]> BSI

Germany stavros.kousidis@bsi.bund.de

MTG AG

Germany falko.strenzke@mtg.de

Proton AG

Switzerland aron@wussler.it

sec Network Working Group Internet-Draft This document defines a post-quantum public-key algorithm extension for the OpenPGP protocol. Given the generally assumed threat of a cryptographically relevant quantum computer, this extension provides a basis for long-term secure OpenPGP signatures and ciphertexts. Specifically, it defines composite public-key encryption based on CRYSTALS-Kyber, composite public-key signatures based on CRYSTALS-Dilithium, both in combination with elliptic curve cryptography, and SPHINCS+ as a standalone public key signature scheme. About This Document Status information for this document may be found at . Discussion of this document takes place on the WG Working Group mailing list (), which is archived at . Subscribe at . Source for this draft and an issue tracker can be found at .

Introduction The OpenPGP protocol supports various traditional public-key algorithms based on the factoring or discrete logarithm problem. As the security of algorithms based on these mathematical problems is endangered by the advent of quantum computers, there is a need to extend OpenPGP by algorithms that remain secure in the presence of quantum computers. Such cryptographic algorithms are referred to as post-quantum cryptography. The algorithms defined in this extension were chosen for standardization by the National Institute of Standards and Technology (NIST) in mid 2022 as the result of the NIST Post-Quantum Cryptography Standardization process initiated in 2016 . Namely, these are CRYSTALS-Kyber as a Key Encapsulation Mechanism (KEM), a KEM being a modern building block for public-key encryption, and CRYSTALS-Dilithium as well as SPHINCS+ as signature schemes. For the two CRYSTALS-* schemes, this document follows the conservative strategy to deploy post-quantum in combination with traditional schemes such that the security is retained even if all schemes but one in the combination are broken. In contrast, the hashed-based signature scheme SPHINCS+ is considered to be sufficiently well understood with respect to its security assumptions in order to be used standalone. To this end, this document specifies the following new set: SPHINCS+ standalone and CRYSTALS-* as composite with ECC-based KEM and digital signature schemes. Here, the term "composite" indicates that any data structure or algorithm pertaining to the combination of the two components appears as single data structure or algorithm from the protocol perspective. The document specifies the conventions for interoperability between compliant OpenPGP implementations that make use of this extension and the newly defined algorithms or algorithm combinations.

Conventions used in this Document

Terminology for Multi-Algorithm Schemes The terminology in this document is oriented towards the definitions in . Specifically, the terms "multi-algorithm", "composite" and "non-composite" are used in correspondence with the definitions therein. The abbreviation "PQ" is used for post-quantum schemes. To denote the combination of post-quantum and traditional schemes, the abbreviation "PQ/T" is used. The short form "PQ(/T)" stands for PQ or PQ/T.

Post-Quantum Cryptography This section describes the individual post-quantum cryptographic schemes. All schemes listed here are believed to provide security in the presence of a cryptographically relevant quantum computer. However, the mathematical problems on which the two CRYSTALS-* schemes and SPHINCS+ are based, are fundamentally different, and accordingly the level of trust commonly placed in them as well as their performance characteristics vary. [Note to the reader: This specification refers to the latest NIST submission papers of each scheme as if it were a specification. This is a temporary solution that is owed to the fact that currently no other specification is available. The goal is to provide a sufficiently precise specification of the algorithms already at the draft stage of this specification, so that it is possible for implementers to create interoperable implementations. As soon as standards by NIST or the IETF for the PQC schemes employed in this specification are available, these will replace the references to the NIST submission papers. Furthermore, we want to point out that, depending on possible changes to the schemes standardized by NIST, this specification may be updated substantially as soon as corresponding information becomes available.]

CRYSTALS-Kyber CRYSTALS-Kyber is based on the hardness of solving the learning-with-errors problem in module lattices (MLWE). The scheme is believed to provide security against cryptanalytic attacks by classical as well as quantum computers. This specification defines CRYSTALS-Kyber only in composite combination with ECC-based encryption schemes in order to provide a pre-quantum security fallback.

CRYSTALS-Dilithium CRYSTALS-Dilithium, defined in , is a signature scheme that, like CRYSTALS-Kyber, is based on the hardness of solving lattice problems in module lattices. Accordingly, this specification only defines CRYSTALS-Dilithium in composite combination with ECC-based signature schemes.

SPHINCS+ SPHINCS+ is a stateless hash-based signature scheme. Its security relies on the hardness of finding preimages for cryptographic hash functions. This feature is generally considered to be a high security guarantee. Therefore, this specification defines SPHINCS+ as a standalone signature scheme. In deployments the performance characteristics of SPHINCS+ should be taken into account. We refer to for a discussion of the performance characteristics of this scheme.

Elliptic Curve Cryptography The ECC-based encryption is defined here as a KEM. This is in contrast to where the ECC-based encryption is defined as a public-key encryption scheme. All elliptic curves for the use in the composite combinations are taken from . However, as explained in the following, in the case of Curve25519 encoding changes are applied to the new composite schemes.

Curve25519 and Curve448 Curve25519 and Curve448 are defined in for use in a Diffie-Hellman key agreement scheme and defined in for use in a digital signature scheme. For Curve25519 this specification adapts the encoding of objects as defined in in contrast to .

Generic Prime Curves For interoperability this extension offers CRYSTALS-* in composite combinations with the NIST curves P-256, P-384 defined in and the Brainpool curves brainpoolP256r1, brainpoolP384r1 defined in .

Standalone and Multi-Algorithm Schemes This section provides a categorization of the new algorithms and their combinations.

Standalone and Composite Multi-Algorithm Schemes This specification introduces new cryptographic schemes, which can be categorized as follows:

• PQ/T multi-algorithm public-key encryption, namely a composite combination of CRYSTALS-Kyber with an ECC-based KEM,
• PQ/T multi-algorithm digital signature, namely composite combinations of CRYSTALS-Dilithium with ECC-based signature schemes,
• PQ digital signature, namely SPHINCS+ as a standalone cryptographic algorithm.

For each of the composite schemes, this specifications mandates that the recipient has to successfully perform the cryptographic algorithms for each of the component schemes used in a cryptrographic message, in order for the message to be deciphered and considered as valid. This means that all component signatures must be verified successfully in order to achieve a successful verification of the composite signature. In the case of the composite public-key decryption, each of the component KEM decapsulation operations must succeed.

Non-Composite Algorithm Combinations As the OpenPGP protocol allows for multiple signatures to be applied to a single message, it is also possible to realize non-composite combinations of signatures. Furthermore, multiple OpenPGP signatures may be combined on the application layer. These latter two cases realize non-composite combinations of signatures. specifies how implementations should handle the verification of such combinations of signatures. Furthermore, the OpenPGP protocol also allows for parallel encryption to different keys held by the same recipient. Accordingly, if the sender makes use of this feature and sends an encrypted message with multiple PKESK packages for different encryption keys held by the same recipient, a non-composite multi-algorithm public-key encryption is realized where the recipient has to decrypt only one of the PKESK packages in order to decrypt the message. See for restrictions on parallel encryption mandated by this specification.

Preliminaries This section provides some preliminaries for the definitions in the subsequent sections.

Elliptic curves

SEC1 EC Point Wire Format Elliptic curve points of the generic prime curves are encoded using the SEC1 (uncompressed) format as the following octet string: where X and Y are coordinates of the elliptic curve point P = (X, Y), and each coordinate is encoded in the big-endian format and zero-padded to the adjusted underlying field size. The adjusted underlying field size is the underlying field size rounded up to the nearest 8-bit boundary, as noted in the "Field size" column in , , or . This encoding is compatible with the definition given in .

Measures to Ensure Secure Implementations The following paragraphs describe measures that ensure secure implementations according to existing best practices and standards defining the operations of Elliptic Curve Cryptography. Even though the zero point, also called the point at infinity, may occur as a result of arithmetic operations on points of an elliptic curve, it MUST NOT appear in any ECC data structure defined in this document. Furthermore, when performing the explicitly listed operations in , or it is REQUIRED to follow the specification and security advisory mandated from the relative elliptic curve specification.

Supported Public Key Algorithms This section specifies the composite Kyber + ECC and Dilithium + ECC schemes as well as the standalone SPHINCS+ signature scheme. The composite schemes are fully specified via their algorithm ID. The SPHINCS+ signature schemes are fully specified by their algorithm ID and an additional parameter ID.

Algorithm Specifications For encryption, the following composite KEM schemes are specified: KEM algorithm specifications

ID	Algorithm	Requirement	Definition
29	Kyber768 + X25519	MUST
30	Kyber1024 + X448	SHOULD
31	Kyber768 + ECDH-NIST-P-256	MAY
32	Kyber1024 + ECDH-NIST-P-384	MAY
33	Kyber768 + ECDH-brainpoolP256r1	MAY
34	Kyber1024 + ECDH-brainpoolP384r1	MAY

For signatures, the following (composite) signature schemes are specified: Signature algorithm specifications

ID	Algorithm	Requirement	Definition
35	Dilithium3 + Ed25519	MUST
36	Dilithium5 + Ed448	SHOULD
37	Dilithium3 + ECDSA-NIST-P-256	MAY
38	Dilithium5 + ECDSA-NIST-P-384	MAY
39	Dilithium3 + ECDSA-brainpoolP256r1	MAY
40	Dilithium5 + ECDSA-brainpoolP384r1	MAY
41	SPHINCS+-simple-SHA2	SHOULD
42	SPHINCS+-simple-SHAKE	MAY

Parameter Specification

SPHINCS+-simple-SHA2 For the SPHINCS+-simple-SHA2 signature algorithm from , the following parameters are specified: SPHINCS+-simple-SHA2 security parameters

Parameter ID	Parameter
1	SPHINCS+-simple-SHA2-128s
2	SPHINCS+-simple-SHA2-128f
3	SPHINCS+-simple-SHA2-192s
4	SPHINCS+-simple-SHA2-192f
5	SPHINCS+-simple-SHA2-256s
6	SPHINCS+-simple-SHA2-256f

All security parameters inherit the requirement of SPHINCS+-simple-SHA2 from . That is, implementations SHOULD implement the parameters specified in . The values 0x00 and 0xFF are reserved for future extensions.

SPHINCS+-simple-SHAKE For the SPHINCS+-simple-SHAKE signature algorithm from , the following parameters are specified: SPHINCS+-simple-SHAKE security parameters

Parameter ID	Parameter
1	SPHINCS+-simple-SHAKE-128s
2	SPHINCS+-simple-SHAKE-128f
3	SPHINCS+-simple-SHAKE-192s
4	SPHINCS+-simple-SHAKE-192f
5	SPHINCS+-simple-SHAKE-256s
6	SPHINCS+-simple-SHAKE-256f

All security parameters inherit the requirement of SPHINCS+-simple-SHAKE from . That is, implementations MAY implement the parameters specified in . The values 0x00 and 0xFF are reserved for future extensions.

Algorithm Combinations

Composite KEMs Kyber + ECC public-key encryption is meant to involve both the Kyber KEM and an ECC-based KEM in an a priori non-separable manner. This is achieved via KEM combination, i.e. both key encapsulations/decapsulations are performed in parallel, and the resulting key shares are fed into a key combiner to produce a single shared secret for message encryption.

Parallel Public-Key Encryption As explained in , the OpenPGP protocol inherently supports parallel encryption to different keys of the same recipient. Implementations MUST NOT encrypt a message to a purely traditional public-key encryption key of a recipient if it is encrypted to a PQ/T key of the same recipient.

Composite Signatures Dilithium + ECC signatures are meant to contain both the Dilithium and the ECC signature data, and an implementation MUST validate both algorithms to state that a signature is valid.

Multiple Signatures The OpenPGP message format allows multiple signatures of a message, i.e. the attachment of multiple signature packets. An implementation MAY sign a message with a traditional key and a PQ(/T) key from the same sender. This ensures backwards compatibility due to Section 5.2.5, since a legacy implementation without PQ(/T) support can fall back on the traditional signature. Newer implementations with PQ(/T) support MAY ignore the traditional signature(s) during validation. Implementations SHOULD consider the message correctly signed if at least one of the non-ignored signatures validates successfully. [Note to the reader: The last requirement, that one valid signature is sufficient to identify a message as correctly signed, is an interpretation of Section 5.2.5.]

Composite KEM schemes

Building Blocks

ECC-Based KEMs In this section we define the encryption, decryption, and data formats for the ECDH component of the composite algorithms. , , and describe the ECC-KEM parameters and artifact lengths. The artefacts in follow the encodings described in . Montgomery curves parameters and artifact lengths

	X25519	X448
Algorithm ID reference	29	30
Field size	32 octets	56 octets
ECC-KEM	x25519Kem ()	x448Kem ()
ECDH public key	32 octets	56 octets
ECDH secret key	32 octets	56 octets
ECDH ephemeral	32 octets	56 octets
ECDH share	32 octets	56 octets
Key share	32 octets	64 octets
Hash	SHA3-256	SHA3-512

NIST curves parameters and artifact lengths

	NIST P-256	NIST P-384
Algorithm ID reference	31	32
Field size	32 octets	48 octets
ECC-KEM	ecdhKem ()	ecdhKem ()
ECDH public key	65 octets of SEC1-encoded public point	97 octets of SEC1-encoded public point
ECDH secret key	32 octets big-endian encoded secret scalar	48 octets big-endian encoded secret scalar
ECDH ephemeral	65 octets of SEC1-encoded ephemeral point	97 octets of SEC1-encoded ephemeral point
ECDH share	65 octets of SEC1-encoded shared point	97 octets of SEC1-encoded shared point
Key share	32 octets	64 octets
Hash	SHA3-256	SHA3-512

Brainpool curves parameters and artifact lengths

	brainpoolP256r1	brainpoolP384r1
Algorithm ID reference	33	34
Field size	32 octets	48 octets
ECC-KEM	ecdhKem ()	ecdhKem ()
ECDH public key	65 octets of SEC1-encoded public point	97 octets of SEC1-encoded public point
ECDH secret key	32 octets big-endian encoded secret scalar	48 octets big-endian encoded secret scalar
ECDH ephemeral	65 octets of SEC1-encoded ephemeral point	97 octets of SEC1-encoded ephemeral point
ECDH share	65 octets of SEC1-encoded shared point	97 octets of SEC1-encoded shared point
Key share	32 octets	64 octets
Hash	SHA3-256	SHA3-512

The SEC1 format for point encoding is defined in . The various procedures to perform the operations of an ECC-based KEM are defined in the following subsections. Specifically, each of these subsections defines the instances of the following operations: and The placeholder eccKem has to be replaced with the specific ECC-KEM from the row "ECC-KEM" of , , and .

X25519-KEM The encapsulation and decapsulation operations of x25519kem are described using the function X25519() and encodings defined in . The eccPrivateKey is denoted as r, the eccPublicKey as R, they are subject to the equation R = X25519(r, U(P)). Here, U(P) denotes the u-coordinate of the base point of Curve25519. The operation x25519Kem.encap() is defined as follows:

1. Generate an ephemeral key pair {v, V} via V = X25519(v,U(P))
2. Compute the shared coordinate X = X25519(v, R) where R is the public key eccPublicKey
3. Set the output eccCipherText to V
4. Set the output eccKeyShare to SHA3-256(X || eccCipherText)

The operation x25519Kem.decap() is defined as follows:

1. Compute the shared coordinate X = X25519(r, V), where r is the eccPrivateKey and V is the eccCipherText
2. Set the output eccKeyShare to SHA3-256(X || eccCipherText)

X448-KEM The encapsulation and decapsulation operations of x448kem are described using the function X448() and encodings defined in . The eccPrivateKey is denoted as r, the eccPublicKey as R, they are subject to the equation R = X25519(r, U(P)). Here, U(P) denotes the u-coordinate of the base point of Curve448. The operation x448.encap() is defined as follows:

1. Generate an ephemeral key pair {v, V} via V = X448(v,U(P))
2. Compute the shared coordinate X = X448(v, R) where R is the public key eccPublicKey
3. Set the output eccCipherText to V
4. Set the output eccKeyShare to SHA3-512(X || eccCipherText)

The operation x448Kem.decap() is defined as follows:

1. Compute the shared coordinate X = X448(r, V), where r is the eccPrivateKey and V is the eccCipherText
2. Set the output eccKeyShare to SHA3-512(X || eccCipherText)

ECDH-KEM The operation ecdhKem.encap() is defined as follows:

1. Generate an ephemeral key pair {v, V=vG} as defined in or
2. Compute the shared point S = vR, where R is the component public key eccPublicKey, according to or
3. Extract the X coordinate from the SEC1 encoded point S = 04 || X || Y as defined in section
4. Set the output eccCipherText to the SEC1 encoding of V
5. Set the output eccKeyShare to Hash(X || eccCipherText), with Hash chosen according to or

The operation ecdhKem.decap() is defined as follows:

1. Compute the shared Point S as rV, where r is the eccPrivateKey and V is the eccCipherText, according to or
2. Extract the X coordinate from the SEC1 encoded point S = 04 || X || Y as defined in section
3. Set the output eccKeyShare to Hash(X || eccCipherText), with Hash chosen according to or

Kyber-KEM Kyber-KEM features the following operations: and The above are the operations Kyber.CCAKEM.Enc() and Kyber.CCAKEM.Dec() defined in . Kyber-KEM has the parameterization with the corresponding artifact lengths in octets as given in . All artifacts are encoded as defined in . Kyber-KEM parameters artifact lengths in octets

Algorithm ID reference	Kyber-KEM	Public key	Secret key	Ciphertext	Key share
29, 31, 33	kyberKem768	1184	2400	1088	32
30, 32, 34	kyberKem1024	1568	3186	1568	32

The placeholder kyberKem has to be replaced with the specific Kyber-KEM from the column "Kyber-KEM" of . The procedure to perform kyberKem.encap() is as follows:

1. Extract the component public key kyberPublicKey that is part of the recipient's composite public key
2. Invoke (kyberCipherText, keyShare) <- kyberKem.encap(kyberPublicKey)
3. Set kyberCipherText as the Kyber ciphertext
4. Set keyShare as the Kyber symmetric key share

The procedure to perform kyberKem.decap() is as follows:

1. Invoke keyShare <- kyberKem.decap(kyberCipherText, kyberPrivateKey)
2. Set keyShare as the Kyber symmetric key

Composite Encryption Schemes with Kyber specifies the following Kyber + ECC composite public-key encryption schemes: Kyber-ECC-composite Schemes

Algorithm ID reference	Kyber-KEM	ECC-KEM	ECDH-KEM curve
29	kyberKem768	x25519Kem	X25519
30	kyberKem1024	x448Kem	X448
31	kyberKem768	ecdhKem	NIST P-256
32	kyberKem1024	ecdhKem	NIST P-384
33	kyberKem768	ecdhKem	brainpoolP256r1
34	kyberKem1024	ecdhKem	brainpoolP384r1

The Kyber + ECC composite public-key encryption schemes are built according to the following principal design:

• The Kyber-KEM encapsulation algorithm is invoked to create a Kyber ciphertext together with a Kyber symmetric key share.
• The encapsulation algorithm of an ECC-based KEM, namely one out of X25519-KEM, X448-KEM, or ECDH-KEM is invoked to create an ECC ciphertext together with an ECC symmetric key share.
• A Key-Encryption-Key (KEK) is computed as the output of a key combiner that receives as input both of the above created symmetric key shares and the protocol binding information.
• The session key for content encryption is then wrapped as described in using AES-256 as algorithm and the KEK as key.
• The v6 PKESK package's algorithm specific parts are made up of the Kyber ciphertext, the ECC ciphertext, and the wrapped session key

Fixed information For the composite KEM schemes defined in the following procedure, justified in , MUST be used to derive a string to use as binding between the KEK and the communication parties. SHA3-256 MUST be used to hash the publicKey of the recipient.

Key combiner For the composite KEM schemes defined in the following procedure MUST be used to compute the KEK that wraps a session key. The construction is a one-step key derivation function compliant to Section 4, based on KMAC256 . It is given by the following algorithm. Note that the values eccKeyShare defined in and kyberKeyShare defined in already use the relative ciphertext in the derivation. The ciphertext is by design included again in the key combiner to provide a robust security proof. The value of domSeparation is the UTF-8 encoding of the string "OpenPGPCompositeKeyDerivationFunction" and MUST be the following octet sequence: The value of counter MUST be set to the following octet sequence: The value of fixedInfo MUST be set according to . The value of customizationString is the UTF-8 encoding of the string "KDF" and MUST be set to the following octet sequence:

Key generation procedure The implementation MUST independently generate the Kyber and the ECC component keys. Kyber key generation follows the specification and the artifacts are encoded as fixed-length octet strings. For ECC this is done following the relative specification in , , or , and encoding the outputs as fixed-length octet strings in the format specified in table , , or .

Encryption procedure The procedure to perform public-key encryption with a Kyber + ECC composite scheme is as follows:

1. Take the recipient's authenticated public-key packet pkComposite and sessionKey as input
2. Parse the algorithm ID from pkComposite
3. Extract the eccPublicKey and kyberPublicKey component from the algorithm specific data encoded in pkComposite with the format specified in .
4. Instantiate the ECC-KEM eccKem.encap() and the Kyber-KEM kyberKem.encap() depending on the algorithm ID according to
5. Compute (eccCipherText, eccKeyShare) := eccKem.encap(eccPublicKey)
6. Compute (kyberCipherText, kyberKeyShare) := kyberKem.encap(kyberPublicKey)
7. Compute fixedInfo as specified in
8. Compute KEK := multiKeyCombine(eccKeyShare, eccCipherText, kyberKeyShare, kyberCipherText, fixedInfo, oBits=256) as defined in
9. Compute C := AESKeyWrap(KEK, sessionKey) with AES-256 as per that includes a 64 bit integrity check
10. Output eccCipherText || kyberCipherText || len(C) || C as specified in

Decryption procedure The procedure to perform public-key decryption with a Kyber + ECC composite scheme is as follows:

1. Take the matching PKESK and own secret key packet as input
2. From the PKESK extract the algorithm ID and the encryptedKey
3. Check that the own and the extracted algorithm ID match
4. Parse the eccSecretKey and kyberSecretKey from the algorithm specific data of the own secret key encoded in the format specified in
5. Instantiate the ECC-KEM eccKem.decap() and the Kyber-KEM kyberKem.decap() depending on the algorithm ID according to
6. Parse eccCipherText, kyberCipherText, and C from encryptedKey encoded as eccCipherText || kyberCipherText || len(C) || C as specified in
7. Compute (eccKeyShare) := eccKem.decap(eccCipherText, eccPrivateKey)
8. Compute (kyberKeyShare) := kyberKem.decap(kyberCipherText, kyberPrivateKey)
9. Compute fixedInfo as specified in
10. Compute KEK := multiKeyCombine(eccKeyShare, eccCipherText, kyberKeyShare, kyberCipherText, fixedInfo, oBits=256) as defined in
11. Compute sessionKey := AESKeyUnwrap(KEK, C) with AES-256 as per , aborting if the 64 bit integrity check fails
12. Output sessionKey

Packet specifications

Public-Key Encrypted Session Key Packets (Tag 1) The composite Kyber algorithms MUST be used only with v6 PKESK, as defined in Section 5.1.2. The algorithm-specific v6 PKESK parameters consists of:

• A fixed-length octet string representing an ECC ephemeral public key in the format associated with the curve as specified in .
• A fixed-length octet string of the Kyber ciphertext, whose length depends on the algorithm ID as specified in .
• A variable-length field containing the symmetric key:
  • A one-octet size of the following field;
  • Octet string of the wrapped symmetric key as described in .

Key Material Packets The algorithm-specific public key is this series of values:

• A fixed-length octet string representing an EC point public key, in the point format associated with the curve specified in .
• A fixed-length octet string containing the Kyber public key, whose length depends on the algorithm ID as specified in .

The algorithm-specific secret key is these two values:

• A fixed-length octet string of the encoded secret scalar, whose encoding and length depend on the algorithm ID as specified in .
• A fixed-length octet string containing the Kyber secret key, whose length depends on the algorithm ID as specified in .

Composite Signature Schemes

Building blocks

EdDSA-Based signatures To sign and verify with EdDSA the following operations are defined: and The public and private keys, as well as the signature MUST be encoded according to as fixed-length octet strings. The following table describes the EdDSA parameters and artifact lengths: EdDSA parameters and artifact lengths in octets

Algorithm ID reference	Curve	Field size	Public key	Secret key	Signature
35	Ed25519	32	32	32	64
36	Ed448	57	57	57	114

ECDSA-Based signatures To sign and verify with ECDSA the following operations are defined: and The public keys MUST be encoded in SEC1 format as defined in section . The secret key, as well as both values R and S of the signature MUST each be encoded as a big-endian integer in a fixed-length octet string of the specified size. The following table describes the ECDSA parameters and artifact lengths: ECDSA parameters and artifact lengths in octets

Algorithm ID reference	Curve	Field size	Public key	Secret key	Signature value R	Signature value S
37	NIST P-256	32	65	32	32	32
38	NIST P-384	48	97	48	48	48
39	brainpoolP256r1	32	65	32	32	32
40	brainpoolP384r1	48	97	48	48	48

Dilithium signatures The procedure for Dilithium signature generation is the function Sign(sk, M) given in Figure 4 in , where sk is the Dilithium private key and M is the data to be signed. OpenPGP does not use the optional randomized signing given as a variant in the definition of this function, i.e. rho' := H(K || mu) is used. The signing function returns the Dilithium signature. That is, to sign with Dilithium the following operation is defined: The procedure for Dilithium signature verification is the function Verify(pk, M, sigma) given in Figure 4 in , where pk is the Dilithium public key, M is the data to be signed and sigma is the Dilithium signature. That is, to verify with Dilithium the following operation is defined: Dilithium has the parameterization with the corresponding artifact lengths in octets as given in . All artifacts are encoded as defined in . Dilithium parameters and artifact lengths in octets

Algorithm ID reference	Dilithium instance	Public key	Secret key	Signature value
35, 37, 39	Dilithium3	1952	4000	3293
36, 38, 40	Dilithium5	2592	4864	4595

Composite Signature Schemes with Dilithium

Binding hashes Composite Dilithium + ECC signatures MUST use SHA3-256 (hash algorithm ID 12) or SHA3-512 (hash algorithm ID 14) as hashing algorithm. Signatures using other hash algorithms MUST be considered invalid. An implementation MUST support SHA3-256 and SHOULD support SHA3-512, in order to support the hash binding with Dilithium + ECC signatures.

Key generation procedure The implementation MUST independently generate the Dilithium and the ECC component keys. Dilithium key generation follows the specification in and the artifacts are encoded as fixed-length octet strings as defined in . For ECC this is done following the relative specification in , , or , and encoding the artifacts as specified in or as fixed-length octet strings.

Signature Generation To sign a message M with Dilithium + EdDSA the following sequence of operations has to be performed:

1. Generate dataDigest according to Section 5.2.4
2. Create the EdDSA signature over dataDigest with eddsa.sign() from
3. Create the Dilithium signature over dataDigest with dilithium.sign() from
4. Encode the EdDSA and Dilithium signatures according to the packet structure given in .

To sign a message M with Dilithium + ECDSA the following sequence of operations has to be performed:

1. Generate dataDigest according to Section 5.2.4
2. Create the ECDSA signature over dataDigest with ecdsa.sign() from
3. Create the Dilithium signature over dataDigest with dilithium.sign() from
4. Encode the ECDSA and Dilithium signatures according to the packet structure given in .

Signature Verification To verify a Dilithium + EdDSA signature the following sequence of operations has to be performed:

1. Verify the EdDSA signature with eddsa.verify() from
2. Verify the Dilithium signature with dilithium.verify() from

To verify a Dilithium + ECDSA signature the following sequence of operations has to be performed:

1. Verify the ECDSA signature with ecdsa.verify() from
2. Verify the Dilithium signature with dilithium.verify() from

As specified in an implementation MUST validate both signatures, i.e. EdDSA/ECDSA and Dilithium, to state that a composite Dilithium + ECC signature is valid.

Packet Specifications

Signature Packet (Tag 2) The composite Dilithium + ECC schemes MUST be used only with v6 signatures, as defined in Section 5.2.3. The algorithm-specific v6 signature parameters for Dilithium + EdDSA signatures consists of:

• A fixed-length octet string representing the EdDSA signature, whose length depends on the algorithm ID as specified in .
• A fixed-length octet string of the Dilithium signature value, whose length depends on the algorithm ID as specified in .

The algorithm-specific v6 signature parameters for Dilithium + ECDSA signatures consists of:

• A fixed-length octet string of the big-endian encoded ECDSA value R, whose length depends on the algorithm ID as specified in .
• A fixed-length octet string of the big-endian encoded ECDSA value S, whose length depends on the algorithm ID as specified in .
• A fixed-length octet string of the Dilithium signature value, whose length depends on the algorithm ID as specified in .

Key Material Packets The composite Dilithium + ECC schemes MUST be used only with v6 keys, as defined in . The algorithm-specific public key for Dilithium + EdDSA keys is this series of values:

• A fixed-length octet string representing the EdDSA public key, whose length depends on the algorithm ID as specified in .
• A fixed-length octet string containing the Dilithium public key, whose length depends on the algorithm ID as specified in .

The algorithm-specific private key for Dilithium + EdDSA keys is this series of values:

• A fixed-length octet string representing the EdDSA secret key, whose length depends on the algorithm ID as specified in .
• A fixed-length octet string containing the Dilithium secret key, whose length depends on the algorithm ID as specified in .

The algorithm-specific public key for Dilithium + ECDSA keys is this series of values:

• A fixed-length octet string representing the ECDSA public key in SEC1 format, as specified in section and with length specified in .
• A fixed-length octet string containing the Dilithium public key, whose length depends on the algorithm ID as specified in .

The algorithm-specific private key for Dilithium + ECDSA keys is this series of values:

• A fixed-length octet string representing the ECDSA secret key as a big-endian encoded integer, whose length depends on the algorithm used as specified in .
• A fixed-length octet string containing the Dilithium secret key, whose length depends on the algorithm ID as specified in .

SPHINCS+

The SPHINCS+ Algorithms The following table describes the SPHINCS+ parameters and artifact lengths: SPHINCS+ parameters and artifact lengths in octets. The values equally apply to the parameter IDs of SPHINCS+-simple-SHA2 and SPHINCS+-simple-SHAKE.

Parameter ID reference	Parameter name suffix	SPHINCS+ public key	SPHINCS+ secret key	SPHINCS+ signature
1	128s	32	64	7856
2	128f	32	64	17088
3	192s	48	96	16224
4	192f	48	96	35664
5	256s	64	128	29792
6	256f	64	128	49856

Binding hashes SPHINCS+ signature packets MUST use the associated hash as specified in . Signature packets using other hashes MUST be considered invalid. Binding between SPHINCS+ and signature hashes

Algorithm ID reference	Parameter ID reference	Hash function	Hash function ID reference
41	1, 2	SHA-256	8
41	3, 4, 5, 6	SHA-512	10
42	1, 2	SHA3-256	12
42	3, 4, 5, 6	SHA3-512	14

An implementation supporting a specific SPHINCS+ algorithm and parameter MUST also support the matching hash algorithm.

Key generation The SPHINCS+ key generation is performed according to the function spx_keygen() specified in , Sec. 6.2 as Alg. 19. The private and public key are encoded as defined in .

Signature Generation The procedure for SPHINCS+ signature generation is the function spx_sign(M, SK) specified in , Sec. 6.4 as Alg. 20. Here, M is the dataDigest generated according to Section 5.2.4 and SK is the SPHINCS+ private key. The global variable RANDOMIZE specified in Alg. 20 is to be considered as not set, i.e. the variable opt shall be initialized with PK.seed. See also . An implementation MUST set the Parameter ID in the signature equal to the issuing private key Parameter ID.

Signature Verification The procedure for SPHINCS+ signature verification is the function spx_verify(M, SIG, PK) specified in , Sec. 6.5 as Alg. 21. Here, M is the dataDigest generated according to Section 5.2.4, SIG is the signature, and PK is the SPHINCS+ public key. An implementation MUST check that the Parameter ID in the signature and in the key match when verifying.

Packet specifications

Signature Packet (Tag 2) The SPHINCS+ algorithms MUST be used only with v6 signatures, as defined in Section 5.2.3. The algorithm-specific v6 Signature parameters consists of:

• A one-octet value specifying the SPHINCS+ parameter ID defined in and . The values 0x00 and 0xFF are reserved for future extensions.
• A fixed-length octet string of the SPHINCS+ signature value, whose length depends on the parameter ID in the format specified in .

Key Material Packets The SPHINCS+ algorithms MUST be used only with v6 keys, as defined in . The algorithm-specific public key is this series of values:

• A one-octet value specifying the SPHINCS+ parameter ID defined in and . The values 0x00 and 0xFF are reserved for future extensions.
• A fixed-length octet string containing the SPHINCS+ public key, whose length depends on the parameter ID as specified in .

The algorithm-specific private key is this value:

• A fixed-length octet string containing the SPHINCS+ secret key, whose length depends on the parameter ID as specified in .

Migration Considerations The post-quantum KEM algorithms defined in and the signature algorithms defined in are a set of new public key algorithms that extend the algorithm selection of . During the transition period, the post-quantum algorithms will not be supported by all clients. Therefore various migration considerations must be taken into account, in particular backwards compatibility to existing implementations that have not yet been updated to support the post-quantum algorithms.

Key preference Implementations SHOULD prefer PQ(/T) keys when multiple options are available. For instance, if encrypting for a recipient for which both a valid PQ/T and a valid ECC certificate are available, the implementation SHOULD choose the PQ/T certificate. In case a certificate has both a PQ/T and an ECC encryption-capable valid subkey, the PQ/T subkey SHOULD be preferred. An implementation MAY sign with both a PQ(/T) and an ECC key using multiple signatures over the same data as described in . Signing only with PQ(/T) key material is not backwards compatible. Note that the confidentiality of a message is not post-quantum secure when encrypting to multiple recipients if at least one recipient does not support PQ/T encryption schemes. An implementation SHOULD NOT abort the encryption process in this case to allow for a smooth transition to post-quantum cryptography.

Key generation strategies It is REQUIRED to generate fresh secrets when generating PQ(/T) keys. Reusing key material from existing ECC keys in PQ(/T) keys does not provide backwards compatibility, and the fingerprint will differ. An OpenPGP (v6) certificate is composed of a certification-capable primary key and one or more subkeys for signature, encryption, and authentication. Two migration strategies are recommended:

1. Generate two independent certificates, one for PQ(/T)-capable implementations, and one for legacy implementations. Implementations not understanding PQ(/T) certificates can use the legacy certificate, while PQ(/T)-capable implementations will prefer the newer certificate. This allows having an older v4 or v6 ECC certificate for compatibility and a v6 PQ(/T) certificate, at a greater complexity in key distribution.
2. Attach PQ(/T) encryption and signature subkeys to an existing v6 ECC certificate. Implementations understanding PQ(/T) will be able to parse and use the subkeys, while PQ(/T)-incapable implementations can gracefully ignore them. This simplifies key distribution, as only one certificate needs to be communicated and verified, but leaves the primary key vulnerable to quantum computer attacks.

Security Considerations

Hashing in ECC-KEM Our construction of the ECC-KEMs, in particular the final hashing step in encapsulation and decapsulation that produces the eccKeyShare, is standard and known as hashed ElGamal key encapsulation, a hashed variant of ElGamal encryption. It ensures IND-CCA2 security in the random oracle model under some Diffie-Hellman intractability assumptions .

Key combiner For the key combination in this specification limits itself to the use of KMAC. The sponge construction used by KMAC was proven to be indifferentiable from a random oracle . This means, that in contrast to SHA2, which uses a Merkle-Damgard construction, no HMAC-based construction is required for key combination. Except for a domain separation it is sufficient to simply process the concatenation of any number of key shares when using a sponge-based construction like KMAC. The construction using KMAC ensures a standardized domain separation. In this case, the processed message is then the concatenation of any number of key shares. More precisely, for a given capacity c the indifferentiability proof shows that assuming there are no weaknesses found in the Keccak permutation, an attacker has to make an expected number of 2^(c/2) calls to the permutation to tell KMAC from a random oracle. For a random oracle, a difference in only a single bit gives an unrelated, uniformly random output. Hence, to be able to distinguish a key K, derived from shared keys K1 and K2 (and ciphertexts C1 and C2) as from a random bit string, an adversary has to know (or correctly guess) both key shares K1 and K2, entirely. The proposed construction in preserves 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. Indeed, the above stated indifferentiability from a random oracle qualifies Keccak as a split-key pseudorandom function as defined in . That is, Keccak behaves like a random function if at least one input shared secret is picked uniformly at random. Our construction can thus be seen as an instantiation of the IND-CCA2 preserving Example 3 in Figure 1 of , up to some reordering of input shared secrets and ciphertexts. In the random oracle setting, the reordering does not influence the arguments in .

Domain separation and binding The domSeparation information defined in provides the domain separation for the key combiner construction. This ensures that the input keying material is used to generate a KEK for a specific purpose or context. The fixedInfo defined in binds the derived KEK to the chosen algorithm and communication parties. The algorithm ID identifies univocally the algorithm, the parameters for its instantiation, and the length of all artifacts, including the derived key. The hash of the recipient's public key identifies the subkey used to encrypt the message, binding the KEK to both the Kyber and the ECC key. Given that both algorithms allow a degree of ciphertext malleability, this prevents transformations onto the ciphertext without the final recipient's knowledge. This is in line with the Recommendation for ECC in section 5.5 of . Other fields included in the recommendation are not relevant for the OpenPGP protocol, since the sender is not required to have a key on their own, there are no pre-shared secrets, and all the other parameters are univocally defined by the algorithm ID.

SPHINCS+ The original specification of SPHINCS+ prescribes an optional randomized hashing. This is not used in this specification, as OpenPGP v6 signatures already provide a salted hash of the appropriate size.

Binding hashes in signatures with signature algorithms In order not to extend the attack surface, we bind the hash algorithm used for message digestion to the hash algorithm used internally by the signature algorithm. Dilithium internally uses a SHAKE256 digest, therefore we require SHA3 in the Dilithium + ECC signature packet. In the case of SPHINCS+ the internal hash algorithm varies based on the algorithm and parameter ID.

Additional considerations

Performance Considerations for SPHINCS+ This specification introduces both Dilithium + ECC as well as SPHINCS+ as PQ(/T) signature schemes. Generally, it can be said that Dilithium + ECC provides a performance in terms of execution time and space requirements that is close to that of traditional ECC signature schemes. Implementers may want to offer SPHINCS+ for applications where a higher degree of trust in the signature scheme is required. However, SPHINCS+ has performance characteristics in terms of execution time of the signature generation as well as space requirements for the signature that can be, depending on the parameter choice, far greater than those of traditional or Dilithium + ECC signature schemes. Pertaining to the execution time, the particularly costly operation in SPHINCS+ is the signature generation. In order to achieve short signature generation times, one of the parameter sets with the name ending in the letter "f" for "fast" should be chosen. This comes at the expense of a larger signature size. In order to minimize the space requirements of a SPHINCS+ signature, a parameter set ending in "s" for "small" should be chosen. This comes at the expense of a larger signature generation time.

IANA Considerations IANA will add the following registries to the Pretty Good Privacy (PGP) registry group at https://www.iana.org/assignments/pgp-parameters:

• Registry name: SPHINCS+-simple-SHA2 parameters Registration procedure: SPECIFICATION REQUIRED Values defined in this document, .
• Registry name: SPHINCS+-simple-SHAKE parameters Registration procedure: SPECIFICATION REQUIRED Values defined in this document, .

Furthermore IANA will add the algorithm IDs defined in and to the registry Public Key Algorithms.

Contributors Stephan Ehlen (BSI)
Carl-Daniel Hailfinger (BSI)
Andreas Huelsing (TU Eindhoven)
Johannes Roth (MTG AG)

References Normative References This memo specifies two elliptic curves over prime fields that offer a high level of practical security in cryptographic applications, including Transport Layer Security (TLS). These curves are intended to operate at the ~128-bit and ~224-bit security level, respectively, and are generated deterministically based on a list of required properties. This document describes elliptic curve signature scheme Edwards-curve Digital Signature Algorithm (EdDSA). The algorithm is instantiated with recommended parameters for the edwards25519 and edwards448 curves. An example implementation and test vectors are provided. Many protocols make use of points of extensibility that use constants to identify various protocol parameters. To ensure that the values in these fields do not have conflicting uses and to promote interoperability, their allocations are often coordinated by a central record keeper. For IETF protocols, that role is filled by the Internet Assigned Numbers Authority (IANA). To make assignments in a given registry prudently, guidance describing the conditions under which new values should be assigned, as well as when and how modifications to existing values can be made, is needed. This document defines a framework for the documentation of these guidelines by specification authors, in order to assure that the provided guidance for the IANA Considerations is clear and addresses the various issues that are likely in the operation of a registry. This is the third edition of this document; it obsoletes RFC 5226. Aiven Proton AG Sequoia-PGP FSIJ This document specifies the message formats used in OpenPGP. OpenPGP provides encryption with public-key or symmetric cryptographic algorithms, digital signatures, compression and key management. This document is maintained in order to publish all necessary information needed to develop interoperable applications based on the OpenPGP format. It is not a step-by-step cookbook for writing an application. It describes only the format and methods needed to read, check, generate, and write conforming packets crossing any network. It does not deal with storage and implementation questions. It does, however, discuss implementation issues necessary to avoid security flaws. This document obsoletes: RFC 4880 (OpenPGP), RFC 5581 (Camellia in OpenPGP) and RFC 6637 (Elliptic Curves in OpenPGP). Informative References This memo proposes several elliptic curve domain parameters over finite prime fields for use in cryptographic applications. The domain parameters are consistent with the relevant international standards, and can be used in X.509 certificates and certificate revocation lists (CRLs), for Internet Key Exchange (IKE), Transport Layer Security (TLS), XML signatures, and all applications or protocols based on the cryptographic message syntax (CMS). This document is not an Internet Standards Track specification; it is published for informational purposes. Standards for Efficient Cryptography Group

Acknowledgments Thanks to Daniel Huigens and Evangelos Karatsiolis for the early review and feedback on this document.