Post-Quantum Key Encapsulation Mechanisms (PQ KEMs) for JOSE and COSE

Introduction Quantum computing is no longer perceived as a conjecture of computational sciences and theoretical physics. Considerable research efforts and enormous corporate and government funding for the development of practical quantum computing systems are being invested currently. As such, as quantum technology advances, there is the potential for future quantum computers to have a significant impact on current cryptographic systems. Researchers have developed Post-Quantum Key Encapsulation Mechanisms (PQ-KEMs) to provide secure key establishment resistant against an adversary with access to a quantum computer. As the National Institute of Standards and Technology (NIST) is still in the process of selecting the new post-quantum cryptographic algorithms that are secure against both quantum and classical computers, the purpose of this document is to propose a PQ-KEMs to protect the confidentiality of content encrypted using JOSE and COSE against the quantum threat. Although this mechanism could thus be used with any PQ-KEM, this document focuses on Module-Lattice-based Key Encapsulation Mechanisms (ML-KEMs). ML-KEM is a one-pass (store-and-forward) cryptographic mechanism for an originator to securely send keying material to a recipient using the recipient's ML-KEM public key. Three parameters sets for ML-KEMs are specified by . In order of increasing security strength (and decreasing performance), these parameter sets are ML-KEM-512, ML-KEM-768, and ML-KEM-1024.

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 . The following terms are repeately used in this specification:

KEM: Key Encapsulation Mechanism
PQ-KEM: Post-Quantum Key Encapsulation Mechanism
CEK: Content Encryption Key
ML-KEM: Module-Lattice-based Key Encapsulation Mechanism

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. Post-quantum algorithms can also be called quantum-resistant or quantum-safe algorithms. Examples of Post-Quantum Algorithm include ML-KEM.

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.

Design Rationales Section 4.6 of the JSON Web Algorithms (JWA) specification, see , defines two ways of using a key agreement:

When Direct Key Agreement is employed, the shared secret established through the Traditional Algorithm will be the content encryption key (CEK).
When Key Agreement with Key Wrapping is employed, the shared secret established through the Traditional Algorithm will wrap the CEK.

For efficient use with multiple recipient the key wrap approach is used since the content can be encrypted once with the CEK but each CEK is encrypted per recipient. Similarly, Section 8.5.4 and Section 8.5.5 of COSE define the Direct Key Agreement and Key Agreement with Key Wrap, respectively. This document proposes the use of PQ-KEMs for these two modes. It is essential to note that in the PQ-KEM, one needs to apply Fujisaki-Okamoto transform or its variant on the PQC KEM part to ensure that the overall scheme is IND-CCA2 secure, as mentioned in . The FO transform is performed using the KDF such that the PQC KEM shared secret achieved is IND-CCA2 secure. As a consequence, one can re-use PQC KEM public keys but there is an upper bound that must be adhered to. Note that during the transition from traditional to post-quantum algorithms, there may be a desire or a requirement for protocols that incorporate both types of algorithms until the post-quantum algorithms are fully trusted. HPKE is a KEM that can be extended to support hybrid post-quantum KEMs and the specification for the use of PQ/T Hybrid Key Encapsulation Mechanism (KEM) in Hybrid Public-Key Encryption (HPKE) for integration with JOSE and COSE is described in .

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): ML-KEM , previously known as Kyber, is a module learning with errors (MLWE)-based KEM. Three security levels have been defined in the NIST PQC Project, namely Level 1, 3, and 5. These levels correspond to the hardness of breaking AES-128, AES-192 and AES-256, respectively.

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.

ML-KEM ML-KEM offers several parameter sets with varying levels of security and performance trade-offs. This document specifies the use of the ML-KEM algorithm at three security levels: ML-KEM-512, ML-KEM-768, and ML-KEM-1024. ML-KEM key generation, encapsulation and decaspulation functions are defined in . The main security property for KEMs standardized in the NIST Post-Quantum Cryptography Standardization Project is indistinguishability under adaptive chosen ciphertext attacks (IND-CCA2) (see Section 10.2 of ). The public/private key sizes, ciphertext key size, and PQ security levels of ML-KEM are detailed in Section 12 of .

PQ-KEM Encapsulation The encapsulation process is as follows:

Generate an inital shared secret SS' and the associated ciphertext CT using the KEM encapsulation function and the recipient's public key recipPubKey.

Derive a final shared secret SS of length SSLen bytes from the initial shared secret SS' using the underlying key derivation function:

In Direct Key Agreement mode, the output of the KDF 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 KDF MUST be a key of the length needed for the specified key wrap algorithm. When Direct Key Agreement is employed, SS is the CEK. When Key Agreement with Key Wrapping is employed, SS is used to wrap the CEK.

PQ-KEM Decapsulation The decapsulation process is as follows:

Decapsulate the ciphertext CT using the KEM decapsulation function and the recipient's private key to retrieve the initial shared secret SS':

Derive the final shared secret SS of length SSLen bytes from the inital secret SS' using the underlying key derivation function:

KDF

Key Derivation for JOSE The key derivation is performed using the Concat KDF leveraged in Section 4.6.2 of for JOSE. A different set of contact KDF parameters would be used to construct the agreed-upon key from the shared secret (SS') established through the ML-KEM algorithm, instead of the key derivation process defined in Section 4.6.2 of RFC7518 for JOSE. The Concat KDF parameters are set as follows: *Z : This is set to the representation of the shared secret (SS'). *keydatalen : This is set to the number of bits in the desired output key. For Direct Key Agreement, this is length of the key used by the "enc" algorithm. For Key Agreement with Key Wrapping, "MLKEM512-AES128KW", "MLKEM768-AES192KW", and "MLKEM1024-AES256KW", this is 128, 192, and 256, respectively. *AlgorithmID: The AlgorithmID value will be set as explained in Section 4.6.2 of . *CipherText: The ciphertext (CT) generated using the KEM encapsulation function to bind the shared secret to the ciphertext (ct), achieving MAL-BIND-K-CT. ML-KEM already is MAL-BIND-K-PK as the hash of the encapsulation key (pk) is an input to the computation of the shared secret (ss).

Key Derivation for COSE The HKDF (HMAC-based Key Derivation Function) defined in Section 5 of is utilized to construct the agreed-upon key from the shared secret (SS') established through the ML-KEM algorithm. The HKDF algorithm leverages HMAC-SHA-256 as the underlying PRF (Pseudo-Random function). It takes the inputs defined in Section 5.1 of , with the exception of the shared secret and context structure inputs. The secret is set to the shared secret established through the ML-KEM algorithm. The context structure, redefined as follows, is used as input to the HKDF. The fields AlgorithmID, SuppPubInfo and SuppPrivInfo in the above array are defined in Section 5.2 of . The CipherText field contains the ciphertext (CT) generated using the KEM encapsulation function to bind the shared secret to the ciphertext (ct).

Post-quantum KEM in JOSE As explained in JWA defines two ways to use public key cryptography with JWE:

Direct Key Agreement
Key Agreement with Key Wrapping

This specification describes these two modes of use for PQ-KEM in JWE. Unless otherwise stated, no changes to the procedures described in have been made.

Direct Key Agreement

The "alg" header parameter MUST be a PQ-KEM algorithm chosen from the JSON Web Signature and Encryption Algorithms registry defined in .
The CEK will be generated using the process explained in . The output of the MUST be a secret key of the same length as that used by the "enc" algorithm. Both header parameters, "alg" and "enc", MUST be placed in the JWE Protected Header. Subsequently, the plaintext will be encrypted using the CEK, as detailed in Step 15 of Section 5.1 of .
The parameter "kem-ct" MUST include the output ('ct') from the PQ-KEM algorithm, encoded using base64url.
The recipient MUST base64url decode the ciphertext from the "kem-ct" and then use it to derive the CEK using the process defined in . The ciphertext sizes of ML-KEMs are discussed in Section 12 of .
The JWE Encrypted Key MUST be absent.

Key Agreement with Key Wrapping

The derived key is generated using the process explained in and used to encrypt the CEK.
The parameter "kem-ct" MUST include the output ('ct') from the PQ-KEM algorithm, encoded using base64url.
The JWE Encrypted Key MUST include the base64url-encoded encrypted CEK.
The 'enc' (Encryption Algorithm) header parameter MUST specify a content encryption algorithm from the JSON Web Signature and Encryption Algorithms registry, as defined in .
The recipient MUST base64url decode the ciphertext from "kem-ct". Subsequently, it is used to derive the key, through the process defined in . The derived key will then be used to decrypt the CEK.

Post-Quantum KEM in COSE This specification supports two uses of PQ-KEM in COSE, namely

PQ-KEM in a single recipient setup. This use case utilizes a one layer COSE structure.
PQ-KEM in a multiple recipient setup. This use case requires a two layer COSE structure.

Single Recipient / One Layer Structure With the one layer structure the information carried inside the COSE_recipient structure is embedded inside the COSE_Encrypt0. The CEK will be generated using the process explained in . Subsequently, the plaintext will be encrypted using the CEK. The resulting ciphertext is either included in the COSE_Encrypt0 or is detached. If a payload is transported separately then it is called "detached content". A nil CBOR object is placed in the location of the ciphertext. See Section 5 of for a description of detached payloads. The sender MUST set the 'alg' parameter in the protected header to indicate the use of the PQ-KEM algorithm. Although the use of the 'kid' parameter in COSE_Encrypt0 is discouraged by , this documents RECOMMENDS the use of the 'kid' parameter (or other parameters) to explicitly identify the recipient public key used by the sender. If the COSE_Encrypt0 contains the 'kid' then the recipient may use it to select the appropriate private key.

Multiple Recipients / Two Layer Structure With the two layer structure the PQ-KEM information is conveyed in the COSE_recipient structure, i.e. one COSE_recipient structure per recipient. In this approach the following layers are involved:

Layer 0 (corresponding to the COSE_Encrypt structure) contains the content (plaintext) encrypted with the CEK. This ciphertext may be detached, and if not detached, then it is included in the COSE_Encrypt structure.
Layer 1 (corresponding to a recipient structure) contains parameters needed for PQ-KEM to generate a shared secret used to encrypt the CEK. This layer conveys
the output ('ct') from the PQ KEM Encaps algorithm in the 'ek' header parameter (Section 7.2 of ) and encrypted CEK in the encCEK structure (Section 3.1.2 of ). The unprotected header MAY contain the kid parameter to identify the static recipient public key the sender has been using with PQ-KEM.

This two-layer structure is used to encrypt content that can also be shared with multiple parties at the expense of a single additional encryption operation. As stated above, the specification uses a CEK to encrypt the content at layer 0.

JOSE Ciphersuite Registration This specification registers a number of PQ-KEM algorithms for use with JOSE. All security levels of ML-KEM internally utilize SHA3-256, SHA3-512, SHAKE128, and SHAKE256. This internal usage influences the selection of the Concat KDF as described in this document. ML-KEM-512 MUST be used with a KDF capable of outputting a key with at least 128 bits of security and with a key wrapping algorithm with a key length of at least 128 bits. ML-KEM-768 MUST be used with a KDF capable of outputting a key with at least 192 bits of security and with a key wrapping algorithm with a key length of at least 192 bits. ML-KEM-1024 MUST be used with a KDF capable of outputting a key with at least 256 bits of security and with a key wrapping algorithm with a key length of at least 256 bits.

In Direct key agreement, the parameter "alg" MUST be specified, and its value MUST be one of the values specified in . (Note that future specifications MAY extend the list of algorithms.)

Direct Key Agreement: Algorithms.

In Key Agreement with Key Wrapping, the parameter "alg" MUST be specified, and its value MUST be one of the values specified in the table .

Key Agreement with Key Wrapping: Algorithms.

COSE Ciphersuite Registration maps the JOSE algorithm names to the COSE algorithm values (for the PQ-KEM ciphersuites defined by this document).

Mapping between JOSE and COSE PQ-KEM Ciphersuites.

Security Considerations 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. ML-KEM has such security properties.

IANA Considerations

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

Parameter Name: "kem-ct"
Parameter Description: PQC KEM ciphertext
Parameter Information Class: Public
Change Controller: IANA
Specification Document(s): [[TBD: This RFC]]
Algorithm Analysis Documents(s): TODO

The following entries are added to the "JSON Web Signature and Encryption Algorithms" registry:

Algorithm Name: MLKEM512
Algorithm Description: PQ-KEM that uses ML-KEM-512 PQ-KEM.
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IANA
Specification Document(s): [[TBD: This RFC]]
Algorithm Analysis Documents(s): TODO
Algorithm Name: MLKEM768
Algorithm Description: PQ-KEM that uses ML-KEM-768 PQ-KEM.
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IANA
Specification Document(s): [[TBD: This RFC]]
Algorithm Analysis Documents(s): TODO
Algorithm Name: MLKEM1024
Algorithm Description: PQ-KEM that uses ML-KEM-1024 PQ-KEM.
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IANA
Specification Document(s): [[TBD: This RFC]]
Algorithm Analysis Documents(s): TODO
Algorithm Name: MLKEM512+A128KW
Algorithm Description: PQ-KEM that uses ML-KEM-512 PQ-KEM and CEK wrapped with "A128KW".
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IANA
Specification Document(s): [[TBD: This RFC]]
Algorithm Analysis Documents(s): TODO
Algorithm Name: MLKEM768+A192KW
Algorithm Description: PQ-KEM that uses ML-KEM-768 and CEK wrapped with "A192KW".
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IANA
Specification Document(s): [[TBD: This RFC]]
Algorithm Analysis Documents(s): TODO
Algorithm Name: MLKEM1024+A256KW
Algorithm Description: PQ-KEM that uses ML-KEM-1024 and CEK wrapped with "A256KW".
Algorithm Usage Location(s): "alg"
JOSE Implementation Requirements: Optional
Change Controller: IANA
Specification Document(s): [[TBD: This RFC]]
Algorithm Analysis Documents(s): TODO

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

Name: MLKEM512
Value: TBD1
Description: PQ-KEM that uses ML-KEM-512 PQ-KEM.
Capabilities: [kty]
Change Controller: IANA
Reference: This document (TBD)
Recommended: No
Name: MLKEM768
Value: TBD2
Description: PQ-KEM that uses ML-KEM-768 PQ-KEM.
Capabilities: [kty]
Change Controller: IANA
Reference: This document (TBD)
Recommended: No
Name: MLKEM1024
Value: TBD3
Description: PQ-KEM that uses ML-KEM-1024 PQ-KEM.
Capabilities: [kty]
Change Controller: IANA
Reference: This document (TBD)
Recommended: No
Name: MLKEM512+A128KW
Value: TBD4
Description: PQ-KEM that uses ML-KEM-512 PQ-KEM and CEK wrapped with "A128KW".
Capabilities: [kty]
Change Controller: IANA
Reference: This document (TBD)
Recommended: No
Name: MLKEM768+192KW
Value: TBD5
Description: PQ-KEM that uses ML-KEM-768 and CEK wrapped with "A192KW".
Capabilities: [kty]
Change Controller: IANA
Reference: This document (TBD)
Recommended: No
Name: MLKEM1024+A256KW
Value: TBD6
Description: PQ-KEM that uses ML-KEM-1024 and CEK wrapped with "A256KW".
Capabilities: [kty]
Change Controller: IANA
Reference: This document (TBD)
Recommended: No

Acknowledgments Thanks to Ilari Liusvaara, Neil Madden and AJITOMI Daisuke for the discussion and comments.