDH. The full list of algorithms registered by
this specification is in Section 6. Backwards compatibility in the
sense of upgraded systems continuing to interoperate with legacy
systems is not directly covered in this specification, but is the
subject of Section 10.2.
Certain jurisdictions have recommended that ML-KEM 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].
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 Cryptography 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 from which any cryptographic algorithm an
organization has deployed today can evolve or transition.
While this specification registers a large number of composite
algorithms, it is expected that organizations will choose to deploy a
single composite algorithm, or a small number of composite
algorithms, that meets the needs of their environment, and very few
implementers will need concern themselves with the entire list. This
specification does not specify any mandatory-to-implement algorithms,
but Section 10.3 provides a short-list of recommended composite
algorithms for common use-cases.
Composite ML-KEM is applicable in any PKIX-related application that
would otherwise use ML-KEM.
1.1. 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 all terminology from [RFC9794].
In addition, the following terms are used in 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.
*Application Backwards Compatibility*: The usual definition of
backwards compatibility, meaning whether an upgraded and non-upgraded
application can successfully establish communication.
*COMBINER*: A combiner specifies how multiple shared secret keys are
combined into a single shared secret key.
*COMPOSITE CRYPTOGRAPHIC ELEMENT*: [RFC9794] defines composites as: A
cryptographic element that incorporates multiple component
cryptographic elements of the same type in a multi-algorithm scheme.
*COMPONENT / PRIMITIVE*: The words "component" or "primitive" are
used interchangeably to refer to a cryptographic algorithm that is
used internally within a composite algorithm. For example this could
be an asymmetric algorithm such as "ML-KEM-768" or "RSA-OAEP".
*DER:* Distinguished Encoding Rules as defined in [X.690].
*KEM:* A key encapsulation mechanism as defined in Section 2.
*PKI:* Public Key Infrastructure, as defined in [RFC5280].
*Post-Quantum Traditional (PQ/T) hybrid scheme*: A multi-algorithm
scheme where at least one component algorithm is a post-quantum
algorithm and at least one is a traditional algorithm.
*Protocol Backwards Compatibility*: A property whereby a new feature
can be added to a protocol without requiring any changes to the
protocol's specification and only minimal changes to its
implementations (such as adding new identifiers). This is notable
because many PQ/T Hybrids require modification of the protocol to
make it "hybrid aware", whereas this specification presents as a
standalone algorithm and thus can take advantage of existing
cryptographic agility mechanisms.
*SHARED SECRET KEY:* A value established between two communicating
parties for use as cryptographic key material suitable for direct use
by symmetric cryptographic algorithms. This specification is
concerned with shared secrets established via public key
cryptographic operations.
1.2. Notation
The algorithm descriptions use python-like syntax. The following
symbols deserve special mention:
* || represents concatenation of two byte arrays.
* [:] represents byte array slicing.
* (a, b) represents a pair of values a and b. Typically this
indicates that a function returns multiple values; the exact
conveyance mechanism -- tuple, struct, output parameters, etc --
is left to the implementer.
* (a, _): represents a pair of values where one -- the second one in
this case -- is ignored.
* Func<TYPE>(): represents a function that is parametrized by <TYPE>
meaning that the function's implementation will have minor
differences depending on the underlying TYPE. Typically this
means that a function will need to look up different constants or
use different underlying cryptographic primitives depending on
which composite algorithm it is implementing.
1.3. Composite Design Philosophy
Composite algorithms, as defined in this specification, follow the
definition in [RFC9794] and should be regarded as a single algorithm
that performs a single cryptographic operation typical of a key
establishment mechanism.This generally means that the complexity of
combining algorithms can and should be handled by the cryptographic
library or cryptographic module. The design intent is that protocols
such as PKCS#10 [RFC2986], CMP [RFC4210], X.509 [RFC5280], the CMS
[RFC5652], and the Trust Anchor Format [RFC5914] can treat composite
algorithms as they would any other algorithm without the protocol
layer to have any "hybrid-awareness". This is a property referred to
as "protocol backwards-compatibility".
Discussion of the specific choices of algorithm pairings can be found
in Section 6.2.
2. Overview of the Composite ML-KEM Scheme
Composite ML-KEM is a PQ/T hybrid Key Encapsulation Mechanism (KEM)
which combines ML-KEM as specified in [FIPS.203] and
[I-D.ietf-lamps-kyber-certificates] with one of RSA-OAEP defined in
[RFC8017], the Elliptic Curve Diffie-Hellman key agreement schemes
ECDH defined in section 5.7.1.2 of [SP.800-56Ar3], and X25519 / X448
defined in [RFC8410]. A KEM combiner function is used to combine the
two component shared secret keys into a single shared secret key.
Composite Key Encapsulation Mechanisms are defined as cryptographic
primitives that consist of three algorithms. These definitions are
borrowed from [RFC9180].
* 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-KEM.
* Encap(pk) -> (ss, ct): A probabilistic encapsulation algorithm,
which takes as input a public key pk and outputs a ciphertext ct
and shared secret key ss. Note: this specification uses Encap()
to conform to [RFC9180], but [FIPS.203] uses Encaps().
* Decap(sk, ct) -> ss: A decapsulation algorithm, which takes as
input a secret key sk and ciphertext ct and outputs a shared
secret ss, or in some cases a distinguished error value. Note:
this specification uses Decap() to conform to [RFC9180], but
[FIPS.203] uses Decaps().
The KEM interface was chosen as the interface for a composite key
establishment because it allows for arbitrary combinations of
component algorithm types since both key transport and key agreement
mechanisms can be promoted into KEMs as described in Section 2.1 and
Section 2.2 below.
The following algorithms are defined for serializing and
deserializing component values. These algorithms are inspired by
similar algorithms in [RFC9180].
* SerializePublicKey(mlkemPK, tradPK) -> bytes: Produce a byte
string encoding of the component public keys.
* DeserializePublicKey(bytes) -> (mlkemPK, tradPK): Parse a byte
string to recover the component public keys.
* SerializeCiphertext(mlkemCT, tradCT) -> bytes: Produce a byte
string encoding of the component ciphertexts.
* DeserializeCiphertext(bytes) -> (mlkemCT, tradCT): Parse a byte
string to recover the component ciphertexts.
* SerializePrivateKey(mlkemSeed, tradSK) -> bytes: Produce a byte
string encoding of the component private keys.
* DeserializePrivateKey(bytes) -> (mlkemSeed, tradSK): Parse a byte
string to recover the component private keys.
Full definitions of serialization and deserialization algorithms can
be found in Section 4.
2.1. Promotion of RSA-OAEP into a KEM
The RSA Optimal Asymmetric Encryption Padding (OAEP), as defined in
section 7.1 of [RFC8017] is a public key encryption algorithm used to
transport key material from a sender to a receiver. A "key
transport" type algorithm has the following API:
* Encrypt(pk, ss) -> ct: Take an existing shared secret key ss and
encrypt it for pk.
* Decrypt(sk, ct) -> ss: Decrypt the ciphertext ct to recover ss.
Note the difference between the API of RSA.Encrypt(pk, ss) -> ct and
KEM.Encap(pk) -> (ss, ct) presented above. For this reason, RSA-OAEP
cannot be directly combined with ML-KEM. Fortunately, a key
transport mechanism such as RSA-OAEP can be easily promoted into a
KEM by having the sender generate a random 256 bit shared secret key
and encrypt it.
RSAOAEPKEM.Encap(pkR):
shared_secret = SecureRandom(ss_len)
enc = RSAES-OAEP-ENCRYPT(pkR, shared_secret)
return shared_secret, enc
Note that the OAEP label L is left to its default value, which is the
empty string as per [RFC8017]. The shared secret key output by the
overall Composite ML-KEM already binds a composite KEM Combiner
Label, so there is no need to also use the component Label.
The value of ss_len as well as concrete values for all the RSA-OAEP
parameters used within this specification can be found in
Section 6.1.
Decap(sk, ct) -> ss is accomplished by direct use of OAEP Decrypt.
RSAOAEPKEM.Decap(skR, enc):
shared_secret = RSAES-OAEP-DECRYPT(skR, enc)
return shared_secret
The encodings for the public key (pkR), private key (skR), and
ciphertext (enc) are described in Section 4.
A quick note on the choice of RSA-OAEP as the supported RSA
encryption primitive. RSA-KEM [RFC5990] is cryptographically robust
and is more straightforward to work with, but it has fairly limited
adoption and therefore is of limited value as a PQ migration
mechanism. Also, while RSA-PKCS#1v1.5 [RFC8017] is still widely
used, it is hard to make secure and no longer FIPS-approved as of the
end of 2023 [SP800-131Ar2], so it is of limited forwards value. This
leaves RSA-OAEP [RFC8017] as the remaining choice. See Section 6.2
for further discussion of algorithm choices.
Note that, at least at the time of writing, the algorithm RSAOAEPKEM
is not defined as a standalone algorithm within PKIX standards and it
does not have an assigned algorithm OID, so it cannot be used
directly with CMS KEMRecipientInfo [RFC9629]; it is merely a building
block for the composite algorithm.
2.2. Promotion of ECDH into a KEM
The elliptic curve Diffie-Hellman algorithm identified by the OID id-
ecDH as defined in [RFC5480] and [SEC1] is a key agreement algorithm
requiring both parties to contribute an asymmetric keypair to the
derivation of the shared secret key. A "key agreement" type
algorithm has the following API:
* DH(skX, pkY) -> ss: Each party combines their secret key skX with
the other party's public key pkY.
Note the difference between the API of DH(skX, pkY) -> ss and
KEM.Encap(pk) -> (ss, ct) presented above. For this reason, a
Diffie-Hellman key exchange cannot be directly combined with ML-KEM.
Fortunately, a Diffie-Hellman key agreement can be easily promoted
into a KEM Encap(pk) -> (ss, ct) by having the sender generate an
ephemeral keypair for themself and sending their public key as the
ciphertext ct. Composite ML-KEM uses a simplified version of the
DHKEM definition from [RFC9180]:
DHKEM.Encap(pkR):
(skE, pkE) = GenerateKeyPair()
ss = DH(skE, pkR)
ct = SerializePublicKey(pkE)
return ss, ct
Decap(sk, ct) -> ss is accomplished in the analogous way.
DHKEM.Decap(skR, ct):
pkE = DeserializePublicKey(ct)
ss = DH(skR, pkE)
return ss
This construction applies for all variants of elliptic curve Diffie-
Hellman used in this specification: ECDH, X25519, and X448.
For ECDH, DH() yields the value Z as described in section 5.7.1.2 of
[SP.800-56Ar3].
For X25519 and X448, DH() yields the value K as described in section
6 of [RFC7748].
The encodings for the public key (pkR), private key (skR), and
ciphertext (pkE) are described in Section 4.
The promotion of DH to a KEM is similar to the DHKEM functions in
[RFC9180], but it is simplified in the following ways:
1. Notation has been aligned to the notation used in this
specification.
2. Since a KEM Combiner Label is included explicitly in the
Composite ML-KEM combiner, there is no need to perform the
labeled steps of ExtractAndExpand().
3. Since the ciphertext and receiver's public key are included
explicitly in the Composite ML-KEM combiner, there is no need to
construct the kem_context object.
Note that here, SerializePublicKey() and DeserializePublicKey() refer
to the underlying encoding of the DH primitive, and not to the
composite serialization functions defined in Section 4.
Note that, at least at the time of writing, the algorithm DHKEM is
not defined as a standalone algorithm within PKIX standards and it
does not have an assigned algorithm OID, so it cannot be used
directly with CMS KEMRecipientInfo [RFC9629]; it is merely a building
block for the composite algorithm.
3. Composite ML-KEM Functions
This section describes the composite ML-KEM functions needed to
instantiate the public API of a Key Encapsulation Mechanism as
defined in Section 2.
3.1. Key Generation
In order to maintain security properties of the composite, this
specification strictly forbids re-using component key material
between composite and non-composite keys, or between multiple
composite keys. This means that an invocation of Composite-ML-
KEM.KeyGen() MUST perform, or otherwise guarantee, fresh generation
of the key material for both underlying algorithms and MUST NOT reuse
existing key material. See Section 9.3 for a discussion.
To generate a new keypair 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>.
Composite-ML-KEM<OID>.KeyGen() -> (pk, sk)
Explicit Inputs:
None
Implicit Inputs mapped from <OID>:
ML-KEM The underlying ML-KEM algorithm and
parameter set, for example "ML-KEM-768".
Trad The underlying traditional algorithm and
parameter, for example "RSA-OAEP"
or "X25519".
Output:
(pk, sk) The composite keypair.
Key Generation Process:
1. Generate component keys
mlkemSeed = Random(64)
(mlkemPK, mlkemSK) = ML-KEM.KeyGen(mlkemSeed)
(tradPK, tradSK) = Trad.KeyGen()
2. Check for component key gen failure
if NOT (mlkemPK, mlkemSK) or NOT (tradPK, tradSK):
output "Key generation error"
3. Output the composite public and private keys
pk = SerializePublicKey(mlkemPK, tradPK)
sk = SerializePrivateKey(mlkemSeed, tradSK)
return (pk, sk)
In order to ensure fresh keys, the key generation functions MUST be
executed for both component algorithms. Compliant parties MUST NOT
use, import or export component keys that are used in other contexts,
combinations, or by themselves as keys for standalone algorithm use.
For more details on the security considerations around key reuse, see
Section 9.3.
Errors produced by the component KeyGen() routines MUST be forwarded
on to the calling application. Further discussion can be found below
in Section 3.5.
3.1.1. Allowed Modifications to the Key Generation Process
Key generation is a process that is entirely internal to a
cryptographic module, and as such it is often customized to fit the
performance or operational requirements of the module. In cases
where the private keys never leave the module or are otherwise not
required to interoperate with other cryptographic modules, it is not
required for interoperability for the private keys to match the
format described in this specification. Therefore, in general,
implementations of Composite ML-KEM MAY use an alternate key
generation process so long as it generates compatible public keys,
and so long as both component keys are freshly-generated and not re-
used in a standalone key or within another composite key. Below are
some examples of modifications that an implementer MAY make to the
key generation process.
Implementations MAY modify this process to additionally output the
expanded mlkemSK or to make use of ML-KEM.KeyGen_internal(mlkemSeed)
as needed to expand the ML-KEM seed into an expanded key prior to
performing a signing operation.
In cases where it is desirable to have a deterministic KeyGen of one
or both component keys from a seed, this process MAY be modified to
expose an interface of Composite-ML-KEM<OID>.KeyGen(seed) such that
one component algorithm is generated from the seed and the other from
random, or the input seed is cryptohraphically expanded to produce
seeds for both components. Security analysis of such a modified key
generation process is outside the scope of this document.
Where interoperable private keys are not required, implementations
MAY choose to use a different private key representation than the one
given in Section 4.2. For example, the component keys MAY be stored
in separate cryptographic modules, or MAY be stored in separate
PKCS#8 objects, or MAY be stored in a format that preserves the ML-
KEM expanded key instead of the ML-KEM seed. The required
modifications to the key generation process, as well as the signature
generation process below, to support these private key
representations are considered compliant with this specification so
long as they generate compatible public keys, and so long as both
component keys are freshly-generated. Note that when implementing
Composite ML-KEM with a private key format that does not preserve the
ML-KEM seed, especially when implementing on top of a cryptographic
module that does not support seeds, it will be impossible to
reconstruct a compliant seed-based private key as described in
Section 4.2
3.2. Encapsulation
The Encap(pk) of a Composite ML-KEM algorithm is designed to behave
exactly the same as ML-KEM.Encaps(ek) defined in Algorithm 20 in
Section 7.2 of [FIPS.203]. Specifically, Composite-ML-KEM.Encap(pk)
produces a 256-bit shared secret key that can be used directly with
any symmetric-key cryptographic algorithm. In this way, Composite
ML-KEM can be used as a direct drop-in replacement anywhere that ML-
KEM is used.
The following describes how to instantiate a Encap(pk) function for a
given composite algorithm represented by <OID>.
Composite-ML-KEM<OID>.Encap(pk) -> (ss, ct)
Explicit Inputs:
pk Composite public key consisting of encryption public keys
for each component.
Implicit inputs mapped from <OID>:
ML-KEM The underlying ML-KEM algorithm and
parameter set, for example "ML-KEM-768".
Trad The underlying ML-KEM algorithm and
parameter set, for example "RSA-OAEP"
or "X25519".
Label KEM Combiner Label value for binding the ciphertext to the
Composite OID. See section on KEM Combiner Labels below.
Output:
ss The shared secret key, a 256-bit key suitable for use with
symmetric cryptographic algorithms.
ct The ciphertext, a byte string.
Encap Process:
1. Separate the public keys.
(mlkemPK, tradPK) = DeserializePublicKey(pk)
2. Perform the respective component Encap operations according to
their algorithm specifications.
(mlkemCT, mlkemSS) = ML-KEM.Encaps(mlkemPK)
(tradCT, tradSS) = TradKEM.Encap(tradPK)
3. If either ML-KEM.Encaps() or TradKEM.Encap() return an error,
then this process must return an error.
if NOT (mlkemCT, mlkemSS) or NOT (tradCT, tradSS):
output "Encapsulation error"
4. Encode the ciphertext
ct = SerializeCiphertext(mlkemCT, tradCT)
5. Combine the KEM secrets and additional context to yield the
composite shared secret key.
ss = KemCombiner(mlkemSS, tradSS, tradCT, tradPK, Label)
6. Output composite shared secret key and ciphertext.
return (ss, ct)
The specific values for Label are defined per Composite ML-KEM
algorithm in Section 6.
Errors produced by the component Encaps() routines MUST be forwarded
on to the calling application. Further discussion can be found below
in Section 3.5.
3.3. Decapsulation
The Decap(sk, ct) -> ss of a Composite ML-KEM algorithm is designed
to behave exactly the same as ML-KEM.Decaps(dk, c) defined in
Algorithm 21 in Section 7.3 of [FIPS.203]. Specifically, Composite-
ML-KEM.Decap(sk, ct) produces a 256-bit shared secret key that can be
used directly with any symmetric-key cryptographic algorithm. In
this way, Composite ML-KEM can be used as a direct drop-in
replacement anywhere that ML-KEM is used.
The following describes how to instantiate a Decap(sk, ct) function
for a given composite algorithm represented by <OID>.
Composite-ML-KEM<OID>.Decap(sk, ct) -> ss
Explicit inputs
sk Composite private key consisting of decryption private
keys for each component.
ct The ciphertext, a byte string.
Implicit inputs mapped from <OID>:
ML-KEM The underlying ML-KEM algorithm and
parameter set, for example "ML-KEM-768".
Trad The underlying traditional algorithm and
parameter set, for example "RSA-OAEP"
or "X25519".
Label KEM Combiner Label value for binding the ciphertext to
the Composite ML-KEM OID.
See section on KEM Combiner Labels below.
Implicit inputs looked up from SK:
tradPK The traditional public key is required for the KEM
combiner.
For discussion of where to get this value, see the
Decapsulation Requires the Public Key section.
Output:
ss The shared secret key, a 256-bit key suitable for use
with symmetric cryptographic algorithms.
Decap Process:
1. Separate the private keys and ciphertexts
(mlkemSeed, tradSK) = DeserializePrivateKey(sk)
(_, mlkemSK) = ML-KEM.KeyGen(mlkemSeed)
(mlkemCT, tradCT) = DeserializeCiphertext(ct)
2. Perform the respective component Decap operations according
to their algorithm specifications.
mlkemSS = ML-KEM.Decaps(mlkemSK, mlkemCT)
tradSS = TradKEM.Decap(tradSK, tradCT)
3. If either ML-KEM.Decaps() or TradKEM.Decap() return an error,
then this process must return an error.
if NOT mlkemSS or NOT tradSS:
output "Decapsulation error"
4. Combine the KEM secrets and additional context to yield the
composite shared secret key.
ss = KemCombiner(mlkemSS, tradSS, tradCT, tradPK, Label)
5. Output composite shared secret key.
return ss
Steps 2, 3, and 4 SHOULD be performed in a timing-invariant way to
prevent side-channel attackers from learning which component
algorithm failed and from learning any of the inputs or output of the
KEM combiner.
Step 4 requires the Decaps() process to have access to tradPK, which
is not carried in the private key format and therefore the
implementation is required to acquire it from some out-of-band means.
The Implementation Considerations Section 10.4 provides further
discussion on this.
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.
In order to properly achieve its security properties, the KEM
combiner requires that all inputs are fixed-length or length-encoded.
Since each Composite ML-KEM algorithm fully specifies its component
algorithms, including key sizes, all inputs should be fixed-length in
non-error scenarios except for minor variations introduced by
encoding. In the cases where there are minor variations introduced
by encoding, those encodings already have a fixed-length prefix
followed by length-encoded data, so the requirements for the KEM
combiner security properties hold (namely that the input is
injective). However some implementations may choose to perform
additional checking to handle certain error conditions. In
particular, the KEM combiner step should not be performed if either
of the component decapsulations returned an error condition
indicating malformed inputs. RSA-based composites MUST ensure that
the modulus size (i.e. the size of tradCT and tradPK) matches that
specified for the given Composite ML-KEM algorithm in Section 6;
depending on the cryptographic library used, this check may be done
by the library or may require an explicit check as part of the
Composite-ML-KEM.Decap() routine. Implementers should keep in mind
that some instances of tradCT and tradPK will be DER-encoded which
could introduce minor length variations such as dropping leading
zeroes; since the underlying KEMs are assumed to be IND-CCA secure,
decapsulation against tampered ciphertexts or public keys is assumed
to fail, these length differences are considered benign to the KEM
combiner.
Errors produced by the component Decaps() routines MUST be forwarded
on to the calling application. Further discussion can be found below
in Section 3.5.
3.4. KEM Combiner Function
This specification provides a combiner construction with SHA3-256 for
all combinations of algorithms.
KemCombiner(mlkemSS, tradSS, tradCT, tradPK, Label) -> ss
Explicit inputs:
The list of input values to be combined.
Output:
ss The shared secret key, a 256-bit key suitable for use with
symmetric cryptographic algorithms.
Process:
ss = SHA3-256(mlkemSS || tradSS || tradCT || tradPK || Label)
return ss
3.5. Error Handling and Explicit Rejection
ML-KEM, particularly its Decaps() defined in Algorithms 18 and 21 of
[FIPS.203], is designed to be implicitly rejecting, meaning that a
failure within the underlying PKE scheme due to a mangled ciphertext
will not cause ML-KEM.Decaps() to return an error, but instead any
errors encountered during decapsulation are handled by producing a
pseudo-random shared secret. ML-KEM.Decaps() can, however return
errors for example if the provided ciphertext or decapsulation
private key is the wrong size.
In Composite ML-KEM, not all component algorithms will be implicitly
rejecting, for example RSA-OAEP's Decrypt() can return an error if
the padding is incorrect. In general, in the case that one of the
component primitives generates an error during Composite ML-KEM
KeyGen, Encaps, or Decaps, Composite ML-KEM MUST clear all buffers
containing key material and forward the error to its caller; i.e.
Composite ML-KEM MUST be explicitly rejecting whenever one of its
components is. The same applies to Composite ML-KEM KeyGen() and
Encaps(): Composite KEM MUST forward any errors produced by component
algorithms.
4. Serialization
This section presents routines for serializing and deserializing
composite public keys, private keys, and ciphertext values to bytes.
The functions defined in this section are considered internal
implementation details and are referenced from within the public API
definitions in Section 3.
Deserialization is possible because ML-KEM has fixed-length public
keys, private keys (seeds), and ciphertext values as shown in the
following table.
+=============+============+=============+============+
| Algorithm | Public Key | Private Key | Ciphertext |
+=============+============+=============+============+
| ML-KEM-768 | 1184 | 64 | 1088 |
+-------------+------------+-------------+------------+
| ML-KEM-1024 | 1568 | 64 | 1568 |
+-------------+------------+-------------+------------+
Table 1: ML-KEM Sizes in bytes
For all serialization routines below, when these values are required
to be carried in an ASN.1 structure, they are wrapped as described in
Section 5.1.
While ML-KEM has a single fixed-size representation for each of
public key, private key, and ciphertext, the traditional component
might allow multiple valid encodings; for example an elliptic curve
public key, and therefore also ciphertext, might be validly encoded
as either compressed or uncompressed [SEC1], or an RSA private key
could be encoded in Chinese Remainder Theorem form [RFC8017]. In
order to obtain interoperability, composite algorithms MUST use the
following encodings of the underlying components:
* *ML-KEM*: MUST be encoded as specified in sections 7.1 and 7.2 of
[FIPS.203], using a 64-byte seed as the private key.
* *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-OAEP ciphertext MUST be encoded as specified in section
7.1.1 of [RFC8017]
* *ECDH*: 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. The private key MUST be encoded as
ECPrivateKey specified in [RFC5915] with 'NamedCurve' parameter
set to the OID of the curve, but without the 'publicKey' field.
The ciphertext MUST be encoded in the same manner as the public
key.
* *X25519 and X448*: the public key MUST be encoded as per section 5
of [RFC7748] and the private key is a 32 or 56 byte raw value for
X25519 and X448 respectively. The ciphertext MUST be encoded in
the same manner as the public key.
All ASN.1 objects SHALL be encoded using DER on serialization.
Even with fixed encodings for the traditional component, there may be
slight differences in size of the encoded value due to, for example,
encoding rules that drop leading zeroes. See Appendix A for further
discussion of encoded size of each composite algorithm.
The deserialization routines described below do not check for well-
formedness of the cryptographic material they are recovering. It is
assumed that underlying cryptographic primitives will catch malformed
values and raise an appropriate error.
4.1. SerializePublicKey and DeserializePublicKey
The serialization routine for keys simply concatenates the public
keys of the component algorithms, as defined below:
Composite-ML-KEM.SerializePublicKey(mlkemPK, tradPK) -> bytes
Explicit inputs:
mlkemPK The ML-KEM 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 mlkemPK || 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>.
Composite-ML-KEM<OID>.DeserializePublicKey(bytes) -> (mlkemPK, tradPK)
Explicit inputs:
bytes An encoded composite public key.
Implicit inputs mapped from <OID>:
ML-KEM The underlying ML-KEM algorithm and
parameter, for example, could be "ML-KEM-768".
Output:
mlkemPK The ML-KEM 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 mlkemPK is known based on the size of
the ML-KEM component key length specified by the Object ID.
switch ML-KEM do
case ML-KEM-768:
mlkemPK = bytes[:1184]
tradPK = bytes[1184:]
case ML-KEM-1024:
mlkemPK = bytes[:1568]
tradPK = bytes[1568:]
Note that while ML-KEM has fixed-length keys, RSA
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 (mlkemPK, tradPK)
4.2. SerializePrivateKey and DeserializePrivateKey
The serialization routine for keys simply concatenates the private
keys of the component algorithms, as defined below:
Composite-ML-KEM.SerializePrivateKey(mlkemSeed, tradSK) -> bytes
Explicit inputs:
mlkemSeed The ML-KEM 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 mlkemSeed || 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-KEM private keys are
64 bytes for all parameter sets, this function does not need to be
parametrized.
Composite-ML-KEM.DeserializePrivateKey(bytes)
-> (mlkemSeed, tradSK)
Explicit inputs:
bytes An encoded composite private key.
Implicit inputs:
That an ML-KEM private key is 64 bytes for all parameter sets.
Output:
mlkemSeed The ML-KEM 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 the ML-KEM seed, which is always a 64 byte seed
for all parameter sets.
mlkemSeed = bytes[:64]
tradSK = bytes[64:]
2. Output the component private keys
output (mlkemSeed,tradSK)
4.3. SerializeCiphertext and DeserializeCiphertext
The serialization routine for the composite ciphertext value simply
concatenates the fixed-length ML-KEM ciphertext with the ciphertext
from the traditional algorithm, as defined below:
Composite-ML-KEM.SerializeCiphertext(mlkemCT, tradCT) -> bytes
Explicit inputs:
mlkemCT The ML-KEM ciphertext, which is bytes.
tradCT The traditional ciphertext in the appropriate
encoding for the underlying component algorithm.
Implicit inputs:
None
Output:
bytes The encoded composite ciphertext value.
Serialization Process:
1. Combine and output the encoded composite ciphertext
output mlkemCT || tradCT
Deserialization reverses this process. Each component ciphertext is
deserialized according to their respective specification as shown in
Appendix B.
The following describes how to instantiate a
DeserializeCiphertext(bytes) function for a given composite algorithm
represented by <OID>.
Composite-ML-KEM<OID>.DeserializeCiphertext(bytes)
-> (mlkemCT, tradCT)
Explicit inputs:
bytes An encoded composite ciphertext value.
Implicit inputs mapped from <OID>:
ML-KEM The underlying ML-KEM algorithm and
parameter, for example, could be "ML-KEM-768".
Output:
mlkemCT The ML-KEM ciphertext, which is bytes.
tradCT The traditional ciphertext in the appropriate
encoding for the underlying component algorithm.
Deserialization Process:
1. Parse each constituent encoded ciphertext.
The length of the mlkemCT is known based on the size of the
ML-KEM component ciphertext length specified by the Object ID.
switch ML-KEM do
case ML-KEM-768:
mlkemCT = bytes[:1088]
tradCT = bytes[1088:]
case ML-KEM-1024:
mlkemCT= bytes[:1568]
tradCT = bytes[1568:]
2. Output the component ciphertext values
output (mlkemCT, tradCT)
5. Use within X.509 and PKIX
The following sections provide processing logic and the necessary
ASN.1 modules necessary to use composite ML-KEM within X.509 and PKIX
protocols. Use within the Cryptographic Message Syntax (CMS) will be
covered in a separate specification.
While composite ML-KEM keys and ciphertext values MAY be used raw,
the following sections provide conventions for using them within
X.509 and other PKIX protocols such that Composite ML-KEM can be used
as a drop-in replacement for KEM algorithms in PKCS#10 [RFC2986], CMP
[RFC4210], X.509 [RFC5280], and related protocols.
5.1. Encoding to DER
The serialization routines presented in Section 4 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 or a
OneAsymmetricKey.privateKey OCTET STRING [RFC5958], then the BIT
STRING or OCTET STRING contains this raw byte string output of the
appropriate serialization routine from Section 4 without further
encoding.
When a Composite ML-KEM 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-KEM-
PublicKey type defined below.
Composite-ML-KEM-PublicKey ::= OCTET STRING
Size constraints MAY be enforced, as appropriate as per Appendix A.
5.2. Key Usage Bits
When any Composite ML-KEM Object Identifier appears within the
SubjectPublicKeyInfo.AlgorithmIdentifier field of an X.509
certificate [RFC5280], the key usage certificate extension MUST only
contain:
keyEncipherment
Composite ML-KEM 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.
5.3. ASN.1 Definitions
Composite ML-KEM uses a substantially non-ASN.1 based encoding, as
specified in Section 4. 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.
pk-CompositeKEM {OBJECT IDENTIFIER:id}
PUBLIC-KEY ::= {
IDENTIFIER id
-- KEY no ASN.1 wrapping --
PARAMS ARE absent
CERT-KEY-USAGE { keyEncipherment }
-- PRIVATE-KEY no ASN.1 wrapping --
}
kema-CompositeKEM {
OBJECT IDENTIFIER:id,
PUBLIC-KEY:publicKeyType }
KEM-ALGORITHM ::= {
IDENTIFIER id
-- VALUE no ASN.1 wrapping --
PARAMS ARE absent
PUBLIC-KEYS { publicKeyType }
SMIME-CAPS { IDENTIFIED BY id }
}
Figure 1: ASN.1 Object Information Classes for Composite ML-KEM
As an example, the public key and KEM algorithm types associated with
id-MLKEM768-ECDH-P256-SHA3-256 are defined as:
pk-MLKEM768-ECDH-P256-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM {
id-MLKEM768-ECDH-P256-SHA3-256 }
kema-MLKEM768-ECDH-P256-SHA3-256 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM768-ECDH-P256-SHA3-256,
pk-MLKEM768-ECDH-P256-SHA3-256 }
The full set of key types defined by this specification can be found
in the ASN.1 Module in Section 7.
Use cases that require an interoperable encoding for composite
private keys will often need to place a composite private key inside
a OneAsymmetricKey structure defined in [RFC5958], such as when
private keys are carried in PKCS #12 [RFC7292], CMP [RFC4210] or CRMF
[RFC4211]. The definition of OneAsymmetricKey is copied here for
convenience:
OneAsymmetricKey ::= SEQUENCE {
version Version,
privateKeyAlgorithm PrivateKeyAlgorithmIdentifier,
privateKey PrivateKey,
attributes [0] Attributes OPTIONAL,
...,
[[2: publicKey [1] PublicKey OPTIONAL ]],
...
}
...
PrivateKey ::= OCTET STRING
-- Content varies based on type of key. The
-- algorithm identifier dictates the format of
-- the key.
Figure 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 6 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 4.2. The publicKey field
remains OPTIONAL. If the publicKey field is present, it MUST be a
composite public key as per Section 4.1.
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 6 provides the necessary mapping
between composite and their component algorithms for doing this
reconstruction.
Component keys of a composite private key 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 9.3.
6. Algorithm Identifiers and Parameters
This section lists the algorithm identifiers and parameters for all
Composite ML-KEM algorithms.
Full specifications for the referenced algorithms can be found in
Appendix B.
As the number of algorithms can be daunting to implementers, see
Section 10.3 for a discussion of choosing a subset to support.
Each Composite ML-KEM algorithm has a unique Label which is used in
constructing the KEM combiner in (Section 3.4). This helps protect
against a different algorithm arriving at the same shared secret key
even if all inputs are the same.
Label values are provided in two forms: where the label value is
alphanumeric ASCII, they are represented below as strings. For
example, "MLKEM768-RSAOAEP2048" below is equivalent to the
hexadecimal value 4D4C4B454D3736382D5253414F41455032303438.
Some of the label values contain problematic characters, such as
backslashes, that can cause issues displaying correctly in rendered
documents or even in source code when the compiler interprets it as
an escape character. Below, these are represented directly in
hexadecimal. For example, the label for id-MLKEM768-X25519-SHA3-256
is "\.//^\", but to avoid transcription errors it is provided only in
hexadecimal as 5c2e2f2f5e5c.
Composite KEM algorithm list:
* id-MLKEM768-RSA2048-SHA3-256
- OID: 1.3.6.1.5.5.7.6.55
- Label: "MLKEM768-RSAOAEP2048"
- ML-KEM variant: ML-KEM-768
- Traditional Algorithm: RSA
o Traditional KEM Algorithm: id-RSAES-OAEP
o RSA size: 2048
o RSAES-OAEP parameters: See Table 2
* id-MLKEM768-RSA3072-SHA3-256
- OID: 1.3.6.1.5.5.7.6.56
- Label: "MLKEM768-RSAOAEP3072"
- ML-KEM variant: ML-KEM-768
- Traditional Algorithm: RSA
o Traditional KEM Algorithm: id-RSAES-OAEP
o RSA size: 3072
o RSAES-OAEP parameters: See Table 2
* id-MLKEM768-RSA4096-SHA3-256
- OID: 1.3.6.1.5.5.7.6.57
- Label: "MLKEM768-RSAOAEP4096"
- ML-KEM variant: ML-KEM-768
- Traditional Algorithm: RSA
o Traditional KEM Algorithm: id-RSAES-OAEP
o RSA size: 4096
o RSAES-OAEP parameters: See Table 2
* id-MLKEM768-X25519-SHA3-256
- OID: 1.3.6.1.5.5.7.6.58
- Label: "5c2e2f2f5e5c" (hex)
- ML-KEM variant: ML-KEM-768
- Traditional Algorithm: X25519
o Traditional KEM Algorithm: id-X25519
* id-MLKEM768-ECDH-P256-SHA3-256
- OID: 1.3.6.1.5.5.7.6.59
- Label: "MLKEM768-P256"
- ML-KEM variant: ML-KEM-768
- Traditional Algorithm: ECDH
o Traditional KEM Algorithm: id-ecDH
o ECDH curve: secp256r1
* id-MLKEM768-ECDH-P384-SHA3-256
- OID: 1.3.6.1.5.5.7.6.60
- Label: "MLKEM768-P384"
- ML-KEM variant: ML-KEM-768
- Traditional Algorithm: ECDH
o Traditional KEM Algorithm: id-ecDH
o ECDH curve: secp384r1
* id-MLKEM768-ECDH-brainpoolP256r1-SHA3-256
- OID: 1.3.6.1.5.5.7.6.61
- Label: "MLKEM768-BP256"
- ML-KEM variant: ML-KEM-768
- Traditional Algorithm: ECDH
o Traditional KEM Algorithm: id-ecDH
o ECDH curve: brainpoolP256r1
* id-MLKEM1024-RSA3072-SHA3-256
- OID: 1.3.6.1.5.5.7.6.62
- Label: "MLKEM1024-RSAOAEP3072"
- ML-KEM variant: ML-KEM-1024
- Traditional Algorithm: RSA
o Traditional KEM Algorithm: id-RSAES-OAEP
o RSA size: 3072
o RSAES-OAEP parameters: See Table 2
* id-MLKEM1024-ECDH-P384-SHA3-256
- OID: 1.3.6.1.5.5.7.6.63
- Label: "MLKEM1024-P384"
- ML-KEM variant: ML-KEM-1024
- Traditional Algorithm: ECDH
o Traditional KEM Algorithm: id-ecDH
o ECDH curve: secp384r1
* id-MLKEM1024-ECDH-brainpoolP384r1-SHA3-256
- OID: 1.3.6.1.5.5.7.6.64
- Label: "MLKEM1024-BP384"
- ML-KEM variant: ML-KEM-1024
- Traditional Algorithm: ECDH
o Traditional KEM Algorithm: id-ecDH
o ECDH curve: brainpoolP384r1
* id-MLKEM1024-X448-SHA3-256
- OID: 1.3.6.1.5.5.7.6.65
- Label: "MLKEM1024-X448"
- ML-KEM variant: ML-KEM-1024
- Traditional Algorithm: X448
o Traditional KEM Algorithm: id-X448
* id-MLKEM1024-ECDH-P521-SHA3-256
- OID: 1.3.6.1.5.5.7.6.66
- Label: "MLKEM1024-P521"
- ML-KEM variant: ML-KEM-1024
- Traditional Algorithm: ECDH
o Traditional KEM Algorithm: id-ecDH
o ECDH curve: secp521r1
In alignment with ML-KEM [FIPS.203], Composite KEM algorithms output
a 256-bit shared secret key at all security levels.
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.
SHA3-256 is used as the KDF for all Composite ML-KEM algorithms.
6.1. RSA-OAEP Parameters
Use of RSA-OAEP [RFC8017] requires additional parameters to be
specified.
The RSA component keys MUST be generated at the specified 2048-bit,
3072-bit, 4096-bit key sizes respectively (up to small differences
such as dropping leading zeros); intermediate sizes are not
acceptable.
As with the other Composite ML-KEM algorithms, AlgorithmIdentifier
parameters MUST be absent. The RSA-OAEP primitive SHALL be
instantiated with the following hard-coded parameters which are the
same for the 2048, 3072 and 4096 bit key sizes since the objective is
to carry and output a 256-bit shared secret key at all security
levels.
+=============================+=================+
| RSAES-OAEP-params | Value |
+=============================+=================+
| hashAlgorithm | id-sha256 |
+-----------------------------+-----------------+
| MaskGenAlgorithm.algorithm | id-mgf1 |
+-----------------------------+-----------------+
| maskGenAlgorithm.parameters | id-sha256 |
+-----------------------------+-----------------+
| pSourceAlgorithm | pSpecifiedEmpty |
+-----------------------------+-----------------+
| ss_len | 256 bits |
+-----------------------------+-----------------+
Table 2: RSA-OAEP Parameters
Full specifications for the referenced algorithms can be found in
Appendix B.
Note: The mask length, according to [RFC8017], is k - hLen - 1, where
k is the size of the RSA modulus. Since the choice of hash function
and the RSA key size is fixed for each composite algorithm,
implementations could choose to pre-compute and hard-code the mask
length.
6.2. 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-KEM security level with commonly-
deployed traditional algorithms. This supports the design goal of
using composites as a stepping stone to efficiently deploy post-
quantum on top of existing hardened and certified traditional
algorithm implementations. This was prioritized rather than
attempting to exactly match the security level of the post-quantum
and traditional components -- which in general is difficult to do
since there is no academic consensus on how to compare the "bits of
security" against classical attackers and "qubits of security"
against quantum attackers.
While it may seem odd to use 256-bit outputs at all security levels,
this aligns with ML-KEM [FIPS.203] which produces a 256-bit shared
secret key at all security levels. SHA3-256 has 256 bits of (2nd)
pre-image resistance, which is the required property for a KDF to
provide 128 bits of security, as allowed in Table 3 of
[SP.800-57pt1r5].
7. ASN.1 Module
<CODE STARTS>
Composite-MLKEM-2025
{ iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-composite-mlkem-2025(TBDMOD) }
DEFINITIONS IMPLICIT TAGS ::= BEGIN
EXPORTS ALL;
IMPORTS
PUBLIC-KEY, AlgorithmIdentifier{}, SMIME-CAPS
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) }
KEM-ALGORITHM
FROM KEMAlgorithmInformation-2023
{ iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-kemAlgorithmInformation-2023(109) }
;
--
-- Object Identifiers
--
--
-- Information Object Classes
--
pk-CompositeKEM {OBJECT IDENTIFIER:id}
PUBLIC-KEY ::= {
IDENTIFIER id
-- KEY no ASN.1 wrapping --
PARAMS ARE absent
CERT-KEY-USAGE { keyEncipherment }
-- PRIVATE-KEY no ASN.1 wrapping --
}
kema-CompositeKEM {
OBJECT IDENTIFIER:id,
PUBLIC-KEY:publicKeyType }
KEM-ALGORITHM ::= {
IDENTIFIER id
-- VALUE no ASN.1 wrapping --
PARAMS ARE absent
PUBLIC-KEYS { publicKeyType }
SMIME-CAPS { IDENTIFIED BY id }
}
--
-- Composite KEM Algorithms
--
-- Composite ML-KEM
id-MLKEM768-RSA2048-SHA3-256 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) alg(6) 55 }
pk-MLKEM768-RSA2048-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM {
id-MLKEM768-RSA2048-SHA3-256 }
kema-MLKEM768-RSA2048-SHA3-256 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM768-RSA2048-SHA3-256,
pk-MLKEM768-RSA2048-SHA3-256 }
id-MLKEM768-RSA3072-SHA3-256 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) alg(6) 56 }
pk-MLKEM768-RSA3072-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM {
id-MLKEM768-RSA3072-SHA3-256 }
kema-MLKEM768-RSA3072-SHA3-256 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM768-RSA3072-SHA3-256,
pk-MLKEM768-RSA3072-SHA3-256 }
id-MLKEM768-RSA4096-SHA3-256 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) alg(6) 57 }
pk-MLKEM768-RSA4096-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM {
id-MLKEM768-RSA4096-SHA3-256 }
kema-MLKEM768-RSA4096-SHA3-256 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM768-RSA4096-SHA3-256,
pk-MLKEM768-RSA4096-SHA3-256 }
id-MLKEM768-X25519-SHA3-256 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) alg(6) 58 }
pk-MLKEM768-X25519-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM {
id-MLKEM768-X25519-SHA3-256 }
kema-MLKEM768-X25519-SHA3-256 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM768-X25519-SHA3-256,
pk-MLKEM768-X25519-SHA3-256 }
id-MLKEM768-ECDH-P256-SHA3-256 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) alg(6) 59 }
pk-MLKEM768-ECDH-P256-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM {
id-MLKEM768-ECDH-P256-SHA3-256 }
kema-MLKEM768-ECDH-P256-SHA3-256 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM768-ECDH-P256-SHA3-256,
pk-MLKEM768-ECDH-P256-SHA3-256 }
id-MLKEM768-ECDH-P384-SHA3-256 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) alg(6) 60 }
pk-MLKEM768-ECDH-P384-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM {
id-MLKEM768-ECDH-P384-SHA3-256 }
kema-MLKEM768-ECDH-P384-SHA3-256 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM768-ECDH-P384-SHA3-256,
pk-MLKEM768-ECDH-P384-SHA3-256 }
id-MLKEM768-ECDH-brainpoolP256r1-SHA3-256 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) alg(6) 61 }
pk-MLKEM768-ECDH-brainpoolP256r1-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM {
id-MLKEM768-ECDH-brainpoolP256r1-SHA3-256 }
kema-MLKEM768-ECDH-brainpoolP256r1-SHA3-256 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM768-ECDH-brainpoolP256r1-SHA3-256,
pk-MLKEM768-ECDH-brainpoolP256r1-SHA3-256 }
id-MLKEM1024-RSA3072-SHA3-256 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) alg(6) 62 }
pk-MLKEM1024-RSA3072-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM {
id-MLKEM1024-RSA3072-SHA3-256 }
kema-MLKEM1024-RSA3072-SHA3-256 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM1024-RSA3072-SHA3-256,
pk-MLKEM1024-RSA3072-SHA3-256 }
id-MLKEM1024-ECDH-P384-SHA3-256 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) alg(6) 63 }
pk-MLKEM1024-ECDH-P384-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM {
id-MLKEM1024-ECDH-P384-SHA3-256 }
kema-MLKEM1024-ECDH-P384-SHA3-256 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM1024-ECDH-P384-SHA3-256,
pk-MLKEM1024-ECDH-P384-SHA3-256 }
id-MLKEM1024-ECDH-brainpoolP384r1-SHA3-256 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) alg(6) 64 }
pk-MLKEM1024-ECDH-brainpoolP384r1-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM{
id-MLKEM1024-ECDH-brainpoolP384r1-SHA3-256 }
kema-MLKEM1024-ECDH-brainpoolP384r1-SHA3-256 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM1024-ECDH-brainpoolP384r1-SHA3-256,
pk-MLKEM1024-ECDH-brainpoolP384r1-SHA3-256 }
id-MLKEM1024-X448-SHA3-256 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) alg(6) 65 }
pk-MLKEM1024-X448-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM {
id-MLKEM1024-X448-SHA3-256 }
kema-MLKEM1024-X448 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM1024-X448-SHA3-256,
pk-MLKEM1024-X448-SHA3-256 }
id-MLKEM1024-ECDH-P521-SHA3-256 OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) alg(6) 66 }
pk-MLKEM1024-ECDH-P521-SHA3-256 PUBLIC-KEY ::=
pk-CompositeKEM {
id-MLKEM1024-ECDH-P521-SHA3-256 }
kema-MLKEM1024-ECDH-P521-SHA3-256 KEM-ALGORITHM ::=
kema-CompositeKEM{
id-MLKEM1024-ECDH-P521-SHA3-256,
pk-MLKEM1024-ECDH-P521-SHA3-256 }
END
<CODE ENDS>
8. IANA Considerations
8.1. Object Identifier Allocations
IANA has registered the Object Identifiers in the "SMI Security for
PKIX Algorithms" registry.
8.1.1. Module Registration
The following is to be registered in "SMI Security for PKIX Module
Identifier":
* Decimal: IANA Assigned - *Replace TBDMOD*
* Description: Composite-MLKEM-2025 - id-mod-composite-mlkem-2025
* References: This Document
8.1.2. Object Identifier Registrations
The following are registered in the "SMI Security for PKIX
Algorithms":
* id-MLKEM768-RSA2048-SHA3-256
- Decimal: 1.3.6.1.5.5.7.6.55
- Description: id-MLKEM768-RSA2048-SHA3-256
- References: This Document
* id-MLKEM768-RSA3072-SHA3-256
- Decimal: 1.3.6.1.5.5.7.6.56
- Description: id-MLKEM768-RSA3072-SHA3-256
- References: This Document
* id-MLKEM768-RSA4096-SHA3-256
- Decimal: 1.3.6.1.5.5.7.6.57
- Description: id-MLKEM768-RSA4096-SHA3-256
- References: This Document
* id-MLKEM768-X25519-SHA3-256
- Decimal: 1.3.6.1.5.5.7.6.58
- Description: id-MLKEM768-X25519-SHA3-256
- References: This Document
* id-MLKEM768-ECDH-P256-SHA3-256
- Decimal: 1.3.6.1.5.5.7.6.59
- Description: id-MLKEM768-ECDH-P256-SHA3-256
- References: This Document
* id-MLKEM768-ECDH-P384-SHA3-256
- Decimal: 1.3.6.1.5.5.7.6.60
- Description: id-MLKEM768-ECDH-P384-SHA3-256
- References: This Document
* id-MLKEM768-ECDH-brainpoolP256r1-SHA3-256
- Decimal: 1.3.6.1.5.5.7.6.61
- Description: id-MLKEM768-ECDH-brainpoolP256r1-SHA3-256
- References: This Document
* id-MLKEM1024-RSA3072-SHA3-256
- Decimal: 1.3.6.1.5.5.7.6.62
- Description: id-MLKEM1024-RSA3072-SHA3-256
- References: This Document
* id-MLKEM1024-ECDH-P384-SHA3-256
- Decimal: 1.3.6.1.5.5.7.6.63
- Description: id-MLKEM1024-ECDH-P384-SHA3-256
- References: This Document
* id-MLKEM1024-ECDH-brainpoolP384r1-SHA3-256
- Decimal: 1.3.6.1.5.5.7.6.64
- Description: id-MLKEM1024-ECDH-brainpoolP384r1-SHA3-256
- References: This Document
* id-MLKEM1024-X448-SHA3-256
- Decimal: 1.3.6.1.5.5.7.6.65
- Description: id-MLKEM1024-X448-SHA3-256
- References: This Document
* id-MLKEM1024-ECDH-P521-SHA3-256
- Decimal: 1.3.6.1.5.5.7.6.66
- Description: id-MLKEM1024-ECDH-P521-SHA3-256
- References: This Document
9. Security Considerations
As this specification uses ML-KEM as a component of all composite
algorithms, all security considerations from
[I-D.ietf-lamps-kyber-certificates] and
[I-D.sfluhrer-cfrg-ml-kem-security-considerations] apply. Note in
particular the "Encapsulation key check" in section 7.2 of [FIPS.203]
and the "Decapsulation input check" in section 7.3 of [FIPS.203]
which are required for correct and secure functioning of ML-KEM, but
which are considered to be external to the Encaps() and Decaps()
algorithms.
9.1. Why Hybrids?
In broad terms, a PQ/T Hybrid can be used either to provide dual-
algorithm security or to provide migration flexibility. Let's
quickly explore both.
Dual-algorithm security. The general idea is that the data is
protected by two algorithms such that an attacker would need to break
both in order to compromise the data. As with most of cryptography,
this property is easy to state in general terms, but becomes more
complicated when expressed in formalisms. The following sections go
into more detail here.
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 application backwards compatibility to allow legacy and
upgraded applications to co-exist and communicate. The composite
algorithms 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-KEM implementation which
immediately starts providing benefits against harvest-now-decrypt-
later attacks even if that ML-KEM 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 10.1.
9.2. KEM Combiner
The KEM combiner from Section 3.4 is reproduced here for reference.
SHA3-256(mlkemSS || tradSS || tradCT || tradPK || Label)
Figure 3: KEM combiner construction
The primary security property of the KEM combiner is that it
preserves indistinguishable (adaptive) chosen-ciphertext (IND-CCA2)
security of the overall Composite ML-KEM so long as at least one
component is IND-CCA2 [X-Wing] [GHP18]. Additionally, we also need
to consider the case where one of the component algorithms is
completely broken; that the private key is known to an attacker. In
this case, we rely on the construction of the KEM combiner to ensure
that the value of the other shared secret key cannot be leaked or the
combined shared secret key predicted via manipulation of the broken
algorithm.
Each registered Composite ML-KEM algorithm specifies a Label -- see
Section 6. Given that each Composite ML-KEM algorithm fully
specifies the component algorithms, including for example the size of
the RSA modulus, all inputs to the KEM combiner are fixed-size and
thus do not require length-prefixing.
* mlkemSS is always 32 bytes.
* tradSS in the case of DH this is derived by the decapsulator and
therefore the length is not controlled by the attacker, however in
the case of RSA-OAEP this value is directly chosen by the sender
and both the length and content could be freely chosen by an
attacker.
* tradCT is either an elliptic curve public key or an RSA-OAEP
ciphertext which is required to have its length checked by step 1b
of RSAES-OAEP-DECRYPT in [RFC8017].
* tradPK is the public key of the traditional component (elliptic
curve or RSA) and therefore fixed-length.
* Label is a fixed value specified in this document.
9.2.1. IND-CCA2 Security of the hybrid scheme
Informally, a Composite ML-KEM algorithm is secure if the combiner
(SHA3) is secure, and either ML-KEM is secure or the traditional
component (RSA-OAEP, ECDH, X25519 or X448) is secure.
The security of ML-KEM and DH hybrids is covered in [X-Wing] and
requires that the first KEM component (ML-KEM in this construction)
is IND-CCA2 and second ciphertext preimage resistant (C2PRI) and that
the DH component is nominal group; i.e. a well-behaved elliptic curve
DH group, but does not require the traditional component to be IND-
CCA. This design choice improves performance by not including the
large ML-KEM public key and ciphertext, but means that an
implementation error in the ML-KEM component that affects the
ciphertext check step of the FO transform could result in the overall
composite no longer achieving IND-CCA2 security. This solution
remains IND-CCA2 due to binding the tradPK and tradCT in the KEM
combiner.
The QSF framework presented in [X-Wing] is extended to cover RSA-OAEP
as the traditional algorithm in place of DH by noting that RSA-OAEP
is also IND-CCA2 secure [RFC8017].
The composite combiner cannot be assumed to be secure when used with
different KEMs and a more cautious approach would bind the public key
and ciphertext of the first KEM as well.
9.2.2. Second pre-image resistance of component KEMs
The notion of a "ciphertext second pre-image resistant KEM" is
defined in [X-Wing] as being the property that it is computationally
difficult to find two different ciphertexts c != c' that will
decapsulate to the same shared secret key under the same public key.
For the purposes of a hybrid KEM combiner, this property means that
given two composite ciphertexts (c1, c2) and (c1', c2'), we must
obtain a unique overall shared secret key so long as either c1 != c1'
or c2 != c2' -- i.e. the overall Composite ML-KEM is ciphertext
second pre-image resistant, and therefore secure so long as one of
the component KEMs is secure.
In [X-Wing] it is proven that ML-KEM is a second pre-image resistant
KEM and therefore the ML-KEM ciphertext can safely be omitted from
the KEM combiner. Note that this makes a fundamental assumption on
ML-KEM remaining ciphertext second pre-image resistant, and therefore
this formulation of KEM combiner does not fully protect against
implementation errors in the ML-KEM component -- particularly around
the ciphertext check step of the Fujisaki-Okamoto transform -- which
could trivially lead to second ciphertext pre-image attacks that
break the IND-CCA2 security of the ML-KEM component and of the
overall Composite ML-KEM. This could be more fully mitigated by
binding the ML-KEM ciphertext in the combiner, but a design decision
was made to settle for protection against algorithmic attacks and not
implementation attacks against ML-KEM in order to increase
performance.
However, since neither RSA-OAEP nor DH guarantee second pre-image
resistance at all, even in a correct implementation, these
ciphertexts are bound to the key derivation in order to guarantee
that c != c' will yield a unique ciphertext, and thus restoring
second pre-image resistance to the overall Composite ML-KEM.
9.2.3. Generifying this construction
It should be clear that the security analysis of the presented KEM
combiner construction relies heavily on the specific choices of
component algorithms and combiner KDF, and this combiner construction
SHOULD NOT by applied to any other combination of ciphers without
performing the appropriate security analysis.
9.3. 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 keying 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 and did
not exist in single-algorithm contexts. One of these is key reuse
where the component keys within a hybrid are also used by themselves
within a single-algorithm context. For example, it might be tempting
for an operator to take already-deployed RSA keys and add an ML-KEM
key to them to form a hybrid. Within a hybrid signature context this
leads to a class of attacks referred to as "stripping attacks" where
one component signature can be extracted and presented as a single-
algorithm signature. Hybrid KEMs using a concatenation-style KEM
combiner, as is done in this specification, do not have the analogous
attack surface because even if an attacker is able to extract and
decrypt one of the component ciphertexts, this will yield a different
shared secret key than the overall shared secret key derived from the
composite, so any subsequent symmetric cryptographic operations will
fail.
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.
9.4. 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.
10. Implementation Considerations
10.1. 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.
Implementers seeking FIPS certification of a composite KEM 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 3.1 invokes ML-KEM.KeyGen(seed) which might not be
available in a cryptographic module running in FIPS-mode, but
Section 3.1 is only a suggested implementation and the composite
KeyGen MAY be implemented using a different available interface for
ML-KEM.KeyGen.
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.
Successful FIPS certification will need to take into account the
"Encapsulation key check" in section 7.2 of [FIPS.203] and the
"Decapsulation input check" in section 7.3 of [FIPS.203] which are
required for correct and secure functioning of ML-KEM, but which are
considered to be external to the Encaps() and Decaps() algorithms.
The following sections go into further detail on specific issues that
relate to FIPS certification.
10.1.1. Combiner Function
For reference, the KEM combiner used in Composite ML-KEM is:
ss = SHA3-256(mlkemSS || tradSS || tradCT || tradPK || Label)
NIST SP 800-227 [SP800-227] allows hybrid key combiners of the
following form:
K <- KDM((S1,S2,...,St), OtherInput) (14)
Composite ML-KEM maps cleanly into this since it places the two
shared secret keys mlkemSS || tradSS at the beginning of the KDF
input such that all other inputs tradCT || tradPK || Label can be
considered part of OtherInput for the purposes of FIPS certification.
For the detailed steps of the Key Derivation Mechanism KDM,
[SP800-227] refers to [SP.800-56Cr2].
Compliance of the Composite ML-KEM variants is achieved in the
following way:
The Composite ML-KEM algorithms use SHA3, and so can be certified
under [SP.800-56Cr2] One-Step Key Derivation Option 1: H(x) =
hash(x).
[SP.800-56Cr2] section 4 "One-Step Key Derivation" requires a counter
which begins at the 4-byte value 0x00000001. However, the counter is
allowed to be omitted when the hash function is executed only once,
as specified on page 159 of the FIPS 140-3 Implementation Guidance
[FIPS-140-3-IG].
10.1.2. Order of KDF inputs with Non-Approved Algorithms
[SP800-227] adds an important stipulation that was not present in
earlier NIST specifications:
This publication approves the use of the key combiner (14) for any
t > 1, so long as at least one shared secret (i.e., S_j for some
j) is a shared secret generated from the key- establishment
methods of SP 800-56A or SP 800-56B, or an approved KEM.
This means that although Composite ML-KEM always places the shared
secret key from ML-KEM in the first slot, a Composite ML-KEM can be
FIPS certified so long as either component is FIPS certified. This
is important for several reasons. First, in the early stages of PQC
migration, composites allow for a non-FIPS certified ML-KEM
implementation to be added to a module that already has a FIPS
certified traditional component, and the resulting composite can be
FIPS certified. Second, when eventually RSA and Elliptic Curve are
no longer FIPS-allowed, the composite can retain its FIPS certified
status on the strength of the ML-KEM component. Third, while this is
outside the scope of this specification, the general composite
construction could be used to create FIPS certified algorithms that
contain a component algorithm from a different jurisdiction. Third,
a composite where both components are FIPS-certified could allow an
implementer to patch one component algorithm while awaiting re-
certification while continuing to use the overall composite in FIPS
mode.
Note that before [SP800-227] was in force, [SP.800-56Cr2] required
the shared secret key from the certified algorithm to be in the first
slot and therefore a Composite ML-KEM implementation using a FIPS-
certified traditional component and a non-FIPS certified ML-KEM is
not believed to be certifiable under [SP.800-56Cr2] alone, and
requires the ammendments made by [SP800-227].
10.2. Backwards Compatibility
The term "application backwards compatibility" is used here to mean
that existing systems as they are deployed today can interoperate
with the upgraded systems of the future. This draft explicitly does
not provide application backwards compatibility, only upgraded
systems will understand the OIDs defined in this specification.
These 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 key establishment and content
encryption, 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], as well as myriad
other standardized and proprietary protocols and applications that
leverage CMS [RFC5652] encrypted structures.
10.3. Profiling down the number of options
One daunting aspect of this specification is the number of composite
algorithm combinations. Each option has been specified because there
is a community that has a direct application for it; typically
because the traditional component is already deployed in a change-
managed environment, or because that specific traditional component
is required for regulatory reasons.
However, this large number of combinations leads either to fracturing
of the ecosystem into non-interoperable sub-groups when different
communities choose non-overlapping subsets to support, or on the
other hand it leads to spreading development resources too thin when
trying to support all options.
This specification does not list any particular composite algorithm
as mandatory-to-implement, however organizations that operate within
specific application domains are encouraged to define profiles that
select a small number of composites appropriate for that application
domain. For applications that do not have any regulatory
requirements or legacy implementations to consider, it is RECOMMENDED
to focus implementation effort on:
id-MLKEM768-X25519-SHA3-256 (aka "X-Wing")
id-MLKEM768-ECDH-P256-SHA3-256
In applications that only allow NIST PQC Level 5, it is RECOMMENDED
to focus implementation effort on:
id-MLKEM1024-ECDH-P384-SHA3-256
10.4. Decapsulation Requires the Public Key
ML-KEM always requires the public key in order to perform various
steps of the Fujisaki-Okamoto decapsulation [FIPS.203], and for this
reason the private key encoding specified in FIPS 203 includes the
public key.
Moreover, the KEM combiner as specified in Section 3.4 requires the
public key of the traditional component in order to achieve the
public-key binding property and ciphertext collision resistance as
described in Section 9.2. Since tradPK is not carried in the
composite private key encoding, the implementation is required to
obtain it from some out-of-band mechanism. This section discusses
several options, but is a non-normative, non-exhaustive list.
1. Derive or extract from private key. Many cryptographic modules
expose functionality to obtain an RSA or EC public key from the
corresponding private key. For applications where such
functionality does not exist, Section 10.4.1 and Section 10.4.2
provide the suggested mechanisms for extracting the public keys
from private keys for RSA and ECDH respectively. It is assumed
that this is not required for X25519 or X448 since those private
keys are seeds from which the public key can be obtained.
2. Fetch it from an external data source, for example from the
public-key certificate corresponding to this private key.
3. If the composite KEM private key is being carried within a PKCS#8
OneAsymmetricKey object, place the full composite public key
within the optional OneAsymmetricKey.publicKey field, which
allows extracting the tradPK (and re-encode as necessary for
correctly using it in the KEM Combiner).
4. Use an alternate private key encoding that explicitly carries the
tradPK.
10.4.1. Extracting RSAPublicKey from RSAPrivateKey
Assuming that the RSA component of the composite private key is
encoded as an RSAPrivateKey, as required by this specification, then,
quoting from [RFC8017] you have:
RSAPrivateKey ::= SEQUENCE {
version Version,
modulus INTEGER, -- n
publicExponent INTEGER, -- e
privateExponent INTEGER, -- d
prime1 INTEGER, -- p
prime2 INTEGER, -- q
exponent1 INTEGER, -- d mod (p-1)
exponent2 INTEGER, -- d mod (q-1)
coefficient INTEGER, -- (inverse of q) mod p
otherPrimeInfos OtherPrimeInfos OPTIONAL
}
This can trivially be converted into an RSAPublicKey through simple
DER decoding / re-encoding since both required values are already
present.
RSAPublicKey ::= SEQUENCE {
modulus INTEGER, -- n
publicExponent INTEGER -- e
}
10.4.2. Deriving the public ECPoint from ECPrivateKey
Unlike RSA, the ECPrivateKey does not contain sufficient information
to simply extract the public key. Note that in the interest of
having a single unique encoding to foster interoperability, this
specification forbids the optional publicKey field.
That said, the EC public key can be derived from the private key in
the following way:
g = generator for the group P256r1, P384r1, etc.
s = ECPrivateKey.getS()
pubKey = ec_multiply_by_scalar(g, s)
where a recommended implementation of ec_multiply_by_scalar() can be
found in [SEC1].
Then encode pubKey as X9.62 uncompressed point.
11. References
11.1. Normative References
[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.203] National Institute of Standards and Technology (NIST),
"Module-Lattice-based Key-Encapsulation Mechanism
Standard", August 2024,
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.203.pdf>.
[FIPS.204] National Institute of Standards and Technology (NIST),
"Module-Lattice-Based Digital Signature Standard", August
2024, <https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.204.pdf>.
[RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
Hashing for Message Authentication", RFC 2104,
DOI 10.17487/RFC2104, February 1997,
<https://www.rfc-editor.org/info/rfc2104>.
[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>.
[RFC5280] Cooper, D., Santesson, S., Farrell, S., Boeyen, S.,
Housley, R., and W. Polk, "Internet X.509 Public Key
Infrastructure Certificate and Certificate Revocation List
(CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, May 2008,
<https://www.rfc-editor.org/info/rfc5280>.
[RFC5480] Turner, S., Brown, D., Yiu, K., Housley, R., and T. Polk,
"Elliptic Curve Cryptography Subject Public Key
Information", RFC 5480, DOI 10.17487/RFC5480, March 2009,
<https://www.rfc-editor.org/info/rfc5480>.
[RFC5652] Housley, R., "Cryptographic Message Syntax (CMS)", STD 70,
RFC 5652, DOI 10.17487/RFC5652, September 2009,
<https://www.rfc-editor.org/info/rfc5652>.
[RFC5869] Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
Key Derivation Function (HKDF)", RFC 5869,
DOI 10.17487/RFC5869, May 2010,
<https://www.rfc-editor.org/info/rfc5869>.
[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>.
[RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", RFC 7748, DOI 10.17487/RFC7748, January
2016, <https://www.rfc-editor.org/info/rfc7748>.
[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>.
[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>.
[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>.
[RFC9629] Housley, R., Gray, J., and T. Okubo, "Using Key
Encapsulation Mechanism (KEM) Algorithms in the
Cryptographic Message Syntax (CMS)", RFC 9629,
DOI 10.17487/RFC9629, August 2024,
<https://www.rfc-editor.org/info/rfc9629>.
[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>.
[SP.800-185]
National Institute of Standards and Technology (NIST),
"SHA-3 Derived Functions: cSHAKE, KMAC, TupleHash, and
ParallelHash", December 2016,
<https://nvlpubs.nist.gov/nistpubs/SpecialPublications/
NIST.SP.800-185.pdf>.
[SP.800-56Ar3]
National Institute of Standards and Technology (NIST),
"Recommendation for Pair-Wise Key-Establishment Schemes
Using Discrete Logarithm Cryptography", April 2018,
<https://nvlpubs.nist.gov/nistpubs/SpecialPublications/
NIST.SP.800-56Ar3.pdf>.
[SP.800-56Cr2]
National Institute of Standards and Technology (NIST),
"Recommendation for Key-Derivation Methods in Key-
Establishment Schemes", August 2020,
<https://nvlpubs.nist.gov/nistpubs/SpecialPublications/
NIST.SP.800-56Cr2.pdf>.
[SP.800-57pt1r5]
National Institute of Standards and Technology (NIST),
"Recommendation for Key Management: Part 1 – General", May
2020,
<https://nvlpubs.nist.gov/nistpubs/SpecialPublications/
NIST.SP.800-57pt1r5.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]
"Public Key Cryptography for the Financial Services
Industry, The Elliptic Curve Digital Signature Algorithm
(ECDSA)", November 2005.
11.2. 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>.
[Aviram22] Aviram, N., Dowling, B., Komargodski, I., Paterson, K. G.,
Ronen, E., and E. Yogev, "Practical (Post-Quantum) Key
Combiners from One-Wayness and Applications to TLS", n.d.,
<https://eprint.iacr.org/2022/065>.
[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>.
[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>.
[ETSI.TS.103.744]
ETSI, "ETSI TS 103 744 V1.2.1 CYBER-QSC; Quantum-safe
Hybrid Key Establishment", March 2025,
<https://www.etsi.org/deliver/
etsi_ts/103700_103799/103744/01.02.01_60/
ts_103744v010201p.pdf>.
[FIPS-140-3-IG]
National Institute of Standards and Technology (NIST),
"Implementation Guidance for FIPS 140-3 and the
Cryptographic Module Validation Program", July 2024,
<https://csrc.nist.gov/csrc/media/Projects/cryptographic-
module-validation-program/documents/fips%20140-3/
FIPS%20140-3%20IG.pdf>.
[GHP18] Giacon, F., Heuer, F., and B. Poettering, "KEM Combiners",
2018, <https://eprint.iacr.org/2018/024>.
[I-D.ietf-lamps-kyber-certificates]
Turner, S., Kampanakis, P., Massimo, J., and B.
Westerbaan, "Internet X.509 Public Key Infrastructure -
Algorithm Identifiers for the Module-Lattice-Based Key-
Encapsulation Mechanism (ML-KEM)", Work in Progress,
Internet-Draft, draft-ietf-lamps-kyber-certificates-11, 22
July 2025, <https://datatracker.ietf.org/doc/html/draft-
ietf-lamps-kyber-certificates-11>.
[I-D.sfluhrer-cfrg-ml-kem-security-considerations]
Fluhrer, S., Dang, Q., Mattsson, J. P., Milner, K., and D.
Shiu, "ML-KEM Security Considerations", Work in Progress,
Internet-Draft, draft-sfluhrer-cfrg-ml-kem-security-
considerations-04, 17 November 2025,
<https://datatracker.ietf.org/doc/html/draft-sfluhrer-
cfrg-ml-kem-security-considerations-04>.
[RFC2986] Nystrom, M. and B. Kaliski, "PKCS #10: Certification
Request Syntax Specification Version 1.7", RFC 2986,
DOI 10.17487/RFC2986, November 2000,
<https://www.rfc-editor.org/info/rfc2986>.
[RFC4210] Adams, C., Farrell, S., Kause, T., and T. Mononen,
"Internet X.509 Public Key Infrastructure Certificate
Management Protocol (CMP)", RFC 4210,
DOI 10.17487/RFC4210, September 2005,
<https://www.rfc-editor.org/info/rfc4210>.
[RFC4211] Schaad, J., "Internet X.509 Public Key Infrastructure
Certificate Request Message Format (CRMF)", RFC 4211,
DOI 10.17487/RFC4211, September 2005,
<https://www.rfc-editor.org/info/rfc4211>.
[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>.
[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>.
[RFC5990] Randall, J., Kaliski, B., Brainard, J., and S. Turner,
"Use of the RSA-KEM Key Transport Algorithm in the
Cryptographic Message Syntax (CMS)", RFC 5990,
DOI 10.17487/RFC5990, September 2010,
<https://www.rfc-editor.org/info/rfc5990>.
[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>.
[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>.
[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>.
[SP800-131Ar2]
Barker, E., Roginksy, A., and National Institute of
Standards and Technology (NIST), "Transitioning the Use of
Cryptographic Algorithms and Key Lengths", n.d.,
<https://nvlpubs.nist.gov/nistpubs/specialpublications/
nist.sp.800-131ar2.pdf>.
[SP800-227]
Alagic, G., Barker, E., Chen, L., Moody, D., Robinson, A.,
Silberg, H., Waller, N., and National Institute of
Standards and Technology (NIST), "Recommendations for Key-
Encapsulation Mechanisms", September 2025,
<https://csrc.nist.gov/pubs/sp/800/227/final>.
[TestVectors]
"Test vectors for Composite-ML-KEM", n.d.,
<https://github.com/lamps-wg/draft-composite-
kem/tree/main/src>.
[X-Wing] Barbosa, M., Connolly, D., Duarte, J., Kaiser, A.,
Schwabe, P., Varner, K., and B. Westerbaan, "X-Wing The
Hybrid KEM You’ve Been Looking For", 9 January 2024,
<https://eprint.iacr.org/2024/039.pdf>.
Appendix A. Maximum Key and Ciphertext Sizes
The sizes listed below are maximum values: several factors could
cause fluctuations in the size of the traditional component. For
example, this could be due to:
* The RSA public key (n, e) allows e to vary in 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.
* When the underlying RSA or EC value is itself DER-encoded, integer
values could occasionally be shorter than expected due to leading
zeros being dropped from the encoding.
By contrast, ML-KEM values are always fixed size, so composite values
can always be correctly de-serialized based on the size of the ML-KEM
component.
Size values marked with an asterisk (*) in the table are not fixed
but maximum possible values for the composite key or ciphertext.
Implementations MUST NOT perform strict length checking based on such
values.
Non-hybrid ML-KEM is included for reference.
+============================+========+=========+============+====+
| Algorithm | Public | Private | Ciphertext | SS |
| | key | key | | |
+============================+========+=========+============+====+
| id-alg-ml-kem-768 | 1184 | 64 | 1088 | 32 |
+----------------------------+--------+---------+------------+----+
| id-alg-ml-kem-1024 | 1568 | 64 | 1568 | 32 |
+----------------------------+--------+---------+------------+----+
| id- | 1454* | 1258* | 1344 | 32 |
| MLKEM768-RSA2048-SHA3-256 | | | | |
+----------------------------+--------+---------+------------+----+
| id- | 1582* | 1834* | 1472 | 32 |
| MLKEM768-RSA3072-SHA3-256 | | | | |
+----------------------------+--------+---------+------------+----+
| id- | 1710* | 2415* | 1600 | 32 |
| MLKEM768-RSA4096-SHA3-256 | | | | |
+----------------------------+--------+---------+------------+----+
| id- | 1216 | 96 | 1120 | 32 |
| MLKEM768-X25519-SHA3-256 | | | | |
+----------------------------+--------+---------+------------+----+
| id-MLKEM768-ECDH- | 1249 | 115 | 1153 | 32 |
| P256-SHA3-256 | | | | |
+----------------------------+--------+---------+------------+----+
| id-MLKEM768-ECDH- | 1281 | 128 | 1185 | 32 |
| P384-SHA3-256 | | | | |
+----------------------------+--------+---------+------------+----+
| id-MLKEM768-ECDH- | 1249 | 116 | 1153 | 32 |
| brainpoolP256r1-SHA3-256 | | | | |
+----------------------------+--------+---------+------------+----+
| id- | 1966* | 1834* | 1952 | 32 |
| MLKEM1024-RSA3072-SHA3-256 | | | | |
+----------------------------+--------+---------+------------+----+
| id-MLKEM1024-ECDH- | 1665 | 128 | 1665 | 32 |
| P384-SHA3-256 | | | | |
+----------------------------+--------+---------+------------+----+
| id-MLKEM1024-ECDH- | 1665 | 132 | 1665 | 32 |
| brainpoolP384r1-SHA3-256 | | | | |
+----------------------------+--------+---------+------------+----+
| id-MLKEM1024-X448-SHA3-256 | 1624 | 120 | 1624 | 32 |
+----------------------------+--------+---------+------------+----+
| id-MLKEM1024-ECDH- | 1701 | 146 | 1701 | 32 |
| P521-SHA3-256 | | | | |
+----------------------------+--------+---------+------------+----+
Table 3: Maximum size values of composite ML-KEM
Appendix B. Component Algorithm Reference
This section provides references to the full specification of the
algorithms used in the composite constructions.
+================+========================+===================+
| Component KEM | OID | Specification |
| Algorithm ID | | |
+================+========================+===================+
| id-ML-KEM-768 | 2.16.840.1.101.3.4.4.2 | [FIPS.203] |
+----------------+------------------------+-------------------+
| id-ML-KEM-1024 | 2.16.840.1.101.3.4.4.3 | [FIPS.203] |
+----------------+------------------------+-------------------+
| id-X25519 | 1.3.101.110 | [RFC7748], |
| | | [RFC8410] |
+----------------+------------------------+-------------------+
| id-X448 | 1.3.101.111 | [RFC7748], |
| | | [RFC8410] |
+----------------+------------------------+-------------------+
| id-ecDH | 1.3.132.1.12 | [RFC5480], |
| | | [RFC5915], [SEC1] |
+----------------+------------------------+-------------------+
| id-RSAES-OAEP | 1.2.840.113549.1.1.7 | [RFC8017] |
+----------------+------------------------+-------------------+
Table 4: Component Encryption Algorithms used in Composite
Constructions
+==================+=======================+===================+
| Elliptic CurveID | OID | Specification |
+==================+=======================+===================+
| secp256r1 | 1.2.840.10045.3.1.7 | [RFC6090], [SEC2] |
+------------------+-----------------------+-------------------+
| secp384r1 | 1.3.132.0.34 | [RFC6090], [SEC2] |
+------------------+-----------------------+-------------------+
| secp521r1 | 1.3.132.0.35 | [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 5: Elliptic Curves used in Composite Constructions
+=============+========================+===============+
| HashID | OID | Specification |
+=============+========================+===============+
| id-sha3-256 | 2.16.840.1.101.3.4.2.8 | [FIPS.202] |
+-------------+------------------------+---------------+
Table 6: Hash algorithms used in Composite Constructions
Appendix C. Fixed Component Algorithm Identifiers
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 ML-KEM 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 for each component
algorithm.
*ML-KEM-768*
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-alg-ml-kem-768 -- (2.16.840.1.101.3.4.4.2)
}
DER:
30 0B 06 07 60 86 48 01 65 03 04 04 02
*ML-KEM-1024*
ASN.1:
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-alg-ml-kem-1024 -- (2.16.840.1.101.3.4.4.3)
}
DER:
30 0B 06 07 60 86 48 01 65 03 04 04 03
*RSA-OAEP - all sizes*
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-RSAES-OAEP, -- (1.2.840.113549.1.1.7)
parameters RSAES-OAEP-params {
hashFunc [0] id-sha256, -- (2.16.840.1.101.3.4.2.1)
maskGenFunc [1] mgf1SHA256Identifier,
pSourceFunc [2] pSpecifiedEmpty }
}
where
mgf1SHA256Identifier AlgorithmIdentifier ::= {
algorithm id-mgf1, -- (1.2.840.113549.1.1.8)
parameters sha256Identifier }
sha256Identifier AlgorithmIdentifier ::= { id-sha256, NULL }
DER:
30 4D 06 09 2A 86 48 86 F7 0D 01 01 07 30 40 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 0F 30 0D 06 09 2A
86 48 86 F7 0D 01 01 09 04 00
*ECDH NIST-P-256*
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
*ECDH NIST-P-384*
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
*ECDH NIST-P-521*
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
*ECDH Brainpool-256*
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
*ECDH Brainpool-384*
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
*X25519*
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-X25519 -- (1.3.101.110)
}
DER:
30 05 06 03 2B 65 6E
*X448*
ASN.1:
algorithm AlgorithmIdentifier ::= {
algorithm id-X448 -- (1.3.101.111)
}
DER:
30 05 06 03 2B 65 6F
Appendix D. Comparison with other Hybrid KEMs
D.1. X-Wing
This specification borrows extensively from the analysis and KEM
combiner construction presented in [X-Wing]. In particular, X-Wing
and id-MLKEM768-X25519-SHA3-256 are largely interchangeable. The one
difference is that X-Wing uses a combined KeyGen function to generate
the two component private keys from the same seed, which gives some
additional binding properties. In order to allow for re-use of
existing hardeneded certified cryptographic modules (for example,
getting the RSA component from an existing smartcard), this
specification keeps the key generation for both components separate
and only loosely-specified so that implementers are free to use an
existing certified hardware or software module for one or both
components.
D.2. ETSI CatKDF
[ETSI.TS.103.744] section 8.2.3 defines CatKDF as:
1) Form secret = psk || k1 || k2.
2) Set context = f(info, MA, MB), where f is a context formatting
function.
3) key_material = KDF(secret, label, context, length).
4) Return key_material.
MA shall contain all of the public keys.
MB shall contain all of the corresponding public keys and ciphertexts.
The main difference between the Composite ML-KEM combiner and the
ETSI CatKDF combiner is that CatKDF makes the more conservative
choice to bind the public keys and ciphertexts of both components,
while Composite ML-KEM follows the analysis presented in [X-Wing]
that while preserving the security properties of the traditional
component requires binding the public key and ciphertext of the
traditional component, it is not necessary to do so for ML-KEM thanks
to the rejection sampling step of the Fujisaki-Okamoto transform.
Additionally, ETSI CatKDF can be instantiated with either HMAC
[RFC2104], KMAC [SP.800-185] or HKDF [RFC5869] as KDF. Since this
specification uses SHA3-256 as the KDF for all variants, there is no
equivalent construction of CatKDF.
Appendix E. Examples of KEM Combiner Intermediate Values
This section provides examples of constructing the input for the KEM
Combiner, showing all intermediate values. This is intended to be
useful for debugging purposes. See Section 3.4 for additional
information.
Each input component is shown. Note that values are shown hex-
encoded for display purposes only, they are actually raw binary
values.
* mlkemSS is the shared secret produced by the ML-KEM encapsulate or
decapsulate function which is always 32 bytes.
* tradSS is the shared secret produce by the traditional algorithm.
* tradCT is either an elliptic curve public key or an RSA-OAEP
ciphertext depending on the algorithm chosen.
* tradPK is the public key of the traditional component (elliptic
curve or RSA) and therefore fixed-length.
* Label is the specific KEM Combiner Label for this composite
algorithm. See Section 6
Next, the Combined KDF Input is given, which is simply the
concatenation of the above values.
Finally, the KDF Function and the ss Output are shown as outputs.
The ss is the Composite ML-KEM shared-secret generated by applying
the KDF to the Combined KDF Input.
Examples are given for each recommended Composite ML-KEM algorithm
from Section 10.3.
Example 1:
Example of id-MLKEM768-ECDH-P256-SHA3-256 Combiner function output.
# Inputs
mlkemSS:
a995e85fd52a32dbb6aaf216887de6f715ba6a0bdb01524ef74987a991a6d30c
tradSS:
de3eb22be5f5734e12335b1a51e27f60841ceb726df844da5b516e0128ab9a18
tradCT: 04570d34d53fd74670cfc77b81912dbe97d3d06242addc327ef6f2c7a9
8e35214ef9723118d600fc3b08e48d8e7f7cd166472d25a86aedbf9f598a404c231
80f0e
tradPK: 04acab079ea214fe047d490cc449e63e93daf879f9565ced0b3dfef5bd
b6c4438db29b33d8c28673cfe16d99dcaea82fba5cf40a5f209b501c437cf3b5ec9
3a4fd
Label: 4d4c4b454d3736382d50323536
(ascii: "MLKEM768-P256")
# Combined KDF Input:
# mlkemSS || tradSS || tradCT || tradPK || Label
Combined KDF Input: a995e85fd52a32dbb6aaf216887de6f715ba6a0bdb01524
ef74987a991a6d30cde3eb22be5f5734e12335b1a51e27f60841ceb726df844da5b
516e0128ab9a1804570d34d53fd74670cfc77b81912dbe97d3d06242addc327ef6f
2c7a98e35214ef9723118d600fc3b08e48d8e7f7cd166472d25a86aedbf9f598a40
4c23180f0e04acab079ea214fe047d490cc449e63e93daf879f9565ced0b3dfef5b
db6c4438db29b33d8c28673cfe16d99dcaea82fba5cf40a5f209b501c437cf3b5ec
93a4fd4d4c4b454d3736382d50323536
# Outputs
# ss = SHA3-256(Combined KDF Input)
ss:
8e6a7a064f64e23331b96d34735197805df17ca2e33776850c3ef65a62e730df
Example 2:
Example of id-MLKEM768-X25519-SHA3-256 Combiner function output.
# Inputs
mlkemSS:
ab7e0ac563e93b5d24a07ef20e6ed78b59972afcd34267a5eb68b3bf73e5d794
tradSS:
c837861b6b11cb40be2201bba20f4713e96fb56dba5afd1a2aecb04dea875215
tradCT:
64979ae712e5465b27651a8830fbd8d6256c19d7875cb55775b78d91c3a7b459
tradPK:
360d0ed7ecbb571c34c381d41e69a42d09a2bb5885be14ec405eb694f06e3941
Label: 5c2e2f2f5e5c
(ascii: "\.//^\")
# Combined KDF Input:
# mlkemSS || tradSS || tradCT || tradPK || Label
Combined KDF Input: ab7e0ac563e93b5d24a07ef20e6ed78b59972afcd34267a
5eb68b3bf73e5d794c837861b6b11cb40be2201bba20f4713e96fb56dba5afd1a2a
ecb04dea87521564979ae712e5465b27651a8830fbd8d6256c19d7875cb55775b78
d91c3a7b459360d0ed7ecbb571c34c381d41e69a42d09a2bb5885be14ec405eb694
f06e39415c2e2f2f5e5c
# Outputs
# ss = SHA3-256(Combined KDF Input)
ss:
f312bd17964443ccc54a2846f6d9f98c5d1e6760c28bd0e87ca15ddba4da040d
Example 3:
Example of id-MLKEM1024-ECDH-P384-SHA3-256 Combiner function output.
# Inputs
mlkemSS:
c44e262d0fbf83217f8140988e51e6952dee399a4098b0fe3c9003e555ea9977
tradSS: 363f4a5fbe2c2109b86c343d390c731c8e417567e71f7d9000d6a34d6f
7e780997dd643754deb5d73af8f4727f1b45b1
tradCT: 0463e6a7252ba898c04be179c0c66e301b4871a07395a636b0d1f66131
ab62bf78cf3f9898f02d8ca3c8a19dea82e95d3eb4b3469a3227669ef785a30de00
d4d2334893a8996b8067fc661c66868eb6a0476c256de177f23dc2a1a0116870d3a
f3
tradPK: 041431c346f091622a10c410be842d1dd4c599681abe9c3c78b5fa7faa
9b7f9eb968cba0cf8410ddda65b89e48beac53c5aae67ad268a1985e6db92c50573
414c4e71b85671a9ce0e8daaa36fa12c8f5584a6c598f9811042c4e7d0b49399c75
9a
Label: 4d4c4b454d313032342d50333834
(ascii: "MLKEM1024-P384")
# Combined KDF Input:
# mlkemSS || tradSS || tradCT || tradPK || Label
Combined KDF Input: c44e262d0fbf83217f8140988e51e6952dee399a4098b0f
e3c9003e555ea9977363f4a5fbe2c2109b86c343d390c731c8e417567e71f7d9000
d6a34d6f7e780997dd643754deb5d73af8f4727f1b45b10463e6a7252ba898c04be
179c0c66e301b4871a07395a636b0d1f66131ab62bf78cf3f9898f02d8ca3c8a19d
ea82e95d3eb4b3469a3227669ef785a30de00d4d2334893a8996b8067fc661c6686
8eb6a0476c256de177f23dc2a1a0116870d3af3041431c346f091622a10c410be84
2d1dd4c599681abe9c3c78b5fa7faa9b7f9eb968cba0cf8410ddda65b89e48beac5
3c5aae67ad268a1985e6db92c50573414c4e71b85671a9ce0e8daaa36fa12c8f558
4a6c598f9811042c4e7d0b49399c759a4d4c4b454d313032342d50333834
# Outputs
# ss = SHA3-256(Combined KDF Input)
ss:
2c50407b7b2e5dd0990f36f0c0362d6d43c6f046105a00a584adc066ad0b28aa
Appendix F. 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 cacert is provided which is used to
sign each KEM certificate.
Within each test case there are the following values:
* tcId the name of the algorithm.
* ek the encapsulation public key.
* x5c the X.509 certificate of the encapsulation key, signed by the
cacert.
* dk the raw decapsulation private key.
* dk_pkcs8 the decapsulation private key in a PKCS#8 object.
* c the ciphertext.
* k the derived shared secret key.
Implementers should be able to perform the following tests using the
test vectors below:
1. Load the public key ek or certificate x5c and perform an
encapsulation for it (you should obtain valid ct and k values,
but they will not match the ones in the test vector since Encap()
is randomized.)
2. Load the decapsulation private key dk or dk_pkcs8 and the
ciphertext c and perform a Decaps() operation to ensure that the
same shared secret key k is derived.
Test vectors are provided for each underlying ML-KEM 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 [TestVectors]. The
reference implementation written in python that generated them is
also available.
{
"cacert": "MIIVpzCCCKSgAwIBAgIUWbwKMXGQsN797exI+7pAKIF/tdkwCwYJYIZIA
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]
}
Appendix G. Contributors and Acknowledgments
This document represents the results of a many-year effort by the
LAMPS working group. Over that time the following working group
members provided valuable review and commentary on the document:
Serge Mister (Entrust), Felipe Ventura (Entrust), Richard Kettlewell
(Entrust), Ali Noman (Entrust), Peter C. (UK NCSC), Tim Hollebeek
(Digicert), Sophie Schmieg (Google), Deirdre Connolly (SandboxAQ),
Chris A. Wood (Apple), Bas Westerbaan (Cloudflare), Falko Strenzke
(MTG AG), Piotr Popis (Enigma), Jean-Pierre Fiset (Crypto4A), Carl
Wallace, Daniel Van Geest (CryptoNext Security), 陳志華 (Abel C. H.
Chen, Chunghwa Telecom), 林邦曄 (Austin Lin, Chunghwa Telecom) and
Douglas Stebila (University of Waterloo).
We wish to acknowledge a few people who have made notable
contributions to specific sections of this document.
We wish to acknowledge particular effort from Carl Wallace and Daniel
Van Geest (CryptoNext Security), who have implemented each successive
version of the draft over multiple years to provide valuable
implementation experience and hackathon testing. Thanks to Stepan
Yakimovich for contributing to the reference implementation to be
able to provide and verify hackathon artifacts.
Thanks to Giacomo Pope (github.com/GiacomoPope) whose ML-DSA and ML-
KEM implementations were used to generate the test vectors.
We are grateful to all who have given feedback over the years,
formally or informally, on mailing lists or in person, including any
contributors who may have been inadvertently omitted from this list.
Finally, we wish to thank the authors of all the referenced documents
upon which this specification was built. "Copying always makes
things easier and less error prone" - [RFC8411].
Authors' Addresses
Mike Ounsworth
Entrust Limited
2500 Solandt Road – Suite 100
Ottawa, Ontario K2K 3G5
Canada
Email: mike.ounsworth@entrust.com
John Gray
Entrust Limited
2500 Solandt Road – Suite 100
Ottawa, Ontario K2K 3G5
Canada
Email: john.gray@entrust.com
Massimiliano Pala
OpenCA Labs
New York City, New York,
United States of America
Email: director@openca.org
Jan Klaussner
Bundesdruckerei GmbH
Kommandantenstr. 18
10969 Berlin
Germany
Email: jan.klaussner@bdr.de
Scott Fluhrer
Cisco Systems
Email: sfluhrer@cisco.com