Hybrid key exchange in JOSE and COSE

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. 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.

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 when, and only when, they appear in all capitals, as shown here. This document makes use of the terms defined in . 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 . In the context of COSE, examples of traditional key exchange algorithms include Ephemeral-Static (ES) DH and Static-Static (SS) DH . "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 . 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.

Key Encapsulation Mechanisms For the purposes of this document, we consider a Key Encapsulation Mechanism (KEM) to be any asymmetric cryptographic scheme comprised of algorithms satisfying the following interfaces .

def kemKeyGen() -> (pk, sk)
def kemEncaps(pk) -> (ct, ss)
def kemDecaps(ct, sk) -> ss

where pk is public key, sk is secret key, ct is the ciphertext representing an encapsulated key, and ss is shared secret. KEMs are typically used in cases where two parties, hereby refereed to as the "encapsulater" and the "decapsulater", wish to establish a shared secret via public key cryptography, where the decapsulater has an asymmetric key pair and has previously shared the public key with the encapsulater.

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 , IKEv2 . 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 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) 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 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.

KEM Combiner The specification uses the KEM combiner defined in 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 . The KDF and Hash functions will be KMAC and SHA3 and the counter will be initialized with a value of 0x00000001 (Section 4 of ). The KMAC and Hash functions used with the PQ/T hybrid algorithms are specified in the table below: KMAC is defined in NIST SP 800-185 . 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 , the key derivation process defined in Section 4.6.2 of 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 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 , 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 ). The KEM combiner instantiation of the first entry of Table 1 would be: 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.

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.

Kyber Kyber offers several parameter sets with varying levels of security and performance trade-offs. This document specifies the use of the Kyber algorithm at two security levels: Kyber512 and Kyber768. Kyber key generation, encapsulation and decaspulation functions are defined in .

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:
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 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 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 encoding.
The parameter "y" MUST be present and contains the y coordinate for the Elliptic Curve point encoded using the base64url 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" The "kem" (KEM) parameter identifies PQC KEM algorithm used with the "kem-pk" key. KEM values used by this specification are: These values are registered in the IANA "JSON PQC KEM" registry defined in . Additional "kem" values can be registered by other specifications.

Example Hybrid Key Agreement Computation This example uses secp256r1_kyber512 Key Agreement and the KEM Combiner to derive the CEK in the manner described in . In this example, the secp256r1_kyber512 Direct Key Agreement mode ("alg" value "secp256r1_kyber512") is used to produce an agreed-upon key for AES GCM with a 128-bit key ("enc" value "A128GCM"). In this example, a producer Alice is encrypting content to a consumer Bob. The producer (Alice) generates an ephemeral key for the key agreement computation. Alice's ephemeral key (in JWK format) used for the key agreement computation in this example (including the private part) is: The consumer's (Bob's) key (in JWK format) used for the key agreement computation in this example (including the private part) is: Header Parameter values used in this example are as follows.

Hybrid Key Representation with COSE The approach taken here matches the work done to support secp256k1 in JOSE and COSE in . The following tables map terms between JOSE and COSE for Key Type Parameters. The following tables map terms between JOSE and COSE for PQ/T Hybrid KEM. The following tables map terms between JOSE and COSE for key types. The following tables map terms between JOSE and COSE for PQC KEM algorithms.

Security Considerations Security considerations from and 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.

IANA Considerations

JOSE The following has to be been added to the "JSON Web Key Types" registry:

Name: "HYBRID"
Description: Hybrid Key Exchange
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): of this document (TBD)

The following has to be added to the "JSON Web Key Parameters" registry:

Parameter Name: "crv"
Parameter Description: The EC used
Parameter Information Class: Public
Used with "kty" Value(s): "HYBRID"
Change Controller: IESG
Specification Document(s): of this document (TBD)
Parameter Name: "d"
Parameter Description: The private key
Parameter Information Class: Private
Used with "kty" Value(s): "HYBRID"
Change Controller: IESG
Specification Document(s): of this document (TBD)
Parameter Name: "x"
Parameter Description: x coordinate for the public key
Parameter Information Class: Public
Used with "kty" Value(s): "HYBRID"
Change Controller: IESG
Specification Document(s): of this document (TBD)
Parameter Name: "y"
Parameter Description: y coordinate for the public key
Parameter Information Class: Public
Used with "kty" Value(s): "HYBRID"
Change Controller: IESG
Specification Document(s): of this document (TBD)
Parameter Name: "kem"
Parameter Description: PQC KEM Algorithm
Parameter Information Class: Public
Used with "kty" Value(s): "HYBRID"
Change Controller: IESG
Specification Document(s): of this document (TBD)
Parameter Name: "kem-pk"
Parameter Description: PQC KEM Public Key
Parameter Information Class: Public
Used with "kty" Value(s): "HYBRID"
Change Controller: IESG
Specification Document(s): of this document (TBD)
Parameter Name: "kem-sk"
Parameter Description: PQC KEM Private Key
Parameter Information Class: Private
Used with "kty" Value(s): "HYBRID"
Change Controller: IESG
Specification Document(s): of this document (TBD)
Parameter Name: "kem-ct"
Parameter Description: PQC KEM ciphertext
Parameter Information Class: Public
Used with "kty" Value(s): "HYBRID"
Change Controller: IESG
Specification Document(s): of this document (TBD)

The following has to be added to the "JSON Web Signature and Encryption Algorithms" registry:

Algorithm Name: "x25519_kyber768"
Algorithm Description: Curve25519 elliptic curve + Kyber768 parameter
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): of this document (TBD)
Algorithm Analysis Documents(s): (TBD20)
Algorithm Name: "secp384r1_kyber768"
Algorithm Description: P-384 + Kyber768 parameter
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): of this document (TBD)
Algorithm Analysis Documents(s): (TBD20)
Algorithm Name: "x25519_kyber512"
Algorithm Description: Curve25519 elliptic curve + Kyber512 parameter
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): of this document (TBD)
Algorithm Analysis Documents(s): (TBD20)
Algorithm Name: "secp256r1_kyber512"
Algorithm Description: P-256 + Kyber512 parameter
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): of this document (TBD)
Algorithm Analysis Documents(s): (TBD20)
Algorithm Name: "x25519_kyber768+A128KW"
Algorithm Description: Curve25519 elliptic curve + Kyber768 parameter and CEK wrapped with "A128KW"
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): of this document (TBD)
Algorithm Analysis Documents(s): (TBD20)
Algorithm Name: "secp384r1_kyber768+A128KW"
Algorithm Description: P-384 + Kyber768 parameter and CEK wrapped with "A128KW"
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): of this document (TBD)
Algorithm Analysis Documents(s): (TBD20)
Algorithm Name: "x25519_kyber512+A128KW"
Algorithm Description: Curve25519 elliptic curve + Kyber512 parameter and CEK wrapped with "A128KW"
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): of this document (TBD)
Algorithm Analysis Documents(s): (TBD20)
Algorithm Name: "secp256r1_kyber512+A128KW"
Algorithm Description: P-256 + Kyber512 parameter and CEK wrapped with "A128KW"
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): of this document (TBD)
Algorithm Analysis Documents(s): (TBD20)
Algorithm Name: "x25519_kyber768+A256KW"
Algorithm Description: Curve25519 elliptic curve + Kyber768 parameter and CEK wrapped with "A256KW"
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): of this document (TBD)
Algorithm Analysis Documents(s): (TBD20)
Algorithm Name: "secp384r1_kyber768+A256KW"
Algorithm Description: P-384 + Kyber768 parameter and CEK wrapped with "A256KW"
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): S of this document (TBD)
Algorithm Analysis Documents(s): (TBD20)
Algorithm Name: "x25519_kyber512+A256KW"
Algorithm Description: Curve25519 elliptic curve + Kyber512 parameter and CEK wrapped with "A256KW"
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): of this document (TBD)
Algorithm Analysis Documents(s): (TBD20)
Algorithm Name: "secp256r1_kyber512+A256KW"
Algorithm Description: P-256 + Kyber512 parameter and CEK wrapped with "A256KW"
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s): of this document (TBD)
Algorithm Analysis Documents(s): (TBD20)

JSON PQC KEM Registry This section establishes the IANA "JSON PQC KEM" registry for JWK "kem" member values. The registry records the PQC KEM name, implementation requirements, and a reference to the specification that defines it. This specification registers the PQC KEM algorithms defined in . The implementation requirements of a PQC KEM may be changed over time as the cryptographic landscape evolves, for instance, to change the status of a PQC KEM to Deprecated or to change the status of a PQC KEM from Optional to Recommended+ or Required. Changes of implementation requirements are only permitted on a Specification Required basis after review by the Designated Experts, with the new specification defining the revised implementation requirements level.

Registration Template PQC KEM name: The name requested (e.g., "Kyber512"). Because a core goal of this specification is for the resulting representations to be compact, it is RECOMMENDED that the name be short -- not to exceed 12 characters without a compelling reason to do so. This name is case sensitive. Names may not match other registered names in a case-insensitive manner unless the Designated Experts state that there is a compelling reason to allow an exception. PQC KEM Description: Brief description of the PQC KEM (e.g., "Kyber512"). JOSE Implementation Requirements: The PQC KEM implementation requirements for JWE, which must be one the words Required, Recommended, Optional, Deprecated, or Prohibited. Optionally, the word can be followed by a "+" or "-". The use of "+" indicates that the requirement strength is likely to be increased in a future version of the specification. The use of "-" indicates that the requirement strength is likely to be decreased in a future version of the specification. Change Controller: For Standards Track RFCs, list "IESG". For others, give the name of the responsible party. Other details (e.g., postal address, email address, home page URI) may also be included. Specification Document(s): Reference to the document or documents that specify the parameter, preferably including URIs that can be used to retrieve copies of the documents. An indication of the relevant sections may also be included but is not required.

Initial Registry Contents

PQC KEM name: "Kyber512"
PQC KEM Description: Kyber512
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s):
PQC KEM name: "Kyber768"
PQC KEM Description: Kyber768
JOSE Implementation Requirements: Optional
Change Controller: IESG
Specification Document(s):

COSE The following has to be been added to the "COSE Key Types" registry:

Name: "HYBRID"
Value: TBD1
Description: Hybrid Key Exchange
Reference: This document (TBD)

The following has to be added to the "COSE Key Type Parameters" registry:

Key Type: TBD1
Name: crv
Label : -1
CBOR Type: int / tstr
Description: The EC used
Reference: This document (TBD)
Key Type: TBD1
Name: d
Label : -4
CBOR Type: bstr
Description: The Private key
Reference: This document (TBD)
Key Type: TBD1
Name: x
Label : -2
CBOR Type: bstr
Description: x coordinate for the public key
Reference: This document (TBD)
Key Type: TBD1
Name: y
Label : -3
CBOR Type: bstr / bool
Description: y coordinate for the public key
Reference: This document (TBD)
Key Type: TBD1
Name: kem
Label : TBD2
CBOR Type: int / tstr
Description: PQC KEM Algorithm
Reference: This document (TBD)
Key Type: TBD1
Name: kem-pk
Label : TBD3
CBOR Type: bstr
Description: PQC KEM Public Key
Reference: This document (TBD)
Key Type: TBD1
Name: kem-sk
Label : TBD4
CBOR Type: bstr
Description: PQC KEM Private Key
Reference: This document (TBD)
Key Type: TBD1
Name: kem-ct
Label : TBD5
CBOR Type: bstr
Description: PQC KEM ciphertext
Reference: This document (TBD)

The following has to be added to the "COSE Algorithms" registry:

Name: x25519_kyber768
Value: TBD10
Description: Curve25519 elliptic curve + Kyber768 parameter
Reference: This document (TBD)
Recommended: No
Name: secp384r1_kyber768
Value: TBD11
Description: P-384 + Kyber768 parameter
Reference: This document (TBD)
Recommended: No
Name: x25519_kyber512
Value: TBD12
Description: Curve25519 elliptic curve + Kyber512 parameter
Reference: This document (TBD)
Recommended: No
Name: secp256r1_kyber512
Value: TBD13
Description: P-256 + Kyber512 parameter
Reference: This document (TBD)
Recommended: No
Name: x25519_kyber768+A128KW
Value: TBD14
Description: Curve25519 elliptic curve + Kyber768 parameter and CEK wrapped with "A128KW"
Reference: This document (TBD)
Recommended: No
Name: secp384r1_kyber768+A128KW
Value: TBD15
Description: P-384 + Kyber768 parameter and CEK wrapped with "A128KW"
Reference: This document (TBD)
Recommended: No
Name: x25519_kyber512+A128KW
Value: TBD16
Description: Curve25519 elliptic curve + Kyber512 parameter and CEK wrapped with "A128KW"
Reference: This document (TBD)
Recommended: No
Name: secp256r1_kyber512+A128KW
Value: TBD17
Description: P-256 + Kyber512 parameter and CEK wrapped with "A128KW"
Reference: This document (TBD)
Recommended: No
Name: x25519_kyber768+A256KW
Value: TBD18
Description: Curve25519 elliptic curve + Kyber768 parameter and CEK wrapped with "A256KW"
Reference: This document (TBD)
Recommended: No
Name: secp384r1_kyber768+A256KW
Value: TBD19
Description: P-384 + Kyber768 parameter and CEK wrapped with "A256KW"
Reference: This document (TBD)
Recommended: No
Name: x25519_kyber512+A256KW
Value: TBD20
Description: Curve25519 elliptic curve + Kyber512 parameter and CEK wrapped with "A256KW"
Reference: This document (TBD)
Recommended: No
Name: secp256r1_kyber512+A256KW
Value: TBD21
Description: P-256 + Kyber512 parameter and CEK wrapped with "A256KW"
Reference: This document (TBD)
Recommended: No

COSE PQC KEM Registry This section establishes the IANA "COSE PQC KEM" registry for "kem" member values. The registry records the PQC KEM name, implementation requirements, and a reference to the specification that defines it. This specification registers the PQC KEM algorithms defined in . The implementation requirements of a PQC KEM may be changed over time as the cryptographic landscape evolves, for instance, to change the status of a PQC KEM to Deprecated or to change the status of a PQC KEM from Optional to Recommended+ or Required. Changes of implementation requirements are only permitted on a Specification Required basis after review by the Designated Experts, with the new specification defining the revised implementation requirements level.

Registration Template Name: The name requested (e.g., "Kyber512"). Because a core goal of this specification is for the resulting representations to be compact, it is RECOMMENDED that the name be short -- not to exceed 12 characters without a compelling reason to do so. This name is case sensitive. Names may not match other registered names in a case-insensitive manner unless the Designated Experts state that there is a compelling reason to allow an exception. Value: This is the value used for the label. The label can be either an integer or a string. Registration in the table is based on the value of the label requested. Integer values between 1 and 255 and strings of length 1 are designated as "Standards Action". Integer values from 256 to 65535 and strings of length 2 are designated as "Specification Required". Integer values of greater than 65535 and strings of length greater than 2 are designated as "Expert Review". Integer values in the range -1 to -65536 are "delegated to the COSE Header Algorithm Parameters registry". Integer values less than -65536 are marked as private use. Description: Brief description of the PQC KEM (e.g., "Kyber512"). Change Controller: For Standards Track RFCs, list "IESG". For others, give the name of the responsible party. Other details (e.g., postal address, email address, home page URI) may also be included. Reference: Reference to the document or documents that specify the parameter, preferably including URIs that can be used to retrieve copies of the documents. An indication of the relevant sections may also be included but is not required.

Initial Registry Contents

Name: "Kyber512"
Value: TBD7
Description: Kyber512
Change Controller: IESG
Reference: This document (TBD)
Recommended: No
Name: "Kyber768"
Value: TBD9
Description: Kyber768
Change Controller: IESG
Reference: This document (TBD)
Recommended: No

Acknowledgments Thanks to Mike Ounsworth for the discussion and comments.