Network Working Group Q. Dang
Internet-Draft NIST
Intended status: Informational S. Ehlen
Expires: 9 January 2025 BSI
J. Roth
F. Strenzke
MTG AG
8 July 2024
PQ/T Composite Schemes for OpenPGP using NIST and Brainpool Elliptic
Curve Domain Parameters
draft-ehlen-openpgp-nist-bp-comp-00
Abstract
This document defines PQ/T composite schemes based on ML-KEM and ML-
DSA combined with ECC algorithms using the NIST and Brainpool domain
parameters for the OpenPGP protocol.
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-ehlen-openpgp-nist-bp-comp/.
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Source for this draft and an issue tracker can be found at
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Conventions used in this Document . . . . . . . . . . . . 3
1.1.1. Terminology for Multi-Algorithm Schemes . . . . . . . 4
1.2. Post-Quantum Cryptography . . . . . . . . . . . . . . . . 4
1.2.1. ML-KEM . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2. ML-DSA . . . . . . . . . . . . . . . . . . . . . . . 4
1.3. Elliptic Curve Cryptography . . . . . . . . . . . . . . . 5
1.4. Applicable Specifications for the use of PQC Algorithms in
OpenPGP . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1. Elliptic curves . . . . . . . . . . . . . . . . . . . . . 5
2.1.1. SEC1 EC Point Wire Format . . . . . . . . . . . . . . 5
2.1.2. Measures to Ensure Secure Implementations . . . . . . 6
3. Supported Public Key Algorithms . . . . . . . . . . . . . . . 6
3.1. Algorithm Specifications . . . . . . . . . . . . . . . . 6
3.1.1. Experimental Codepoints for Interop Testing . . . . . 7
4. Algorithm Combinations . . . . . . . . . . . . . . . . . . . 7
4.1. Composite KEMs . . . . . . . . . . . . . . . . . . . . . 7
4.2. Composite Signatures . . . . . . . . . . . . . . . . . . 8
5. Composite KEM schemes . . . . . . . . . . . . . . . . . . . . 8
5.1. Building Blocks . . . . . . . . . . . . . . . . . . . . . 8
5.1.1. ECC-Based KEMs . . . . . . . . . . . . . . . . . . . 8
5.1.2. ML-KEM . . . . . . . . . . . . . . . . . . . . . . . 11
5.2. Composite Encryption Schemes with ML-KEM . . . . . . . . 12
5.2.1. Fixed information . . . . . . . . . . . . . . . . . . 13
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5.2.2. Key combiner . . . . . . . . . . . . . . . . . . . . 14
5.2.3. Key generation procedure . . . . . . . . . . . . . . 15
5.2.4. Encryption procedure . . . . . . . . . . . . . . . . 15
5.2.5. Decryption procedure . . . . . . . . . . . . . . . . 16
5.3. Packet specifications . . . . . . . . . . . . . . . . . . 17
5.3.1. Public-Key Encrypted Session Key Packets (Tag 1) . . 17
5.3.2. Key Material Packets . . . . . . . . . . . . . . . . 18
6. Composite Signature Schemes . . . . . . . . . . . . . . . . . 18
6.1. Building blocks . . . . . . . . . . . . . . . . . . . . . 18
6.1.1. ECDSA-Based signatures . . . . . . . . . . . . . . . 18
6.1.2. ML-DSA signatures . . . . . . . . . . . . . . . . . . 20
6.2. Composite Signature Schemes with ML-DSA . . . . . . . . . 20
6.2.1. Signature data digest . . . . . . . . . . . . . . . . 20
6.2.2. Key generation procedure . . . . . . . . . . . . . . 21
6.2.3. Signature Generation . . . . . . . . . . . . . . . . 21
6.2.4. Signature Verification . . . . . . . . . . . . . . . 21
6.3. Packet Specifications . . . . . . . . . . . . . . . . . . 22
6.3.1. Signature Packet (Tag 2) . . . . . . . . . . . . . . 22
6.3.2. Key Material Packets . . . . . . . . . . . . . . . . 22
7. Security Considerations . . . . . . . . . . . . . . . . . . . 23
8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 23
9. Changelog . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10. Contributors . . . . . . . . . . . . . . . . . . . . . . . . 23
11. References . . . . . . . . . . . . . . . . . . . . . . . . . 24
11.1. Normative References . . . . . . . . . . . . . . . . . . 24
11.2. Informative References . . . . . . . . . . . . . . . . . 24
Appendix A. Test Vectors . . . . . . . . . . . . . . . . . . . . 26
A.1. Sample v6 PQC Subkey Artifacts . . . . . . . . . . . . . 26
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 27
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 27
1. Introduction
This document defines PQ/T composite schemes based on ML-KEM and ML-
DSA combined with ECDH and ECDSA using the NIST and Brainpool domain
parameters for the OpenPGP protocol. As such it extends
[draft-ietf-openpgp-pqc-03], which introduces post-quantum
cryptography in OpenPGP. The ML-KEM and ML-DSA composite schemes
defined in that document are built with ECC algorithms using the
Edwards Curves defined in [RFC8032] and [RFC7748]. This document
extends the set of algorithms given in [draft-ietf-openpgp-pqc-03] by
further combinations of ML-KEM and ML-DSA with the NIST [SP800-186]
and Brainpool [RFC5639] domain parameters. The support of NIST and
Brainpool domain parameters is required in various applications
related to certain regulatory environments.
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.
[Note to the reader: This specification refers to the NIST PQC draft
standards FIPS 203 and FIPS 204 as if they were a final
specification. This is a temporary solution until the final versions
of these documents are 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. Furthermore,
we want to point out that, depending on possible future changes to
the draft standards by NIST, this specification may be updated as
soon as corresponding information becomes available.]
1.2.1. ML-KEM
ML-KEM [FIPS-203] 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
ML-KEM only in composite combination with ECC-based encryption
schemes in order to provide a pre-quantum security fallback.
1.2.2. ML-DSA
ML-DSA [FIPS-204] is a signature scheme that, like ML-KEM, is based
on the hardness of solving the Learning With Errors problem and a
variant of the Short Integer Solution problem in module lattices
(MLWE and SelfTargetMSIS). Accordingly, this specification only
defines ML-DSA in composite combination with ECC-based signature
schemes.
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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].
For interoperability this extension offers ML-* in composite
combinations with the NIST curves P-256, P-384 defined in [SP800-186]
and the Brainpool curves brainpoolP256r1, brainpoolP384r1 defined in
[RFC5639].
1.4. Applicable Specifications for the use of PQC Algorithms in OpenPGP
This document is to be understood as an extension of
[draft-ietf-openpgp-pqc-03], which introduced PQC in OpenPGP, in that
it defines further algorithm code points. All general specifications
in [draft-ietf-openpgp-pqc-03] that pertain to the ML-KEM and ML-DSA
composite schemes or generally cryptographic schemes defined therein
equally apply to the schemes specified in this document.
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 3, Table 4, or Table 7. This encoding is compatible with the
definition given in [SEC1].
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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 it is REQUIRED to follow the specification and
security advisory mandated from the respective elliptic curve
specification.
3. Supported Public Key Algorithms
This section specifies the composite ML-KEM + ECC and ML-DSA + ECC
schemes. All of these schemes are fully specified via their
algorithm ID, i.e., they are not parametrized.
3.1. Algorithm Specifications
For encryption, the following composite KEM schemes are specified:
+===+==================================+=============+=============+
| ID| Algorithm | Requirement | Definition |
+===+==================================+=============+=============+
|TBD| ML-KEM-512+ECDH-NIST-P-256 | MAY | Section 5.2 |
+---+----------------------------------+-------------+-------------+
|TBD| ML-KEM-768+ECDH-NIST-P-384 | MAY | Section 5.2 |
+---+----------------------------------+-------------+-------------+
|TBD| ML-KEM-1024+ECDH-NIST-P-384 | MAY | Section 5.2 |
+---+----------------------------------+-------------+-------------+
|TBD| ML-KEM-768+ECDH-brainpoolP256r1 | MAY | Section 5.2 |
+---+----------------------------------+-------------+-------------+
|TBD| ML-KEM-1024+ECDH-brainpoolP384r1 | MAY | Section 5.2 |
+---+----------------------------------+-------------+-------------+
Table 1: KEM algorithm specifications
For signatures, the following (composite) signature schemes are
specified:
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+=====+=================================+=============+=============+
| ID | Algorithm | Requirement | Definition |
+=====+=================================+=============+=============+
| TBD | ML-DSA-44+ECDSA-NIST-P-256 | MAY | Section |
| | | | 6.2 |
+-----+---------------------------------+-------------+-------------+
| TBD | ML-DSA-65+ECDSA-NIST-P-384 | MAY | Section |
| | | | 6.2 |
+-----+---------------------------------+-------------+-------------+
| TBD | ML-DSA-87+ECDSA-NIST-P-384 | MAY | Section |
| | | | 6.2 |
+-----+---------------------------------+-------------+-------------+
| TBD | ML-DSA-65+ECDSA-brainpoolP256r1 | MAY | Section |
| | | | 6.2 |
+-----+---------------------------------+-------------+-------------+
| TBD | ML-DSA-87+ECDSA-brainpoolP384r1 | MAY | Section |
| | | | 6.2 |
+-----+---------------------------------+-------------+-------------+
Table 2: Signature algorithm specifications
3.1.1. Experimental Codepoints for Interop Testing
[ Note: this section to be removed before publication ]
Algorithms indicated as MAY are not assigned a codepoint in the
current state of the draft since there are not enough private/
experimental code points available to cover all newly introduced
public-key algorithm identifiers.
The use of private/experimental codepoints during development are
intended to be used in non-released software only, for
experimentation and interop testing purposes only. An OpenPGP
implementation MUST NOT produce a formal release using these
experimental codepoints. This draft will not be sent to IANA without
every listed algorithm having a non-experimental codepoint.
4. Algorithm Combinations
4.1. Composite KEMs
The ML-KEM + ECC public-key encryption involves both the ML-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.
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4.2. Composite Signatures
The ML-DSA + ECC signature consists of independent ML-DSA and ECC
signatures, and an implementation MUST successfully validate both
signatures to state that the ML-DSA + ECC signature is valid.
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 3 and Table 4 describe the ECC-KEM parameters and artifact
lengths.
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+=========+============================+============================+
| |NIST P-256 |NIST P-384 |
+=========+============================+============================+
|Algorithm|TBD (ML-KEM-512+ECDH-NIST- |TBD (ML-KEM-768+ECDH-NIST- |
|ID |P-256) |P-384, ML-KEM-1024+ECDH- |
|reference| |NIST-P-384, ) |
+---------+----------------------------+----------------------------+
|Field |32 octets |48 octets |
|size | | |
+---------+----------------------------+----------------------------+
|ECC-KEM |ecdhKem (Section 5.1.1.1) |ecdhKem (Section 5.1.1.1) |
+---------+----------------------------+----------------------------+
|ECDH |65 octets of SEC1-encoded |97 octets of SEC1-encoded |
|public |public point |public point |
|key | | |
+---------+----------------------------+----------------------------+
|ECDH |32 octets big-endian encoded|48 octets big-endian encoded|
|secret |secret scalar |secret scalar |
|key | | |
+---------+----------------------------+----------------------------+
|ECDH |65 octets of SEC1-encoded |97 octets of SEC1-encoded |
|ephemeral|ephemeral point |ephemeral point |
+---------+----------------------------+----------------------------+
|ECDH |65 octets of SEC1-encoded |97 octets of SEC1-encoded |
|share |shared point |shared point |
+---------+----------------------------+----------------------------+
|Key share|32 octets |64 octets |
+---------+----------------------------+----------------------------+
|Hash |SHA3-256 |SHA3-512 |
+---------+----------------------------+----------------------------+
Table 3: NIST curves parameters and artifact lengths
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+==============+===========================+========================+
| | brainpoolP256r1 | brainpoolP384r1 |
+==============+===========================+========================+
| Algorithm ID | TBD (ML-KEM-768+ECDH- | TBD (ML-KEM-1024+ECDH- |
| reference | brainpoolP256r1) | brainpoolP384r1) |
+--------------+---------------------------+------------------------+
| Field size | 32 octets | 48 octets |
+--------------+---------------------------+------------------------+
| ECC-KEM | ecdhKem | ecdhKem |
| | (Section 5.1.1.1) | (Section 5.1.1.1) |
+--------------+---------------------------+------------------------+
| ECDH public | 65 octets of | 97 octets of |
| key | SEC1-encoded public | SEC1-encoded public |
| | point | point |
+--------------+---------------------------+------------------------+
| ECDH secret | 32 octets big-endian | 48 octets big-endian |
| key | encoded secret scalar | encoded secret scalar |
+--------------+---------------------------+------------------------+
| ECDH | 65 octets of | 97 octets of |
| ephemeral | SEC1-encoded | SEC1-encoded ephemeral |
| | ephemeral point | point |
+--------------+---------------------------+------------------------+
| ECDH share | 65 octets of | 97 octets of |
| | SEC1-encoded shared | SEC1-encoded shared |
| | point | point |
+--------------+---------------------------+------------------------+
| Key share | 32 octets | 64 octets |
+--------------+---------------------------+------------------------+
| Hash | SHA3-256 | SHA3-512 |
+--------------+---------------------------+------------------------+
Table 4: 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) <- ECC-KEM.Encaps(eccPublicKey)
and
(eccKeyShare) <- ECC-KEM.Decaps(eccSecretKey, eccCipherText, eccPublicKey)
To instantiate ECC-KEM, one must select a parameter set from Table 3
or Table 4.
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5.1.1.1. ECDH-KEM
The operation ecdhKem.Encaps() 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 with 0 < v < n, n being the base point
order of the elliptic curve domain parameters
1. Compute the shared point S = vR, where R is the component public
key eccPublicKey, 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 eccCipherText to the SEC1 encoding of V
4. Set the output eccKeyShare to Hash(X || eccCipherText ||
eccPublicKey), with Hash chosen according to Table 3 or Table 4
The operation ecdhKem.Decaps() is defined as follows:
1. Compute the shared Point S as rV, where r is the eccSecretKey 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 3 or Table 4
5.1.2. ML-KEM
ML-KEM features the following operations:
(mlkemCipherText, mlkemKeyShare) <- ML-KEM.Encaps(mlkemPublicKey)
and
(mlkemKeyShare) <- ML-KEM.Decaps(mlkemCipherText, mlkemSecretKey)
The above are the operations ML-KEM.Encaps and ML-KEM.Decaps defined
in [FIPS-203]. Note that mlkemPublicKey is the encapsulation and
mlkemSecretKey is the decapsulation key.
ML-KEM has the parametrization with the corresponding artifact
lengths in octets as given in Table 5. All artifacts are encoded as
defined in [FIPS-203].
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+==============+=============+========+========+============+=======+
| Algorithm | ML-KEM | Public | Secret | Ciphertext | Key |
| ID | | key | key | | share |
| reference | | | | | |
+==============+=============+========+========+============+=======+
| TBD | ML-KEM-512 | 800 | 1632 | 768 | 32 |
+--------------+-------------+--------+--------+------------+-------+
| TBD | ML-KEM-768 | 1184 | 2400 | 1088 | 32 |
+--------------+-------------+--------+--------+------------+-------+
| TBD | ML-KEM-1024 | 1568 | 3168 | 1568 | 32 |
+--------------+-------------+--------+--------+------------+-------+
Table 5: ML-KEM parameters artifact lengths in octets
To instantiate ML-KEM, one must select a parameter set from the
column "ML-KEM" of Table 5.
The procedure to perform ML-KEM.Encaps() is as follows:
1. Invoke (mlkemCipherText, mlkemKeyShare) <- ML-
KEM.Encaps(mlkemPublicKey), where mlkemPublicKey is the
recipient's public key
2. Set mlkemCipherText as the ML-KEM ciphertext
3. Set mlkemKeyShare as the ML-KEM symmetric key share
The procedure to perform ML-KEM.Decaps() is as follows:
1. Invoke mlkemKeyShare <- ML-KEM.Decaps(mlkemCipherText,
mlkemSecretKey)
2. Set mlkemKeyShare as the ML-KEM symmetric key share
5.2. Composite Encryption Schemes with ML-KEM
Table 1 specifies the following ML-KEM + ECC composite public-key
encryption schemes:
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+========================+========+=========+=================+
| Algorithm ID reference | ML-KEM | ECC-KEM | ECC-KEM curve |
+========================+========+=========+=================+
| TBD (ML-KEM-512+ECDH- | ML-KEM | ecdhKem | NIST P-256 |
| NIST-P-256) | -512 | | |
+------------------------+--------+---------+-----------------+
| TBD (ML-KEM-768+ECDH- | ML-KEM | ecdhKem | NIST P-384 |
| NIST-P-384) | -768 | | |
+------------------------+--------+---------+-----------------+
| TBD (ML-KEM-1024+ECDH- | ML-KEM | ecdhKem | NIST P-384 |
| NIST-P-384) | -1024 | | |
+------------------------+--------+---------+-----------------+
| TBD (ML-KEM-768+ECDH- | ML-KEM | ecdhKem | brainpoolP256r1 |
| brainpoolP256r1) | -768 | | |
+------------------------+--------+---------+-----------------+
| TBD (ML-KEM-1024+ECDH- | ML-KEM | ecdhKem | brainpoolP384r1 |
| brainpoolP384r1) | -1024 | | |
+------------------------+--------+---------+-----------------+
Table 6: ML-KEM + ECC composite schemes
The ML-KEM + ECC composite public-key encryption schemes are built
according to the following principal design:
* The ML-KEM encapsulation algorithm is invoked to create an ML-KEM
ciphertext together with an ML-KEM symmetric key share.
* The encapsulation algorithm of an 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 encrypted with the
AES Key Wrap Algorithm [RFC3394] with AES-256 as the encryption
algorithm and using the KEK as the encryption key.
* The PKESK package's algorithm-specific parts are made up of the
ML-KEM ciphertext, the ECC ciphertext, and the wrapped session
key.
5.2.1. Fixed information
For the composite KEM schemes defined in Table 1 the following fixed
information, which is identical to one specified in
[draft-ietf-openpgp-pqc-03], MUST be used in the subsequently
described key combiner Section 5.2.2.
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// Input:
// algID - the algorithm ID encoded as octet
//
// Constants:
// domSeparation - the UTF-8 encoding of the string
// "OpenPGPCompositeKDFv1"
fixedInfo = algID || domSeparation
The value of domSeparation is the UTF-8 encoding of the string
"OpenPGPCompositeKDFv1" 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
44 46 76 31
5.2.2. Key combiner
For the composite KEM schemes defined in Table 1 the following
procedure, which is identical to one described in
[draft-ietf-openpgp-pqc-03], 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 SHA3-256. It
is given by the following algorithm, which computes the key
encryption key KEK that is used to wrap, i.e., encrypt, the session
key.
[Note to the reader: the key combiner defined in the current version
of this draft is not actually compliant to [SP800-56C], since the
NIST standard requires that the shared secret is fed to the KDF first
whereas the combiner defined here feeds the key shares of the two
component schemes, which together form the shared secret, in two
parts with public information in between. The combiner will be
reworked to fix this defect in conformance to the combiner defined in
draft-ietf-openpgp-pqc. The change is planned to be integrated into
both drafts prior to IETF 121.]
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// multiKeyCombine(ecdhKeyShare, ecdhCipherText, ecdhPublicKey, mlkemKeyShare,
// mlkemCipherText, mlkemPublicKey, fixedInfo)
//
// Input:
// ecdhKeyShare - the ECDH key share encoded as an octet string
// ecdhCipherText - the ECDH ciphertext encoded as an octet string
// mlkemKeyShare - the ML-KEM key share encoded as an octet string
// mlkemCipherText - the ML-KEM ciphertext encoded as an octet string
// ecdhPublicKey - The ECDH public key of the recipient as an octet string
// mlkemPublicKey - The ML-KEM public key of the recipient as an octet string
// fixedInfo - the fixed information octet string
//
// Constants:
// counter - the 4 byte value 00 00 00 01
ecdhData = ecdhKeyShare || ecdhCipherText || ecdhPublicKey
mlkemData = mlkemKeyShare || mlkemCipherText || mlkemPublicKey
KEK = SHA3-256(counter || ecdhData || mlkemData || fixedInfo)
return KEK
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.
5.2.3. Key generation procedure
The implementation MUST independently generate the ML-KEM and the ECC
component keys. ML-KEM key generation follows the specification
[FIPS-203] and the artifacts are encoded as fixed-length octet
strings as defined in Section 5.1.2. For ECC this is done following
the relative specification in [SP800-186] or [RFC5639], and encoding
the outputs as fixed-length octet strings in the format specified in
Table 3 or Table 4.
5.2.4. Encryption procedure
The procedure to perform public-key encryption with an ML-KEM + 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
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3. Extract the eccPublicKey and mlkemPublicKey component from the
algorithm specific data encoded in pkComposite with the format
specified in Section 5.3.2.
4. Instantiate the ECC-KEM and the ML-KEM depending on the
algorithm ID according to Table 6
5. Compute (eccCipherText, eccKeyShare) := ECC-
KEM.Encaps(eccPublicKey)
6. Compute (mlkemCipherText, mlkemKeyShare) := ML-
KEM.Encaps(mlkemPublicKey)
7. Compute fixedInfo as specified in Section 5.2.1
8. Compute KEK := multiKeyCombine(eccKeyShare, eccCipherText,
eccPublicKey, mlkemKeyShare, mlkemCipherText, mlkemPublicKey,
fixedInfo) 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 the algorithm specific part of the PKESK as
eccCipherText || mlkemCipherText len(symAlgId, C) || (||
symAlgId) || C, where both symAlgId and len(C, symAlgId) are
single octet fields, symAlgId denotes the symmetric algorithm ID
used and is present only for a v3 PKESK, and len(C, symAlgId)
denotes the combined octet length of the fields specified as the
arguments.
5.2.5. Decryption procedure
The procedure to perform public-key decryption with an ML-KEM + 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,
i.e., the wrapped session key
3. Check that the own and the extracted algorithm ID match
4. Parse the eccSecretKey and mlkemSecretKey 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 and the ML-KEM depending on the
algorithm ID according to Table 6
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6. Parse eccCipherText, mlkemCipherText, and C from encryptedKey
encoded as eccCipherText || mlkemCipherText || len(symAlgId, C)
(|| symAlgId) || C as specified in Section 5.3.1, where symAlgId
is present only in the case of a v3 PKESK.
7. Compute (eccKeyShare) := ECC-KEM.Decaps(eccCipherText,
eccSecretKey, eccPublicKey)
8. Compute (mlkemKeyShare) := ML-KEM.Decaps(mlkemCipherText,
mlkemSecretKey)
9. Compute fixedInfo as specified in Section 5.2.1
10. Compute KEK := multiKeyCombine(eccKeyShare, eccCipherText,
eccPublicKey, mlkemKeyShare, mlkemCipherText, mlkemPublicKey,
fixedInfo) 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 the output of the
encryption procedure described in Section 5.2.4:
* 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 ML-KEM ciphertext, whose length
depends on the algorithm ID as specified in Table 5.
* A one-octet size of the following fields.
* Only in the case of a v3 PKESK packet: a one-octet symmetric
algorithm identifier.
* The wrapped session key represented as an octet string.
Note that like in the case of the algorithms X25519 and X448
specified in [I-D.ietf-openpgp-crypto-refresh], for the ML-KEM+ECC
composite schemes, in the case of a v3 PKESK packet, the symmetric
algorithm identifier is not encrypted. Instead, it is placed in
plaintext after the mlkemCipherText and before the length octet
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preceding the wrapped session key. In the case of v3 PKESK packets
for ML-KEM composite schemes, the symmetric algorithm used MUST be
AES-128, AES-192 or AES-256 (algorithm ID 7, 8 or 9).
In the case of a v3 PKESK, a receiving implementation MUST check if
the length of the unwrapped symmetric key matches the symmetric
algorithm identifier, and abort if this is not the case.
5.3.2. 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
Section 5.1.1.
* A fixed-length octet string containing the ML-KEM public key,
whose length depends on the algorithm ID as specified in Table 5.
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 ML-KEM secret key,
whose length depends on the algorithm ID as specified in Table 5.
6. Composite Signature Schemes
6.1. Building blocks
6.1.1. ECDSA-Based signatures
To sign and verify with ECDSA the following operations are defined:
(ecdsaSignatureR, ecdsaSignatureS) <- ECDSA.Sign(ecdsaSecretKey,
dataDigest)
and
(verified) <- ECDSA.Verify(ecdsaPublicKey, ecdsaSignatureR,
ecdsaSignatureS, dataDigest)
Here, the operation ECDSA.Sign() is defined as the algorithm in
Section "6.4.1 ECDSA Signature Generation Algorithm" of
[SP800-186-5], however, excluding Step 1: H = Hash(M) in that
algorithm specification, as in this specification the message digest
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H is a direct input to the operation ECDSA.Sign(). Equivalently, the
operation ECDSA.Sign() can be understood as representing the
algorithm under Section "4.2.1.1. Signature Algorithm" in
[TR-03111], again with the difference that in this specification the
message digest H_Tau(M) appearing in Step 5 of the algorithm
specification is the direct input to the operation ECDSA.Sign() and
thus the hash computation is not carried out. The same statement
holds for the definition of the verification operation
ECDSA.Verify(): it is given either through the algorithm defined in
Section "6.4.2 ECDSA Signature Verification Algorithm" of
[SP800-186-5] omitting the message digest computation in Step 2 or by
the algorithm in Section "4.2.1.2. Verification Algorithm" of
[TR-03111] omitting the message digest computation in Step 3.
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 ID|Curve |Field|Public|Secret|Signature|Signature|
| reference| |size |key |key |value R |value S |
+================+===============+=====+======+======+=========+=========+
| TBD (ML-DSA-|NIST P-256 |32 |65 |32 |32 |32 |
| 44+ECDSA-NIST-| | | | | | |
| P-256)| | | | | | |
+----------------+---------------+-----+------+------+---------+---------+
| TBD (ML-DSA-|NIST P-384 |48 |97 |48 |48 |48 |
|65+ECDSA-NIST-P-| | | | | | |
| 384,ML-DSA-| | | | | | |
| 87+ECDSA-NIST-| | | | | | |
| P-384)| | | | | | |
+----------------+---------------+-----+------+------+---------+---------+
| TBD (ML-DSA-|brainpoolP256r1|32 |65 |32 |32 |32 |
| 65+ECDSA-| | | | | | |
|brainpoolP256r1)| | | | | | |
+----------------+---------------+-----+------+------+---------+---------+
| TBD (ML-DSA-|brainpoolP384r1|48 |97 |48 |48 |48 |
| 87+ECDSA-| | | | | | |
|brainpoolP384r1)| | | | | | |
+----------------+---------------+-----+------+------+---------+---------+
Table 7: ECDSA parameters and artifact lengths in octets
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6.1.2. ML-DSA signatures
For ML-DSA signature generation the default hedged version of ML-
DSA.Sign given in [FIPS-204] is used. That is, to sign with ML-DSA
the following operation is defined:
(mldsaSignature) <- ML-DSA.Sign(mldsaSecretKey, dataDigest)
For ML-DSA signature verification the algorithm ML-DSA.Verify given
in [FIPS-204] is used. That is, to verify with ML-DSA the following
operation is defined:
(verified) <- ML-DSA.Verify(mldsaPublicKey, dataDigest, mldsaSignature)
ML-DSA has the parametrization with the corresponding artifact
lengths in octets as given in Table 8. All artifacts are encoded as
defined in [FIPS-204].
+========================+===========+========+========+===========+
| Algorithm ID reference | ML-DSA | Public | Secret | Signature |
| | | key | key | value |
+========================+===========+========+========+===========+
| TBD | ML-DSA-44 | 1312 | 2528 | 2420 |
+------------------------+-----------+--------+--------+-----------+
| TBD | ML-DSA-65 | 1952 | 4032 | 3293 |
+------------------------+-----------+--------+--------+-----------+
| TBD | ML-DSA-87 | 2592 | 4896 | 4595 |
+------------------------+-----------+--------+--------+-----------+
Table 8: ML-DSA parameters and artifact lengths in octets
6.2. Composite Signature Schemes with ML-DSA
6.2.1. Signature data digest
Signature data (i.e. the data to be signed) is digested prior to
signing operations, see [I-D.ietf-openpgp-crypto-refresh],
Section 5.2.4. Composite ML-DSA + ECC signatures MUST use the
associated hash algorithm as specified in Table 9 for the signature
data digest. Signatures using other hash algorithms MUST be
considered invalid.
An implementation supporting a specific ML-DSA + ECC algorithm MUST
also support the matching hash algorithm.
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+========================+===============+===============+
| Algorithm ID reference | Hash function | Hash function |
| | | ID reference |
+========================+===============+===============+
| TBD (ML-DSA-44 IDs) | SHA3-256 | 12 |
+------------------------+---------------+---------------+
| TBD (ML-DSA-65 IDs) | SHA3-512 | 14 |
+------------------------+---------------+---------------+
| TBD (ML-DSA-87 IDs) | SHA3-512 | 14 |
+------------------------+---------------+---------------+
Table 9: Binding between ML-DSA + ECDSA and signature
data digest
6.2.2. Key generation procedure
The implementation MUST independently generate the ML-DSA and the ECC
component keys. ML-DSA key generation follows the specification
[FIPS-204] and the artifacts are encoded as fixed-length octet
strings as defined in Section 6.1.2. For ECC this is done following
the relative specification in [SP800-186] or [RFC5639], and encoding
the artifacts as specified in Section 6.1.1 as fixed-length octet
strings.
6.2.3. Signature Generation
To sign a message M with ML-DSA + 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 6.1.1
3. Create the ML-DSA signature over dataDigest with ML-DSA.Sign()
from Section 6.1.2
4. Encode the ECDSA and ML-DSA signatures according to the packet
structure given in Section 6.3.1.
6.2.4. Signature Verification
To verify an ML-DSA + ECDSA signature the following sequence of
operations has to be performed:
1. Verify the ECDSA signature with ECDSA.Verify() from Section 6.1.1
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2. Verify the ML-DSA signature with ML-DSA.Verify() from
Section 6.1.2
As specified in Section 4.2 an implementation MUST validate both
signatures, i.e. ECDSA and ML-DSA, successfully to state that a
composite ML-DSA + ECC signature is valid.
6.3. Packet Specifications
6.3.1. Signature Packet (Tag 2)
The composite ML-DSA + ECC schemes MUST be used only with v6
signatures, as defined in [I-D.ietf-openpgp-crypto-refresh].
The algorithm-specific v6 signature parameters for ML-DSA + ECDSA
signatures consist 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 7.
* A fixed-length octet string of the big-endian encoded ECDSA value
S, whose length depends on the algorithm ID as specified in
Table 7.
* A fixed-length octet string of the ML-DSA signature value, whose
length depends on the algorithm ID as specified in Table 8.
6.3.2. Key Material Packets
The composite ML-DSA + ECC schemes MUST be used only with v6 keys, as
defined in [I-D.ietf-openpgp-crypto-refresh].
The algorithm-specific public key for ML-DSA + 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 7.
* A fixed-length octet string containing the ML-DSA public key,
whose length depends on the algorithm ID as specified in Table 8.
The algorithm-specific secret key for ML-DSA + ECDSA keys is this
series of values:
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* 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 7.
* A fixed-length octet string containing the ML-DSA secret key,
whose length depends on the algorithm ID as specified in Table 8.
7. Security Considerations
TBD
8. IANA Considerations
IANA is requested to add the algorithm IDs defined in Table 10 to the
existing registry OpenPGP Public Key Algorithms. The field
specifications enclosed in brackets for the ML-KEM + ECDH composite
algorithms denote fields that are only conditionally contained in the
data structure.
[Note: Once the working group has agreed on the actual algorithm
choice, the following table with the requested IANA updates will be
filled out.]
+===+===============+==========+=========+=========+======+=========+
|ID | Algorithm | Public| Secret|Signature| PKESK|Reference|
| | | Key| Key| Format|Format| |
| | | Format| Format| | | |
+===+===============+==========+=========+=========+======+=========+
|TBD| ML-DSA-65+TBD | TBD| TBD| TBD| N/A| Section|
| | | octets| octets| octets| | 6.2|
| | | TBD| TBD| TBD| | |
| | | public| secret|signature| | |
| | | key , TBD|key , TBD| , TBD| | |
| | | octets| octets| octets| | |
| | | ML-DSA-65|ML-DSA-65|ML-DSA-65| | |
| | | public| secret|signature| | |
| | | key|(Table 8)|(Table 8)| | |
| | | (Table 8)| | | | |
+---+---------------+----------+---------+---------+------+---------+
Table 10: IANA updates for registry 'OpenPGP Public Key Algorithms'
9. Changelog
10. Contributors
Stavros Kousidis
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11. References
11.1. Normative References
[draft-ietf-openpgp-pqc-03]
Kousidis, S., Roth, J., Strenzke, F., and A. Wussler,
"Post-Quantum Cryptography in OpenPGP (draft-ietf-openpgp-
pqc-03)", 2024, .
[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-13, 4 January 2024,
.
[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, .
[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,
.
11.2. 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,
.
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[draft-driscoll-pqt-hybrid-terminology]
Driscoll, F., "Terminology for Post-Quantum Traditional
Hybrid Schemes", March 2023,
.
[FIPS-203] National Institute of Standards and Technology, "Module-
Lattice-Based Key-Encapsulation Mechanism Standard",
August 2023, .
[FIPS-204] National Institute of Standards and Technology, "Module-
Lattice-Based Digital Signature Standard", August 2023,
.
[FIPS-205] National Institute of Standards and Technology, "Stateless
Hash-Based Digital Signature Standard", August 2023,
.
[GHP18] Giacon, F., Heuer, F., and B. Poettering, "KEM Combiners",
2018, .
[NIST-PQC] Chen, L., Moody, D., and Y. Liu, "Post-Quantum
Cryptography Standardization", December 2016,
.
[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,
.
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[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,
.
[SP800-186-5]
Information Technology Laboratory, National Institute of
Standards and Technology, "Digital Signature Standard
(DSS)", 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,
.
[TR-03111] Federal Office for Information Security, Germany,
"Technical Guideline BSI TR-03111 – Elliptic Curve
Cryptography, Version 2.1", June 2018,
.
Appendix A. Test Vectors
TBD
A.1. Sample v6 PQC Subkey Artifacts
TBD ## V4 PQC Subkey Artifacts
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TBD
Acknowledgments
Authors' Addresses
Quynh Dang
NIST
United States of America
Email: quynh.dang@nist.gov
Stephan Ehlen
BSI
Germany
Email: stephan.ehlen@bsi.bund.de
Johannes Roth
MTG AG
Germany
Email: johannes.roth@mtg.de
Falko Strenzke
MTG AG
Germany
Email: falko.strenzke@mtg.de
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