| Internet-Draft | QSC Keys for CRYSTALS-Dilithium | October 2022 |
| Vredendaal, et al. | Expires 26 April 2023 | [Page] |
This proposal defines key management approaches for the Quantum Safe Cryptographic (QSC) algorithm CRYSTALS-Dilithium which has been selected for standardization by the NIST Post Quantum Cryptography (PQC) process. This includes key identification, key serialization, and key compression. The purpose is to provide guidance such that the adoption of quantum safe algorithms is not hampered with the fragmented evolution of necessary key management standards. Early definition of key material standards will help expedite the adoption of new quantum safe algorithms and at the same time as improving interoperability between implementations and minimizing divergence across standards.¶
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QSC algorithms being standardized in the NIST PQC Process have evolved through several rounds and iterations. Keys are neither easily identifiable nor compatible across rounds. It is also expected that algorithms will evolve after final candidates have been selected. The lack of binary compatibility between algorithm versions and variants means that it is important to clearly identify key material. Parallel to the NIST process, industry is evaluating the impact of adopting new PQC algorithms, in particular key management. Here it is important to define and standardize key serialization and encoding formats. Finally, we have seen that many platforms and protocols are very constrained when it comes to the amount of memory or space available for key objects. This makes it important to define and standardize key compression formats. This proposal addresses aspects of key identification, key serialization, and key compression for the future primary NIST PQC Digital Signature standard, CRYSTALS-Dilithium. For the other schemes, see draft-uni-qsckeys-kyber, draft-uni-qsckeys-falcon, draft-uni-qsckeys-sphincsplus and the previous Internet-Draft [draft-uni-qsckeys-01]. This proposal will be updated when the final NIST standard for CRYSTALS-Dilithium becomes available.¶
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119 [RFC2119] .¶
Algorithm identification is important for several reasons:¶
The current standardization of quantum safe algorithms does not address the definition of serialization structures for keys. As a result, it has become commonplace for the cryptographic community working on and with these algorithms to define their own approaches. This leads to proprietary and internal representations for key material. This has certain advantages in terms of ease of experimentation while focusing on finding the best-performing QSC algorithms. In terms of longer-term support where algorithm versions change this is a problem. This proposal defines in section 2 a long-term structured key representation format useful to address the goals outlined above.¶
Algorithm and algorithm parameter information shall have ASN.1 type AlgorithmIdentifier as given in [RFC5280] and shall be extended by an pqcAlgorithmParameterName type in the optional parameters field:¶
AlgorithmIdentifier ::= SEQUENCE {
algorithm OBJECT IDENTIFIER, - OID: algorithm and algo parameter
parameters pqcAlgorithmParameterName OPTIONAL
}
pqcAlgorithmParameterName ::= PrintableString
¶
CRYSTALS-Dilithium consists of six parameter sets. This memo attributes a name and a placeholder for an OID to the different parameter sets of CRYSTALS-Dilithium. The following table gives an overview of the possible OIDs in the algorithm field and possible parameters set names in the parameters field of the AlgorithmIdentifier type. Each name or OID represents a single parameter set of given security. Details can be found in the next section.¶
|=========+=====+===============================================|
| CRYSTALS-Dilithium (PQC Digital Signature) |
|=========+=====+===============================================|
| dilithium-4x4-r3 |
|---------+-----+-----------------------------------------------|
| |ASN.1|{..*.. pqc-ds-dilithium dilithium-4x4-r3} |
| |dot | |
|---------------+-----+-----------------------------------------|
| dilithium-4x4-aes-r3 |
|---------+-----+-----------------------------------------------|
| |ASN.1| {..*.. pqc-ds-dilithium dilithium-4x4-aes-r3} |
| | dot | |
|---------+-----+-----------------------------------------------|
| dilithium-6x5-r3 |
|---------+-----+-----------------------------------------------|
| |ASN.1| {..*.. pqc-ds-dilithium dilithium-6x5-r3} |
| | Dot | |
|---------+-----+-----------------------------------------------|
| dilithium-6x5-aes-r3 |
|---------+-----+-----------------------------------------------|
| |ASN.1| {..*.. pqc-ds-dilithium dilithium-6x5-aes-r3} |
| | Dot | |
|---------+-----+-----------------------------------------------|
| dilithium-8x7-r3 |
|---------+-----+-----------------------------------------------|
| |ASN.1| {..*.. pqc-ds-dilithium dilithium-8x7-r3} |
| |Dot | |
|---------+-----+-----------------------------------------------|
| dilithium-8x7-aes-r3 |
|---------+-----+-----------------------------------------------|
| |ASN.1| {..*.. pqc-ds-dilithium dilithium-8x7-aes-r3} |
| |dot. | |
|=========+=====+===============================================|
The private key format defined is from PKCS#8 [RFC5208] . PKCS#8 PrivateKeyInfo is defined as:¶
PrivateKeyInfo ::= SEQUENCE {
version INTEGER -- PKCS#8 syntax ver
privateKeyAlgorithm AlgorithmIdentifier -- see chapter above
privateKey OCTET STRING, -- see chapter below
attributes [0] IMPLICIT Attributes OPTIONAL
}
¶
Distributing a PQC private key requires a PKCS#8 PrivateKeyInfo with a joined PQC algorithm and algorithm parameter OID in the algorithm field of AlgorithmIdentifier and a PQC algorithm specific private key object in the privateKey field of PrivateKeyInfo. Both objects are defined in the specific algorithm sections of this document. For an overview see tables above and below.¶
RFC5280 subjectPublicKeyInfo is defined in as:¶
SubjectPublicKeyInfo := SEQUENCE {
algorithm AlgorithmIdentifier -- see chapter above
subjectPublicKey BIT STRING -- see chapter below
}
¶
Distributing a PQC public key requires a [RFC5480] subjectPublicKeyInfo with a joined PQC algorithm and algorithm parameter OID in the algorithm field of AlgorithmIdentifier and a PQC algorithm specific public key object in the subjectPublicKey field of subjectPublicKeyInfo. Both objects are defined in the specific algorithm sections of this document. For an overview see tables above and below.¶
The privateKey field in the PrivateKeyInfo type [RFC5480] is an OCTET STRING whose contents are the value of the private key. The interpretation of the content differs from PQC algorithm to algorithm. The subjectPublicKey field in the subjectPublicKeyInfo type [RFC5480] is a BIT STRING whose contents are the value of the public key. Here also the interpretation of the content differs from PQC algorithm to algorithm.¶
CRYSTALS-Dilithium is a digital signature scheme that is based on the hardness of lattice problems over module lattices.¶
CRYSTALS-Dilithium uses OIDs to identify parameters sets.¶
|=========================+=====================================|
| dilithium-4x4-r3 |
|=========================+=====================================|
| Parameter OID | {..*.. dilithium-4x4-r3} |
| | <.> |
| NIST Level Security | Level 2 |
|-------------------------|-------------------------------------|
| Parameters | Polynomial Ring Zq[x]/( x^n+1 ) |
| | Dimension/Degree n=256 |
| | Modulus q=8380417 |
| | Dropped bits from t: d=13 |
| | # of +-1's in c: tau=39 |
| | challenge entropy=192 |
| | gamma coefficient range: gamma1=2^17|
| | low-order rounding range: gamma2=(q-|
| | 1)/88 |
| | Private key Range eta=2 |
| | Dimensions of A: (k,l)=(4,4) |
| | Max # of 1's in the hint h: w=80 |
| | Repetitions=4.25 |
|=========================+=====================================|
| dilithium-4x4-aes-r3 |
|=========================+=====================================|
| Parameter OID | {..*.. dilithium-4x4-aes-r3} |
| | <.> |
| NIST Level Security | Level 2 |
|-------------------------|-------------------------------------|
| Parameters | Polynomial Ring Zq[x]/( x^n + 1 ) |
| | Dimension/Degree n=256 |
| | Modulus q=8380417 |
| | Dropped bits from t: d=13 |
| | # of +-1's in c: tau=39 |
| | challenge entropy=192 |
| | y coefficient range: gamma1=2^17 |
| | low-order rounding range:gamma2=(q- |
| | -1)/88 |
| | Private key Range eta=2 |
| | Dimensions of A: (k,l)=(4,4) |
| | Max # of 1's in the hint h: w=80 |
| | Repetitions=4.25 |
|=========================+=====================================|
| dilithium-6x5-r3 |
|=========================+=====================================|
| Parameter OID | {..*.. dilithium-6x5-r3} |
| | <.> |
| NIST Level Security | Level 3 |
|-------------------------|-------------------------------------|
| Parameters | Polynomial Ring Zq[x]/( x^n + 1 ) |
| | Dimension/Degree n=256 |
| | Modulus q=8380417 |
| | Dropped bits from t: d=13 |
| | # of +-1's in c: tau=49 |
| | challenge entropy=225 |
| | y coefficient range: gamma1=2^19 |
| | low-order rounding range:gamma2=(q- |
| | -1)/32 |
| | Private key Range eta=4 |
| | Dimensions of A: (k,l)=(6,5) |
| | Max # of 1's in the hint h: w=55 |
| | Repetitions=5.1 |
|=========================+=====================================|
| dilithium-6x5-aes-r3 |
|=========================+=====================================|
| Parameter OID | {..*.. dilithium-6x5-aes-r3} |
| | <.> |
| NIST Level Security | Level 3 |
|-------------------------|-------------------------------------|
| Parameters | Polynomial Ring Zq[x]/( x^n +1 ) |
| | Dimension/Degree n=256 |
| | Modulus q=8380417 |
| | Dropped bits from t: d=13 |
| | # of +-1's in c: tau=49 |
| | challenge entropy=225 |
| | y coefficient range: gamma1=2^19 |
| | low-order rounding range:gamma2=(q- |
| | -1)/32 |
| | Private key Range eta=4 |
| | Dimensions of A: (k,l)=(6,5) |
| | Max # of 1's in the hint h: w=55 |
| | Repetitions=5.1 |
|=========================+=====================================|
| dilithium-8x7-r3 |
|=========================+=====================================|
| Parameter OID | {..*.. dilithium-8x7-r3} |
| | <.> |
| NIST Level Security | Level 5 |
|-------------------------|-------------------------------------|
| Parameters | Polynomial Ring Zq[x]/( x^n + 1 ) |
| | Dimension/Degree n=256 |
| | Modulus q=8380417 |
| | Dropped bits from t: d=13 |
| | # of +-1's in c: tau=60 |
| | challenge entropy=257 |
| | y coefficient range: gamma1=2^19 |
| | low-order rounding range:gamma2=(q- |
| | -1)/32 |
| | Private key Range eta=2 |
| | Dimensions of A: (k,l)=(8,7) |
| | Max # of 1's in the hint h: w=75 |
| | Repetitions=3.85 |
|=========================+=====================================|
| dilithium-8x7-aes-r3 |
|=========================+=====================================|
| Parameter OID | {..*.. dilithium-8x7-aes-r3} |
| | <.> |
| NIST Level Security | Level 5 |
|-------------------------|-------------------------------------|
| Parameters | Polynomial Ring Zq[x]/( x^n + 1 ) |
| | Dimension/Degree n=256 |
| | Modulus q=8380417 |
| | Dropped bits from t: d=13 |
| | # of +-1's in c: tau=60 |
| | challenge entropy=257 |
| | y coefficient range: gamma1=2^19 |
| | low-order rounding range:gamma2=(q- |
| | -1)/32 |
| | Private key Range eta=2 |
| | Dimensions of A: (k,l)=(8,7) |
| | Max # of 1's in the hint h: w=75 |
| | Repetitions=3.85 |
|=========================+=====================================|
The AES variants listed above differ from the other variants in that they use AES, rather than SHAKE internally to expand the key parameters from an initial seed. While the parameters listed in the table are the same, the key-pairs will not be compatible with the 'aes' variants.¶
Public key. The public-key consists of two parameters:¶
The size necessary to hold all public key elements accounts to 32+320*k bytes.¶
Private key. The private key consists of 6 parameters:¶
If the private key is fully populated, it consists of 6 parameters. The size necessary to hold all private key elements accounts to 32+32+32+32*[(k+l)*ceiling(log(2*eta+1))+13*k] bytes. The resulting public key and private key sizes can be found in the table below.¶
|=========================+========+=========+=========+=========| | Algorithm | Public | Private | Partial | Partial | | | Key | Key SK | SK (V1) | SK (V2) | | | Length | Length | Length | Length | |=========================+========+=========+=========+=========+ | dilithium-4x4-r3 | 1312 | 2528 | 64 | 32 | | dilithium-4x4-aes-r3 | 1312 | 2528 | 64 | 32 | | dilithium-6x5-r3 | 1952 | 4000 | 64 | 32 | | dilithium-6x5-aes-r3 | 1952 | 4000 | 64 | 32 | | dilithium-8x7-r3 | 2592 | 4864 | 64 | 32 | | dilithium-8x7-aes-r3 | 2592 | 4864 | 64 | 32 | |=========================+========+=========+=========+=========|
Encoding a CRYSTALS-Dilithium private key with PKCS#8 must include the following two fields:¶
CRYSTALS-Dilithium public keys are optionally distributed in the PublicKey field of the PrivateKeyInfo structure.¶
ASN.1 Encoding for a CRYSTALS-Dilithium private key when fully populated:¶
DilithiumPrivateKey ::= SEQUENCE {
version INTEGER {v0(0)} -- version (round 3)
nonce BIT STRING, -- rho
key BIT STRING, -- key/seed/D
tr BIT STRING, -- PRF bytes (CRH in spec)
s1 BIT STRING, -- vector(L)
s2 BIT STRING, -- vector(K)
t0 BIT STRING,
publicKey [0] IMPLICIT DilithiumPublicKey OPTIONAL
-- see next section
}
¶
In option 1 ofCRYSTALS-Dilithium partial encoding the rho (nonce) and the seed (key) are used to regenerate the full key. Note: There are a number of alternative ways to encode a partially filled structure that include defining fields as optional and defining fields as 'EMPTY'. As an example partial RSA keys are encoded using EMPTY fields. It can be argued that defining fields as EMPTY significantly simplifies the implementation of parsing ASN.1 frames. The ASN.1 format for the partially populated versions is the same as for the fully populated version. The ASN.1 encoding for the first variant (rho and seed) is defined as follows:¶
DilithiumPrivateKey ::= SEQUENCE {
version INTEGER {v0(0)} -- version (round 3)
nonce BIT STRING, -- rho
key BIT STRING, -- key/seed/D
tr BIT STRING, -- EMPTY
s1 BIT STRING, -- EMPTY
s2 BIT STRING, -- EMPTY
t0 BIT STRING, -- EMPTY
publicKey [0] IMPLICIT DilithiumPublicKey OPTIONAL
-- see next section
}
¶
In option 2 of CRYSTALS-Dilithium partial encoding only zeta (nonce) is used to regenerate the full key. The ASN.1 encoding for this is defined as follows:¶
DilithiumPrivateKey ::= SEQUENCE {
version INTEGER {v0(0)} -- version (round 3)
nonce BIT STRING, -- zeta
key BIT STRING, -- EMPTY
tr BIT STRING, -- EMPTY
s1 BIT STRING, -- EMPTY
s2 BIT STRING, -- EMPTY
t0 BIT STRING, -- EMPTY
publicKey [0] IMPLICIT DilithiumPublicKey OPTIONAL
-- see next section
}
¶
Components are individual OCTET STRINGs, without unused bits, encoded with the exact size. There is no removal of leading zeroes.¶
DilithiumPublicKey ::= SEQUENCE {
rho OCTET STRING,
t1 OCTET STRING
}
¶
This template was derived from an initial version written by Pekka Savola and contributed by him to the xml2rfc project.¶
This document is part of a plan to make xml2rfc indispensable.¶
This memo includes no request to IANA.¶
Any processing of the ASN.1 private key structures, such as base64 en/decoding shall be performed in "constant-time", meaning without secret-dependent control flow and table lookups. The ASN.1 structures in this document are defined with fixed tag-lengths. The purpose is to prevent side-channel leakage of variable lengths during DER parsing. Any DER parsing of the private key ASN.1 key structures shall be performed with these fixed lengths.¶
This becomes an Appendix.¶