Composite KEM For Use In Internet PKI

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 cryptagraphic 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 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 relies on the RSA-KEM construction defined in [I-D.ietf-lamps-rfc5990bis] and the Elliptic Curve DHKEM defined in [I-D.ounsworth-lamps-cms-dhkem].¶

A composite KEM allows two or more underlying key transport, key agreement, or KEM algorithms to be combined into a single cryptographic operation by performing each operation, transformed to a KEM as outline above, and using a specified combiner function to combine the two or more component shared secrets into a single shared secret.¶

Encaps(pk):
  # Split the component public keys
  pk1 = pk[0]
  pk2 = pk[1]

  # Perform the respective component Encaps operations
  (ct1, ss1) = ComponentKEM1.Encaps(pk1)
  (ct2, ss2) = ComponentKEM2.Encaps(pk2)

  # combine
  ct = CompositeCiphertextValue(ct1, ct2)
  ss = Combiner(ct1, ss1, ct2, ss2, algName)

  return (ct, ss)

Decaps(sk, ct):
  # Sptil the component ciphertexts
  ct1 = ct[0]
  ct2 = ct[1]

  # Perform the respective component Decaps operations
  ss1 = ComponentKEM1.Encaps(sk1, ct1)
  ss2 = ComponentKEM2.Encaps(sk2, ct2)

  # combine
  ss = Combiner(ct1, ss1, ct2, ss2, algName)

  return ss

2.4. 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.¶

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-KMAC128 is defined as:¶

pk-MLKEM512-ECDH-P256-KMAC128 PUBLIC-KEY ::=
  pk-CompositeKEM {
    id-MLKEM512-ECDH-P256-KMAC128,
    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 6.¶

Some applications may need to reconstruct the SubjectPublicKeyInfo objects corresponding to each component public key. Table 2 in Section 6 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

Usecases that require an interoperable 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 6, 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 usecases 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 {sec-fips} 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)

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

A composite KEM and CompositeCipherTextValue MAY be associated with a composite KEM public key, but MAY also be associated with multiple public keys from different sources, for example multiple X.509 certificates, or multiple cryptographic modules. In the latter case, composite KEMs MAY be used as the mechanism for carrying multiple ciphertexts, for example, in a non-composite hybrid encryption equivalent of those described for digital signatures in [I-D.becker-guthrie-noncomposite-hybrid-auth].¶

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 probility.¶

This document follows the construction of [I-D.ounsworth-cfrg-kem-combiners], which is repeated here for clarity and simplified to take two imput shared secrets:¶

Combiner(ct1, ss1, ct2, ss2, fixedInfo) =
  KDF(counter || ct1 || ss1 || ct2 || ss2 || fixedInfo, outputBits)

where:¶

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

• fixedInfo SHALL be the ASCII-encoded string name of the composite KEM algorithm as listed in Table 2.¶

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

• || represents concatenation.¶

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

See Section 9.2 for further discussion of the security coniserations of this KEM combiner.¶

6.1. RSA-KEM Parameters

Use of RSA-KEM [I-D.ietf-lamps-rfc5990bis] within id-MLKEM512-RSA2048-KMAC128 and id-MLKEM512-RSA3072-KMAC128 requires additional specification.¶

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

As with the other composite KEM algorithms, when id-MLKEM512-RSA2048-KMAC128 or id-MLKEM512-RSA3072-KMAC128 is used in an AlgorithmIdentifier, the parameters MUST be absent. The RSA-KEM SHALL be instantiated with the following parameters:¶

where:¶

• kda-kdf3 is defined in [I-D.ietf-lamps-rfc5990bis] which references it from [ANS-X9.44].¶

• mda-shake256 is defined in [I-D.housley-lamps-cms-sha3-hash].¶

8.1. Object Identifier Allocations

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

9.1. 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 indpendently from that of their component algorithms. For example a cryptographic policy might continue to allow id-MLKEM512-ECDH-P256-KMAC128 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.¶

9.2. KEM Combiner

This document uses directly the KEM Combiner defined in [I-D.ounsworth-cfrg-kem-combiners] and therefore IND-CCA2 of any of its ingredient KEMs, i.e. the newly formed combined KEM is IND-CCA2 secure as long as at least one of the ingredient KEMs is¶

[I-D.ounsworth-cfrg-kem-combiners] provides two different constructions depending on the properties of the component KEMs:¶

• If both the secret share ss_i and the ciphertext ct_i are constant length, then k_i MAY be constructed concatenating the two values. If ss_i or ct_i are not guaranteed to have constant length, it is REQUIRED to append the rlen encoded length when concatenating, prior to inclusion in the overall construction.¶

The component KEMs used in this specification are RSA-KEM [I-D.ietf-lamps-rfc5990bis], ECDH KEM [I-D.ounsworth-lamps-cms-dhkem] and ML-KEM [FIPS.203-ipd] all of which meet the criteria of having constant-length shared secrets and ciphertexts and therefore we justify using the simpler construction that omits the length tag.¶

B.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.¶

Implementors 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 algorith 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.¶

B.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 interoperate 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.¶