Network Working Group S. Kousidis
Internet-Draft BSI
Intended status: Informational F. Strenzke
Expires: 11 January 2024 MTG AG
A. Wussler
Proton AG
10 July 2023
Post-Quantum Cryptography in OpenPGP
draft-wussler-openpgp-pqc-02
Abstract
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
This note is to be removed before publishing as an RFC.
Status information for this document may be found at
https://datatracker.ietf.org/doc/draft-wussler-openpgp-pqc/.
Discussion of this document takes place on the WG Working Group
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Source for this draft and an issue tracker can be found at
https://github.com/openpgp-pqc/draft-openpgp-pqc.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1. Conventions used in this Document . . . . . . . . . . . . 4
1.1.1. Terminology for Multi-Algorithm Schemes . . . . . . . 5
1.2. Post-Quantum Cryptography . . . . . . . . . . . . . . . . 5
1.2.1. CRYSTALS-Kyber . . . . . . . . . . . . . . . . . . . 5
1.2.2. CRYSTALS-Dilithium . . . . . . . . . . . . . . . . . 6
1.2.3. SPHINCS+ . . . . . . . . . . . . . . . . . . . . . . 6
1.3. Elliptic Curve Cryptography . . . . . . . . . . . . . . . 6
1.3.1. Curve25519 and Curve448 . . . . . . . . . . . . . . . 6
1.3.2. Generic Prime Curves . . . . . . . . . . . . . . . . 6
1.4. Standalone and Multi-Algorithm Schemes . . . . . . . . . 7
1.4.1. Standalone and Composite Multi-Algorithm Schemes . . 7
1.4.2. Non-Composite Algorithm Combinations . . . . . . . . 7
2. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1. Elliptic curves . . . . . . . . . . . . . . . . . . . . . 8
2.1.1. SEC1 EC Point Wire Format . . . . . . . . . . . . . . 8
2.1.2. Measures to Ensure Secure Implementations . . . . . . 8
3. Supported Public Key Algorithms . . . . . . . . . . . . . . . 9
3.1. Algorithm Specifications . . . . . . . . . . . . . . . . 9
3.2. Parameter Specification . . . . . . . . . . . . . . . . . 10
3.2.1. SPHINCS+-simple-SHA2 . . . . . . . . . . . . . . . . 10
3.2.2. SPHINCS+-simple-SHAKE . . . . . . . . . . . . . . . . 11
4. Algorithm Combinations . . . . . . . . . . . . . . . . . . . 12
4.1. Composite KEMs . . . . . . . . . . . . . . . . . . . . . 12
4.2. Parallel Public-Key Encryption . . . . . . . . . . . . . 12
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4.3. Composite Signatures . . . . . . . . . . . . . . . . . . 12
4.4. Multiple Signatures . . . . . . . . . . . . . . . . . . . 12
5. Composite KEM schemes . . . . . . . . . . . . . . . . . . . . 13
5.1. Building Blocks . . . . . . . . . . . . . . . . . . . . . 13
5.1.1. ECC-Based KEMs . . . . . . . . . . . . . . . . . . . 13
5.1.2. Kyber-KEM . . . . . . . . . . . . . . . . . . . . . . 17
5.2. Composite Encryption Schemes with Kyber . . . . . . . . . 19
5.2.1. Fixed information . . . . . . . . . . . . . . . . . . 20
5.2.2. Key combiner . . . . . . . . . . . . . . . . . . . . 20
5.2.3. Key generation procedure . . . . . . . . . . . . . . 21
5.2.4. Encryption procedure . . . . . . . . . . . . . . . . 21
5.2.5. Decryption procedure . . . . . . . . . . . . . . . . 22
5.3. Packet specifications . . . . . . . . . . . . . . . . . . 23
5.3.1. Public-Key Encrypted Session Key Packets (Tag 1) . . 23
5.3.2. Key Material Packets . . . . . . . . . . . . . . . . 23
6. Composite Signature Schemes . . . . . . . . . . . . . . . . . 24
6.1. Building blocks . . . . . . . . . . . . . . . . . . . . . 24
6.1.1. EdDSA-Based signatures . . . . . . . . . . . . . . . 24
6.1.2. ECDSA-Based signatures . . . . . . . . . . . . . . . 25
6.1.3. Dilithium signatures . . . . . . . . . . . . . . . . 25
6.2. Composite Signature Schemes with Dilithium . . . . . . . 26
6.2.1. Binding hashes . . . . . . . . . . . . . . . . . . . 26
6.2.2. Key generation procedure . . . . . . . . . . . . . . 26
6.2.3. Signature Generation . . . . . . . . . . . . . . . . 27
6.2.4. Signature Verification . . . . . . . . . . . . . . . 27
6.3. Packet Specifications . . . . . . . . . . . . . . . . . . 28
6.3.1. Signature Packet (Tag 2) . . . . . . . . . . . . . . 28
6.3.2. Key Material Packets . . . . . . . . . . . . . . . . 28
7. SPHINCS+ . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7.1. The SPHINCS+ Algorithms . . . . . . . . . . . . . . . . . 29
7.1.1. Binding hashes . . . . . . . . . . . . . . . . . . . 30
7.1.2. Key generation . . . . . . . . . . . . . . . . . . . 31
7.1.3. Signature Generation . . . . . . . . . . . . . . . . 31
7.1.4. Signature Verification . . . . . . . . . . . . . . . 31
7.2. Packet specifications . . . . . . . . . . . . . . . . . . 31
7.2.1. Signature Packet (Tag 2) . . . . . . . . . . . . . . 31
7.2.2. Key Material Packets . . . . . . . . . . . . . . . . 32
8. Migration Considerations . . . . . . . . . . . . . . . . . . 32
8.1. Key preference . . . . . . . . . . . . . . . . . . . . . 32
8.2. Key generation strategies . . . . . . . . . . . . . . . . 33
9. Security Considerations . . . . . . . . . . . . . . . . . . . 33
9.1. Hashing in ECC-KEM . . . . . . . . . . . . . . . . . . . 33
9.2. Key combiner . . . . . . . . . . . . . . . . . . . . . . 34
9.3. Domain separation and binding . . . . . . . . . . . . . . 34
9.4. SPHINCS+ . . . . . . . . . . . . . . . . . . . . . . . . 36
9.5. Binding hashes in signatures with signature algorithms . 36
10. Additional considerations . . . . . . . . . . . . . . . . . . 36
10.1. Performance Considerations for SPHINCS+ . . . . . . . . 36
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11. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 37
12. Contributors . . . . . . . . . . . . . . . . . . . . . . . . 37
13. References . . . . . . . . . . . . . . . . . . . . . . . . . 37
13.1. Normative References . . . . . . . . . . . . . . . . . . 37
13.2. Informative References . . . . . . . . . . . . . . . . . 38
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 40
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 40
1. 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 [NISTIR-8413] as the result of the NIST
Post-Quantum Cryptography Standardization process initiated in 2016
[NIST-PQC]. 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.
1.1. Conventions used in this Document
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1.1.1. Terminology for Multi-Algorithm Schemes
The terminology in this document is oriented towards the definitions
in [draft-driscoll-pqt-hybrid-terminology]. 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.
1.2. 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.]
1.2.1. CRYSTALS-Kyber
CRYSTALS-Kyber [KYBER-Subm] 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.
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1.2.2. CRYSTALS-Dilithium
CRYSTALS-Dilithium, defined in [DILITHIUM-Subm], 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.
1.2.3. SPHINCS+
SPHINCS+ [SPHINCS-Subm] 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 Section 10.1 for a discussion of the
performance characteristics of this scheme.
1.3. Elliptic Curve Cryptography
The ECC-based encryption is defined here as a KEM. This is in
contrast to [I-D.ietf-openpgp-crypto-refresh] 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 [I-D.ietf-openpgp-crypto-refresh]. However, as explained
in the following, in the case of Curve25519 encoding changes are
applied to the new composite schemes.
1.3.1. Curve25519 and Curve448
Curve25519 and Curve448 are defined in [RFC7748] for use in a Diffie-
Hellman key agreement scheme and defined in [RFC8032] for use in a
digital signature scheme. For Curve25519 this specification adapts
the encoding of objects as defined in [RFC7748] in contrast to
[I-D.ietf-openpgp-crypto-refresh].
1.3.2. Generic Prime Curves
For interoperability this extension offers CRYSTALS-* in composite
combinations with the NIST curves P-256, P-384 defined in [SP800-186]
and the Brainpool curves brainpoolP256r1, brainpoolP384r1 defined in
[RFC5639].
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1.4. Standalone and Multi-Algorithm Schemes
This section provides a categorization of the new algorithms and
their combinations.
1.4.1. 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 specification 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.
1.4.2. Non-Composite Algorithm Combinations
As the OpenPGP protocol [I-D.ietf-openpgp-crypto-refresh] 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. Section 4.4 specifies how
implementations should handle the verification of such combinations
of signatures.
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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 Section 4.2 for
restrictions on parallel encryption mandated by this specification.
2. Preliminaries
This section provides some preliminaries for the definitions in the
subsequent sections.
2.1. Elliptic curves
2.1.1. 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:
B = 04 || X || Y
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
Table 6, Table 7, or Table 11. This encoding is compatible with the
definition given in [SEC1].
2.1.2. Measures to Ensure Secure Implementations
In the following measures are described 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
Section 5.1.1.1, Section 5.1.1.2 or Section 5.1.1.3 it is REQUIRED to
follow the specification and security advisory mandated from the
respective elliptic curve specification.
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3. 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.
3.1. Algorithm Specifications
For encryption, the following composite KEM schemes are specified:
+====+==================================+=============+=============+
| ID | Algorithm | Requirement | Definition |
+====+==================================+=============+=============+
| 29 | Kyber768 + X25519 | MUST | Section 5.2 |
+----+----------------------------------+-------------+-------------+
| 30 | Kyber1024 + X448 | SHOULD | Section 5.2 |
+----+----------------------------------+-------------+-------------+
| 31 | Kyber768 + ECDH-NIST-P-256 | MAY | Section 5.2 |
+----+----------------------------------+-------------+-------------+
| 32 | Kyber1024 + ECDH-NIST-P-384 | MAY | Section 5.2 |
+----+----------------------------------+-------------+-------------+
| 33 | Kyber768 + ECDH-brainpoolP256r1 | MAY | Section 5.2 |
+----+----------------------------------+-------------+-------------+
| 34 | Kyber1024 + ECDH- | MAY | Section 5.2 |
| | brainpoolP384r1 | | |
+----+----------------------------------+-------------+-------------+
Table 1: KEM algorithm specifications
For signatures, the following (composite) signature schemes are
specified:
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+====+===============================+=============+=============+
| ID | Algorithm | Requirement | Definition |
+====+===============================+=============+=============+
| 35 | Dilithium3 + Ed25519 | MUST | Section 6.2 |
+----+-------------------------------+-------------+-------------+
| 36 | Dilithium5 + Ed448 | SHOULD | Section 6.2 |
+----+-------------------------------+-------------+-------------+
| 37 | Dilithium3 + ECDSA-NIST-P-256 | MAY | Section 6.2 |
+----+-------------------------------+-------------+-------------+
| 38 | Dilithium5 + ECDSA-NIST-P-384 | MAY | Section 6.2 |
+----+-------------------------------+-------------+-------------+
| 39 | Dilithium3 + ECDSA- | MAY | Section 6.2 |
| | brainpoolP256r1 | | |
+----+-------------------------------+-------------+-------------+
| 40 | Dilithium5 + ECDSA- | MAY | Section 6.2 |
| | brainpoolP384r1 | | |
+----+-------------------------------+-------------+-------------+
| 41 | SPHINCS+-simple-SHA2 | SHOULD | Section |
| | | | 1.2.3 |
+----+-------------------------------+-------------+-------------+
| 42 | SPHINCS+-simple-SHAKE | MAY | Section |
| | | | 1.2.3 |
+----+-------------------------------+-------------+-------------+
Table 2: Signature algorithm specifications
3.2. Parameter Specification
3.2.1. SPHINCS+-simple-SHA2
For the SPHINCS+-simple-SHA2 signature algorithm from Table 2, the
following parameters are specified:
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+==============+===========================+
| 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 |
+--------------+---------------------------+
Table 3: SPHINCS+-simple-SHA2 security
parameters
All security parameters inherit the requirement of SPHINCS+-simple-
SHA2 from Table 2. That is, implementations SHOULD implement the
parameters specified in Table 3. The values 0x00 and 0xFF are
reserved for future extensions.
3.2.2. SPHINCS+-simple-SHAKE
For the SPHINCS+-simple-SHAKE signature algorithm from Table 2, the
following parameters are specified:
+==============+============================+
| 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 |
+--------------+----------------------------+
Table 4: SPHINCS+-simple-SHAKE security
parameters
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All security parameters inherit the requirement of SPHINCS+-simple-
SHAKE from Table 2. That is, implementations MAY implement the
parameters specified in Table 4. The values 0x00 and 0xFF are
reserved for future extensions.
4. Algorithm Combinations
4.1. 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.
4.2. Parallel Public-Key Encryption
As explained in Section 1.4.2, the OpenPGP protocol inherently
supports parallel encryption to different keys of the same recipient.
Implementations MUST NOT encrypt a message with a purely traditional
public-key encryption key of a recipient if it is encrypted with a
PQ/T key of the same recipient.
4.3. 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.
4.4. 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 [I-D.ietf-openpgp-crypto-refresh] 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.
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[Note to the reader: The last requirement, that one valid signature
is sufficient to identify a message as correctly signed, is an
interpretation of [I-D.ietf-openpgp-crypto-refresh] Section 5.2.5.]
5. Composite KEM schemes
5.1. Building Blocks
5.1.1. ECC-Based KEMs
In this section we define the encryption, decryption, and data
formats for the ECDH component of the composite algorithms.
Table 5, Table 6, and Table 7 describe the ECC-KEM parameters and
artifact lengths. The artefacts in Table 5 follow the encodings
described in [RFC7748].
+========================+===================+==================+
| | X25519 | X448 |
+========================+===================+==================+
| Algorithm ID reference | 29 | 30 |
+------------------------+-------------------+------------------+
| Field size | 32 octets | 56 octets |
+------------------------+-------------------+------------------+
| ECC-KEM | x25519Kem | x448Kem (Section |
| | (Section 5.1.1.1) | 5.1.1.2) |
+------------------------+-------------------+------------------+
| ECDH public key | 32 octets | 56 octets |
| | [RFC7748] | [RFC7748] |
+------------------------+-------------------+------------------+
| ECDH secret key | 32 octets | 56 octets |
| | [RFC7748] | [RFC7748] |
+------------------------+-------------------+------------------+
| ECDH ephemeral | 32 octets | 56 octets |
| | [RFC7748] | [RFC7748] |
+------------------------+-------------------+------------------+
| ECDH share | 32 octets | 56 octets |
| | [RFC7748] | [RFC7748] |
+------------------------+-------------------+------------------+
| Key share | 32 octets | 64 octets |
+------------------------+-------------------+------------------+
| Hash | SHA3-256 | SHA3-512 |
+------------------------+-------------------+------------------+
Table 5: Montgomery curves parameters and artifact lengths
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+==============+===========================+==================+
| | NIST P-256 | NIST P-384 |
+==============+===========================+==================+
| Algorithm ID | 31 | 32 |
| reference | | |
+--------------+---------------------------+------------------+
| Field size | 32 octets | 48 octets |
+--------------+---------------------------+------------------+
| ECC-KEM | ecdhKem (Section 5.1.1.3) | ecdhKem (Section |
| | | 5.1.1.3) |
+--------------+---------------------------+------------------+
| ECDH public | 65 octets of SEC1-encoded | 97 octets of |
| key | public point | SEC1-encoded |
| | | public point |
+--------------+---------------------------+------------------+
| ECDH secret | 32 octets big-endian | 48 octets big- |
| key | encoded secret scalar | endian encoded |
| | | secret scalar |
+--------------+---------------------------+------------------+
| ECDH | 65 octets of SEC1-encoded | 97 octets of |
| ephemeral | ephemeral point | SEC1-encoded |
| | | ephemeral point |
+--------------+---------------------------+------------------+
| ECDH share | 65 octets of SEC1-encoded | 97 octets of |
| | shared point | SEC1-encoded |
| | | shared point |
+--------------+---------------------------+------------------+
| Key share | 32 octets | 64 octets |
+--------------+---------------------------+------------------+
| Hash | SHA3-256 | SHA3-512 |
+--------------+---------------------------+------------------+
Table 6: NIST curves parameters and artifact lengths
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+==============+===========================+==================+
| | brainpoolP256r1 | brainpoolP384r1 |
+==============+===========================+==================+
| Algorithm ID | 33 | 34 |
| reference | | |
+--------------+---------------------------+------------------+
| Field size | 32 octets | 48 octets |
+--------------+---------------------------+------------------+
| ECC-KEM | ecdhKem (Section 5.1.1.3) | ecdhKem (Section |
| | | 5.1.1.3) |
+--------------+---------------------------+------------------+
| ECDH public | 65 octets of SEC1-encoded | 97 octets of |
| key | public point | SEC1-encoded |
| | | public point |
+--------------+---------------------------+------------------+
| ECDH secret | 32 octets big-endian | 48 octets big- |
| key | encoded secret scalar | endian encoded |
| | | secret scalar |
+--------------+---------------------------+------------------+
| ECDH | 65 octets of SEC1-encoded | 97 octets of |
| ephemeral | ephemeral point | SEC1-encoded |
| | | ephemeral point |
+--------------+---------------------------+------------------+
| ECDH share | 65 octets of SEC1-encoded | 97 octets of |
| | shared point | SEC1-encoded |
| | | shared point |
+--------------+---------------------------+------------------+
| Key share | 32 octets | 64 octets |
+--------------+---------------------------+------------------+
| Hash | SHA3-256 | SHA3-512 |
+--------------+---------------------------+------------------+
Table 7: Brainpool curves parameters and artifact lengths
The SEC1 format for point encoding is defined in Section 2.1.1.
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:
(eccCipherText, eccKeyShare) <- eccKem.encap(eccPublicKey)
and
(eccKeyShare) <- eccKem.decap(eccPrivateKey, eccCipherText)
The placeholder eccKem has to be replaced with the specific ECC-KEM
from the row "ECC-KEM" of Table 5, Table 6, and Table 7.
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5.1.1.1. X25519-KEM
The encapsulation and decapsulation operations of x25519kem are
described using the function X25519() and encodings defined in
[RFC7748]. 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))
where v is a random scalar
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 ||
eccPublicKey)
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 ||
eccPublicKey)
5.1.1.2. X448-KEM
The encapsulation and decapsulation operations of x448kem are
described using the function X448() and encodings defined in
[RFC7748]. 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)) where
v is a random scalar
2. Compute the shared coordinate X = X448(v, R) where R is the
public key eccPublicKey
3. Set the output eccCipherText to V
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4. Set the output eccKeyShare to SHA3-512(X || eccCipherText ||
eccPublicKey)
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 ||
eccPublicKey)
5.1.1.3. ECDH-KEM
The operation ecdhKem.encap() is defined as follows:
1. Generate an ephemeral key pair {v, V=vG} as defined in
[SP800-186] or [RFC5639] where v is a random scalar
2. Compute the shared point S = vR, where R is the component public
key eccPublicKey, according to [SP800-186] or [RFC5639]
3. Extract the X coordinate from the SEC1 encoded point S = 04 ||
X || Y as defined in section Section 2.1.1
4. Set the output eccCipherText to the SEC1 encoding of V
5. Set the output eccKeyShare to Hash(X || eccCipherText ||
eccPublicKey), with Hash chosen according to Table 6 or Table 7
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 [SP800-186] or [RFC5639]
2. Extract the X coordinate from the SEC1 encoded point S = 04 ||
X || Y as defined in section Section 2.1.1
3. Set the output eccKeyShare to Hash(X || eccCipherText ||
eccPublicKey), with Hash chosen according to Table 6 or Table 7
5.1.2. Kyber-KEM
Kyber-KEM features the following operations:
(kyberCipherText, kyberKeyShare) <- kyberKem.encap(kyberPublicKey)
and
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(kyberKeyShare) <- kyberKem.decap(kyberCipherText, kyberPrivateKey)
The above are the operations Kyber.CCAKEM.Enc() and
Kyber.CCAKEM.Dec() defined in [KYBER-Subm].
Kyber-KEM has the parameterization with the corresponding artifact
lengths in octets as given in Table 8. All artifacts are encoded as
defined in [KYBER-Subm].
+===========+==============+========+========+============+=======+
| Algorithm | Kyber-KEM | Public | Secret | Ciphertext | Key |
| ID | | key | key | | share |
| reference | | | | | |
+===========+==============+========+========+============+=======+
| 29, 31, | kyberKem768 | 1184 | 2400 | 1088 | 32 |
| 33 | | | | | |
+-----------+--------------+--------+--------+------------+-------+
| 30, 32, | kyberKem1024 | 1568 | 3186 | 1568 | 32 |
| 34 | | | | | |
+-----------+--------------+--------+--------+------------+-------+
Table 8: Kyber-KEM parameters artifact lengths in octets
The placeholder kyberKem has to be replaced with the specific Kyber-
KEM from the column "Kyber-KEM" of Table 8.
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
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5.2. Composite Encryption Schemes with Kyber
Table 1 specifies the following Kyber + ECC composite public-key
encryption schemes:
+==============+==============+===========+=================+
| Algorithm ID | Kyber-KEM | ECC-KEM | ECDH-KEM curve |
| reference | | | |
+==============+==============+===========+=================+
| 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 |
+--------------+--------------+-----------+-----------------+
Table 9: Kyber-ECC-composite Schemes
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 [RFC3394] using AES-256 as algorithm and the KEK as
key.
* The PKESK package's algorithm-specific parts are made up of the
Kyber ciphertext, the ECC ciphertext, and the wrapped session key.
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5.2.1. Fixed information
For the composite KEM schemes defined in Table 1 the following
procedure, justified in Section 9.3, MUST be used to derive a string
to use as binding between the KEK and the communication parties.
// Input:
// algID - the algorithm ID encoded as octet
fixedInfo = algID
SHA3-256 MUST be used to hash the publicKey of the recipient.
5.2.2. Key combiner
For the composite KEM schemes defined in Table 1 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
[SP800-56C] Section 4, based on KMAC256 [SP800-185]. It is given by
the following algorithm.
// multiKeyCombine(eccKeyShare, eccCipherText,
// kyberKeyShare, kyberCipherText,
// fixedInfo, oBits)
//
// Input:
// eccKeyShare - the ECC key share encoded as an octet string
// eccCipherText - the ECC ciphertext encoded as an octet string
// kyberKeyShare - the Kyber key share encoded as an octet string
// kyberCipherText - the Kyber ciphertext encoded as an octet string
// fixedInfo - the fixed information octet string
// oBits - the size of the output keying material in bits
//
// Constants:
// domSeparation - the UTF-8 encoding of the string
// "OpenPGPCompositeKeyDerivationFunction"
// counter - the fixed 4 byte value 0x00000001
// customizationString - the UTF-8 encoding of the string "KDF"
eccKemData = eccKeyShare || eccCipherText
kyberKemData = kyberKeyShare || kyberCipherText
encData = counter || eccKemData || kyberKemData || fixedInfo
MB = KMAC256(domSeparation, encData, oBits, customizationString)
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Note that the values eccKeyShare defined in Section 5.1.1 and
kyberKeyShare defined in Section 5.1.2 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:
domSeparation := 4F 70 65 6E 50 47 50 43 6F 6D 70 6F 73 69 74 65
4B 65 79 44 65 72 69 76 61 74 69 6F 6E 46 75 6E
63 74 69 6F 6E
The value of counter MUST be set to the following octet sequence:
counter := 00 00 00 01
The value of fixedInfo MUST be set according to Section 5.2.1.
The value of customizationString is the UTF-8 encoding of the string
"KDF" and MUST be set to the following octet sequence:
customizationString := 4B 44 46
5.2.3. Key generation procedure
The implementation MUST independently generate the Kyber and the ECC
component keys. Kyber key generation follows the specification
[KYBER-Subm] and the artifacts are encoded as fixed-length octet
strings. For ECC this is done following the relative specification
in [RFC7748], [SP800-186], or [RFC5639], and encoding the outputs as
fixed-length octet strings in the format specified in table Table 5,
Table 6, or Table 7.
5.2.4. 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 Section 5.3.2.
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4. Instantiate the ECC-KEM eccKem.encap() and the Kyber-KEM
kyberKem.encap() depending on the algorithm ID according to
Table 9
5. Compute (eccCipherText, eccKeyShare) :=
eccKem.encap(eccPublicKey)
6. Compute (kyberCipherText, kyberKeyShare) :=
kyberKem.encap(kyberPublicKey)
7. Compute fixedInfo as specified in Section 5.2.1
8. Compute KEK := multiKeyCombine(eccKeyShare, eccCipherText,
kyberKeyShare, kyberCipherText, fixedInfo, oBits=256) as defined
in Section 5.2.2
9. Compute C := AESKeyWrap(KEK, sessionKey) with AES-256 as per
[RFC3394] that includes a 64 bit integrity check
10. Output eccCipherText || kyberCipherText || len(C) || C
5.2.5. 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 Section 5.3.2
5. Instantiate the ECC-KEM eccKem.decap() and the Kyber-KEM
kyberKem.decap() depending on the algorithm ID according to
Table 9
6. Parse eccCipherText, kyberCipherText, and C from encryptedKey
encoded as eccCipherText || kyberCipherText || len(C) || C as
specified in Section 5.3.1
7. Compute (eccKeyShare) := eccKem.decap(eccCipherText,
eccPrivateKey)
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8. Compute (kyberKeyShare) := kyberKem.decap(kyberCipherText,
kyberPrivateKey)
9. Compute fixedInfo as specified in Section 5.2.1
10. Compute KEK := multiKeyCombine(eccKeyShare, eccCipherText,
kyberKeyShare, kyberCipherText, fixedInfo, oBits=256) as defined
in Section 5.2.2
11. Compute sessionKey := AESKeyUnwrap(KEK, C) with AES-256 as per
[RFC3394], aborting if the 64 bit integrity check fails
12. Output sessionKey
5.3. Packet specifications
5.3.1. Public-Key Encrypted Session Key Packets (Tag 1)
The algorithm-specific fields consists of:
* A fixed-length octet string representing an ECC ephemeral public
key in the format associated with the curve as specified in
Section 5.1.1.
* A fixed-length octet string of the Kyber ciphertext, whose length
depends on the algorithm ID as specified in Table 8.
* The one-octet algorithm identifier, if it was passed (in the case
of a v3 PKESK packet).
* A variable-length field containing the wrapped session key:
- A one-octet size of the following field;
- The wrapped session key represented as an octet string, i.e.,
the output of the encryption procedure described in
Section 5.2.4.
Note that unlike most public-key algorithms, in the case of a v3
PKESK packet, the symmetric algorithm identifier is not encrypted.
Instead, it is prepended to the encrypted session key in plaintext.
In this case, the symmetric algorithm used MUST be AES-128, AES-192
or AES-256 (algorithm ID 7, 8 or 9).
5.3.2. Key Material Packets
The algorithm-specific public key is this series of values:
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* A fixed-length octet string representing an EC point public key,
in the point format associated with the curve specified in
Section 5.1.1.
* A fixed-length octet string containing the Kyber public key, whose
length depends on the algorithm ID as specified in Table 8.
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
Section 5.1.1.
* A fixed-length octet string containing the Kyber secret key, whose
length depends on the algorithm ID as specified in Table 8.
6. Composite Signature Schemes
6.1. Building blocks
6.1.1. EdDSA-Based signatures
To sign and verify with EdDSA the following operations are defined:
(eddsaSignature) <- eddsa.sign(eddsaPrivateKey, dataDigest)
and
(verified) <- eddsa.verify(eddsaPublicKey, eddsaSignature, dataDigest)
The public and private keys, as well as the signature MUST be encoded
according to [RFC8032] as fixed-length octet strings. The following
table describes the EdDSA parameters and artifact lengths:
+==============+=========+=======+========+========+===========+
| Algorithm ID | Curve | Field | Public | Secret | Signature |
| reference | | size | key | key | |
+==============+=========+=======+========+========+===========+
| 35 | Ed25519 | 32 | 32 | 32 | 64 |
+--------------+---------+-------+--------+--------+-----------+
| 36 | Ed448 | 57 | 57 | 57 | 114 |
+--------------+---------+-------+--------+--------+-----------+
Table 10: EdDSA parameters and artifact lengths in octets
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6.1.2. ECDSA-Based signatures
To sign and verify with ECDSA the following operations are defined:
(ecdsaSignatureR, ecdsaSignatureS) <- ecdsa.sign(ecdsaPrivateKey,
dataDigest)
and
(verified) <- ecdsa.verify(ecdsaPublicKey, ecdsaSignatureR,
ecdsaSignatureS, dataDigest)
The public keys MUST be encoded in SEC1 format as defined in section
Section 2.1.1. 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:
+=========+===============+=====+======+======+=========+=========+
|Algorithm|Curve |Field|Public|Secret|Signature|Signature|
| ID| |size |key |key |value R |value S |
|reference| | | | | | |
+=========+===============+=====+======+======+=========+=========+
| 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 |
+---------+---------------+-----+------+------+---------+---------+
Table 11: ECDSA parameters and artifact lengths in octets
6.1.3. Dilithium signatures
The procedure for Dilithium signature generation is the function
Sign(sk, M) given in Figure 4 in [DILITHIUM-Subm], 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:
(dilithiumSignature) <- dilithium.sign(dilithiumPrivateKey,
dataDigest)
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The procedure for Dilithium signature verification is the function
Verify(pk, M, sigma) given in Figure 4 in [DILITHIUM-Subm], 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:
(verified) <- dilithium.verify(dilithiumPublicKey, dataDigest,
dilithiumSignature)
Dilithium has the parameterization with the corresponding artifact
lengths in octets as given in Table 12. All artifacts are encoded as
defined in [DILITHIUM-Subm].
+========================+============+========+========+===========+
| Algorithm ID | Dilithium | Public | Secret | Signature |
| reference | instance | key | key | value |
+========================+============+========+========+===========+
| 35, 37, 39 | Dilithium3 | 1952 | 4000 | 3293 |
+------------------------+------------+--------+--------+-----------+
| 36, 38, 40 | Dilithium5 | 2592 | 4864 | 4595 |
+------------------------+------------+--------+--------+-----------+
Table 12: Dilithium parameters and artifact lengths in octets
6.2. Composite Signature Schemes with Dilithium
6.2.1. 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.
6.2.2. Key generation procedure
The implementation MUST independently generate the Dilithium and the
ECC component keys. Dilithium key generation follows the
specification in [DILITHIUM-Subm] and the artifacts are encoded as
fixed-length octet strings as defined in Section 6.1.3. For ECC this
is done following the relative specification in [RFC7748],
[SP800-186], or [RFC5639], and encoding the artifacts as specified in
Section 6.1.1 or Section 6.1.2 as fixed-length octet strings.
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6.2.3. Signature Generation
To sign a message M with Dilithium + EdDSA the following sequence of
operations has to be performed:
1. Generate dataDigest according to
[I-D.ietf-openpgp-crypto-refresh] Section 5.2.4
2. Create the EdDSA signature over dataDigest with eddsa.sign() from
Section 6.1.1
3. Create the Dilithium signature over dataDigest with
dilithium.sign() from Section 6.1.3
4. Encode the EdDSA and Dilithium signatures according to the packet
structure given in Section 6.3.1.
To sign a message M with Dilithium + ECDSA the following sequence of
operations has to be performed:
1. Generate dataDigest according to
[I-D.ietf-openpgp-crypto-refresh] Section 5.2.4
2. Create the ECDSA signature over dataDigest with ecdsa.sign() from
Section 6.1.2
3. Create the Dilithium signature over dataDigest with
dilithium.sign() from Section 6.1.3
4. Encode the ECDSA and Dilithium signatures according to the packet
structure given in Section 6.3.1.
6.2.4. 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 Section 6.1.1
2. Verify the Dilithium signature with dilithium.verify() from
Section 6.1.3
To verify a Dilithium + ECDSA signature the following sequence of
operations has to be performed:
1. Verify the ECDSA signature with ecdsa.verify() from Section 6.1.2
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2. Verify the Dilithium signature with dilithium.verify() from
Section 6.1.3
As specified in Section 4.3 an implementation MUST validate both
signatures, i.e. EdDSA/ECDSA and Dilithium, to state that a composite
Dilithium + ECC signature is valid.
6.3. Packet Specifications
6.3.1. Signature Packet (Tag 2)
The composite Dilithium + ECC schemes MUST be used only with v6
signatures, as defined in [I-D.ietf-openpgp-crypto-refresh]
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 Table 10.
* A fixed-length octet string of the Dilithium signature value,
whose length depends on the algorithm ID as specified in Table 12.
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
Table 11.
* A fixed-length octet string of the big-endian encoded ECDSA value
S, whose length depends on the algorithm ID as specified in
Table 11.
* A fixed-length octet string of the Dilithium signature value,
whose length depends on the algorithm ID as specified in Table 12.
6.3.2. Key Material Packets
The composite Dilithium + ECC schemes MUST be used only with v6 keys,
as defined in [I-D.ietf-openpgp-crypto-refresh].
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 Table 10.
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* A fixed-length octet string containing the Dilithium public key,
whose length depends on the algorithm ID as specified in Table 12.
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 Table 10.
* A fixed-length octet string containing the Dilithium secret key,
whose length depends on the algorithm ID as specified in Table 12.
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 Section 2.1.1 and with length
specified in Table 11.
* A fixed-length octet string containing the Dilithium public key,
whose length depends on the algorithm ID as specified in Table 12.
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 Table 11.
* A fixed-length octet string containing the Dilithium secret key,
whose length depends on the algorithm ID as specified in Table 12.
7. SPHINCS+
7.1. The SPHINCS+ Algorithms
The following table describes the SPHINCS+ parameters and artifact
lengths:
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+==============+=============+============+============+===========+
| Parameter ID | Parameter | SPHINCS+ | SPHINCS+ | SPHINCS+ |
| reference | name suffix | public key | secret key | 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 |
+--------------+-------------+------------+------------+-----------+
Table 13: SPHINCS+ parameters and artifact lengths in octets.
The values equally apply to the parameter IDs of SPHINCS+-
simple-SHA2 and SPHINCS+-simple-SHAKE.
7.1.1. Binding hashes
SPHINCS+ signature packets MUST use the associated hash as specified
in Table 14. Signature packets using other hashes MUST be considered
invalid.
+========================+==============+==========+===============+
| Algorithm ID reference | Parameter ID | Hash | Hash function |
| | reference | 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 |
+------------------------+--------------+----------+---------------+
Table 14: Binding between SPHINCS+ and signature hashes
An implementation supporting a specific SPHINCS+ algorithm and
parameter MUST also support the matching hash algorithm.
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7.1.2. Key generation
The SPHINCS+ key generation is performed according to the function
spx_keygen() specified in [SPHINCS-Subm], Sec. 6.2 as Alg. 19. The
private and public key are encoded as defined in [SPHINCS-Subm].
7.1.3. Signature Generation
The procedure for SPHINCS+ signature generation is the function
spx_sign(M, SK) specified in [SPHINCS-Subm], Sec. 6.4 as Alg. 20.
Here, M is the dataDigest generated according to
[I-D.ietf-openpgp-crypto-refresh] 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 Section 9.4.
An implementation MUST set the Parameter ID in the signature equal to
the issuing private key Parameter ID.
7.1.4. Signature Verification
The procedure for SPHINCS+ signature verification is the function
spx_verify(M, SIG, PK) specified in [SPHINCS-Subm], Sec. 6.5 as Alg.
21. Here, M is the dataDigest generated according to
[I-D.ietf-openpgp-crypto-refresh] 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.
7.2. Packet specifications
7.2.1. Signature Packet (Tag 2)
The SPHINCS+ algorithms MUST be used only with v6 signatures, as
defined in [I-D.ietf-openpgp-crypto-refresh] Section 5.2.3.
The algorithm-specific v6 Signature parameters consists of:
* A one-octet value specifying the SPHINCS+ parameter ID defined in
Table 3 and Table 4. 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
Table 13.
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7.2.2. Key Material Packets
The SPHINCS+ algorithms MUST be used only with v6 keys, as defined in
[I-D.ietf-openpgp-crypto-refresh].
The algorithm-specific public key is this series of values:
* A one-octet value specifying the SPHINCS+ parameter ID defined in
Table 3 and Table 4. 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 Table 13.
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 Table 11.
8. Migration Considerations
The post-quantum KEM algorithms defined in Table 1 and the signature
algorithms defined in Table 2 are a set of new public key algorithms
that extend the algorithm selection of
[I-D.ietf-openpgp-crypto-refresh]. 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.
8.1. 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 Section 4.4.
Signing only with PQ(/T) key material is not backwards compatible.
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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.
8.2. 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.
9. Security Considerations
9.1. Hashing in ECC-KEM
Our construction of the ECC-KEMs, in particular the inclusion of
eccCipherText in 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 [CS03]. The
additional inclusion of eccPublicKey follows the security advice in
Section 6.1 of [RFC7748].
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9.2. Key combiner
For the key combination in Section 5.2.2 this specification limits
itself to the use of KMAC. The sponge construction used by KMAC was
proven to be indifferentiable from a random oracle [BDPA08]. 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
K = KMAC(domainSeparation, counter || K1 || C1 || K2 || C2 || fixedInfo,
outputBits, customization)
from a random bit string, an adversary has to know (or correctly
guess) both key shares K1 and K2, entirely.
The proposed construction in Section 5.2.2 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
[GHP18]. 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 [GHP18], up to some reordering of
input shared secrets and ciphertexts. In the random oracle setting,
the reordering does not influence the arguments in [GHP18].
9.3. Domain separation and binding
The domSeparation information defined in Section 5.2.2 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.
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The fixedInfo defined in Section 5.2.1 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.
This is in line with the Recommendation for ECC in section 5.5 of
[SP800-56A]. Other fields included in the recommendation are not
relevant for the OpenPGP protocol, since the sender is not required
to have a key of their own, there are no pre-shared secrets, and all
the other parameters are univocally defined by the algorithm ID.
Furthermore, we do not require the recipients public key into the key
combiner as the public key material is already included in the
component key derivation functions. Given two KEMs which we assume
to be multi-user secure, we combine their outputs using a KEM-
combiner:
K = H(K1, C1, K2, C2), C = (C1, C2)
Our aim is to preserve multi-user security. A common approach to
this is to add the public key into the key derivation for K.
However, it turns out that this is not necessary here. To break
security of the combined scheme in the multi-user setting, the
adversary has to distinguish a set of challenge keys
K__u = H(K1__u, C1__u, K2__u, C2*_u)
for users u in some set from random, also given ciphertexts C*_u =
(C1*_u, C2*_u). For each of these K* it holds that if the adversary
never makes a query
H(K1*_u, C1*_u, K2*_u, C2*_u)
they have a zero advantage over guessing.
The only multi-user advantage that the adversary could gain therefore
consists of queries to H that are meaningful for two different users
u1 != u2 and their associated public keys. This is only the case if
(c1*_u1, c2*_u1) = (c1*_u2, c2*_u2)
as the ciphertext values decide for which challenge the query is
meaningful. This means that a ciphertext collision is needed between
challenges. Assuming that the randomness used in the generation of
the two challenges is uncorrelated, this is negligible.
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In consequence, the ciphertexts already work sufficiently well as
domain-separator.
9.4. SPHINCS+
The original specification of SPHINCS+ [SPHINCS-Subm] 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.
9.5. 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.
10. Additional considerations
10.1. 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.
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11. 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 [RFC8126]
Values defined in this document, Table 3.
* Registry name: SPHINCS+-simple-SHAKE parameters
Registration procedure: SPECIFICATION REQUIRED [RFC8126]
Values defined in this document, Table 4.
Furthermore IANA will add the algorithm IDs defined in Table 1 and
Table 2 to the registry Public Key Algorithms.
12. Contributors
Stephan Ehlen (BSI)
Carl-Daniel Hailfinger (BSI)
Andreas Huelsing (TU Eindhoven)
Johannes Roth (MTG AG)
13. References
13.1. Normative References
[I-D.ietf-openpgp-crypto-refresh]
Wouters, P., Huigens, D., Winter, J., and N. Yutaka,
"OpenPGP", Work in Progress, Internet-Draft, draft-ietf-
openpgp-crypto-refresh-10, 21 June 2023,
.
[RFC3394] Schaad, J. and R. Housley, "Advanced Encryption Standard
(AES) Key Wrap Algorithm", RFC 3394, DOI 10.17487/RFC3394,
September 2002, .
[RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", RFC 7748, DOI 10.17487/RFC7748, January
2016, .
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[RFC8032] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital
Signature Algorithm (EdDSA)", RFC 8032,
DOI 10.17487/RFC8032, January 2017,
.
[RFC8126] Cotton, M., Leiba, B., and T. Narten, "Guidelines for
Writing an IANA Considerations Section in RFCs", BCP 26,
RFC 8126, DOI 10.17487/RFC8126, June 2017,
.
13.2. Informative References
[BDPA08] Bertoni, G., Daemen, J., Peters, M., and G. Assche, "On
the Indifferentiability of the Sponge Construction", 2008,
.
[CS03] Cramer, R. and V. Shoup, "Design and Analysis of Practical
Public-Key Encryption Schemes Secure against Adaptive
Chosen Ciphertext Attack", 2003,
.
[DILITHIUM-Subm]
Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V.,
Schwabe, P., Seiler, G., and D. Stehle, "CRYSTALS-
Dilithium - Algorithm Specifications and Supporting
Documentation (Version 3.1)", 8 February 2021.
[draft-driscoll-pqt-hybrid-terminology]
Driscoll, F., "Terminology for Post-Quantum Traditional
Hybrid Schemes", March 2023,
.
[GHP18] Giacon, F., Heuer, F., and B. Poettering, "KEM Combiners",
2018, .
[KYBER-Subm]
Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T.,
Lyubashevsky, V., Schanck, J. M., Schwabe, P., Seiler, G.,
and D. Stehle, "CRYSTALS-Kyber (version 3.02) - Submission
to round 3 of the NIST post-quantum project", 4 August
2021.
[NIST-PQC] Chen, L., Moody, D., and Y. Liu, "Post-Quantum
Cryptography Standardization", December 2016,
.
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[NISTIR-8413]
Alagic, G., Apon, D., Cooper, D., Dang, Q., Dang, T.,
Kelsey, J., Lichtinger, J., Miller, C., Moody, D.,
Peralta, R., Perlner, R., Robinson, A., Smith-Tone, D.,
and Y. Liu, "Status Report on the Third Round of the NIST
Post-Quantum Cryptography Standardization Process", NIST
IR 8413 , September 2022,
.
[RFC5639] Lochter, M. and J. Merkle, "Elliptic Curve Cryptography
(ECC) Brainpool Standard Curves and Curve Generation",
RFC 5639, DOI 10.17487/RFC5639, March 2010,
.
[SEC1] Standards for Efficient Cryptography Group, "Standards for
Efficient Cryptography 1 (SEC 1)", May 2009,
.
[SP800-185]
Kelsey, J., Chang, S., and R. Perlner, "SHA-3 Derived
Functions: cSHAKE, KMAC, TupleHash, and ParallelHash",
NIST Special Publication 800-185 , December 2016,
.
[SP800-186]
Chen, L., Moody, D., Regenscheid, A., and K. Randall,
"Recommendations for Discrete Logarithm-Based
Cryptography: Elliptic Curve Domain Parameters", NIST
Special Publication 800-186 , February 2023,
.
[SP800-56A]
Barker, E., Chen, L., Roginsky, A., Vassilev, A., and R.
Davis, "Recommendation for Pair-Wise Key-Establishment
Schemes Using Discrete Logarithm Cryptography", NIST
Special Publication 800-56A Rev. 3 , April 2018,
.
[SP800-56C]
Barker, E., Chen, L., and R. Davis, "Recommendation for
Key-Derivation Methods in Key-Establishment Schemes", NIST
Special Publication 800-56C Rev. 2 , August 2020,
.
[SPHINCS-Subm]
Aumasson, J., Bernstein, D. J., Beullens, W., Dobraunig,
C., Eichlseder, M., Fluhrer, S., Gazdag, S., Huelsing, A.,
Kampanakis, P., Koelb, S., Lange, T., Lauridsen, M. M.,
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Mendel, F., Niederhagen, R., Rechberger, C., Rijneveld,
J., Schwabe, P., and B. Westerbaan, "SPHINCS+ - Submission
to the 3rd round of the NIST post-quantum project. v3.1",
10 June 2021.
Acknowledgments
Thanks to Daniel Huigens and Evangelos Karatsiolis for the early
review and feedback on this document.
Authors' Addresses
Stavros Kousidis
BSI
Germany
Email: stavros.kousidis@bsi.bund.de
Falko Strenzke
MTG AG
Germany
Email: falko.strenzke@mtg.de
Aron Wussler
Proton AG
Switzerland
Email: aron@wussler.it
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