Internet-Draft Composite ML-KEM May 2025
Ounsworth, et al. Expires 26 November 2025 [Page]
Workgroup:
LAMPS
Internet-Draft:
draft-ietf-lamps-pq-composite-kem-latest
Published:
Intended Status:
Standards Track
Expires:
Authors:
M. Ounsworth
Entrust
J. Gray
Entrust
M. Pala
OpenCA Labs
J. Klaussner
Bundesdruckerei GmbH
S. Fluhrer
Cisco Systems

Composite ML-KEM for use in X.509 Public Key Infrastructure

Abstract

This document defines combinations of 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 requirements. 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 mailing list (mailto:spams@ietf.org), which is archived at https://datatracker.ietf.org/wg/lamps/about/. Subscribe at https://www.ietf.org/mailman/listinfo/spams/.

Source for this draft and an issue tracker can be found at https://github.com/lamps-wg/draft-composite-kem.

Status of This Memo

This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79.

Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at https://datatracker.ietf.org/drafts/current/.

Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress."

This Internet-Draft will expire on 26 November 2025.

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Table of Contents

1. Changes in version -07

Interop-affecting changes:

Editorial changes:

Still to do in a future version:

2. Introduction

The advent of quantum computing poses a significant threat to current cryptographic systems. Traditional cryptographic key establishment algorithms such as RSA-OAEP and ECDH are vulnerable to quantum attacks. During the transition to post-quantum cryptography (PQC), there is considerable uncertainty regarding the robustness of both existing and new cryptographic algorithms. While we can no longer fully trust traditional cryptography, we also cannot immediately place complete trust in post-quantum replacements until they have undergone extensive scrutiny and real-world testing to uncover and rectify potential implementation flaws.

Unlike previous migrations between cryptographic algorithms, the decision of when to migrate and which algorithms to adopt is far from straightforward. Even after the migration period, it may be advantageous for an entity's cryptographic identity to incorporate multiple public-key algorithms to enhance security.

Cautious implementers may opt to combine cryptographic algorithms in such a way that an attacker would need to break all of them simultaneously to compromise the protected data. These mechanisms are referred to as Post-Quantum/Traditional (PQ/T) Hybrids [I-D.ietf-pquip-pqt-hybrid-terminology].

Certain jurisdictions are already recommending or mandating that PQC lattice schemes be used exclusively within a PQ/T hybrid framework. The use of Composite scheme provides a straightforward implementation of hybrid solutions compatible with (and advocated by) some governments and cybersecurity agencies [BSI2021].

In addition, [BSI2021] specifically references the composite specification as a concrete example of hybrid X.509 certificates.

A more recent example is [ANSSI2024], a document co-authored by 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 which makes the following statement:

This specification represents the straightforward implementation of the hybrid solutions called for by European cyber security agencies.

PQ/T Hybrid cryptography can, in general, provide solutions to two migration problems:

This document 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) key and ciphertext such that they can be treated as a single atomic algorithm at the protocol level. Composite algorithms address algorithm strength uncertainty because the composite algorithm remains strong so long as one of its components remains strong. Concrete instantiations of composite ML-KEM algorithms are provided based on ML-KEM, RSA-OAEP and ECDH. Backwards compatibility is not directly covered in this document, but is the subject of Appendix D.2.

Composite ML-KEM is intended for general applicability anywhere that key establishment or enveloped content encryption is used within PKIX protocols.

2.1. Conventions and Terminology

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here. These words may also appear in this document in lower case as plain English words, absent their normative meanings.

This document is consistent with all terminology from [I-D.ietf-pquip-pqt-hybrid-terminology]. In addition, the following terms are used in this document:

ALGORITHM: The usage of the term "algorithm" within this document generally refers to any function which has a registered Object Identifier (OID) for use within an ASN.1 AlgorithmIdentifier. This loosely, but not precisely, aligns with the definitions of "cryptographic algorithm" and "cryptographic scheme" given in [I-D.ietf-pquip-pqt-hybrid-terminology].

COMBINER: A combiner specifies how multiple shared secrets are combined into a single shared secret.

DER: Distinguished Encoding Rules as defined in [X.690].

KEM: A key encapsulation mechanism as defined in Section 3.

PKI: Public Key Infrastructure, as defined in [RFC5280].

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 document is concerned with shared secrets established via public key cryptographic operations.

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.

2.2. Composite Design Philosophy

[I-D.ietf-pquip-pqt-hybrid-terminology] defines composites as:

  • Composite Cryptographic Element: A cryptographic element that incorporates multiple component cryptographic elements of the same type in a multi-algorithm scheme.

Composite keys, as defined here, follow this definition and should be regarded as a single key that performs a single cryptographic operation such as key generation, signing, verifying, encapsulating, or decapsulating -- using its internal sequence of component keys as if they form a single key. This generally means that the complexity of combining algorithms can and should be handled by the cryptographic library or cryptographic module, and the single composite public key, private key, ciphertext and signature can be carried in existing fields in protocols such as PKCS#10 [RFC2986], CMP [RFC4210], X.509 [RFC5280], CMS [RFC5652], and the Trust Anchor Format [RFC5914]. In this way, composites achieve "protocol backwards-compatibility" in that they will drop cleanly into any protocol that accepts an analogous single-algorithm cryptographic scheme without requiring any modification of the protocol to handle multiple algorithms.

3. Overview of the Composite ML-KEM Scheme

We borrow here the definition of a key encapsulation mechanism (KEM) from [I-D.ietf-tls-hybrid-design], in which a KEM is a cryptographic primitive that consists of three algorithms:

We define the following algorithms which are used to serialize and deserialize component values. These algorithms are inspired by similar algorithms in [RFC9180].

Full definitions of serialization and deserialization algorithms can be found in Section 5.

The KEM interface defined above differs from both traditional key transport mechanism (for example for use with KeyTransRecipientInfo defined in [RFC5652]), and key agreement (for example for use with KeyAgreeRecipientInfo defined in [RFC5652]).

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 3.1 and Section 3.2 below.

This specification uses the Post-Quantum KEM ML-KEM as specified in [FIPS.203] and [I-D.ietf-lamps-kyber-certificates]. For Traditional KEMs, this document uses the RSA-OAEP algorithm 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 which are defined in [RFC8410]. A combiner function is used to combine the two component shared secrets into a single shared secret.

3.1. 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. It is promoted into a KEM by having the sender generate a random 256 bit secret and encrypt it.

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.

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 output by the overall Composite ML-KEM already binds a composite domain separator, so there is no need to also utilize the component domain separators.

The value of ss_len as well as the RSA-OAEP parameters used within this specification can be found in Section 7.4.

Decap(sk, ct) -> ss is accomplished in the analogous way.

RSAOAEPKEM.Decap(skR, enc):
  shared_secret = RSAES-OAEP-DECRYPT(skR, enc)

  return shared_secret

3.2. Promotion of ECDH into a KEM

An elliptic curve Diffie-Hellman key agreement is promoted into a KEM Encap(pk) -> (ss, ct) using a simplified version of the DHKEM definition from [RFC9180]; simplified to remove the context-binding labels since the shared secret output by the overall Composite ML-KEM already binds a composite domain separator, so there is no need to also utilize labels within DHKEM.

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.

DHKEM.Encap(pkR):
  skE, pkE = GenerateKeyPair()
  shared_secret = DH(skE, pkR)
  enc = SerializePublicKey(pkE)

  return shared_secret, enc

Decap(sk, ct) -> ss is accomplished in the analogous way.

DHKEM.Decap(skR, enc):
  pkE = DeserializePublicKey(enc)
  shared_secret = DH(skR, pkE)

  return shared_secret

This construction applies for all variants of elliptic curve Diffie-Hellman used in this specification: ECDH, X25519, and X448.

The simplifications from the DHKEM definition in [RFC9180] is that 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, and since a domain separator is included explicitly in the Composite ML-KEM combiner there is no need to perform the labeled steps of ExtractAndExpand().

4. Composite ML-KEM Functions

This section describes the composite ML-KEM functions needed to instantiate the KEM API in Section 3.

4.1. Key Generation

In order to maintain security properties of the composite, applications that use composite keys MUST always perform fresh key generations of both component keys and MUST NOT reuse existing key material. See Section 10.3 for a discussion.

To generate a new keypair for Composite schemes, the KeyGen() -> (pk, sk) function is used. The KeyGen() function calls the two key generation functions of the component algorithms for the Composite keypair in no particular order. Multi-process or multi-threaded applications might choose to execute the key generation functions in parallel for better key generation performance.

The following process is used to generate composite keypair values:

KeyGen() -> (pk, sk)

Explicit Inputs:
     None

Implicit Input:
  ML-KEM     A placeholder for the specific ML-KEM algorithm and
             parameter set to use, for example, could be "ML-KEM-768".

  Trad       A placeholder for the specific traditional algorithm and
             parameter set to use, for example "RSA-OAEP"
             or "X25519".

Output:
  (pk, sk)  The composite keypair.

Key Generation Process:

  1. Generate component keys

    (mlkemPK, mlkemSK) = ML-KEM.KeyGen()
    (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 = mlkemPK || tradPK
    sk = mlkemSK || tradSK
    return (pk, sk)
Figure 1: Composite KeyGen() -> (pk, sk)

In order to ensure fresh keys, the key generation functions MUST be executed for both component algorithms. Compliant parties MUST NOT use or import component keys that are used in other contexts, combinations, or by themselves as keys for standalone algorithm use.

Note that in step 2 above, both component key generation processes are invoked, and no indication is given about which one failed. This SHOULD be done in a timing-invariant way to prevent side-channel attackers from learning which component algorithm failed.

4.2. 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.

Composite-ML-KEM.Encap(pk) -> (ss, ct)

Explicit Input:

  pk          Composite public key consisting of encryption public keys
              for each component.

Implicit inputs:

  ML-KEM   A placeholder for the specific ML-KEM algorithm and
           parameter set to use, for example "ML-KEM-768".

  Trad     A placeholder for the specific ML-KEM algorithm and
           parameter set to use, for example "RSA-OAEP"
           or "X25519".

  KDF      The KDF specified for the given Composite ML-KEM algorithm.
           See algorithm specifications below.

  Domain   Domain separator value for binding the ciphertext to the
           Composite OID. See section on Domain Separators 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) = 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 = mlkemCT || tradCT

  5. Combine the KEM secrets and additional context to yield the composite shared secret
      if KDF is "SHA3-256"
        ss = SHA3-256(mlkemSS || tradSS || tradCT || tradPK || Domain)
      else if KDF is "HKDF"
        ss = HKDF-Extract(salt="", IKM=mlkemSS || tradSS || tradCT || tradPK || Domain)
          # Note: salt is the empty string (0 octets), which will internally be mapped
          # to the zero vector `0x00..00` of the correct input size for the underlying
          # hash function as per [RFC5869].

  6. Output composite shared secret key and ciphertext

     return (ss, ct)
Figure 2: Composite-ML-KEM.Encap(pk)

The specific values for KDF are defined per Composite ML-KEM algorithm in Table 2 and the specific values for Domain are defined per Composite ML-KEM algorithm in Section 7.

4.3. 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.

Composite-ML-KEM.Decap(sk, ct) -> ss

Explicit Input:

  sk    Composite private key consisting of decryption private keys for
        each component.

  ct      The ciphertext, a byte string.

Implicit inputs:

  ML-KEM   A placeholder for the specific ML-KEM algorithm and
           parameter set to use, for example, could be "ML-KEM-768".

  Trad     A placeholder for the specific traditional algorithm and
           parameter set to use, for example "RSA-OAEP"
           or "X25519".

  KDF      The KDF specified for the given Composite ML-KEM algorithm.
           See algorithm specifications below.

  Domain   Domain separator value for binding the ciphertext to the
           Composite OID. See section on Domain Separators below.

Output:

  ss      The shared secret key, a 256-bit key suitable for use with
          symmetric cryptographic algorithms.

Decap Process:

  1. Separate the private keys

      (mlkemSK, tradSK) = sk

  2. Parse the ciphertext

      (mlkemCT, tradCT) = ct

  3.  Perform the respective component Encap operations according to
      their algorithm specifications.

      mlkemSS = MLKEM.Decaps(mlkemSK, mlkemCT)
      tradSS  = TradKEM.Decap(tradSK, tradCT)

  4. 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 "Encapsulation error"

  5. Combine the KEM secrets and additional context to yield the composite shared secret

      if KDF is "SHA3-256"
        ss = SHA3-256(mlkemSS || tradSS || tradCT || tradPK || Domain)
      else if KDF is "HKDF"
        ss = HKDF-Extract(salt="", IKM=mlkemSS || tradSS || tradCT || tradPK || Domain)
          # Note: salt is the empty string (0 octets), which will internally be mapped
          # to the zero vector `0x00..00` of the correct input size for the underlying
          # hash function as per [RFC5869].

  6. Output composite shared secret key

     return ss
Figure 3: Composite-ML-KEM.Decap(sk, ct)

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 document 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. Since each Composite ML-KEM algorithm fully specifies its component algorithms, including key sizes, all inputs should be fixed-length in non-error scenarios, however some implementations may need 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. For timing-invariance reasons, it is RECOMMENDED to perform both decapsulation operations and check for errors afterwards to prevent an attacker from using a timing channel to tell which component failed decapsulation. Also, 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 Table 2; depending on the cryptographic library used, this check may be done by the library or may require an explicit check as part of the CompositeKEM.Decap() routine.

4.4. KEM Combiner Function

As noted in the Encapsulation and Decapsulation proceedures above, this specification defines two KEM combiner constructions, one with SHA3 and one with HKDF-SHA2.

``` if KDF is "SHA3-256" ss = SHA3-256(mlkemSS || tradSS || tradCT || tradPK || Domain) else if KDF is "HKDF" ss = HKDF-Extract(salt="", IKM=mlkemSS || tradSS || tradCT || tradPK || Domain) # Note: salt is the empty string (0 octets), which will internally be mapped # to the zero vector 0x00..00 of the correct input size for the underlying # hash function as per [RFC5869].

```

Implementation note: many cryptographic libraries provide only a combined interface for HKDF and do not expose HKDF-Extract() and HKDF-Expand() separately. Note that HKDF() even with the correct output length and empty info param is not equivalent to HKDF-Extract() since an extra iteration of HMAC will be performed. If HKDF-Extract() is not exposed, then it can be implemented directly with the HMAC primitive as:

HKDF-Extract(salt="", IKM=mlkemSS || tradSS || tradCT || tradPK || Domain) = HMAC-Hash(salt="", IKM=mlkemSS || tradSS || tradCT || tradPK || Domain)

5. Serialization

This section presents routines for serializing and deserializing composite public keys, private keys (seeds), and ciphertext values to bytes via simple concatenation of the underlying encodings of the component algorithms. Deserialization is possible because ML-KEM has fixed-length public keys, private keys (seeds), and ciphertext values as shown in the following table.

Table 1: ML-KEM Key and Ciphertext Sizes
Algorithm Public Key Private Key Ciphertext
ML-KEM-768 1184 64 1088
ML-KEM-1024 1568 64 1568

When these values are required to be carried in an ASN.1 structure, they are wrapped as described in Section 6.1.

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:

In the event that a composite implementation uses an underlying implementation of the traditional component that requires a different encoding, it is the responsibility of the composite implementation to perform the necessary transcoding. Even with fixed encodings for the traditional component, there may be slight differences in encoded size of the traditional component due to, for example, encoding rules that drop leading zeroes. See Appendix A for further discussion of encoded size of each composite algorithm.

5.1. SerializePublicKey and DeserializePublicKey

The serialization routine for keys simply concatenates the fixed-length public keys of the component algorithms, as defined below:

Composite-ML-KEM.SerializePublicKey(mlkemPK, tradPK) -> bytes

Explicit Input:

  mlkemPK  The ML-KEM public key, which is bytes.

  tradPK   The traditional public key in the appropriate
           bytes-like encoding for the underlying component algorithm.

Output:

  bytes   The encoded composite public key

Serialization Process:

  1. Combine and output the encoded public key

     output mlkemPK || tradPK
Figure 4: SerializePublicKey(mlkemKey, tradKey) -> bytes

Deserialization reverses this process. key is deserialized according to their respective standard as shown in Appendix B.

Composite-ML-KEM.DeserializePublicKey(bytes) -> (mlkemPK, tradPK)

Explicit Input:

  bytes   An encoded public key

Implicit inputs:

  ML-KEM   A placeholder for the specific ML-KEM algorithm and
           parameter set to use, 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
           bytes-like encoding for the underlying component algorithm.

Deserialization Process:

  1. Parse each constituent encoded public key.
       The length of the mlkemKey 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 and ECDH
     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)
Figure 5: DeserializePublicKey(bytes) -> (mlkemPK, tradPK)

5.2. SerializePrivateKey and DeserializePrivateKey

The serialization routine for keys simply concatenates the fixed-length private keys of the component algorithms, as defined below:

Composite-ML-KEM.SerializePrivateKey(mlkemSeed, tradSK) -> bytes

Explicit Input:

  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.

Output:

  bytes   The encoded composite private key

Serialization Process:

  1. Combine and output the encoded private key

     output mlkemSeed || tradKey
Figure 6: SerializePrivateKey(mlkemSeed, tradSK) -> bytes

Deserialization reverses this process.

Composite-ML-KEM.DeserializePrivateKey(bytes) -> (mlkemSeed, tradSK)

Explicit Input:

  bytes   An encoded composite private key

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 each constituent encoded key.
       The length of an ML-KEM private key is always a 64 byte seed
       for all parameter sets.

      mlkemSeed = bytes[:64]
      tradSK  = bytes[64:]

     Note that while ML-KEM has fixed-length keys (seeds), RSA and ECDH
     may not, depending on encoding, so rigorous length-checking
     of the overall composite key is not always possible.

  2. Output the component private keys

     output (mlkemSeed, tradSK)
Figure 7: DeserializeKey(bytes) -> (mlkemSeed, tradSK)

5.3. SerializeCiphertext and DeserializeCiphertext

The serialization routine for the CompositeCiphertextValue 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.

Output:

  bytes   The encoded CompositeCiphertextValue

Serialization Process:

  1. Combine and output the encoded composite ciphertext

     output mlkemCT || tradCT
Figure 8: SerializeCiphertext(mlkemCT, tradCT) -> bytes

Deserialization reverses this process.

Composite-ML-KEM.DeserializeCiphertext(bytes) -> (mldkemCT, tradCT)

Explicit Input:

  bytes   An encoded CompositeCiphertextValue

Implicit inputs:

  ML-KEM   A placeholder for the specific ML-KEM algorithm and
           parameter set to use, 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:]

     Note that while ML-KEM has fixed-length ciphertexts, RSA and ECDH
     may not, depending on encoding, so rigorous length-checking is
     not always possible here.

  2. Output the component ciphertext values

     output (mlkemCT, tradCT)
Figure 9: DeserializeCiphertext(bytes) -> (mldkemCT, tradCT)

6. 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.

While composite ML-KEM keys and ciphertexts MAY be used raw, the following sections provide conventions for using them within X.509 and other PKIX protocols, including defining ASN.1-based wrappers for the binary composite values, such that these structures can be used as a drop-in replacement for existing public key and ciphertext fields such as those found in PKCS#10 [RFC2986], CMP [RFC4210], X.509 [RFC5280], CMS [RFC5652].

6.1. Encoding to DER

The serialization routines presented in Section 5 produce raw binary values. When these values are required to be carried within a DER-encoded message format such as an X.509's subjectPublicKey BIT STRING [RFC5280] or a CMS KEMRecipientInfo.kemct OCTET STRING [RFC9629], then the composite value MUST be wrapped into a DER BIT STRING or OCTET STRING in the obvious ways:

When an OCTET STRING is required, the DER encoding of the composite data value SHALL be used directly.

When a BIT STRING is required, the octets of the composite data value SHALL be used as the bits of the bit string, with the most significant bit of the first octet becoming the first bit, and so on, ending with the least significant bit of the last octet becoming the last bit of the bit string.

6.2. Key Usage Bits

When any Composite ML-KEM AlgorithmIdentifier appears in the SubjectPublicKeyInfo 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.

6.3. ASN.1 Definitions

The following ASN.1 Information Object Class is 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 BIT STRING
    PARAMS ARE absent
    CERT-KEY-USAGE { keyEncipherment }
  }

The full set of key types defined by this specification can be found in the ASN.1 Module in Section 8.

The ASN.1 algorithm object for a Composite ML-KEM is:

kema-CompositeKEM {
  OBJECT IDENTIFIER:id,
    PUBLIC-KEY:publicKeyType }
    KEM-ALGORITHM ::= {
         IDENTIFIER id
         VALUE OCTET STRING
         PARAMS ARE absent
         PUBLIC-KEYS { publicKeyType }
        }

Use cases that require an interoperable encoding for composite private keys will often need to place a CompositeKEMPrivateKey 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.

When a composite private key is conveyed inside a OneAsymmetricKey structure (version 1 of which is also known as PrivateKeyInfo) [RFC5958], the privateKeyAlgorithm field SHALL be set to the corresponding composite algorithm identifier defined according to Section 7 and its parameters field MUST be absent. The privateKey field SHALL contain the OCTET STRING reperesentation of the serialized composite private key as per Section 5.2. The publicKey field remains OPTIONAL.

Some applications may need to reconstruct the OneAsymmetricKey objects corresponding to each component private key. Section 7 and Appendix B provide the necessary mapping between composite and their component algorithms for doing this reconstruction.

Component keys of a CompositeKEMPrivateKey MUST NOT be used in any other type of key or as a standalone key. For more details on the security considerations around key reuse, see Section 10.3.

7. Algorithm Identifiers

This table summarizes the list of Composite ML-KEM algorithms and lists the OID, two component algorithms, and the KDF to be used within combiner function. Domain separator values are defined below in Section 7.2.

EDNOTE: these are prototyping OIDs to be replaced by IANA.

<CompKEM> is equal to 2.16.840.1.114027.80.5.2

7.1. Composite-ML-KEM Algorithm Identifiers

Table 2: Composite ML-KEM key types
Composite ML-KEM Algorithm OID First Algorithm Second Algorithm KDF
id-MLKEM768-RSA2048-HKDF-SHA256 <CompKEM>.50 MLKEM768 RSA-OAEP 2048 HKDF-SHA256
id-MLKEM768-RSA3072-HKDF-SHA256 <CompKEM>.51 MLKEM768 RSA-OAEP 3072 HKDF-SHA256
id-MLKEM768-RSA4096-HKDF-SHA256 <CompKEM>.52 MLKEM768 RSA-OAEP 4096 HKDF-SHA256
id-MLKEM768-X25519-SHA3-256 <CompKEM>.53 MLKEM768 X25519 SHA3-256
id-MLKEM768-ECDH-P256-HKDF-SHA256 <CompKEM>.54 MLKEM768 ECDH-P256 HKDF-SHA256
id-MLKEM768-ECDH-P384-HKDF-SHA256 <CompKEM>.55 MLKEM768 ECDH-P384 HKDF-SHA256
id-MLKEM768-ECDH-brainpoolP256r1-HKDF-SHA256 <CompKEM>.56 MLKEM768 ECDH-brainpoolp256r1 HKDF-SHA256
id-MLKEM1024-ECDH-P384-HKDF-SHA384 <CompKEM>.57 MLKEM1024 ECDH-P384 HKDF-SHA384/256
id-MLKEM1024-ECDH-brainpoolP384r1-HKDF-SHA384 <CompKEM>.58 MLKEM1024 ECDH-brainpoolP384r1 SHA3-256
id-MLKEM1024-X448-SHA3-256 <CompKEM>.59 MLKEM1024 X448 SHA3-256
id-MLKEM1024-ECDH-P521-HKDF-SHA384 <CompKEM>.60 MLKEM1024 ECDH-P521 HKDF-SHA384/256

Note that in alignment with ML-KEM which outputs a 256-bit shared secret key at all security levels, all Composite KEM algorithms output a 256-bit shared secret key.

For the use of HKDF [RFC5869]: a salt is not provided; i.e. the default salt (all zeroes of length HashLen) will be used. For HKDF-SHA256 the output of 256 bit output is used directly; for HKDF-SHA384/256, HKDF is invoked with SHA384 and then the output is truncated to 256 bits, meaning that only the first 256 bits of output are used.

As the number of algorithms can be daunting to implementers, see Appendix D.4 for a discussion of choosing a subset to support.

Full specifications for the referenced component algorithms can be found in Appendix B.

7.2. Domain Separators

The KEM combiner used in this document requires a domain separator Domain input. The following table shows the HEX-encoded domain separator for each Composite ML-KEM AlgorithmID; to use it, the value MUST be HEX-decoded and used in binary form. The domain separator is simply the DER encoding of the composite algorithm OID.

Table 3: Composite ML-KEM fixedInfo Domain Separators
Composite Signature Algorithm Domain Separator (in Hex encoding)
id-MLKEM768-RSA2048-HKDF-SHA256 060B6086480186FA6B50050232
id-MLKEM768-RSA3072-HKDF-SHA256 060B6086480186FA6B50050233
id-MLKEM768-RSA4096-HKDF-SHA256 060B6086480186FA6B50050234
id-MLKEM768-X25519-SHA3-256 060B6086480186FA6B50050235
id-MLKEM768-ECDH-P256-HKDF-SHA256 060B6086480186FA6B50050236
id-MLKEM768-ECDH-P384-HKDF-SHA256 060B6086480186FA6B50050237
id-MLKEM768-ECDH-brainpoolP256r1-HKDF-SHA256 060B6086480186FA6B50050238
id-MLKEM1024-ECDH-P384-HKDF-SHA384 060B6086480186FA6B50050239
id-MLKEM1024-ECDH-brainpoolP384r1-HKDF-SHA384 060B6086480186FA6B5005023A
id-MLKEM1024-X448-SHA3-256 060B6086480186FA6B5005023B
id-MLKEM1024-ECDH-P521-HKDF-SHA384 060B6086480186FA6B5005023C

EDNOTE: these domain separators are based on the prototyping OIDs assigned on the Entrust arc. We will need to ask for IANA early allocation of these OIDs so that we can re-compute the domain separators over the final OIDs.

7.3. Rationale for choices

In generating the list of Composite algorithms, the following general guidance was used, however, during development of this specification several algorithms were added by direct request even though they do not fit this guidance.

  • Pair equivalent security levels between

  • NIST-P-384 is CNSA approved [CNSA2.0] for all classification levels.

  • SHA256 and SHA512 generally have better adoption than SHA384.

A single invocation of SHA3 is known to behave as a dual-PRF, and thus is sufficient for use as a KDF, see Section 10.2, however SHA2 is not so must be wrapped in the HKDF construction.

The lower security levels (i.e. ML-KEM768) are provided with HKDF-SHA2 as the KDF in order to facilitate implementations that do not have easy access to SHA3 outside of the ML-KEM function. Higher security levels (i.e. ML-KEM1024) are paired with SHA3 for computational efficiency except for one variant paired with HKDF-SHA384 for compliance with [CNSA2.0], and the Edwards Curve (X25519 and X448) combinations are paired with SHA3 for compatibility with other similar specifications.

While it may seem odd to use 256-bit hash functions at all security levels, this aligns with ML-KEM which produces a 256-bit shared secret key at all security levels. SHA-256 and SHA3-256 both have >= 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].

7.4. RSA-OAEP Parameters

Use of RSA-OAEP [RFC8017] within id-MLKEM768-RSA2048-HKDF-SHA256, id-MLKEM768-RSA3072-HKDF-SHA256, and id-MLKEM768-RSA4096-HKDF-SHA256 requires additional specification.

First, a quick note on the choice of RSA-OAEP as the supported RSA encryption primitive. RSA-KEM [RFC5990] is more straightforward to work with, but it has fairly limited adoption and therefore is of limited backwards compatibility value. Also, while RSA-PKCS#1v1.5 [RFC8017] is still everywhere, but 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.

The RSA component keys MUST be generated at the 2048-bit and 3072-bit security levels respectively.

As with the other Composite ML-KEM algorithms, when id-MLKEM768-RSA2048-HKDF-SHA256, id-MLKEM768-RSA3072-HKDF-SHA256, or id-MLKEM-RSA4096 is used in an AlgorithmIdentifier, the parameters MUST be absent. The RSA-OAEP SHALL be instantiated with the following hard-coded parameters which are the same for the 2048, 3072 and 4096 bit security levels.

Table 4: RSA-OAEP Parameters
RSAES-OAEP-params Value
hashAlgorithm id-sha256
maskGenAlgorithm mgf1SHA256Identifier
pSourceAlgorithm pSpecifiedEmpty
ss_len 256 bits

where:

  • id-sha256 is defined in [RFC8017].

  • mgf1SHA256Identifier is defined in [RFC4055], which refers to the MFG1 function defined in [RFC8017] appendix B.2.1.

  • pSpecifiedEmpty is defined in [RFC8017] to indicate that the empty string is used for the label.

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.

8. 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
--

-- Defined in ITU-T X.690
der OBJECT IDENTIFIER ::=
  {joint-iso-itu-t asn1(1) ber-derived(2) distinguished-encoding(1)}


--
-- Information Object Classes
--

pk-CompositeKEM {OBJECT IDENTIFIER:id}
  PUBLIC-KEY ::= {
    IDENTIFIER id
    KEY BIT STRING
    PARAMS ARE absent
    CERT-KEY-USAGE { keyEncipherment }
  }

kema-CompositeKEM {
  OBJECT IDENTIFIER:id,
    PUBLIC-KEY:publicKeyType }
    KEM-ALGORITHM ::= {
         IDENTIFIER id
         VALUE OCTET STRING
         PARAMS ARE absent
         PUBLIC-KEYS { publicKeyType }
         SMIME-CAPS { IDENTIFIED BY id }
        }



--
-- Composite KEM Algorithms
--


-- TODO: OID to be replaced by IANA
id-MLKEM768-RSA2048-HKDF-SHA256 OBJECT IDENTIFIER ::= {
  joint-iso-itu-t(2) country(16) us(840) organization(1)
  entrust(114027) algorithm(80) explicitcomposite(5) kem(2) 50 }

pk-MLKEM768-RSA2048-HKDF-SHA256 PUBLIC-KEY ::=
  pk-CompositeKEM {
    id-MLKEM768-RSA2048-HKDF-SHA256 }

kema-MLKEM768-RSA2048-HKDF-SHA256 KEM-ALGORITHM ::=
    kema-CompositeKEM{
      id-MLKEM768-RSA2048-HKDF-SHA256,
      pk-MLKEM768-RSA2048-HKDF-SHA256 }



-- TODO: OID to be replaced by IANA
id-MLKEM768-RSA3072-HKDF-SHA256 OBJECT IDENTIFIER ::= {
  joint-iso-itu-t(2) country(16) us(840) organization(1)
  entrust(114027) algorithm(80) explicitcomposite(5) kem(2) 51 }

pk-MLKEM768-RSA3072 PUBLIC-KEY ::=
  pk-CompositeKEM {
    id-MLKEM768-RSA3072-HKDF-SHA256 }

kema-MLKEM768-RSA3072-HKDF-SHA256 KEM-ALGORITHM ::=
    kema-CompositeKEM{
      id-MLKEM768-RSA3072-HKDF-SHA256,
      pk-MLKEM768-RSA3072-HKDF-SHA256 }



-- TODO: OID to be replaced by IANA
id-MLKEM768-RSA4096-HKDF-SHA256 OBJECT IDENTIFIER ::= {
  joint-iso-itu-t(2) country(16) us(840) organization(1)
  entrust(114027) algorithm(80) explicitcomposite(5) kem(2) 52 }

pk-MLKEM768-RSA4096-HKDF-SHA256 PUBLIC-KEY ::=
  pk-CompositeKEM {
    id-MLKEM768-RSA4096-HKDF-SHA256 }

kema-MLKEM768-RSA4096 KEM-ALGORITHM ::=
    kema-CompositeKEM{
      id-MLKEM768-RSA4096-HKDF-SHA256,
      pk-MLKEM768-RSA4096-HKDF-SHA256 }



-- TODO: OID to be replaced by IANA
id-MLKEM768-X25519-SHA3-256 OBJECT IDENTIFIER ::= {
  joint-iso-itu-t(2) country(16) us(840) organization(1)
  entrust(114027) algorithm(80) explicitcomposite(5) kem(2) 53 }

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 }


-- TODO: OID to be replaced by IANA
id-MLKEM768-ECDH-P256-HKDF-SHA256 OBJECT IDENTIFIER ::= {
  joint-iso-itu-t(2) country(16) us(840) organization(1)
  entrust(114027) algorithm(80) explicitcomposite(5) kem(2) 54 }

pk-MLKEM768-ECDH-P256-HKDF-SHA256 PUBLIC-KEY ::=
  pk-CompositeKEM {
    id-MLKEM768-ECDH-P256-HKDF-SHA256 }

kema-MLKEM768-ECDH-P256-HKDF-SHA256 KEM-ALGORITHM ::=
    kema-CompositeKEM{
      id-MLKEM768-ECDH-P256-HKDF-SHA256,
      pk-MLKEM768-ECDH-P256-HKDF-SHA256 }



-- TODO: OID to be replaced by IANA
id-MLKEM768-ECDH-P384-HKDF-SHA256 OBJECT IDENTIFIER ::= {
  joint-iso-itu-t(2) country(16) us(840) organization(1)
  entrust(114027) algorithm(80) explicitcomposite(5) kem(2) 55 }

pk-MLKEM768-ECDH-P384-HKDF-SHA256 PUBLIC-KEY ::=
  pk-CompositeKEM {
    id-MLKEM768-ECDH-P384-HKDF-SHA256 }

kema-MLKEM768-ECDH-P384-HKDF-SHA256 KEM-ALGORITHM ::=
    kema-CompositeKEM{
      id-MLKEM768-ECDH-P384-HKDF-SHA256,
      pk-MLKEM768-ECDH-P384-HKDF-SHA256 }



-- TODO: OID to be replaced by IANA
id-MLKEM768-ECDH-brainpoolP256r1-HKDF-SHA256 OBJECT IDENTIFIER ::= {
  joint-iso-itu-t(2) country(16) us(840) organization(1)
  entrust(114027) algorithm(80) explicitcomposite(5) kem(2) 56 }

pk-MLKEM768-ECDH-brainpoolP256r1-HKDF-SHA256 PUBLIC-KEY ::=
  pk-CompositeKEM {
    id-MLKEM768-ECDH-brainpoolP256r1-HKDF-SHA256 }

kema-MLKEM768-ECDH-brainpoolP256r1-HKDF-SHA256 KEM-ALGORITHM ::=
    kema-CompositeKEM{
      id-MLKEM768-ECDH-brainpoolP256r1-HKDF-SHA256,
      pk-MLKEM768-ECDH-brainpoolP256r1-HKDF-SHA256 }



-- TODO: OID to be replaced by IANA
id-MLKEM1024-ECDH-P384-HKDF-SHA384 OBJECT IDENTIFIER ::= {
  joint-iso-itu-t(2) country(16) us(840) organization(1)
  entrust(114027) algorithm(80) explicitcomposite(5) kem(2) 57 }

pk-MLKEM1024-ECDH-P384-HKDF-SHA384 PUBLIC-KEY ::=
  pk-CompositeKEM {
    id-MLKEM1024-ECDH-P384-HKDF-SHA384 }

kema-MLKEM1024-ECDH-P384-HKDF-SHA384 KEM-ALGORITHM ::=
    kema-CompositeKEM{
      id-MLKEM1024-ECDH-P384-HKDF-SHA384,
      pk-MLKEM1024-ECDH-P384-HKDF-SHA384 }


-- TODO: OID to be replaced by IANA
id-MLKEM1024-ECDH-brainpoolP384r1-HKDF-SHA384 OBJECT IDENTIFIER ::= {
  joint-iso-itu-t(2) country(16) us(840) organization(1)
  entrust(114027) algorithm(80) explicitcomposite(5) kem(2) 58 }

pk-MLKEM1024-ECDH-brainpoolP384r1-HKDF-SHA384 PUBLIC-KEY ::=
  pk-CompositeKEM{
    id-MLKEM1024-ECDH-brainpoolP384r1-HKDF-SHA384 }

kema-MLKEM1024-ECDH-brainpoolP384r1-HKDF-SHA384 KEM-ALGORITHM ::=
    kema-CompositeKEM{
      id-MLKEM1024-ECDH-brainpoolP384r1-HKDF-SHA384,
      pk-MLKEM1024-ECDH-brainpoolP384r1-HKDF-SHA384 }


-- TODO: OID to be replaced by IANA
id-MLKEM1024-X448-SHA3-256 OBJECT IDENTIFIER ::= {
  joint-iso-itu-t(2) country(16) us(840) organization(1)
  entrust(114027) algorithm(80) explicitcomposite(5) kem(2) 59 }

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 }


-- TODO: OID to be replaced by IANA
id-MLKEM1024-ECDH-P521-HKDF-SHA384 OBJECT IDENTIFIER ::= {
  joint-iso-itu-t(2) country(16) us(840) organization(1)
  entrust(114027) algorithm(80) explicitcomposite(5) kem(2) 60 }

pk-MLKEM1024-ECDH-P521-HKDF-SHA384 PUBLIC-KEY ::=
  pk-CompositeKEM {
    id-MLKEM1024-ECDH-P521-HKDF-SHA384 }

kema-MLKEM1024-ECDH-P521-HKDF-SHA384 KEM-ALGORITHM ::=
    kema-CompositeKEM{
      id-MLKEM1024-ECDH-P521-HKDF-SHA384,
      pk-MLKEM1024-ECDH-P521-HKDF-SHA384 }

END

<CODE ENDS>

9. IANA Considerations

9.1. Object Identifier Allocations

EDNOTE to IANA: OIDs will need to be replaced in both the ASN.1 module and in Table 2.

9.1.1. Module Registration - SMI Security for PKIX Module Identifier

  • Decimal: IANA Assigned - Replace TBDMOD

  • Description: Composite-KEM-2023 - id-mod-composite-kems

  • References: This Document

9.1.2. Object Identifier Registrations - SMI Security for PKIX Algorithms

  • id-MLKEM768-RSA2048-HKDF-SHA256

    • Decimal: IANA Assigned

    • Description: id-MLKEM768-RSA2048-HKDF-SHA256

    • References: This Document

  • id-MLKEM768-RSA3072-HKDF-SHA256

    • Decimal: IANA Assigned

    • Description: id-MLKEM768-RSA3072-HKDF-SHA256

    • References: This Document

  • id-MLKEM768-RSA4096-HKDF-SHA256

    • Decimal: IANA Assigned

    • Description: id-MLKEM768-RSA4096-HKDF-SHA256

    • References: This Document

  • id-MLKEM768-ECDH-P256-HKDF-SHA256

    • Decimal: IANA Assigned

    • Description: id-MLKEM768-ECDH-P256-HKDF-SHA256

    • References: This Document

  • id-MLKEM768-ECDH-P384-HKDF-SHA256

    • Decimal: IANA Assigned

    • Description: id-MLKEM768-ECDH-P384-HKDF-SHA256

    • References: This Document

  • id-MLKEM768-ECDH-brainpoolP256r1-HKDF-SHA256

    • Decimal: IANA Assigned

    • Description: id-MLKEM768-ECDH-brainpoolP256r1-HKDF-SHA256

    • References: This Document

  • id-MLKEM768-X25519-SHA3-256

    • Decimal: IANA Assigned

    • Description: id-MLKEM768-X25519-SHA3-256

    • References: This Document

  • id-MLKEM1024-ECDH-P384-HKDF-SHA384

    • Decimal: IANA Assigned

    • Description: id-MLKEM1024-ECDH-P384-HKDF-SHA384

    • References: This Document

  • id-MLKEM1024-ECDH-brainpoolP384r1-HKDF-SHA384

    • Decimal: IANA Assigned

    • Description: id-MLKEM1024-ECDH-brainpoolP384r1-HKDF-SHA384

    • References: This Document

  • id-MLKEM1024-X448-SHA3-256

    • Decimal: IANA Assigned

    • Description: id-MLKEM1024-X448-SHA3-256

    • References: This Document

  • id-MLKEM1024-ECDH-P521-HKDF-SHA384

    • Decimal: IANA Assigned

    • Description: id-MLKEM1024-ECDH-P521-HKDF-SHA384

    • References: This Document

10. Security Considerations

10.1. Why Hybrids?

In broad terms, a PQ/T Hybrid can be used either to provide dual-algorithm security or to provide migration flexibility. Let's quickly explore both.

Dual-algorithm security. The general idea is that the data is proctected 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 client can choose to use one algorithm or the other or both. The intention is that the PQ/T hybrid mechanism builds in backwards compatibility to allow legacy and upgraded clients to co-exist and communicate. The Composites presented in this specification do not provide this since they operate in a strict "AND" mode, but they do 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 to this an ML-KEM implementation which immediately starts providing benefits against harvest-now-decrypt-later attacks even if that ML-KEM implemtation is still experimental, non-validated, non-certified, non-hardened implementation. More details of obtaining FIPS certification of a composite algorithm can be found in Appendix D.1.

10.2. KEM Combiner

The following KEM combiner construction is as follows is used by both Composite-ML-KEM.Encap() and Composite-ML-KEM.Decap() and is split out here for easier analysis.

  KDF(mlkemSS || tradSS || tradCT || tradPK || Domain)
Figure 10: KEM combiner construction

where:

  • KDF(message) represents a key derivation function suitable to the chosen KEMs according to Table 2. All KDFs produce a 256-bit shared secret key, which matches ML-KEM.

  • mlkemSS is the shared secret key from the ML-KEM component.

  • tradSS is the shared secret from the traditional component (elliptic curve or RSA).

  • tradCT is the ciphertext from the traditional component (elliptic curve or RSA).

  • tradPK is the public key of the traditional component (elliptic curve or RSA).

  • Domain is the DER encoded value of the object identifier of the Composite ML-KEM algorithm as listed in Section 7.2.

  • || represents concatenation.

Each registered Composite ML-KEM algorithm specifies the choice of KDF and Domain to be used in Section 7 and Section 7.2 below. 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. The CompositeKEM.Decap() specified in Section 4.3 adds further error handling to protect the KEM combiner from malicious inputs.

The primary security property of the KEM combiner is that it preserves IND-CCA2 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, or worse that the public key, private key, and ciphertext are manipulated by the attacker. In this case, we rely on the construction of the KEM combiner to ensure that the value of the other shared secret cannot be leaked or the combined shared secret predicted via manipulation of the broken algorithm. The following sections continue this discussion.

Note that length-tagging of the inputs to the KDF is not required:

  • mlkemSS is always 32 bytes.

  • tradSS in the case of ECDH 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.

  • Domain is a fixed value specified in this document.

In the case of a composite with ECDH, all inputs to the KDF are fixed-length. In the case of a composite with RSA-OAEP the tradSS is controlled by the attacker but this still does not require length tagging because, unless there is a weakness in the KDF, length-manipulation of only one input is not sufficient to trivially produce collisions.

10.2.1. Security of the hybrid scheme

Informally, a Composite ML-KEM algorithm is secure if the combiner (HKDF-SHA2 or SHA3) is secure, and either ML-KEM is secure or the traditional component (RSA-OAEP, ECDH, or X25519) is secure.

The security of ML-KEM and ECDH hybrids is covered in [X-Wing] and requires that the first KEM component (ML-KEM in this construction) is IND-CCA and second ciphertext preimage resistant (C2PRI) and that the second traditional component is 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. Note that ciphertext collisions exist in the traditional component by the composite design choice to support any underlying encoding of the traditional component, such as compressed vs uncompressed EC points as the ECDH KEM ciphertext. This solution remains IND-CCA 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 ECDH by noting that RSA-OAEP is also IND-CCA secure [RFC8017].

Note that X-Wing uses SHA3 as the combiner KDF whereas Composite ML-KEM uses either SHA3 or HKDF-SHA2 which are interchangeable in the X-Wing proof since both behave as random oracles under multiple concatenated inputs.

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.

10.2.2. Second pre-image resistance of component KEMs

The notion of a second pre-image resistant KEM is defined in [X-Wing] being the property that it is computationally difficult to find two different ciphertexts c != c' that will decapsulate to the same shared secret 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 so long as either c1 != c1' or c2 != c2' -- i.e. the overall Composite ML-KEM is 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 ECDH 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.

10.2.3. SHA3 vs HKDF-SHA2

In order to achieve the desired security property that the Composite ML-KEM is IND-CCA2 whenever at least one of the component KEMs is, the KDF used in the KEM combiner needs to possess collision and second pre-image resistance with respect to each of its inputs independently; a property sometimes called "dual-PRF" [Aviram22]. Collision and second-pre-image resistance protects against compromise of one component algorithm from resulting in the ability to construct multiple different ciphertexts which result in the same shared secret. Pre-image resistance protects against compromise of one component algorithm being used to attack and learn the value of the other shared secret.

SHA3 is known to have all of the necessary dual-PRF properties [X-Wing], but SHA2 does not and therefore all SHA2-based constructions MUST use SHA2 within an HMAC construction such as HKDF-SHA2 [GHP18].

10.2.4. 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.

10.3. Key Reuse

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. With composite keys we have a much stricter security requirement. However this reasoning does not hold in the PQ / Traditional hybrid setting.

Within the broader context of PQ / Traditional 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 document, 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 than the overall shared secret derived from the composite, so any subsequent symmetric cryptographic operations will fail. However there is still a risk of key reuse which relates to certificate revocation, as well as general key reuse security issues.

Upon receiving a new certificate enrollment 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, even if 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, it is RECOMMENDED to avoid key reuse and always generate fresh component keys for a new composite. It is also RECOMMENDED that CAs performing revocation checks on a composite key should also check both component keys independently.

10.4. Decapsulation failure

Provided all inputs are well-formed, the key establishment procedure of ML-KEM will never explicitly fail. Specifically, the ML-KEM.Encaps and ML-KEM.Decaps algorithms from [FIPS.203] will always output a value with the same data type as a shared secret key, and will never output an error or failure symbol. However, it is possible (though extremely unlikely) that the process will fail in the sense that ML-KEM.Encaps and ML-KEM.Decaps will produce different outputs, even though both of them are behaving honestly and no adversarial interference is present. In this case, the sender and recipient clearly did not succeed in producing a shared secret key. This event is called a decapsulation failure. Estimates for the decapsulation failure probability (or rate) for each of the ML-KEM parameter sets are provided in Table 1 of [FIPS.203] and reproduced here in Table 5.

Table 5: ML-KEM decapsulation failure rates
Parameter set Decapsulation failure rate
ML-KEM-512 2^(-139)
ML-KEM-768 2^(-164)
ML-KEM-1024 2^(-174)

In the case of ML-KEM decapsulation failure, Composite ML-KEM MUST preserve the same behaviour and return a well-formed output.

10.5. Policy for Deprecated and Acceptable Algorithms

Traditionally, a public key or certificate contains a single cryptographic algorithm. If and when an algorithm becomes deprecated (for example, RSA-512, or SHA1), the path to deprecating it and removing it from operational environments is, at least is principle, straightforward.

In the composite model this is less obvious since implementers may decide that certain cryptographic algorithms have complementary security properties and are acceptable in combination even though one or both algorithms are deprecated for individual use. As such, a single composite public key or certificate may contain a mixture of deprecated and non-deprecated algorithms.

Since composite algorithms are registered independently of their component algorithms, their deprecation can be handled independently from that of their component algorithms. For example a cryptographic policy might continue to allow id-MLKEM512-ECDH-P256 even after ECDH-P256 is deprecated.

The Composite ML-KEM design specified in this document, and especially that of the KEM combiner specified in this document, and discussed in Section 10.2, means that the overall Composite ML-KEM algorithm should be considered to have the security strength of the strongest of its component algorithms; i.e. as long as one component algorithm remains strong, then the overall composite algorithm remains strong.

11. References

11.1. Normative References

[FIPS.180-4]
National Institute of Standards and Technology (NIST), "FIPS Publication 180-4: Secure Hash Standard", , <https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf>.
[FIPS.202]
National Institute of Standards and Technology (NIST), "SHA-3 Standard: Permutation-Based Hash and Extendable-Output Functions", , <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", , <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", , <https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.204.pdf>.
[I-D.ietf-lamps-cms-sha3-hash]
Housley, R., "Use of the SHA3 One-way Hash Functions in the Cryptographic Message Syntax (CMS)", Work in Progress, Internet-Draft, draft-ietf-lamps-cms-sha3-hash-04, , <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-cms-sha3-hash-04>.
[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-06, , <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-kyber-certificates-06>.
[RFC2119]
Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, , <https://www.rfc-editor.org/info/rfc2119>.
[RFC4055]
Schaad, J., Kaliski, B., and R. Housley, "Additional Algorithms and Identifiers for RSA Cryptography for use in the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile", RFC 4055, DOI 10.17487/RFC4055, , <https://www.rfc-editor.org/info/rfc4055>.
[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, , <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, , <https://www.rfc-editor.org/info/rfc5480>.
[RFC5652]
Housley, R., "Cryptographic Message Syntax (CMS)", STD 70, RFC 5652, DOI 10.17487/RFC5652, , <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, , <https://www.rfc-editor.org/info/rfc5869>.
[RFC5958]
Turner, S., "Asymmetric Key Packages", RFC 5958, DOI 10.17487/RFC5958, , <https://www.rfc-editor.org/info/rfc5958>.
[RFC6234]
Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms (SHA and SHA-based HMAC and HKDF)", RFC 6234, DOI 10.17487/RFC6234, , <https://www.rfc-editor.org/info/rfc6234>.
[RFC7748]
Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves for Security", RFC 7748, DOI 10.17487/RFC7748, , <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, , <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, , <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, , <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, , <https://www.rfc-editor.org/info/rfc8411>.
[RFC8619]
Housley, R., "Algorithm Identifiers for the HMAC-based Extract-and-Expand Key Derivation Function (HKDF)", RFC 8619, DOI 10.17487/RFC8619, , <https://www.rfc-editor.org/info/rfc8619>.
[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, , <https://www.rfc-editor.org/info/rfc9629>.
[SEC1]
Certicom Research, "SEC 1: Elliptic Curve Cryptography", , <https://www.secg.org/sec1-v2.pdf>.
[SEC2]
Certicom Research, "SEC 2: Recommended Elliptic Curve Domain Parameters", , <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", , <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", , <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", , <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", , <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, .

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]
Yogev, E., "Practical (Post-Quantum) Key Combiners from One-Wayness and Applications to TLS", n.d., <https://eprint.iacr.org/2022/065>.
[BSI2021]
Federal Office for Information Security (BSI), "Quantum-safe cryptography - fundamentals, current developments and recommendations", , <https://www.bsi.bund.de/SharedDocs/Downloads/EN/BSI/Publications/Brochure/quantum-safe-cryptography.pdf>.
[CNSA2.0]
"Commercial National Security Algorithm Suite 2.0", n.d., <https://media.defense.gov/2022/Sep/07/2003071834/-1/-1/0/CSA_CNSA_2.0_ALGORITHMS_.PDF>.
[ETSI.TS.103.744]
ETSI, "ETSI TS 103 744 V1.2.1 CYBER-QSC; Quantum-safe Hybrid Key Establishment", , <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", , <https://csrc.nist.gov/csrc/media/Projects/cryptographic-module-validation-program/documents/fips%20140-3/FIPS%20140-3%20IG.pdf>.
[GHP18]
Poettering, B., "KEM Combiners", , <https://eprint.iacr.org/2018/024>.
[I-D.ietf-lamps-cms-kyber]
Prat, J., Ounsworth, M., and D. Van Geest, "Use of ML-KEM in the Cryptographic Message Syntax (CMS)", Work in Progress, Internet-Draft, draft-ietf-lamps-cms-kyber-05, , <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-cms-kyber-05>.
[I-D.ietf-pquip-pqt-hybrid-terminology]
D, F., P, M., and B. Hale, "Terminology for Post-Quantum Traditional Hybrid Schemes", Work in Progress, Internet-Draft, draft-ietf-pquip-pqt-hybrid-terminology-04, , <https://datatracker.ietf.org/doc/html/draft-ietf-pquip-pqt-hybrid-terminology-04>.
[I-D.ietf-tls-hybrid-design]
Stebila, D., Fluhrer, S., and S. Gueron, "Hybrid key exchange in TLS 1.3", Work in Progress, Internet-Draft, draft-ietf-tls-hybrid-design-04, , <https://datatracker.ietf.org/doc/html/draft-ietf-tls-hybrid-design-04>.
[RFC2986]
Nystrom, M. and B. Kaliski, "PKCS #10: Certification Request Syntax Specification Version 1.7", RFC 2986, DOI 10.17487/RFC2986, , <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, , <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, , <https://www.rfc-editor.org/info/rfc4211>.
[RFC4262]
Santesson, S., "X.509 Certificate Extension for Secure/Multipurpose Internet Mail Extensions (S/MIME) Capabilities", RFC 4262, DOI 10.17487/RFC4262, , <https://www.rfc-editor.org/info/rfc4262>.
[RFC5083]
Housley, R., "Cryptographic Message Syntax (CMS) Authenticated-Enveloped-Data Content Type", RFC 5083, DOI 10.17487/RFC5083, , <https://www.rfc-editor.org/info/rfc5083>.
[RFC5639]
Lochter, M. and J. Merkle, "Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation", RFC 5639, DOI 10.17487/RFC5639, , <https://www.rfc-editor.org/info/rfc5639>.
[RFC5914]
Housley, R., Ashmore, S., and C. Wallace, "Trust Anchor Format", RFC 5914, DOI 10.17487/RFC5914, , <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, , <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, , <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, , <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, , <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, , <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, , <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, , <https://www.rfc-editor.org/info/rfc9180>.
[SP-800-227ipd]
Alagic, G., Barker, E., Chen, L., Moody, D., Robinson, A., Silberg, H., and N. Waller, "Recommendations for Key-Encapsulation Mechanisms (Initial Public Draft)", n.d., <https://csrc.nist.gov/pubs/sp/800/227/ipd>.
[SP800-131Ar2]
Barker, E. and A. Roginksy, "Transitioning the Use of Cryptographic Algorithms and Key Lengths", n.d., <https://nvlpubs.nist.gov/nistpubs/specialpublications/nist.sp.800-131ar2.pdf>.
[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", , <https://eprint.iacr.org/2024/039.pdf>.

Appendix A. Approximate Key and Ciphertext Sizes

Note that the sizes listed below are approximate: these values are measured from the test vectors, but other implementations could produce values where the traditional component has a different size. For example, this could be due to:

Note that 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.

Implementations MUST NOT perform strict length checking based on the values in this table.

Non-hybrid ML-KEM is included for reference.

Table 6: Approximate size values of composite ML-KEM
Algorithm Public key Private key Ciphertext SS
id-alg-ml-kem-768 1184 64 1088 32
id-alg-ml-kem-1024 1568 64 1568 32
id-MLKEM768-RSA2048-HKDF-SHA256 1454 1281 1344 32
id-MLKEM768-RSA3072-HKDF-SHA256 1582 1857 1472 32
id-MLKEM768-RSA4096-HKDF-SHA256 1710 2438 1600 32
id-MLKEM768-X25519-SHA3-256 1216 96 1120 32
id-MLKEM768-ECDH-P256-HKDF-SHA256 1249 202 1153 32
id-MLKEM768-ECDH-P384-HKDF-SHA256 1281 249 1185 32
id-MLKEM768-ECDH-brainpoolP256r1-HKDF-SHA256 1249 203 1153 32
id-MLKEM1024-ECDH-P384-HKDF-SHA384 1665 249 1665 32
id-MLKEM1024-ECDH-brainpoolP384r1-HKDF-SHA384 1665 253 1665 32
id-MLKEM1024-X448-SHA3-256 1624 120 1624 32
id-MLKEM1024-ECDH-P521-HKDF-SHA384 1701 305 1701 32

Appendix B. Component Algorithm Reference

This section provides references to the full specification of the algorithms used in the composite constructions.

Table 7: Component Encryption Algorithms used in Composite Constructions
Component KEM Algorithm ID OID Specification
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], [SEC1]
id-RSAES-OAEP 1.2.840.113549.1.1.7 [RFC8017]
Table 8: Elliptic Curves 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 9: Hash algorithms used in Composite Constructions
HashID OID Specification
id-sha256 2.16.840.1.101.3.4.2.1 [RFC6234]
id-sha512 2.16.840.1..101.3.4.2.3 [RFC6234]
id-alg-hkdf-with-sha256 1.2.840.113549.1.9.16.3.28 [RFC8619]
id-alg-hkdf-with-sha384 1.2.840.113549.1.9.16.3.29 [RFC8619]
id-sha3-256 2.16.840.1.101.3.4.2.8 [FIPS.202]

Appendix C. Fixed Component Algorithm Identifiers

The following sections list explicitly the DER encoded AlgorithmIdentifier that MUST be used when reconstructing SubjectPublicKeyInfo objects for each component public key, which may be required for example if cryptographic library requires the public key in this form in order to process each component algorithm. The public key BIT STRING should be taken directly from the respective component of the CompositeKEMPublicKey.

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-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. Implementation Considerations

D.1. FIPS Certification

TODO: update this to NIST SP 800-227, once it is published.

D.1.1. Combiner Function

For reference, the KEM Combiner used in Composite KEM is:

ss = KDF(mlkemSS || tradSS || tradCT || tradPK || Domain)

where KDF is either SHA3 or HKDF-SHA2.

NIST SP 800-227 [SP-800-227ipd], which at the time of writing is in its initial public draft period, allows hybrid key combiners of the following form:

K ← KDM(S1‖S2‖ · · · ‖St , OtherInput) (14)

The key derivation method KDM can take one of two forms, either

K ← KDF(Z‖OtherInput) (12)

or

K ← Expand(Extract(salt, Z), OtherInput) (13)

The Composite KEM variants that use SHA3 as a combiner fit form (12) while the variants that use HKDF-SHA2 fit form (13).

In terms of the order of inputs, Composite KEM places the two shared secret keys mlkemSS || tradSS at the beginning of the KDF input such that all other inputs tradCT || tradPK || Domain can be considered part of OtherInput for the purposes of FIPS certification.

For detailed steps [SP-800-227ipd] refers to NIST SP.800-56Cr2 [SP.800-56Cr2]. Compliance of the Composite KEM variants is achieved in the following way:

[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].

The HKDF-SHA2 options can be certified under [SP.800-56Cr2] One-Step Key Derivation Option 2: H(x) = HMAC-hash(salt, x) where salt is the empty (0 octet) string, which will internally be mapped to the zero vector 0x00..00 of the correct input size for the underlying hash function in order to satisfy the requirement in [SP.800-56Cr2] that "in the absence of an agreed-upon alternative – the default_salt shall be an all-zero byte string whose bit length equals that specified as the bit length of an input block for the hash function, hash". Note that since the desired shared secret key output length of 256 bits for all security levels aligns with the block size of SHA256, we do not need to use the HKDF-Expand step specified in [RFC5869], which further simplifies FIPS certification by allowing us to use the One-Step KDF rather than the Two-Step KDF from [SP.800-56Cr2].

The SHA3 options can be certified under [SP.800-56Cr2] One-Step Key Derivation Option 1: H(x) = hash(x).

D.1.2. Mixing with Non-Approved Algorithms

[SP-800-227ipd] 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 KEM always places the shared secret key from ML-KEM in the first slot, a Composite 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 document, the general composite construction could be used to create FIPS certified algorithms that contain a component algorithm from a different jurisdiction.

D.2. Backwards Compatibility

As noted in the introduction, the post-quantum cryptographic migration will face challenges in both ensuring cryptographic strength against adversaries of unknown capabilities, as well as providing ease of migration. The composite mechanisms defined in this document primarily address cryptographic strength, however this section contains notes on how backwards compatibility may be obtained.

The term "ease of migration" is used here to mean that existing systems can be gracefully transitioned to the new technology without requiring large service disruptions or expensive upgrades. The term "backwards compatibility" is used here to mean something more specific; that existing systems as they are deployed today can inter-operate with the upgraded systems of the future.

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.

D.3. 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. Moveover, the KEM combiner as specified in Section 4.4 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 10.2.

The mechanism by which an application transmits the public keys is out of scope of this specification, but it MAY be accomplished by placing a serialized composite public key into the optional OneAsymmetricKey.publicKey field of the private key object.

Implementers who choose to use a different private key encoding than the one specified in this document MUST consider how to provide the component public keys to the decapsulate routine. While some implementations might contain routines to computationally derive the public key from the private key, it is not guaranteed that all implementations will support this.

D.4. Profiling down the number of options

One immediately 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 implemtation effort on:

id-MLKEM768-X25519-SHA3-256
id-MLKEM768-ECDH-P256-HKDF-SHA256

In applications that only allow NIST PQC Level 5, it is RECOMMENDED to focus implemtation effort on:

id-MLKEM1024-ECDH-P384-HKDF-SHA384

Appendix E. Comparison with other Hybrid KEMs

E.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 properies. However, using a derived value as the seed for ML-KEM.KeyGen_internal() is, at time of writing, explicitely disallowed by [FIPS.203] which makes it impossible to create a FIPS-compliant implentation of X-Wing KeyGen / private key import. For this reason, this specification keeps the key generatation for both components separate so that implementers are free to use an existing certified hardware or software module for one or both components.

Due to the difference in key generation and security properties, X-Wing and id-MLKEM768-X25519-SHA3-256 have been registered as separate algorithms with separate OIDs, and they use a different domain separator string in order to ensure that their ciphertexts are not inter-compatible.

E.2. ETSI CatKDF

[ETSI.TS.103.744] section 8.2.3 defines CatKDF as:

1) Form secret = psk || k1 || k 2.
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 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 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. Using HKDF aligns with some of the KDF variants in this specification, but not the ones that use SHA3.

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:

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.

  2. Load the decapsulation private key dk and the ciphertext c and ensure that the same shared secret key k can be derived.

Test vectors are provided for each underlying component in isolation for the purposes of debugging.

Due to the length of the test vectors, you may prefer to retrieve them from GitHub. The reference implementation that generated them is also available:

https://github.com/lamps-wg/draft-composite-kem/tree/main/src

{
"cacert": "MIIVpzCCCKSgAwIBAgIUQHpY3ftTzRM60D0oGU4bbYJKYZ8wCwYJYIZ
IAWUDBAMSMD0xDTALBgNVBAoMBElFVEYxDjAMBgNVBAsMBUxBTVBTMRwwGgYDVQQDDBN
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"tests": [
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}
]
}

Appendix G. Intellectual Property Considerations

The following IPR Disclosure relates to this draft:

https://datatracker.ietf.org/ipr/3588/

EDNOTE TODO: Check with Max Pala whether this IPR actually applies to this draft.

Appendix H. Contributors and Acknowledgments

This document incorporates contributions and comments from a large group of experts. The Editors would especially like to acknowledge the expertise and tireless dedication of the following people, who attended many long meetings and generated millions of bytes of electronic mail and VOIP traffic over the past year in pursuit of this document:

Serge Mister (Entrust), Ali Noman (Entrust), Peter C. (UK NCSC), Sophie Schmieg (Google), Deirdre Connolly (SandboxAQ), Falko Strenzke (MTG AG), Dan van Geest (Crypto Next), Piotr Popis (Enigma), and Douglas Stebila (University of Waterloo).

Thanks to Giacomo Pope (github.com/GiacomoPope) whose ML-DSA and ML-KEM implementation was used to generate the test vectors.

We are grateful to all, including any contributors who may have been inadvertently omitted from this list.

This document borrows text from similar documents, including those referenced below. Thanks go to the authors of those documents. "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
John Gray
Entrust Limited
2500 Solandt Road – Suite 100
Ottawa, Ontario K2K 3G5
Canada
Massimiliano Pala
OpenCA Labs
New York City, New York,
United States of America
Jan Klaussner
Bundesdruckerei GmbH
Kommandantenstr. 18
10969 Berlin
Germany
Scott Fluhrer
Cisco Systems