Hybrid key exchange in JOSE and COSE

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Table of Contents

1. Introduction

The migration to PQC is unique in the history of modern digital cryptography in that neither the traditional algorithms nor the post-quantum algorithms are fully trusted to protect data for the required data lifetimes. The traditional algorithms, such as RSA and elliptic curve, will fall to quantum cryptalanysis, while the post-quantum algorithms face uncertainty about the underlying mathematics, compliance issues, unknown vulnerabilities, hardware and software implementations that have not had sufficient maturing time to rule out classical cryptanalytic attacks and implementation bugs.¶

During the transition from traditional to post-quantum algorithms, there is a desire or a requirement for protocols that use both algorithm types. [I-D.ietf-pquip-pqt-hybrid-terminology] defines terminology for the Post-Quantum and Traditional Hybrid Schemes.¶

This document gives a construction for hybrid key exchange in Javascript Object Signing and Encryption (JOSE) and CBOR Object Signing and Encryption (COSE). The overall design approach is a simple, "hash and concatenation" based approach to use a “hybrid” shared secret.¶

2. Conventions and Definitions

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 makes use of the terms defined in [I-D.ietf-pquip-pqt-hybrid-terminology]. For the purposes of this document, it is helpful to be able to divide cryptographic algorithms into two classes:¶

"Traditional Algorithm": An asymmetric cryptographic algorithm based on integer factorisation, finite field discrete logarithms or elliptic curve discrete logarithms. In the context of JOSE, examples of traditional key exchange algorithms include Elliptic Curve Diffie-Hellman Ephemeral Static [RFC6090] [RFC8037]. In the context of COSE, examples of traditional key exchange algorithms include Ephemeral-Static (ES) DH and Static-Static (SS) DH [RFC9052].¶

"Post-Quantum Algorithm": An asymmetric cryptographic algorithm that is believed to be secure against attacks using quantum computers as well as classical computers. Examples of PQC key exchange algorithms include Kyber.¶

"Hybrid" key exchange, in this context, means the use of two key exchange algorithms based on different cryptographic assumptions, e.g., one traditional algorithm and one Post-Quantum algorithm, with the purpose of the final shared secret key being secure as long as at least one of the component key exchange algorithms remains unbroken. It is referred to as PQ/T Hybrid Scheme in [I-D.ietf-pquip-pqt-hybrid-terminology].¶

PQ/T Hybrid Key Encapsulation Mechanism: A Key Encapsulation mechanism (KEM) made up of two or more component KEM algorithms where at least one is a post-quantum algorithm and at least one is a traditional algorithm.¶

3. Construction

Building a PQ/T hybrid KEM requires a secure function which combines the output of both component KEMs to form a single output. Several IETF protocols are adding PQ/T hybrid KEM mechanisms as part of their overall post-quantum migration strategies, examples include TLS 1.3 [I-D.ietf-tls-hybrid-design], IKEv2 [RFC9370].¶

The migration to PQ/T Hybrid KEM calls for performing multiple key encapsulations in parallel and then combining their outputs to derive a single shared secret. It is compatible with NIST SP 800-56Cr2 [SP800-56C] when viewed as a key derivation function. The hybrid scheme defined in this document is the combination of Traditional and Post-Quantum Algorithms. The Key agreement Traditional and Post-Quantum Algorithms are used in parallel to generate shared secrets. The two shared secrets are hashed and concatenated together and used as the shared secret in JOSE and COSE.¶

The JSON Web Algorithms (JWA) [RFC7518] in Section 4.6 defines two ways using the key agreement result. When Direct Key Agreement is employed, the shared secret established through the ECDH algorithm will be the content encryption key (CEK). When Key Agreement with Key Wrapping is employed, the shared secret established through the ECDH algorithm will wrap the CEK. Simiarly, COSE in Sections 8.5.4 and 8.5.5 [RFC9052] define the Direct Key Agreement and Key Agreement with Key Wrap classes. If multiple recipients are needed, then the version with key wrap is used.¶

4. KEM Combiner

The specification uses the KEM combiner defined in [I-D.ounsworth-cfrg-kem-combiners] that takes in two or more shared secrets and returns a combined shared secret. In case of PQ/T Hybrid KEM, the shared secrets are the output of the traditional key exchange and PQC KEM. The KEM combiner function is defined in Section 3 of [I-D.ounsworth-cfrg-kem-combiners]. The KDF and Hash functions will be KMAC and SHA3 and the counter will be initialized with a value of 0x00000001 (Section 4 of [I-D.ounsworth-cfrg-kem-combiners]). The KMAC and Hash functions used with the PQ/T hybrid algorithms are specified in the table below:¶

        +==============+=========+=========+==========+
        | PQ/T hybrid algorithm  | KDF     | H        |
        +========================+=========+==========+
        | x25519_kyber512        | KMAC128 | SHA3-256 |
        +------------------------+---------+----------+
        | secp384r1_kyber768     | KMAC256 | SHA3-384 |
        +------------------------+---------+----------+
        | x25519_kyber768        | KMAC256 | SHA3-384 |
        +-----------------------+----------+----------+
        | secp256r1_kyber512     | KMAC128 | SHA3-256 |
        +-----------------------+----------+----------+

                         Table 1

KMAC is defined in NIST SP 800-185 [SP800-185]. The KMAC(K, X, L, S) parameters are instantiated as follows:¶

• K: context-specific string. In case of JOSE, the context-specific string will be set to concat("JOSE", "", Name of the PQ/T hybrid algorithm). In case of COSE, the context-specific string will be set to concat("COSE", "-", Name of the PQ/T hybrid algorithm). For example, concat("JOSE", "","x25519_kyber512") = "JOSE_x25519_kyber512".¶
• X: concat(0x00000001, k_1, ... , k_n).¶
• L: length of the output key in bits.¶
• S: empty string.¶

In the case of a traditional key exchange algorithm (e.g., x25519, secp384r1) since there is no associated ciphertext present when calculating the constant-length input key (k1) defined in Section 3.1 of [I-D.ounsworth-cfrg-kem-combiners], the key derivation process defined in Section 4.6.2 of [RFC7518] for JOSE would be used to construct k. However, in case of COSE, the the HKDF (HMAC based Key Derivation Function) defined in Section 5 of [RFC9053] would be used. The HKDF algorithm leverages HMAC SHA-256 as the underlying PRF (Pseudo-Random function) for secp256r1 and x25519, and HMAC SHA-384 for secp384r1. The context structure defined in Section 5.2 of [RFC9053], salt and secret from DH key agreement are used as inputs to the HKDF. Note that the result of an ECDH key agreement process does not provide a uniformly random secret and it needs to be run through a KDF in order to produce a usable key (see Section 6.3.1 of [RFC9053]).¶

The KEM combiner instantiation of the first entry of Table 1 would be:¶

  ss = KMAC128("COSE_x25519_kyber512", "0x00000001 ||
                HKDF-256(DH-Shared-Secret, salt, context) ||
                SHA3-256(ss_1 || ct_1)" , 256, "")

In Direct Key Agreement mode, the output of the KEM combiner MUST be a key of the same length as that used by encryption algorithm. In Key Agreement with Key Wrapping mode, the output of the KEM combiner MUST be a key of the length needed for the specified key wrap algorithm.¶

5. KEM PQC Algorithms

The National Institute of Standards and Technology (NIST) started a process to solicit, evaluate, and standardize one or more quantum-resistant public-key cryptographic algorithms, as seen here. Said process has reached its first announcement in July 5, 2022, which stated which candidates to be standardized for KEM:¶

• Key Encapsulation Mechanisms (KEMs): CRYSTALS-Kyber: Kyber is a module learning with errors (MLWE)-based key encapsulation mechanism.¶

NIST announced as well that they will be opening a fourth round to standardize an alternative KEM, and a call for new candidates for a post-quantum signature algorithm.¶

6. Hybrid Key Representation with JOSE

A new key type (kty) value "HYBRID" is defined for expressing the cryptographic keys for PQ/T Hybrid KEM in JSON Web Key (JWK) form, the following rules apply:¶

• The parameter "kty" MUST be present and set to "HYBRID".¶

• The parameter "alg" MUST be specified, and its value MUST be one of the values specified in the table below:¶

          +============================+===================================+
          | alg                        | Description                       |
          +============================+===================================+
          | x25519_kyber512            | Curve25519 elliptic curve +       |
          |                            | Kyber512 parameter                |
          |                            | Direct Key Agreement              |
          +============================+===================================+
          | secp384r1_kyber768         | P-384 + Kyber768 parameter        |
          |                            | Direct Key Agreement              |
          +============================+===================================+
          | x25519_kyber768            | Curve25519 elliptic curve +       |
          |                            | Kyber768 parameter                |
          |                            | Direct Key Agreement              |
          +============================+===================================+
          | secp256r1_kyber512         | P-256 +  Kyber512 parameter       |
          |                            | Direct Key Agreement              |
          +============================+===================================+
          | x25519_kyber512+A128KW     | Curve25519 elliptic curve +       |
          |                            | Kyber512 parameter + CEK wrapped  |
          |                            | with "A128KW"                     |
          +========+===================+===================================+
          | secp384r1_kyber768+A128KW  | P-384 + Kyber768 parameter        |
          |                            |  + CEK wrapped with "A128KW"      |
          +========+===================+===================================+
          | x25519_kyber768+A128KW     | Curve25519 elliptic curve +       |
          |                            | Kyber768 parameter + CEK wrapped  |
          |                            | with "A128KW"                     |
          +========+===================+===================================+
          | secp256r1_kyber512+A128KW  | P-256 +  Kyber512 parameter       |
          |                            | + CEK wrapped with "A128KW"       |
          +============================+===================================+
          | x25519_kyber512+A256KW     | Curve25519 elliptic curve +       |
          |                            | Kyber512 parameter + CEK wrapped  |
          |                            | with "A256KW"                     |
          +============================+==================================+
          | secp384r1_kyber768+A256KW  | P-384 + Kyber768 parameter        |
          |                            |  + CEK wrapped  with "A256KW"     |
          +========+===================+===================================+
          | x25519_kyber768+A256KW     | Curve25519 elliptic curve +       |
          |                            | Kyber768 parameter + CEK wrapped  |
          |                            | with "A256KW"                     |
          +========+===================+===================================+
          | secp256r1_kyber512+A256KW  | P-256 +  Kyber512 parameter       |
          |                            | + CEK wrapped with "A256KW"       |
          +============================+===================================+
  
                             Table 2
  

  ¶
• The parameter "kem" MUST be present and set to the PQC KEM algorithm.¶
• The parameter "kem-pk" MUST be present and contains the PQC KEM public key encoded using the base64url [RFC4648] encoding.¶
• The parameter "kem-sk" MUST be present for private key and contains the PQC KEM private key encoded using the base64url encoding. This parameter MUST NOT be present for public key.¶
• The parameter "kem-ct" MUST be present for KEM ciphertext encoded using the base64url [RFC4648] encoding.¶
• The parameter "crv" MUST be present and contains the Elliptic Curve Algorithm used (from the "JSON Web Key Elliptic Curve" registry).¶
• The parameter "x" MUST be present and contains the x coordinate for the Elliptic Curve point encoded using the base64url [RFC4648] encoding.¶
• The parameter "y" MUST be present and contains the y coordinate for the Elliptic Curve point encoded using the base64url [RFC4648] encoding. This parameter is not present for "X25519".¶
• The parameter "d" MUST be present for private keys and contains the Elliptic Curve Algorithm private key encoded using the base64url encoding. This parameter MUST NOT be present for public keys.¶

In Table 1, "A128KW" and "A256KW" are AES Key Wrap with 128-bit key and 256-bit key respectively.¶

  "kem"            PQC KEM Applied
  Kyber512            Kyber512
  Kyber768            Kyber768

 {"kty":"EC",
  "crv":"P-256",
  "x":"alice_eph_public_key_x",
  "y":"alice_eph_public_key_y",
  "d":"alice_eph_private_key"
 }

 {"kty":"HYBRID",
  "kem": "kyber512",
  "kem-pk":"bob_kyber_public_key",
  "kem-sk":"bob_kyber_private_key"
  "crv":"P-256",
  "x":"bob_public_key_x",
  "y":"bob_public_key_y",
  "d":"bob_private_key"
 }

 {"alg":"secp256r1_kyber512",
  "enc":"A128GCM",
  "apu":"QWxpY2U",  // base64url encoding of the UTF-8 string "Alice"
  "apv":"Qm9i",    // base64url encoding of the UTF-8 string "Bob"
  "epk":
   {"kty":"EC",
    "crv":"P-256",
    "x":"alice_eph_public_key_x",
    "y":"alice_eph_public_key_y",
   }
 }

7. Hybrid Key Representation with COSE

The approach taken here matches the work done to support secp256k1 in JOSE and COSE in [RFC8812]. The following tables map terms between JOSE and COSE for Key Type Parameters.¶

    +======================+========================================+==+
    | Name                 | Value | Description                       |
    +======================+===========================================+
    | crv                  | -1    | EC used                           |
    +----------------------+-------------------------------------------+
    | d                    | -4    | Private key                       |
    +----------------------+-------------------------------------------+
    | x                    | -2    | x coordinate for the public key   |
    +----------------- ----+-------------------------------------------+
    | y                    | -3    | y coordinate for the public key   |
    +---------------- -----+-------------------------------------------+
    | kem                  | TBD2  | PQC KEM Algorithm                 |
    +----------------------+-------------------------------------------+
    | kem-pk               | TBD3  | PQC KEM Public Key                |
    +----------------------+-------------------------------------------+
    | kem-sk               | TBD4  | PQC KEM Private Key               |
    +----------------------+-------------------------------------------+
    | kem-ct               | TBD5  | PQC KEM ciphertext                |
    +----------------------+-------------------------------------------+

                             Table 3

The following tables map terms between JOSE and COSE for PQ/T Hybrid KEM.¶

    +==============+===================+====================+============================+
    | Name                          | Value  | Description                 | Recommended |
    +===================+===========+========+=============================+=============+
    | x25519_kyber512               | TBD10  | Curve25519 elliptic curve + | No          |
    |                               |        | Kyber512 parameter          |             |
    +-------------------------------+--------+-----------------------------+-------------+
    | secp384r1_kyber768            | TBD11  | P-384 + Kyber768 parameter  | No          |
    |                               |        |                             |             |
    +-------------------------------+--------+-----------------------------+-------------+
    | x25519_kyber768               | TBD12  | Curve25519 elliptic curve   | No          |
    |                               |        | + Kyber768 parameter        |             |
    +-------------------------------+--------+-----------------------------+-------------+
    | secp256r1_kyber512            | TBD13  | P-256 + Kyber512 parameter  | No          |
    |                               |        |                             |             |
    +-------------------------------+--------+-----------------------------+-------------+
    | x25519_kyber512+A128KW        | TBD14  | Curve25519 elliptic curve + | No          |
    |                               |        | Kyber512 parameter +        |             |
    |                               |        | CEK wrapped with "A128KW"   |             |
    +-------------------------------+--------+-----------------------------+-------------+
    | secp384r1_kyber768+A128KW     | TBD15  | P-384 + Kyber768 parameter  | No          |
    |                               |        | + CEK wrapped with "A128KW" |             |
    +-------------------------------+--------+-----------------------------+-------------+
    | x25519_kyber768+A128KW        | TBD16  | Curve25519 elliptic curve   | No          |
    |                               |        | + Kyber768 parameter        |             |
    |                               |        | + CEK wrapped with "A128KW" |             |
    +-------------------------------+--------+-----------------------------+-------------+
    | secp256r1_kyber512+A128KW     | TBD17  | P-256 + Kyber512 parameter  | No          |
    |                               |        | + CEK wrapped with "A128KW" |             |
    +-------------------------------+--------+-----------------------------+-------------+
    | x25519_kyber512+A256KW        | TBD18  | Curve25519 elliptic curve + | No          |
    |                               |        | Kyber512 parameter +        |             |
    |                               |        | CEK wrapped with "A256KW"   |             |
    +-------------------------------+--------+-----------------------------+-------------+
    | secp384r1_kyber768+A256KW     | TBD19  | P-384 + Kyber768 parameter  | No          |
    |                               |        | + CEK wrapped with "A256KW" |             |
    +-------------------------------+--------+-----------------------------+-------------+
    | x25519_kyber768+A256KW        | TBD20  | Curve25519 elliptic curve   | No          |
    |                               |        | + Kyber768 parameter        |             |
    |                               |        | + CEK wrapped with "A256KW" |             |
    +-------------------------------+--------+-----------------------------+-------------+
    | secp256r1_kyber512+A256KW     | TBD21  | P-256 + Kyber512 parameter  | No          |
    |                               |        | + CEK wrapped with "A256KW" |             |
    +-------------------------------+--------+-----------------------------+-------------+


                                   Table 4

The following tables map terms between JOSE and COSE for key types.¶

    +==============+=======+====================+===============================+
    | Name                 | Value | Description                 | Recommended  |
    +==============+=======+====================+=============--------==========+
    | HYBRID               | TBD1  | kty for PQ/T Hybrid KEM     | No           |
    |                      |       |                             |              |
    +---------------------+--------+-----------------------------+--------------+

                                   Table 5

The following tables map terms between JOSE and COSE for PQC KEM algorithms.¶

    +==============+=======+====================+===============================+
    | Name                 | Value | Description                 | Recommended  |
    +==============+=======+====================+=============--------==========+
    | Kyber512             | TBD7  | Kyber512                    | No           |
    |                      |       |                             |              |
    +---------------------+--------+-----------------------------+--------------+
    | Kyber768             | TBD9  | Kyber768                    | No           |
    |                      |       |                             |              |
    +---------------------+--------+-----------------------------+--------------+

                                   Table 6

8. Security Considerations

Security considerations from [RFC7748] and [I-D.ounsworth-cfrg-kem-combiners] apply here. The shared secrets computed in the hybrid key exchange should be computed in a way that achieves the "hybrid" property: the resulting secret is secure as long as at least one of the component key exchange algorithms is unbroken.¶

PQC KEMs used in the manner described in this document MUST explicitly be designed to be secure in the event that the public key is reused, such as achieving IND-CCA2 security. Kyber has such security properties.¶

9. IANA Considerations

Recommended:  Does the IETF have a consensus recommendation to use
  the algorithm?  The legal values are 'Yes', 'No', and
  'Deprecated'.

Acknowledgments

Thanks to Mike Ounsworth for the discussion and comments.¶

Authors' Addresses