Composite ML-KEM for Use in the Internet X.509 Public Key Infrastructure and CMS

2.1. 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.¶

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

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 2.3.¶

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

SHARED SECRET: A value established between two communicating parties for use as cryptographic key material, but which cannot be learned by an active or passive adversary. This document is concerned with shared secrets established via public key cryptographic operations.¶

2.2. Composite Design Philosophy

[I-D.driscoll-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, and ciphertext 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 KEM algorithms without requiring any modification of the protocol to handle multiple keys.¶

2.3. Composite Key Encapsulation Mechanisms (KEMs)

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:¶

• KeyGen() -> (pk, sk): A probabilistic key generation algorithm, which generates a public key pk and a secret key sk.¶

• Encaps(pk) -> (ct, ss): A probabilistic encapsulation algorithm, which takes as input a public key pk and outputs a ciphertext ct and shared secret ss.¶

• Decaps(sk, ct) -> ss: A decapsulation algorithm, which takes as input a secret key sk and ciphertext ct and outputs a shared secret ss, or in some cases a distinguished error value.¶

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. This specification uses the Post-Quantum KEM ML-KEM as specified in [I-D.ietf-lamps-kyber-certificates] and [FIPS.203-ipd]. For Traditional KEMs, this document uses the RSA-OAEP algorithm defined in [RFC3560], 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.¶

CompositeKEM.KeyGen():
  (compositePK[0], compositeSK[0]) = MLKEM.KeyGen()
  (compositePK[1], compositeSK[1]) = TradKEM.KeyGen()

  return (compositePK, compositeSK)

DHKEM.Encaps(pkR):
  shared_secret = SecureRandom(ss_len)
  enc = RSA-OAEP.Encrypt(pkR, shared_secret)

  return enc, shared_secret

DHKEM.Decap(skR, enc):
  shared_secret = RSA-OAEP.Decrypt(skR, enc)

  return shared_secret

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

  return enc, shared_secret

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

  return shared_secret

CompositeKEM.Encaps(pk):
  # Split the component public keys
  mlkemPK = pk[0]
  tradPK  = pk[1]

  # Perform the respective component Encaps operations
  (mlkemCT, mlkemSS) = MLKEM.Encaps(mlkemPK)
  (tradCT, tradSS) = TradKEM.Encaps(tradPK)

  # Combine
  # note that the order of the traditional and ML-KEM components
  # is flipped here in order to satisfy NIST SP800-56Cr2.
  ct = CompositeCiphertextValue(ct1, ct2)
  ss = Combiner(tradSS, mlkemSS, tradCT, tradPK, domSep)

  return (ct, ss)

CompositeKEM.Decaps(ct, mlkemSK, tradSK):
  # split the component ciphertexts
  mlkemCT = ct[0]
  tradCT  = ct[1]

  # Perform the respective component Decaps operations
  mlkemSS = MLKEM.Decaps(mlkemSK, mlkemCT)
  tradSS  = TradKEM.Decaps(tradSK, tradCT)

  # Combine
  # note that the order of the traditional and ML-KEM components
  # is flipped here in order to satisfy NIST SP800-56Cr2.
  ss = Combiner(tradSS, mlkemSS, tradCT, tradPK, domSep)

  return ss

3.1. pk-CompositeKEM

The following ASN.1 Information Object Class is a template to be used in defining all composite KEM public key types.¶

pk-CompositeKEM {
  OBJECT IDENTIFIER:id, FirstPublicKeyType,
  SecondPublicKeyType} PUBLIC-KEY ::=
  {
    IDENTIFIER id
    KEY SEQUENCE {
     BIT STRING (CONTAINING FirstPublicKeyType)
     BIT STRING (CONTAINING SecondPublicKeyType)
    }
    PARAMS ARE absent
    CERT-KEY-USAGE { keyEncipherment }
  }

As an example, the public key type pk-MLKEM512-ECDH-P256 is defined as:¶

pk-MLKEM512-ECDH-P256 PUBLIC-KEY ::=
  pk-CompositeKEM {
    id-MLKEM512-ECDH-P256,
    OCTET STRING, ECPoint }

The full set of key types defined by this specification can be found in the ASN.1 Module in Section 7.¶

3.2. CompositeKEMPublicKey

Composite public key data is represented by the following structure:¶

CompositeKEMPublicKey ::= SEQUENCE SIZE (2) OF BIT STRING

A composite key MUST contain two component public keys. The order of the component keys is determined by the definition of the corresponding algorithm identifier as defined in section Section 5.¶

Some applications may need to reconstruct the SubjectPublicKeyInfo objects corresponding to each component public key. Table 1 in Section 5 provides the necessary mapping between composite and their component algorithms for doing this reconstruction. This also motivates the design choice of SEQUENCE OF BIT STRING instead of SEQUENCE OF OCTET STRING; using BIT STRING allows for easier transcription between CompositeKEMPublicKey and SubjectPublicKeyInfo.¶

When the CompositeKEMPublicKey must be provided in octet string or bit string format, the data structure is encoded as specified in Section 3.4.¶

3.3. CompositeKEMPrivateKey

Use cases that require an inter-operable encoding for composite private keys, such as when private keys are carried in PKCS #12 [RFC7292], CMP [RFC4210] or CRMF [RFC4211] MUST use the following structure.¶

CompositeKEMPrivateKey ::= SEQUENCE SIZE (2) OF OneAsymmetricKey

Each element is a OneAsymmetricKey` [RFC5958] object for a component private key.¶

The parameters field MUST be absent.¶

The order of the component keys is the same as the order defined in Section 3.2 for the components of CompositeKEMPublicKey.¶

When a CompositePrivateKey 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 5, the privateKey field SHALL contain the CompositeKEMPrivateKey, and the publicKey field MUST NOT be present. Associated public key material MAY be present in the CompositeKEMPrivateKey.¶

In some use-cases the private keys that comprise a composite key may not be represented in a single structure or even be contained in a single cryptographic module; for example if one component is within the FIPS boundary of a cryptographic module and the other is not; see Appendix C.1 for more discussion. The establishment of correspondence between public keys in a CompositeKEMPublicKey and private keys not represented in a single composite structure is beyond the scope of this document.¶

3.4. Encoding Rules

Many protocol specifications will require that the composite public key and composite private key data structures be represented by an octet string or bit string.¶

When an octet string is required, the DER encoding of the composite data structure SHALL be used directly.¶

CompositeKEMPublicKeyOs ::= OCTET STRING (CONTAINING CompositeKEMPublicKey ENCODED BY der)

When a bit string is required, the octets of the DER encoded composite data structure 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.¶

CompositeKEMPublicKeyBs ::= BIT STRING (CONTAINING CompositeKEMPublicKey ENCODED BY der)

3.5. Key Usage Bits

For protocols such as X.509 [RFC5280] that specify key usage along with the public key, then the composite public key associated with a composite KEM algorithm MUST contain only a keyEncipherment key usage, all other key usages MUST NOT be used. This is because the composite public key can only be used in situations that are appropriate for both component algorithms, so even if the classical component key supports both signing and encryption, the post-quantum algorithms do not.¶

4.1. kema-CompositeKEM

The ASN.1 algorithm object for a composite KEM is:¶

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

4.2. CompositeCiphertextValue

The compositeCipherTextValue is a concatenation of the ciphertexts of the underlying component algorithms. It is represented in ASN.1 as follows:¶

CompositeCiphertextValue ::= SEQUENCE SIZE (2) OF OCTET STRING

The order of the component ciphertexts is the same as the order defined in Section 3.2.¶

4.3. KEM Combiner

TODO: as per https://www.enisa.europa.eu/publications/post-quantum-cryptography-integration-study section 4.2, might need to specify behaviour in light of KEMs with a non-zero failure probability.¶

The KEM combiner construction is as follows:¶

KEK <- Combiner(tradSS, mlkemSS, tradCT, tradPK, domSep) =
  KDF(counter || tradSS || mlkemSS || tradCT || tradPK ||
       domSep, outputBits)

where:¶

• KDF(message, outputBits) represents a hash function suitable to the chosen KEMs according to {tab-kem-combiners}.¶

• counter SHALL be the fixed 32-bit value 0x00000001 which is placed here solely for the purposes of compliance with [SP.800-56Cr2].¶

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

• mlkemSS is the shared secret from the ML-KEM componont.¶

• 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).¶

• domSep SHALL be the DER encoded value of the object identifier of the composite KEM algorithm as listed in Section 5.1.¶

• || represents concatenation.¶

Each registered composite KEM algorithm must specify the choice of KDF, demSep, and outputBits to be used.¶

Some of the design choices for the combiner, specifically to place tradSS first, and to allow tradCT || tradPK || domSep to be treated together as a FixedInfo block are made for the purposes of compliance with [SP.800-56Cr2]; see Section 4.4 for more discussion.¶

See Section 9.3 for further discussion of the security considerations of this KEM combiner.¶

4.4. FIPS Compliance

This specification is compliant with [SP.800-56Cr2] which allows for multiple sources of shared secret material to be combined into a single shared secret and the combined shared secret to be considered FIPS compliant so long as the first input shared secret is the result of a FIPS compliant algorithm. In order to ease FIPS compliance issues during the transition period, this specification uses the traditional algorithm as the first input to the combiner so that the combiner is FIPS compliant so long as the traditional component is FIPS compliant.¶

This construction is specifically designed to conform with Section 4.1 Option 1 (when KDF is SHA3) or Option 3 (when KDF is KMAC) in the following way:¶

In both cases we match exactly the construction using the allowed "hybrid" shared secret of the form Z' = Z || T to yield the construction¶

counter || Z || T || FixedInfo¶

where:¶

• Z = tradSS is the algorithm assumed to always be FIPS-approved from a FIPS-certified implementation which is expected to be true during the period where organizations are migrating their existing deployments to add ML-KEM implementations which may not yet have received FIPS certification,¶

• T = mlkemSS, and¶

• FixedInfo = tradCT || tradPK || domSep.¶

In the case that KDF is KMAC, the message to be hashed MUST be post-pended with H_outputBits and the byte string 01001011 || 01000100 || 01000110, which represents the sequence of characters "K", "D," and "F" in 8-bit ASCII, as required by [SP.800-56Cr2] section 4.1 Option 3. salt is left empty since KMAC is only required to behave as a hash function and not as a keyed MAC.¶

5.1. Domain Separators

The KEM combiner defined in section Section 4.3 requires a domain separator domSep input. The following table shows the HEX-encoded domain separator for each Composite KEM AlgorithmID; to use it, the value should be HEX-decoded and used in binary form. The domain separator is simply the DER encoding of the composite algorithm OID.¶

EDNOTE: Should the domain separator values be the SHA-256 hash of the DER encoding of the corresponding composite algorithm OID? That way they would be fixed-length even if the OIDs are different lengths. See https://github.com/lamps-wg/draft-composite-sigs/issues/19¶

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.¶

5.2. RSA-OAEP Parameters

Use of RSA-OAEP [RFC3560] within id-MLKEM512-RSA2048 and id-MLKEM512-RSA3072 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 [RFC3560] 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 KEM algorithms, when id-MLKEM512-RSA2048 or id-MLKEM512-RSA3072 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 both the 2048 and 3072 bit security levels.¶

where:¶

• id-sha256 is defined in [RFC8017].¶

• mgf1SHA256Identifier is defined in [RFC4055].¶

• pSpecifiedEmptyIdentifier is defined in [RFC3560]¶

6.1. Underlying Components

A CMS implementation that supports a composite KEM algorithm MUST support at least the following underlying components:¶

When a particular Composite KEM OID is supported, an implementation MUST support the corresponding KDF algorithm identifier in Table 4.¶

When a particular Composite KEM OID is supported, an implementation MUST support the corresponding key-encryption algorithm identifier in Table 4.¶

The following table lists the REQUIRED KDF and key-encryption algorithms to preserve security and performance characteristics of each composite algorithm.¶

Note: id-aes256-Wrap is stronger than necessary for the MLKEM768 combinations at the NIST level 3 192 bit security level, however id-aes256-Wrap was chosen because it has better general adoption than id-aes192-Wrap.¶

where:¶

• SHA3-* KDF instantiations are defined in [I-D.ietf-lamps-cms-sha3-hash].¶

• id-aes*-Wrap are defined in [RFC3394].¶

6.2. RecipientInfo Conventions

When a composite KEM Algorithm is employed for a recipient, the RecipientInfo alternative for that recipient MUST be OtherRecipientInfo using the KEMRecipientInfo structure [I-D.ietf-lamps-cms-kemri]. The fields of the KEMRecipientInfo MUST have the following values:¶

version is the syntax version number; it MUST be 0.¶

rid identifies the recipient's certificate or public key.¶

kem identifies the KEM algorithm; it MUST contain one of the OIDs listed in Table 1.¶

kemct is the ciphertext produced for this recipient; it contains the ct output from Encaps(pk) of the KEM algorithm identified in the kem parameter.¶

kdf identifies the key-derivation function (KDF). Note that the KDF used for CMS RecipientInfo process MAY be different than the KDF used within the composite KEM Algorithm, which MAY be different than the KDFs (if any) used within the component KEMs of the composite KEM Algorithm.¶

kekLength is the size of the key-encryption key in octets.¶

ukm is an optional random input to the key-derivation function.¶

wrap identifies a key-encryption algorithm used to encrypt the keying material.¶

encryptedKey is the result of encrypting the keying material with the key-encryption key. When used with the CMS enveloped-data content type [RFC5652], the keying material is a content-encryption key. When used with the CMS authenticated-data content type [RFC5652], the keying material is a message-authentication key. When used with the CMS authenticated-enveloped-data content type [RFC5083], the keying material is a content-authenticated-encryption key.¶

6.3. Certificate Conventions

The conventions specified in this section augment RFC 5280 [RFC5280].¶

The willingness to accept a composite KEM Algorithm MAY be signaled by the use of the SMIMECapabilities Attribute as specified in Section 2.5.2. of [RFC8551] or the SMIMECapabilities certificate extension as specified in [RFC4262].¶

The intended application for the public key MAY be indicated in the key usage certificate extension as specified in Section 4.2.1.3 of [RFC5280]. If the keyUsage extension is present in a certificate that conveys a composite KEM public key, then the key usage extension MUST contain only the following value:¶

keyEncipherment¶

The digitalSignature and dataEncipherment values MUST NOT be present. That is, a public key intended to be employed only with a composite KEM algorithm MUST NOT also be employed for data encryption or for digital signatures. This requirement does not carry any particular security consideration; only the convention that KEM keys be identified with the keyEncipherment key usage.¶

6.4. SMIMECapabilities Attribute Conventions

Section 2.5.2 of [RFC8551] defines the SMIMECapabilities attribute to announce a partial list of algorithms that an S/MIME implementation can support. When constructing a CMS signed-data content type [RFC5652], a compliant implementation MAY include the SMIMECapabilities attribute that announces support for the RSA-OAEP Algorithm.¶

The SMIMECapability SEQUENCE representing a composite KEM Algorithm MUST include the appropriate object identifier as per Table 1 in the capabilityID field.¶

8.1. Object Identifier Allocations

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

9.1. Component Algorithm Selection Criteria

The composite algorithm combinations defined in this document were chosen according to the following guidelines:¶

1. RSA combinations are provided at key sizes of 2048 and 3072 bits. Since RSA 2048 and 3072 are considered to have 112 and 128 bits of classical security respectively, they are both matched with NIST PQC Level 1 algorithms and 128-bit symmetric algorithms.¶

2. Elliptic curve algorithms are provided with combinations on each of the NIST [RFC6090], Brainpool [RFC5639], and Edwards [RFC7748] curves. NIST PQC Levels 1 - 3 algorithms are matched with 256-bit curves, while NIST levels 4 - 5 are matched with 384-bit elliptic curves. This provides a balance between matching classical security levels of post-quantum and traditional algorithms, and also selecting elliptic curves which already have wide adoption.¶

3. NIST level 1 candidates are provided, matched with 256-bit elliptic curves, intended for constrained use cases.¶

If other combinations are needed, a separate specification should be submitted to the IETF LAMPS working group. To ease implementation, these specifications are encouraged to follow the construction pattern of the algorithms specified in this document.¶

The composite structures defined in this specification allow only for pairs of algorithms. This also does not preclude future specification from extending these structures to define combinations with three or more components.¶

9.2. 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), it is obvious that the public keys or certificates using that algorithm are to be considered revoked.¶

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 KEM design specified in this document, and especially that of the KEM combiner specified in Section 4.3 means that the overall composite KEM algorithm should be considered to have the security strength of the strongest of its component algorithms; ie as long as one component algorithm remains strong, then the overall composite algorithm remains strong.¶

9.3. KEM Combiner Security Analysis

TODO¶

EDNOTE: the exact text to put here depends on the outcome of the CFRG KEM Combiners and X-Wing discussion. If CFRG doesn't move fast enough for us, then we may need to leverage this security consideration directly on top of the X-Wing paper [X-Wing].¶

C.1. FIPS certification

One of the primary design goals of this specification is for the overall composite algorithm to be able to be considered FIPS-approved even when one of the component algorithms is not. The combiner presented in Section 4.3 was chosen to align with [SP.800-56Cr2] for this reason.¶

Implementers seeking FIPS certification of a composite KEM algorithm where only one of the component algorithms has been FIPS-validated or FIPS-approved should credit the FIPS-validated component algorithm with full security strength, the non-FIPS-validated component algorithm with zero security, and the overall composite should be considered full strength and thus FIPS-approved.¶

The authors wish to note that this gives composite algorithms great future utility both for future cryptographic migrations as well as bridging across jurisdictions; for example defining composite algorithms which combine FIPS cryptography with cryptography from a different national standards body.¶

C.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.¶