Internet DRAFT - draft-ounsworth-pq-composite-keys
draft-ounsworth-pq-composite-keys
LAMPS M. Ounsworth
Internet-Draft J. Gray
Intended status: Standards Track Entrust
Expires: 14 September 2023 M. Pala
CableLabs
J. Klaussner
D-Trust GmbH
13 March 2023
Composite Public and Private Keys For Use In Internet PKI
draft-ounsworth-pq-composite-keys-04
Abstract
The migration to post-quantum cryptography is unique in the history
of modern digital cryptography in that neither the old outgoing nor
the new incoming algorithms are fully trusted to protect data for the
required data lifetimes. The outgoing algorithms, such as RSA and
elliptic curve, may fall to quantum cryptalanysis, while the incoming
post-quantum algorithms face uncertainty about both the underlying
mathematics as well as hardware and software implementations that
have not had sufficient maturing time to rule out classical
cryptanalytic attacks and implementation bugs.
Cautious implementers may wish to layer cryptographic algorithms such
that an attacker would need to break all of them in order to
compromise the data being protected using either a Post-Quantum /
Traditional Hybrid, Post-Quantum / Post-Quantum Hybrid, or
combinations thereof. This document, and its companions, defines a
specific instantiation of hybrid paradigm called "composite" where
multiple cryptographic algorithms are combined to form a single key,
signature, or key encapsulation mechanism (KEM) such that they can be
treated as a single atomic object at the protocol level.
This document defines the structures CompositePublicKey and
CompositePrivateKey, which are sequences of the respective structure
for each component algorithm. Explicit pairings of algorithms are
defined which should meet most Internet needs. The generic composite
key type is also defined which allows arbitrary combinations of key
types to be placed in the CompositePublicKey and CompositePrivateKey
structures without needing the combination to be pre-registered or
pre-agreed.
This document is intended to be coupled with corresponding documents
that define the structure and semantics of composite signatures and
encryption, such as [I-D.ounsworth-pq-composite-sigs] and
[I-D.ounsworth-pq-composite-kem].
Ounsworth, et al. Expires 14 September 2023 [Page 1]
Internet-Draft PQ Composite Keys March 2023
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-ounsworth-pq-composite-keys/.
Discussion of this document takes place on the Limited Additional
Mechanisms for PKIX and SMIME (lamps) Working Group mailing list
(mailto:spasm@ietf.org), which is archived at
https://mailarchive.ietf.org/arch/browse/spasm/. Subscribe at
https://www.ietf.org/mailman/listinfo/spasm/.
Source for this draft and an issue tracker can be found at
https://github.com/EntrustCorporation/draft-ounsworth-pq-composite-
keys.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
Drafts is at https://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on 14 September 2023.
Copyright Notice
Copyright (c) 2023 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents (https://trustee.ietf.org/
license-info) in effect on the date of publication of this document.
Please review these documents carefully, as they describe your rights
and restrictions with respect to this document. Code Components
extracted from this document must include Revised BSD License text as
described in Section 4.e of the Trust Legal Provisions and are
provided without warranty as described in the Revised BSD License.
Ounsworth, et al. Expires 14 September 2023 [Page 2]
Internet-Draft PQ Composite Keys March 2023
Table of Contents
1. Changes in version -04 . . . . . . . . . . . . . . . . . . . 4
2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1. Algorithm Selection Criteria . . . . . . . . . . . . . . 6
2.2. Terminology . . . . . . . . . . . . . . . . . . . . . . . 7
3. Composite Key Structures . . . . . . . . . . . . . . . . . . 7
3.1. pk-Composite . . . . . . . . . . . . . . . . . . . . . . 8
3.2. CompositePublicKey . . . . . . . . . . . . . . . . . . . 8
3.2.1. Key Usage . . . . . . . . . . . . . . . . . . . . . . 9
3.2.2. Component Matching . . . . . . . . . . . . . . . . . 9
3.3. CompositePrivateKey . . . . . . . . . . . . . . . . . . . 10
3.4. As a PrivateKeyInfo or OneAsymmetricKey . . . . . . . . . 10
3.5. Encoding Rules . . . . . . . . . . . . . . . . . . . . . 10
4. Algorithm Identifiers . . . . . . . . . . . . . . . . . . . . 11
4.1. Signature public key types . . . . . . . . . . . . . . . 11
4.2. KEM public key types . . . . . . . . . . . . . . . . . . 14
5. ASN.1 Module . . . . . . . . . . . . . . . . . . . . . . . . 16
6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 26
7. Security Considerations . . . . . . . . . . . . . . . . . . . 27
7.1. Reuse of keys in a Composite public key . . . . . . . . . 27
7.2. Key mismatch in explicit composite . . . . . . . . . . . 27
7.3. Policy for Deprecated and Acceptable Algorithms . . . . . 27
7.4. Protection of Private Keys . . . . . . . . . . . . . . . 28
7.5. Checking for Compromised Key Reuse . . . . . . . . . . . 28
8. References . . . . . . . . . . . . . . . . . . . . . . . . . 28
8.1. Normative References . . . . . . . . . . . . . . . . . . 28
8.2. Informative References . . . . . . . . . . . . . . . . . 31
Appendix A. Work in Progress . . . . . . . . . . . . . . . . . . 33
A.1. Combiner modes (KofN) . . . . . . . . . . . . . . . . . . 33
Appendix B. Samples . . . . . . . . . . . . . . . . . . . . . . 33
B.1. Generic Composite Public Key Samples . . . . . . . . . . 33
B.2. Explicit Composite Public Key Samples . . . . . . . . . . 36
B.2.1. id-Dilithium3-ECDSA-P256 . . . . . . . . . . . . . . 36
B.2.2. id-Dilithium3-RSA . . . . . . . . . . . . . . . . . . 40
B.2.3. id-Falcon512-ECDSA-P256 . . . . . . . . . . . . . . . 44
B.2.4. id-SPHINCSplusSHA256256frobust-ECDSA-P256 . . . . . . 46
Appendix C. Implementation Considerations . . . . . . . . . . . 48
C.1. Textual encoding of Composite Private Keys . . . . . . . 48
C.2. Backwards Compatibility . . . . . . . . . . . . . . . . . 48
C.2.1. OR modes . . . . . . . . . . . . . . . . . . . . . . 49
C.2.2. Parallel PKIs . . . . . . . . . . . . . . . . . . . . 49
Appendix D. Intellectual Property Considerations . . . . . . . . 50
Appendix E. Contributors and Acknowledgements . . . . . . . . . 50
E.1. Making contributions . . . . . . . . . . . . . . . . . . 51
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 51
Ounsworth, et al. Expires 14 September 2023 [Page 3]
Internet-Draft PQ Composite Keys March 2023
1. Changes in version -04
* General restructuring of the document.
* Aligned composite pairings with OpenPGP () and JOSE/COSE WGs,
particularly draft-wussler-openpgp-pqc-00.
* We have dropped the MAY / RECOMMENDED column as well as per-
algorithm usage guidance because in the end we think it does not
belong at the X.509 level because we believe these recommendations
belong at the application profile level; for example what is
RECOMMENDED for X.509-based client authentication may be very
different from what is RECOMMENDED for X.509-based code-signing.
* Renamed "id-SPHINCSsha256256frobust-ECDSA-P256" to "id-
SPHINCSplusSHA256-ECDSA-P256" because the public key format does
not depend on the signature algorithm parameters.
* The following algorithms were removed:
- pk-example-ECandRSA
- id-Dilithium5-Falcon1024-ECDSA-P521
- id-Dilithium5-Falcon1024-RSA
- id-Kyber512-RSA
* The following algorithms were added:
- id-Dilithium3-EDSA-brainpoolP256r1
- id-Dilithium3-Ed25519
- id-Dilithium5-ECDSA-P384
- id-Dilithium5-ECDSA-brainpoolP384r1
- id-Dilithium5-Ed448
- id-Falcon512-ECDSA-brainpoolP256r1
- id-SPHINCSplusSHA256-ECDSA-brainpoolP256r1
- id-SPHINCSplusSHA256-Ed25519
- id-Kyber512-ECDH-brainpoolP256r1-KMAC128
Ounsworth, et al. Expires 14 September 2023 [Page 4]
Internet-Draft PQ Composite Keys March 2023
- id-Kyber768-RSA-KMAC256
- id-Kyber768-ECDH-P256-KMAC256
- id-Kyber768-ECDH-brainpoolP256r1-KMAC256
- id-Kyber768-X25519-KMAC256
- id-Kyber1024-ECDH-P384-KMAC256
- id-Kyber1024-ECDH-brainpoolP384r1-KMAC256
- id-Kyber1024-X448-KMAC256
* Changed "examples" to "samples" when referring to Appendix B.
2. Introduction
During the transition to post-quantum cryptography (PQ or PQC), there
will be uncertainty as to the strength of cryptographic algorithms;
we will no longer fully trust traditional cryptography such as RSA,
Diffie-Hellman, DSA and their elliptic curve variants, but we may
also not fully trust their post-quantum replacements until further
time has passed to allow additional scrutiny and the discovery of
implementation bugs. Unlike previous cryptographic algorithm
migrations, the choice of when to migrate and which algorithms to
migrate to, is not so clear. Even after the migration period, it may
be advantageous for an entity's cryptographic identity to be composed
of multiple public-key algorithms by using a Post-Quantum/Traditional
(PQ/T) or Post-Quantum/Post-Quantum (PQ/PQ) Hybrid scheme.
The transition to PQC will face two challenges:
* Algorithm strength uncertainty: During the transition period, some
post-quantum signature and encryption algorithms will not be fully
trusted, while also the trust in legacy public key algorithms will
start to erode. A relying party may learn some time after
deployment that a public key algorithm has become untrustworthy,
but in the interim, they may not know which algorithm an adversary
has compromised.
* Migration: During the transition period, systems will require
mechanisms that allow for staged migrations from fully traditional
to fully post-quantum-aware cryptography.
This document provides the composite mechanism, which is a specific
instantiation of the PQ/T hybrid paradigm to address algorithm
strength uncertainty concerns by providing formats for encoding
Ounsworth, et al. Expires 14 September 2023 [Page 5]
Internet-Draft PQ Composite Keys March 2023
multiple public key and private key values into existing public key
and private key fields. Backwards compatibility is not directly
addressed via the composite mechanisms defined in the document, but
some notes on how it can be obtained can be found in Appendix C.2.
This document only specifies key formats; usage of these keys are
covered in the corresponding composite signatures
[I-D.ounsworth-pq-composite-sigs] and composite KEM
[I-D.ounsworth-pq-composite-kem] specifications.
This document is intended for general applicability anywhere that
keys are used within PKIX or CMS structures.
2.1. Algorithm Selection Criteria
The composite algorithm combinations defined in this document were
chosen according to the following guidelines:
1. A single RSA combination is provided (but RSA modulus size not
mandated), matched with NIST PQC Level 3 algorithms.
2. Elliptic curve algorithms are provided with combinations on each
of the NIST [RFC6090], Brainpool [RFC5639], and Edwards [RFC7748]
curves. NIST PQC Levels 1 - 3 algorithms are matched with
256-bit curves, while NIST levels 4 - 5 are matched with 384-bit
elliptic curves. This provides a balance between matching
classical security levels of post-quantum and traditional
algorithms, and also selecting elliptic curves which already have
wide adoption.
3. NIST level 1 candidates (Falcon512 and Kyber512) are provided,
matched with 256-bit elliptic curves, intended for constrained
use cases.
4. A single SPHINCS+ combination is provided for use cases that wish
to put hash-based signatures into hybrid combination.
5. A generic composite algorithm is provided for implementers who
wish to use combinations not listed here, without the overhead of
defining new OIDs. Caution should be exercised to avoid issues
with compatibility and complex cryptographic policy mechanisms.
The authors wish to note that although all the composite structures
defined in this and the companion composite signatures
[I-D.ounsworth-pq-composite-sigs] and composite KEM
[I-D.ounsworth-pq-composite-kem] specifications are defined in such a
way as to easily allow 3 or more component algorithms, it was decided
to only specify explicit pairs. The generic composite specified in
Ounsworth, et al. Expires 14 September 2023 [Page 6]
Internet-Draft PQ Composite Keys March 2023
this document allows for an arbitrary number of components. This
also does not preclude future specification of explicit combinations
with three or more components.
2.2. Terminology
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in
BCP14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here.
This document is consistent with all terminology from
[I-D.driscoll-pqt-hybrid-terminology].
In addition, the following terms are used in this document:
BER: Basic Encoding Rules (BER) as defined in [X.690].
CLIENT: Any software that is making use of a cryptographic key. This
includes a signer, verifier, encrypter, decrypter.
DER: Distinguished Encoding Rules as defined in [X.690].
PKI: Public Key Infrastructure, as defined in [RFC5280].
3. Composite Key Structures
In order to represent public keys and private keys that are composed
of multiple algorithms, we define encodings consisting of a sequence
of public key or private key primitives (aka "components") such that
these structures can be used directly in existing public key fields
such as those found in PKCS#10 [RFC2986], CMP [RFC4210], X.509
[RFC5280], CMS [RFC5652], and the Trust Anchor Format [RFC5914].
[I-D.driscoll-pqt-hybrid-terminology] defines composites as:
_Composite Cryptographic Element_: A cryptographic element that
incorporates multiple component cryptographic elements of the same
type in a multi-algorithm scheme.
Composite keys as defined here follow this definition and should be
regarded as a single key that performs a single cryptographic
operation such key generation, signing, verifying, encapsulating, or
decapsulating -- using its encapsulated sequence of component keys as
if it was a single key. This generally means that the complexity of
combining algorithms can and should be ignored by application and
protocol layers and deferred to the cryptographic library layer.
Ounsworth, et al. Expires 14 September 2023 [Page 7]
Internet-Draft PQ Composite Keys March 2023
3.1. pk-Composite
The following ASN.1 Information Object Class applies to all composite
key types, with suitable replacements for the ASN.1 identifier pk-
Composite and the OID id-composite-key as appropriate. See the ASN.1
Module in Section 5 for parmeterized as well as signature and KEM
versions.
pk-Composite PUBLIC-KEY ::= {
id id-composite-key
KeyValue CompositePublicKey
Params ARE ABSENT
PrivateKey CompositePrivateKey
}
keyUsage is omitted here because composites may be formed for keys of
any type, provided that any key usage specified MUST apply to all
component keys. Composites MAY NOT be used to combine key types, for
example to make a "dual-usage" key by combining a signing key with a
KEM key.
3.2. CompositePublicKey
Composite public key data is represented by the following structure:
CompositePublicKey ::= SEQUENCE SIZE (2..MAX) OF SubjectPublicKeyInfo
A composite key MUST contain at least two component public keys.
When the composite key is used in conjunction with an explicit
composite algorithm identifier defined under section Section 4, the
order of the component keys is determined by that algorithm
identifier's definition.
A CompositePublicKey MUST NOT contain a component public key which
itself describes a composite key; i.e. recursive CompositePublicKeys
are not allowed. The purpose is a general reduction in complexity by
not needing to consider nested key types.
Each element of a CompositePublicKey is a SubjectPublicKeyInfo object
encoding a component public key. Each component SubjectPublicKeyInfo
SHALL contain an AlgorithmIdentifier OID which identifies the public
key type and parameters for the public key contained within it. See
Section 4 for specific algorithms defined in this document.
When the CompositePublicKey must be provided in octet string or bit
string format, the data structure is encoded as specified in
Section 3.5.
Ounsworth, et al. Expires 14 September 2023 [Page 8]
Internet-Draft PQ Composite Keys March 2023
3.2.1. Key Usage
Protocols such as X.509 [RFC5280] that specify a key usage along with
the public key. For composite keys, a single key usage is specified
for the entire public key and it MUST apply to all component keys.
For example if a composite key is marked with a key usage of
digitalSignature, then all component keys MUST be capable of
producing digital signatures and handled with policies appropriate
for digital signature keys. The composite mechanism MUST NOT be used
to implement mixed-usage keys, for example, where a digitalSignature
and a keyEncipherment key are combined together into a single
composite key.
Specifications of explicit composite key types must specify allowable
key usages for that type based on the types of the components.
3.2.2. Component Matching
Many cryptographic libraries will require treating each component key
independently and thus expect a full SubjectPublicKeyInfo for each
component at some layer of the software stack. This left two design
choices: either we carry full SPKI for each component within the
CompositePublicKey, or we compress it by only carrying the raw key
bytes and force implementations to carry OID and parameter mapping
tables to be able to reconstruct component SPKIs.
The authors decided to carry the full SPKIs in order to lessen the
implementation complexity at the expense of a small amount of
redundant data to transmit. This also leads to the same wire format
between explicitly specified combinations and generic composites
where the component OIDs cannot be infered and thus must be carried.
This design choice has a non-obvious security risk in that the
algorithm carried within each component SPKI is redundant information
which MUST match -- and can be inferred from -- the specification of
the explicit algorithm.
Security consideration: Implementations SHOULD check that the
component AlgorithmIdentifier OIDs and parameters match those
expected by the definition of the explicit algorithm.
Implementations SHOULD first parse a component's
SubjectPublicKeyInfo.algorithm, and ensure that it matches what is
expected for that position in the explicit key, and then proceed to
parse the SubjectPublicKeyInfo.subjectPublicKey. This is to reduce
the attack surface associated with parsing the public key data of an
unexpected key type, or worse; to parse and use a key which does not
match the explicit algorithm definition. Similar checks SHOULD be
done when handling the corresponding private key.
Ounsworth, et al. Expires 14 September 2023 [Page 9]
Internet-Draft PQ Composite Keys March 2023
3.3. CompositePrivateKey
This section provides an encoding for composite private keys intended
for PKIX protocols and other applications that require an
interoperable format for transmitting private keys, such as PKCS #12
[RFC7292] or CMP / CRMF [RFC4210], [RFC4211]. It is not intended to
dictate a storage format in implementations not requiring
interoperability of private key formats.
In some cases the private keys that comprise a composite key may not
be represented in a single structure or even be contained in a single
cryptographic module. The establishment of correspondence between
public keys in a CompositePublicKey and private keys not represented
in a single composite structure is beyond the scope of this document.
The composite private key data is represented by the following
structure:
CompositePrivateKey ::= SEQUENCE SIZE (2..MAX) OF OneAsymmetricKey
Each element is a OneAsymmetricKey [RFC5958] object for a component
private key.
The parameters field MUST be absent.
A CompositePrivateKey MUST contain at least two component private
keys, and the order of the component keys is the same as the order
defined in Section 3.2 for the components of CompositePublicKey.
3.4. As a PrivateKeyInfo or OneAsymmetricKey
A CompositePrivateKey can be stored in a OneAsymmetricKey structure
(version 1 of which is also known as PrivateKeyInfo) [RFC5958]. When
this is done, the privateKeyAlgorithm field SHALL be set to the
corresponding composite algorithm identifier defined according to
Section 4, the privateKey field SHALL contain the
CompositePrivateKey, and the publicKey field MUST NOT be present.
Associated public key material MAY be present in the
CompositePrivateKey.
3.5. Encoding Rules
Many protocol specifications will require that the composite public
key and composite private key data structures be represented by an
octet string or bit string.
When an octet string is required, the DER encoding of the composite
data structure SHALL be used directly.
Ounsworth, et al. Expires 14 September 2023 [Page 10]
Internet-Draft PQ Composite Keys March 2023
CompositePublicKeyOs ::= OCTET STRING (CONTAINING CompositePublicKey ENCODED BY der)
When a bit string is required, the octets of the DER encoded
composite data structure SHALL be used as the bits of the bit string,
with the most significant bit of the first octet becoming the first
bit, and so on, ending with the least significant bit of the last
octet becoming the last bit of the bit string.
CompositePublicKeyBs ::= BIT STRING (CONTAINING CompositePublicKey ENCODED BY der)
4. Algorithm Identifiers
This section defines algorithm identifiers, component algorithms and
their ordering for composite combinations. The combinations
registered in this section are intended to strike a balance between
the overall number of combinations ("the combinatorial explosion
problem"), while also covering the needs of a wide range of
protocols, applications, and regulatory environments in which
X.509-based technologies are used.
This section is not intended to be exhaustive and other authors may
define OIDs for new combinations so long as they are compatible with
the structures and processes defined in this and the companion
signature and encryption documents.
4.1. Signature public key types
This table summarizes the list of explicit composite Signature
algorithms by the key and signature OID and the two component
algorithms which make up the explicit composite algorithm. These are
denoted by First Signature Alg, and Second Signature Alg.
The OID referenced are TBD and MUST be used only for prototyping and
replaced with the final IANA-assigned OIDS. The following prefix is
used for each: replace <CompSig> with the String
"2.16.840.1.114027.80.5.1"
Therefore <CompSig>.1 is equal to 2.16.840.1.114027.80.5.1.1
Note that a single OID is used for both the key type and the
signature algorithm; ie there is a one-to-one correspondance between
key types and signature algorithms, hence why these key type names
contain more information than they strictly need to define a key
type.
Ounsworth, et al. Expires 14 September 2023 [Page 11]
Internet-Draft PQ Composite Keys March 2023
+============================+===============+===========================+===============+
|Composite Signature Key Type|OID |First Key Type |Second Key Type|
+============================+===============+===========================+===============+
|id-Dilithium3-RSA-PSS |<CompSig>.14 |Dilithium3 |RSASSA-PSS |
+----------------------------+---------------+---------------------------+---------------+
|id-Dilithium3-RSA- |<CompSig>.1 |Dilithium3 |RSAES-PKCS-v1_5|
|PKCS15-SHA256 | | | |
+----------------------------+---------------+---------------------------+---------------+
|id-Dilithium3-ECDSA- |<CompSig>.2 |Dilithium3 |EC-P256 |
|P256-SHA256 | | | |
+----------------------------+---------------+---------------------------+---------------+
|id-Dilithium3-ECDSA- |<CompSig>.3 |Dilithium3 |EC- |
|brainpoolP256r1-SHA256 | | |brainpoolP256r1|
+----------------------------+---------------+---------------------------+---------------+
|id-Dilithium3-Ed25519 |<CompSig>.4 |Dilithium3 |Ed25519 |
+----------------------------+---------------+---------------------------+---------------+
|id-Dilithium5-ECDSA- |<CompSig>.5 |Dilithium5 |EC-P384 |
|P384-SHA384 | | | |
+----------------------------+---------------+---------------------------+---------------+
|id-Dilithium5-ECDSA- |<CompSig>.6 |Dilithium5 |EC- |
|brainpoolP384r1-SHA384 | | |brainpoolP384r1|
+----------------------------+---------------+---------------------------+---------------+
|id-Dilithium5-Ed448 |<CompSig>.7 |Dilithium5 |Ed448 |
+----------------------------+---------------+---------------------------+---------------+
|id-Falcon512-ECDSA- |<CompSig>.8 |Falcon512 |EC-P256 |
|P256-SHA256 | | | |
+----------------------------+---------------+---------------------------+---------------+
|id-Falcon512-ECDSA- |<CompSig>.9 |Falcon512 |EC- |
|brainpoolP256r1-SHA256 | | |brainpoolP256r1|
+----------------------------+---------------+---------------------------+---------------+
|id-Falcon512-Ed25519 |<CompSig>.10 |Falcon512 |Ed25519 |
+----------------------------+---------------+---------------------------+---------------+
|id- |<CompSig>.11 |SPHINCSplusSHA256128sSimple|EC-P256 |
|SPHINCSplusSHA256128sSimple-| | | |
|ECDSA-P256-SHA256 | | | |
+----------------------------+---------------+---------------------------+---------------+
|id- |<CompSig>.12 |SPHINCSplusSHA256128sSimple|EC- |
|SPHINCSplusSHA256128sSimple-| | |brainpoolP256r1|
|ECDSA-brainpoolP256r1-SHA256| | | |
+----------------------------+---------------+---------------------------+---------------+
|id- |<CompSig>.13 |SPHINCSplusSHA256128sSimple|Ed25519 |
|SPHINCSplusSHA256128sSimple-| | | |
|Ed25519 | | | |
+----------------------------+---------------+---------------------------+---------------+
|id-composite-sig |(1) identified-|Any |Any |
| |organization(3)| | |
| |dod(6) | | |
| |internet(1) | | |
Ounsworth, et al. Expires 14 September 2023 [Page 12]
Internet-Draft PQ Composite Keys March 2023
| |private(4) | | |
| |enterprise(1) | | |
| |OpenCA(18227) | | |
| |Algorithms(2) | | |
| |id-alg- | | |
| |composite(1) | | |
+----------------------------+---------------+---------------------------+---------------+
Table 1
The table above contains everything needed to implement the listed
explicit composite algorithms. See the ASN.1 module in section
Section 5 for the explicit definitions of the above Composite
signature algorithms.
Full specifications for the referenced algorithms can be found as
follows:
* _Dilithium_: [I-D.ietf-lamps-dilithium-certificates]
* _EC_: [RFC5480]
- _EC-P256_: AlgorithmIdentifier.parameters MUST be secp256r1 as
defined in [RFC5480].
- _EC-brainpoolP256r1_: AlgorithmIdentifier.parameters MUST be
brainpoolP256r1 as defined in [RFC5639].
- _EC-P384_: AlgorithmIdentifier.parameters MUST be secp384r1 as
defined in [RFC5480].
- _EC-brainpoolP384r1_: AlgorithmIdentifier.parameters MUST be
brainpoolP384r1 as defined in [RFC5639].
* _Ed25519 / Ed448_: [RFC8410]
* _Falcon_: TBD
* _RSAES-PKCS-v1_5_: [RFC8017]
* _RSASSA-PSS_: [RFC8017]
* _SPHICNCSplus_: [I-D.ietf-lamps-cms-sphincs-plus]
Ounsworth, et al. Expires 14 September 2023 [Page 13]
Internet-Draft PQ Composite Keys March 2023
The intended application for the key is indicated in the keyUsage
certificate extension; see Section 4.2.1.3 of [RFC5280]. If the
keyUsage extension is present in a certificate that indicates
signature public key types above in the SubjectPublicKeyInfo, then
the at least one of following MUST be present:
digitalSignature; or
nonRepudiation; or
keyCertSign; or
cRLSign.
Requirements about the keyUsage extension bits defined in [RFC5280]
still apply.
4.2. KEM public key types
This table summarizes the list of explicit composite Signature
algorithms by the key and signature OID and the two component
algorithms which make up the explicit composite algorithm. These are
denoted by First Signature Alg, and Second Signature Alg.
The OID referenced are TBD and MUST be used only for prototyping and
replaced with the final IANA-assigned OIDS. The following prefix is
used for each: replace <CompKEM> with the String
"2.16.840.1.114027.80.5.2"
Therefore <CompKEM>.1 is equal to 2.16.840.1.114027.80.5.2.1.
Note that a single OID is used for both the key type and the KEM
algorithm; ie there is a one-to-one correspondance between key types
and KEM algorithms, hence why these key type names contain more
information than they strictly need to define a key type.
Ounsworth, et al. Expires 14 September 2023 [Page 14]
Internet-Draft PQ Composite Keys March 2023
+=======================+========================+=========+===============++
|Composite KEM Key Type |OID |First Key|Second Key Type||
| | |Type | ||
+=======================+========================+=========+===============++
|id-Kyber512-ECDH- |<CompKEM>.1 |Kyber512 |EC-P256 ||
|P256-KMAC128 | | | ||
+-----------------------+------------------------+---------+---------------++
|id-Kyber512-ECDH- |<CompKEM>.2 |Kyber512 |EC- ||
|brainpoolP256r1-KMAC128| | |brainpoolP256r1||
+-----------------------+------------------------+---------+---------------++
|id- |<CompKEM>.3 |Kyber512 |X25519 ||
|Kyber512-X25519-KMAC128| | | ||
+-----------------------+------------------------+---------+---------------++
|id-Kyber768-RSA-KMAC256|<CompKEM>.4 |Kyber768 |RSA-KEM ||
+-----------------------+------------------------+---------+---------------++
|id-Kyber768-ECDH- |<CompKEM>.5 |Kyber768 |EC-P256 ||
|P256-KMAC256 | | | ||
+-----------------------+------------------------+---------+---------------++
|id-Kyber768-ECDH- |<CompKEM>.6 |Kyber768 |EC- ||
|brainpoolP256r1-KMAC256| | |brainpoolP256r1||
+-----------------------+------------------------+---------+---------------++
|id- |<CompKEM>.7 |Kyber768 |X25519 ||
|Kyber768-X25519-KMAC256| | | ||
+-----------------------+------------------------+---------+---------------++
|id-Kyber1024-ECDH- |<CompKEM>.8 |Kyber1024|EC-P384 ||
|P384-KMAC256 | | | ||
+-----------------------+------------------------+---------+---------------++
|id-Kyber1024-ECDH- |<CompKEM>.9 |Kyber1024|EC- ||
|brainpoolP384r1-KMAC256| | |brainpoolP384r1||
+-----------------------+------------------------+---------+---------------++
|id- |<CompKEM>.10 |Kyber1024|X448 ||
|Kyber1024-X448-KMAC256 | | | ||
+-----------------------+------------------------+---------+---------------++
|id-composite-kem- |2.16.840.1.114027.80.4.1|Any |Any ||
|KMAC128 | | | ||
+-----------------------+------------------------+---------+---------------++
|id-composite-kem- |2.16.840.1.114027.80.4.1|Any |Any ||
|KMAC256 |NEEDS NEW OID | | ||
+-----------------------+------------------------+---------+---------------++
Table 2: Composite KEM key types
The table above contains everything needed to implement the listed
explicit composite algorithms. See the ASN.1 module in section
Section 5 for the explicit definitions of the above Composite
signature algorithms.
Ounsworth, et al. Expires 14 September 2023 [Page 15]
Internet-Draft PQ Composite Keys March 2023
Full specifications for the referenced algorithms can be found as
follows:
* _EC_: [RFC5480]
- _EC-P256_: AlgorithmIdentifier.parameters within the component
SKPI belonging to the EC key MUST be secp256r1 as defined in
[RFC5480].
- _EC-brainpoolP256r1_: AlgorithmIdentifier.parameters within the
component SKPI belonging to the EC key MUST be brainpoolP256r1
as defined in [RFC5639].
- _EC-P384_: AlgorithmIdentifier.parameters within the component
SKPI belonging to the EC key MUST be secp384r1 as defined in
[RFC5480].
- _EC-brainpoolP384r1_: AlgorithmIdentifier.parameters within the
component SKPI belonging to the EC key MUST be brainpoolP384r1
as defined in [RFC5639].
* _Kyber_: [I-D.ietf-lamps-kyber-certificates]
* _RSA-KEM_: [RFC5990]
* _X25519 / X448_: [RFC8410]
Note: the inclusion of a hash function is so that these algorithm
identifiers can double as both key types and KEM algorithms.
The intended application for the key is indicated in the keyUsage
certificate extension; see Section 4.2.1.3 of [RFC5280]. If the
keyUsage extension is present in a certificate that indicates any of
the KEM public key types above in the SubjectPublicKeyInfo, then the
following MUST be present:
keyEncipherment
Requirements about the keyUsage extension bits defined in [RFC5280]
still apply.
5. ASN.1 Module
Ounsworth, et al. Expires 14 September 2023 [Page 16]
Internet-Draft PQ Composite Keys March 2023
<CODE STARTS>
-- command for easily copying it into a compiler (ubuntu with xclip)
-- cat ASN1ModuleIncludes.asn Composite-Keys-2023.asn | xclip -sel clip
Composite-Keys-2023
{iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) id-mod(0) id-mod-composite-keys(98)}
DEFINITIONS IMPLICIT TAGS ::= BEGIN
EXPORTS ALL;
IMPORTS
PUBLIC-KEY, SIGNATURE-ALGORITHM, ParamOptions, AlgorithmIdentifier{}
FROM AlgorithmInformation-2009 -- RFC 5912 [X509ASN1]
{ iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-algorithmInformation-02(58) }
SubjectPublicKeyInfo
FROM PKIX1Explicit-2009
{ iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-pkix1-explicit-02(51) }
OneAsymmetricKey
FROM AsymmetricKeyPackageModuleV1
{ iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1)
pkcs-9(9) smime(16) modules(0)
id-mod-asymmetricKeyPkgV1(50) }
NamedCurve
FROM PKIXAlgs-2009 { iso(1) identified-organization(3) dod(6)
internet(1) security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-pkix1-algorithms2008-02(56) }
pk-Ed25519, pk-X25519, pk-X448
FROM Safecurves-pkix-18
{ iso(1) identified-organization(3) dod(6) internet(1)
security(5) mechanisms(5) pkix(7) id-mod(0)
id-mod-safecurves-pkix(93) } ;
Ounsworth, et al. Expires 14 September 2023 [Page 17]
Internet-Draft PQ Composite Keys March 2023
--
-- Object Identifiers
--
der OBJECT IDENTIFIER ::=
{joint-iso-itu-t asn1(1) ber-derived(2) distinguished-encoding(1)}
-- TODO: To be replaced by IANA
id-composite-key OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) composite(4) compositekey(1) }
-- COMPOSITE-KEY-ALGORITHM
--
-- Describes the basic properties of a composite key algorithm
--
-- &id - contains the OID identifying the composite algorithm
-- &Params - if present, contains the type for the algorithm
-- parameters; if absent, implies no parameters
-- ¶mPresence - parameter presence requirement
--
-- }
COMPOSITE-KEY-ALGORITHM ::= CLASS {
&id OBJECT IDENTIFIER UNIQUE,
&Params OPTIONAL,
¶mPresence ParamOptions DEFAULT absent
} WITH SYNTAX {
IDENTIFIER &id
[PARAMS [TYPE &Params] ARE ¶mPresence ]
}
--
-- Public Key
--
-- Generic Composite
-- TODO: To be replaced by IANA
id-composite-key OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) composite(4) compositekey(1) }
pk-Composite PUBLIC-KEY ::= {
IDENTIFIER id-composite-key
Ounsworth, et al. Expires 14 September 2023 [Page 18]
Internet-Draft PQ Composite Keys March 2023
KEY CompositePublicKey
PARAMS TYPE CompositeAlgorithmIdentifier ARE optional
PRIVATE-KEY CompositePrivateKey
}
CompositePublicKey ::= SEQUENCE SIZE (2..MAX) OF SubjectPublicKeyInfo
CompositePublicKeyOs ::= OCTET STRING (CONTAINING CompositePublicKey ENCODED BY der)
CompositePublicKeyBs ::= BIT STRING (CONTAINING CompositePublicKey ENCODED BY der)
CompositePrivateKey ::= SEQUENCE SIZE (2..MAX) OF OneAsymmetricKey
--
-- Composite public key information objects
--
-- The following ASN.1 object class then automatically generates the
-- public key structure from the types defined in pk-explicitComposite.
-- ExplicitCompositePublicKey - The data structure for a composite
-- public key sec-composite-pub-keys and SecondPublicKeyType are needed
-- because PUBLIC-KEY contains a set of public key types, not a single
-- type.
-- TODO The parameters should be optional only if they are marked
-- optional in the PUBLIC-KEY
ExplicitCompositePublicKey{PUBLIC-KEY:firstPublicKey, FirstPublicKeyType,
PUBLIC-KEY:secondPublicKey, SecondPublicKeyType} ::= SEQUENCE {
firstPublicKey SEQUENCE {
params firstPublicKey.&Params OPTIONAL,
publicKey FirstPublicKeyType
},
secondPublicKey SEQUENCE {
params secondPublicKey.&Params OPTIONAL,
publicKey SecondPublicKeyType
}
}
pk-explicitCompositeSignature{OBJECT IDENTIFIER:id, PUBLIC-KEY:firstPublicKey,
FirstPublicKeyType, PUBLIC-KEY:secondPublicKey, SecondPublicKeyType}
PUBLIC-KEY ::= {
IDENTIFIER id
KEY ExplicitCompositePublicKey{firstPublicKey, FirstPublicKeyType,
secondPublicKey, SecondPublicKeyType}
PARAMS ARE absent
Ounsworth, et al. Expires 14 September 2023 [Page 19]
Internet-Draft PQ Composite Keys March 2023
CERT-KEY-USAGE { digitalSignature, nonRepudiation, keyCertSign, cRLSign }
}
pk-explicitCompositeKEM{OBJECT IDENTIFIER:id, PUBLIC-KEY:firstPublicKey,
FirstPublicKeyType, PUBLIC-KEY:secondPublicKey, SecondPublicKeyType}
PUBLIC-KEY ::= {
IDENTIFIER id
KEY ExplicitCompositePublicKey{firstPublicKey, FirstPublicKeyType,
secondPublicKey, SecondPublicKeyType}
PARAMS ARE absent
CERT-KEY-USAGE { keyEncipherment }
}
-- TODO this is one possible way to reference specific named curves.
-- But I don't think this compiles.
--pk-ECDSA-P256 PUBLIC-KEY ::= {
-- IDENTIFIER id-ecPublicKey
-- KEY ECPoint
-- PARAMS TYPE NamedCurve.secp256r1 ARE required }
--
--pk-ECDSA-brainpoolP256r1 PUBLIC-KEY ::= {
-- IDENTIFIER id-ecPublicKey
-- KEY ECPoint
-- PARAMS NamedCurve{brainpoolP256r1} }
--
--pk-ECDSA-P384 PUBLIC-KEY ::= {
-- IDENTIFIER id-ecPublicKey
-- KEY ECPoint
-- PARAMS TYPE NamedCurve{secp384r1} }
--
--pk-ECDSA-brainpoolP384r1 PUBLIC-KEY ::= {
-- IDENTIFIER id-ecPublicKey
-- KEY ECPoint
-- PARAMS NamedCurve{brainpoolP384r1} }
-- Explicit Composite Signature Keys
-- TODO: To be replaced by IANA
id-Dilithium3-RSA-PSS OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature(1) dilithium3-rsa-pss(14) }
pk-Dilithium3-RSA-PSS PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-Dilithium3-RSA-PSS, pk-Dilithium3TBD,
Ounsworth, et al. Expires 14 September 2023 [Page 20]
Internet-Draft PQ Composite Keys March 2023
OCTET STRING, pk-rsaSSA-PSS, OCTET STRING}
-- TODO: To be replaced by IANA
id-Dilithium3-RSA-PKCS15-SHA256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature(1) dilithium3-rsa(1) }
pk-Dilithium3-RSA-PKCS15-SHA256 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-Dilithium3-RSA-PKCS15-SHA256,
pk-Dilithium3TBD, OCTET STRING, pk-rsa, RSAPublicKey}
-- TODO: To be replaced by IANA
id-Dilithium3-ECDSA-P256-SHA256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature(1) dilithium3-rsa(2) }
pk-Dilithium3-ECDSA-P256-SHA256 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-Dilithium3-ECDSA-P256-SHA256,
pk-Dilithium3TBD, OCTET STRING, pk-ECDSA-P256, ECPoint}
--TODO: this is missing `PARAMS secp256r1`
-- TODO: To be replaced by IANA
id-Dilithium3-ECDSA-brainpoolP256r1 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature(1)
dilithium3-ecdsa-brainpoolp256r1(3) }
pk-Dilithium3-ECDSA-brainpoolP256r1 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-Dilithium3-ECDSA-brainpoolP256r1,
pk-Dilithium3TBD, OCTET STRING, pk-ec, ECPoint}
--TODO: this is missing `PARAMS brainpoolP256r1`
-- TODO: To be replaced by IANA
id-Dilithium3-Ed25519 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature(1) dilithium3-ed25519(4) }
pk-Dilithium3-Ed25519 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-Dilithium3-Ed25519,
pk-Dilithium3TBD, OCTET STRING, pk-Ed25519, OCTET STRING}
Ounsworth, et al. Expires 14 September 2023 [Page 21]
Internet-Draft PQ Composite Keys March 2023
-- TODO: To be replaced by IANA
id-Dilithium5-ECDSA-P384 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature(1) dilithium5-ecdsa-p384(5) }
pk-Dilithium5-ECDSA-P384 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-Dilithium5-ECDSA-P384,
pk-Dilithium5TBD, OCTET STRING, pk-ec, ECPoint}
--TODO: this is missing `PARAMS secp384r1`
-- TODO: To be replaced by IANA
id-Dilithium5-ECDSA-brainpoolP384r1 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature(1) dilithium5-ecdsa-brainpoolp384r1(6) }
pk-Dilithium5-ECDSA-brainpoolP384r1 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-Dilithium5-ECDSA-brainpoolP384r1,
pk-Dilithium5TBD, OCTET STRING, pk-ec, ECPoint}
--TODO: this is missing `PARAMS brainpoolP384r1`
-- TODO: To be replaced by IANA
id-Dilithium5-Ed448 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature dilithium5-ed448(7) }
pk-Dilithium5-Ed448 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-Dilithium5-Ed448,
pk-Dilithium5TBD, OCTET STRING, pk-Ed25519, OCTET STRING}
--TODO: I have a question out to LAMPS about why there is no pk-Ed448. See: https://mailarchive.ietf.org/arch/msg/spasm/bJHcxCA3bXoqKHqXnZ85Vrixu68/
-- TODO: To be replaced by IANA
id-Falcon512-ECDSA-P256-SHA256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature falcon512-ecdsa-p256-sha256(8) }
pk-Falcon512-ECDSA-P256-SHA256 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-Falcon512-ECDSA-P256-SHA256,
pk-falcon512TBD, OCTET STRING, pk-ec, ECPoint}
--TODO: this is missing `PARAMS secp256r1`
Ounsworth, et al. Expires 14 September 2023 [Page 22]
Internet-Draft PQ Composite Keys March 2023
-- TODO: To be replaced by IANA
id-Falcon512-ECDSA-brainpoolP256r1-SHA256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature(1) falcon512-ecdsa-brainpoolp256r1-sha256(9) }
pk-Falcon512-ECDSA-brainpoolP256r1-SHA256 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-Falcon512-ECDSA-brainpoolP256r1-SHA256,
pk-falcon512TBD, OCTET STRING, pk-ec, ECPoint}
--TODO: this is missing `PARAMS brainpoolp256r1`
-- TODO: To be replaced by IANA
id-Falcon512-Ed25519 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signatur(1) falcon512-ed25519(10) }
pk-Falcon512-Ed25519 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-Falcon512-Ed25519,
pk-falcon512TBD, OCTET STRING, pk-Ed25519, OCTET STRING}
-- TODO: To be replaced by IANA
id-SPHINCSplusSHA256128sSimple-ECDSA-P256-SHA256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature(1) sphincsplussha256128ssimple-ecdsa-p256-sha256(11) }
pk-SPHINCSplusSHA256-ECDSA-P256 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-SPHINCSplusSHA256-ECDSA-P256,
pk-sphincs-plus-256, SPHINCS-Plus-PublicKey, pk-ec, ECPoint}
--TODO: this is missing `PARAMS secp256r1`
-- TODO: To be replaced by IANA
id-SPHINCSplusSHA256128sSimple-ECDSA-brainpoolP256r1-SHA256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature(1)
id-sphincsplussha256128ssimple-ecdsa-brainpoolp256r1-sha256(12) }
pk-SPHINCSplusSHA256128sSimple-ECDSA-brainpoolP256r1-SHA256 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-SPHINCSplusSHA256128sSimple-ECDSA-brainpoolP256r1-SHA256,
pk-sphincs-plus-256, SPHINCS-Plus-PublicKey, pk-ec, ECPoint}
--TODO: this is missing `PARAMS brainpoolp256r1`
Ounsworth, et al. Expires 14 September 2023 [Page 23]
Internet-Draft PQ Composite Keys March 2023
-- TODO: To be replaced by IANA
id-SPHINCSplusSHA256128sSimple-Ed25519 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) signature(1)
sphincsplussha256128ssimple-ed25519(13) }
pk-SPHINCSplusSHA256128sSimple-Ed25519 PUBLIC-KEY ::=
pk-explicitCompositeSignature{id-SPHINCSplusSHA256128sSimple-Ed25519,
pk-sphincs-plus-256, SPHINCS-Plus-PublicKey, pk-Ed25519, OCTET STRING}
-- Explicit Composite KEM Keys
-- TODO: To be replaced by IANA
id-Kyber512-ECDH-P256-KMAC128 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) explicitcomposite-kem(2) id-kyber512-ecdh-p256(1) }
pk-Kyber512-ECDH-P256-KMAC128 PUBLIC-KEY ::=
pk-explicitCompositeKEM{id-Kyber512-ECDH-P256-KMAC128,
pk-Kyber512TBD, OCTET STRING, pk-ec, ECPoint}
--TODO: this is missing `PARAMS secp256r1`
-- TODO: To be replaced by IANA
id-Kyber512-ECDH-brainpoolP256r1-KMAC128 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) explicitcomposite-kem(2) id-kyber512-ecdh-brainpoolp256r1(2) }
pk-Kyber512-ECDH-brainpoolP256r1-KMAC128 PUBLIC-KEY ::=
pk-explicitCompositeKEM{id-Kyber512-ECDH-brainpoolP256r1-KMAC128,
pk-Kyber512TBD, OCTET STRING, pk-ec, ECPoint}
--TODO: this is missing `PARAMS brainpoolp256r1`
-- TODO: To be replaced by IANA
id-Kyber512-X25519-KMAC128 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) kem(2)
id-kyber512-x25519(3) }
pk-Kyber512-X25519-KMAC128 PUBLIC-KEY ::=
pk-explicitCompositeKEM{id-Kyber512-X25519-KMAC128,
pk-Kyber512TBD, OCTET STRING, pk-X25519, OCTET STRING}
Ounsworth, et al. Expires 14 September 2023 [Page 24]
Internet-Draft PQ Composite Keys March 2023
-- TODO: To be replaced by IANA
id-Kyber768-RSA-KMAC256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) kem(2)
id-kyber768-rsa(4) }
pk-Kyber768-RSA-KMAC256 PUBLIC-KEY ::=
pk-explicitCompositeKEM{id-Kyber768-RSA-KMAC256,
pk-Kyber768TBD, OCTET STRING, pk-rsa, RSAPublicKey}
-- TODO: To be replaced by IANA
id-Kyber768-ECDH-P256-KMAC256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) kem(2)
id-kyber768-ecdh-p256(5) }
pk-Kyber768-ECDH-P256-KMAC256 PUBLIC-KEY ::=
pk-explicitCompositeKEM{id-Kyber768-ECDH-P256-KMAC256,
pk-Kyber768TBD, OCTET STRING, pk-ec, ECPoint}
--TODO: this is missing `PARAMS secp256r1`
id-Kyber768-ECDH-brainpoolP256r1-KMAC256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) kem(2)
id-kyber768-ecdh-p256(6) }
pk-Kyber768-ECDH-brainpoolP256r1-KMAC256 PUBLIC-KEY ::=
pk-explicitCompositeKEM{id-Kyber768-ECDH-brainpoolP256r1-KMAC256,
pk-Kyber768TBD, OCTET STRING, pk-ec, ECPoint}
--TODO: this is missing `PARAMS brainpoolp256r1`
-- TODO: To be replaced by IANA
id-Kyber768-X25519-KMAC256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) kem(2)
id-kyber768-x25519(7) }
pk-Kyber768-X25519-KMAC256 PUBLIC-KEY ::=
pk-explicitCompositeKEM{id-Kyber768-X25519-KMAC256,
pk-Kyber768TBD, OCTET STRING, pk-X25519, OCTET STRING}
Ounsworth, et al. Expires 14 September 2023 [Page 25]
Internet-Draft PQ Composite Keys March 2023
-- TODO: To be replaced by IANA
id-Kyber1024-ECDH-P384-KMAC256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) kem(2)
id-kyber1024-ecdh-p384(8) }
pk-Kyber1024-ECDH-P384-KMAC256 PUBLIC-KEY ::=
pk-explicitCompositeKEM{id-Kyber1024-ECDH-P384-KMAC256,
pk-Kyber1024TBD, OCTET STRING, pk-ec, ECPoint}
--TODO: this is missing `PARAMS secp384r1`
-- TODO: To be replaced by IANA
id-Kyber1024-ECDH-brainpoolP384r1-KMAC256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) kem(2)
id-kyber1024-ecdh-brainpoolp384r1(9) }
pk-Kyber1024-ECDH-brainpoolP384r1-KMAC256 PUBLIC-KEY ::=
pk-explicitCompositeKEM{id-Kyber1024-ECDH-brainpoolP384r1-KMAC256,
pk-Kyber1024TBD, OCTET STRING, pk-ec, ECPoint}
--TODO: this is missing `PARAMS brainpoolp384r1`
-- TODO: To be replaced by IANA
id-Kyber1024-X448-KMAC256 OBJECT IDENTIFIER ::= {
joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
algorithm(80) explicitcomposite(5) kem(2)
id-kyber1024-x448(10) }
pk-Kyber1024-X448-KMAC256 PUBLIC-KEY ::=
pk-explicitCompositeKEM{id-Kyber1024-X448-KMAC256,
pk-Kyber1024TBD, OCTET STRING, pk-X448, OCTET STRING}
END
<CODE ENDS>
6. IANA Considerations
All sorts of OIDs in the ASN.1 module. Too many to list here
(sorry).
This document registers the following in the SMI "Security for PKIX
Algorithms (1.3.6.1.5.5.7.6)" registry:
Ounsworth, et al. Expires 14 September 2023 [Page 26]
Internet-Draft PQ Composite Keys March 2023
id-composite-key OBJECT IDENTIFIER ::= {
iso(1) identified-organization(3) dod(6) internet(1) security(5)
mechanisms(5) pkix(7) algorithms(6) id-composite-key(??) }
7. Security Considerations
7.1. Reuse of keys in a Composite public key
There is an additional security consideration that some use cases
such as signatures remain secure against downgrade attacks if and
only if component keys are never used outside of their composite
context and therefore it is RECOMMENDED that component keys in a
composite key are not to be re-used in other contexts. In
particular, the components of a composite key SHOULD NOT also appear
in single-key certificates. This is particularly relevant for
protocols that use composite keys in a logical AND mode since the
appearance of the same component keys in single-key contexts
undermines the binding of the component keys into a single composite
key by allowing messages signed in a multi-key AND mode to be
presented as if they were signed in a single key mode in what is
known as a "stripping attack".
7.2. Key mismatch in explicit composite
This security consideration copied from Section 3.2.2.
Implementations SHOULD check that the component AlgorithmIdentifier
OIDs and parameters match those expected by the definition of the
explicit algorithm. Implementations SHOULD first parse a component's
SubjectPublicKeyInfo.algorithm, and ensure that it matches what is
expected for that position in the explicit key, and then proceed to
parse the SubjectPublicKeyInfo.subjectPublicKey. This is to reduce
the attack surface associated with parsing the public key data of an
unexpected key type, or worse; to parse and use a key which does not
match the explicit algorithm definition. Similar checks SHOULD be
done when handling the corresponding private key.
7.3. Policy for Deprecated and Acceptable Algorithms
Traditionally, a public key, certificate, or signature contains a
single cryptographic algorithm. If and when an algorithm becomes
deprecated (for example, RSA-512, or SHA1), it is obvious that
clients performing signature verification or encryption operations
should be updated to fail to validate or refuse to encrypt for these
algorithms.
Ounsworth, et al. Expires 14 September 2023 [Page 27]
Internet-Draft PQ Composite Keys March 2023
In the composite model this is less obvious since implementers may
decide that certain cryptographic algorithms have complementary
security properties and are acceptable in combination even though one
or both algorithms are deprecated for individual use. As such, a
single composite public key, certificate, signature, or ciphertext
MAY contain a mixture of deprecated and non-deprecated algorithms.
Specifying behaviour in these cases is beyond the scope of this
document, but should be considered by implementers and potentially in
additional standards.
EDNOTE: Max had proposed a CRL mechanism to accomplish this, which
could be revived if necessary.
7.4. Protection of Private Keys
Structures described in this document do not protect private keys in
any way unless combined with a security protocol or encryption
properties of the objects (if any) where the CompositePrivateKey is
used.
Protection of the private keys is vital to public key cryptography.
The consequences of disclosure depend on the purpose of the private
key. If a private key is used for signature, then the disclosure
allows unauthorized signing. If a private key is used for key
management, then disclosure allows unauthorized parties to access the
managed keying material. The encryption algorithm used in the
encryption process must be at least as 'strong' as the key it is
protecting.
7.5. Checking for Compromised Key Reuse
Certification Authority (CA) implementations need to be careful when
checking for compromised key reuse, for example as required by
WebTrust regulations; when checking for compromised keys, you MUST
unpack the CompositePublicKey structure and compare individual
component keys. In other words, for the purposes of key reuse
checks, the composite public key structures need to be un-packed so
that primitive keys are being compared. For example if the composite
key {RSA1, PQ1} is revoked for key compromise, then the keys RSA1 and
PQ1 need to be individually considered revoked. If the composite key
{RSA1, PQ2} is submitted for certification, it SHOULD be rejected
because the key RSA1 was previously declared compromised even though
the key PQ2 is unique.
8. References
8.1. Normative References
Ounsworth, et al. Expires 14 September 2023 [Page 28]
Internet-Draft PQ Composite Keys March 2023
[I-D.ietf-lamps-cms-sphincs-plus]
Housley, R., Fluhrer, S., Kampanakis, P., and B.
Westerbaan, "Use of the SPHINCS+ Signature Algorithm in
the Cryptographic Message Syntax (CMS)", Work in Progress,
Internet-Draft, draft-ietf-lamps-cms-sphincs-plus-01, 21
November 2022, <https://datatracker.ietf.org/doc/html/
draft-ietf-lamps-cms-sphincs-plus-01>.
[I-D.ietf-lamps-dilithium-certificates]
Massimo, J., Kampanakis, P., Turner, S., and B.
Westerbaan, "Internet X.509 Public Key Infrastructure:
Algorithm Identifiers for Dilithium", Work in Progress,
Internet-Draft, draft-ietf-lamps-dilithium-certificates-
00, 29 September 2022,
<https://datatracker.ietf.org/doc/html/draft-ietf-lamps-
dilithium-certificates-00>.
[I-D.ietf-lamps-kyber-certificates]
Turner, S., Kampanakis, P., Massimo, J., and B.
Westerbaan, "Internet X.509 Public Key Infrastructure -
Algorithm Identifiers for Kyber", Work in Progress,
Internet-Draft, draft-ietf-lamps-kyber-certificates-00, 26
September 2022, <https://datatracker.ietf.org/doc/html/
draft-ietf-lamps-kyber-certificates-00>.
[I-D.ounsworth-pq-composite-kem]
Ounsworth, M. and J. Gray, "Composite KEM For Use In
Internet PKI", Work in Progress, Internet-Draft, draft-
ounsworth-pq-composite-kem-00, 11 July 2022,
<https://datatracker.ietf.org/doc/html/draft-ounsworth-pq-
composite-kem-00>.
[I-D.ounsworth-pq-composite-sigs]
Ounsworth, M. and M. Pala, "Composite Signatures For Use
In Internet PKI", Work in Progress, Internet-Draft, draft-
ounsworth-pq-composite-sigs-05, 12 July 2021,
<https://datatracker.ietf.org/doc/html/draft-ounsworth-pq-
composite-sigs-05>.
[RFC1421] Linn, J., "Privacy Enhancement for Internet Electronic
Mail: Part I: Message Encryption and Authentication
Procedures", RFC 1421, DOI 10.17487/RFC1421, February
1993, <https://www.rfc-editor.org/info/rfc1421>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/info/rfc2119>.
Ounsworth, et al. Expires 14 September 2023 [Page 29]
Internet-Draft PQ Composite Keys March 2023
[RFC2986] Nystrom, M. and B. Kaliski, "PKCS #10: Certification
Request Syntax Specification Version 1.7", RFC 2986,
DOI 10.17487/RFC2986, November 2000,
<https://www.rfc-editor.org/info/rfc2986>.
[RFC5280] Cooper, D., Santesson, S., Farrell, S., Boeyen, S.,
Housley, R., and W. Polk, "Internet X.509 Public Key
Infrastructure Certificate and Certificate Revocation List
(CRL) Profile", RFC 5280, DOI 10.17487/RFC5280, May 2008,
<https://www.rfc-editor.org/info/rfc5280>.
[RFC5480] Turner, S., Brown, D., Yiu, K., Housley, R., and T. Polk,
"Elliptic Curve Cryptography Subject Public Key
Information", RFC 5480, DOI 10.17487/RFC5480, March 2009,
<https://www.rfc-editor.org/info/rfc5480>.
[RFC5639] Lochter, M. and J. Merkle, "Elliptic Curve Cryptography
(ECC) Brainpool Standard Curves and Curve Generation",
RFC 5639, DOI 10.17487/RFC5639, March 2010,
<https://www.rfc-editor.org/info/rfc5639>.
[RFC5652] Housley, R., "Cryptographic Message Syntax (CMS)", STD 70,
RFC 5652, DOI 10.17487/RFC5652, September 2009,
<https://www.rfc-editor.org/info/rfc5652>.
[RFC5914] Housley, R., Ashmore, S., and C. Wallace, "Trust Anchor
Format", RFC 5914, DOI 10.17487/RFC5914, June 2010,
<https://www.rfc-editor.org/info/rfc5914>.
[RFC5958] Turner, S., "Asymmetric Key Packages", RFC 5958,
DOI 10.17487/RFC5958, August 2010,
<https://www.rfc-editor.org/info/rfc5958>.
[RFC5990] Randall, J., Kaliski, B., Brainard, J., and S. Turner,
"Use of the RSA-KEM Key Transport Algorithm in the
Cryptographic Message Syntax (CMS)", RFC 5990,
DOI 10.17487/RFC5990, September 2010,
<https://www.rfc-editor.org/info/rfc5990>.
[RFC6090] McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic
Curve Cryptography Algorithms", RFC 6090,
DOI 10.17487/RFC6090, February 2011,
<https://www.rfc-editor.org/info/rfc6090>.
[RFC7468] Josefsson, S. and S. Leonard, "Textual Encodings of PKIX,
PKCS, and CMS Structures", RFC 7468, DOI 10.17487/RFC7468,
April 2015, <https://www.rfc-editor.org/info/rfc7468>.
Ounsworth, et al. Expires 14 September 2023 [Page 30]
Internet-Draft PQ Composite Keys March 2023
[RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", RFC 7748, DOI 10.17487/RFC7748, January
2016, <https://www.rfc-editor.org/info/rfc7748>.
[RFC8017] Moriarty, K., Ed., Kaliski, B., Jonsson, J., and A. Rusch,
"PKCS #1: RSA Cryptography Specifications Version 2.2",
RFC 8017, DOI 10.17487/RFC8017, November 2016,
<https://www.rfc-editor.org/info/rfc8017>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/info/rfc8174>.
[RFC8410] Josefsson, S. and J. Schaad, "Algorithm Identifiers for
Ed25519, Ed448, X25519, and X448 for Use in the Internet
X.509 Public Key Infrastructure", RFC 8410,
DOI 10.17487/RFC8410, August 2018,
<https://www.rfc-editor.org/info/rfc8410>.
[RFC8411] Schaad, J. and R. Andrews, "IANA Registration for the
Cryptographic Algorithm Object Identifier Range",
RFC 8411, DOI 10.17487/RFC8411, August 2018,
<https://www.rfc-editor.org/info/rfc8411>.
[X.690] ITU-T, "Information technology - ASN.1 encoding Rules:
Specification of Basic Encoding Rules (BER), Canonical
Encoding Rules (CER) and Distinguished Encoding Rules
(DER)", ISO/IEC 8825-1:2015, November 2015.
8.2. Informative References
[codeSigningBRsv2.8]
CAB Forum, "Baseline Requirements for the Issuance and
Management of Publicly-Trusted Code Signing Certificates
v2.8", May 2022, <https://cabforum.org/wp-content/uploads/
Baseline-Requirements-for-the-Issuance-and-Management-of-
Code-Signing.v2.8.pdf>.
[eIDAS2014]
"REGULATION (EU) No 910/2014 OF THE EUROPEAN PARLIAMENT
AND OF THE COUNCIL of 23 July 2014 on electronic
identification and trust services for electronic
transactions in the internal market and repealing
Directive 1999/93/EC", July 2014,
<https://ec.europa.eu/futurium/en/system/files/ged/
eidas_regulation.pdf>.
Ounsworth, et al. Expires 14 September 2023 [Page 31]
Internet-Draft PQ Composite Keys March 2023
[I-D.becker-guthrie-noncomposite-hybrid-auth]
Becker, A., Guthrie, R., and M. J. Jenkins, "Non-Composite
Hybrid Authentication in PKIX and Applications to Internet
Protocols", Work in Progress, Internet-Draft, draft-
becker-guthrie-noncomposite-hybrid-auth-00, 22 March 2022,
<https://datatracker.ietf.org/doc/html/draft-becker-
guthrie-noncomposite-hybrid-auth-00>.
[I-D.driscoll-pqt-hybrid-terminology]
D, F., "Terminology for Post-Quantum Traditional Hybrid
Schemes", Work in Progress, Internet-Draft, draft-
driscoll-pqt-hybrid-terminology-01, 20 October 2022,
<https://datatracker.ietf.org/doc/html/draft-driscoll-pqt-
hybrid-terminology-01>.
[I-D.guthrie-ipsecme-ikev2-hybrid-auth]
Guthrie, R., "Hybrid Non-Composite Authentication in
IKEv2", Work in Progress, Internet-Draft, draft-guthrie-
ipsecme-ikev2-hybrid-auth-00, 25 March 2022,
<https://datatracker.ietf.org/doc/html/draft-guthrie-
ipsecme-ikev2-hybrid-auth-00>.
[RFC4210] Adams, C., Farrell, S., Kause, T., and T. Mononen,
"Internet X.509 Public Key Infrastructure Certificate
Management Protocol (CMP)", RFC 4210,
DOI 10.17487/RFC4210, September 2005,
<https://www.rfc-editor.org/info/rfc4210>.
[RFC4211] Schaad, J., "Internet X.509 Public Key Infrastructure
Certificate Request Message Format (CRMF)", RFC 4211,
DOI 10.17487/RFC4211, September 2005,
<https://www.rfc-editor.org/info/rfc4211>.
[RFC7292] Moriarty, K., Ed., Nystrom, M., Parkinson, S., Rusch, A.,
and M. Scott, "PKCS #12: Personal Information Exchange
Syntax v1.1", RFC 7292, DOI 10.17487/RFC7292, July 2014,
<https://www.rfc-editor.org/info/rfc7292>.
[RFC7296] Kaufman, C., Hoffman, P., Nir, Y., Eronen, P., and T.
Kivinen, "Internet Key Exchange Protocol Version 2
(IKEv2)", STD 79, RFC 7296, DOI 10.17487/RFC7296, October
2014, <https://www.rfc-editor.org/info/rfc7296>.
[RFC8446] Rescorla, E., "The Transport Layer Security (TLS) Protocol
Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
<https://www.rfc-editor.org/info/rfc8446>.
Ounsworth, et al. Expires 14 September 2023 [Page 32]
Internet-Draft PQ Composite Keys March 2023
[RFC8551] Schaad, J., Ramsdell, B., and S. Turner, "Secure/
Multipurpose Internet Mail Extensions (S/MIME) Version 4.0
Message Specification", RFC 8551, DOI 10.17487/RFC8551,
April 2019, <https://www.rfc-editor.org/info/rfc8551>.
Appendix A. Work in Progress
A.1. Combiner modes (KofN)
For content commitment use-cases, such as legally-binding non-
repudiation, the signer (whether it be a CA or an end entity) needs
to be able to specify how its signature is to be interpreted and
verified.
For now we have removed combiner modes (AND, OR, KofN) from this
draft, but we are still discussing how to incorporate this for the
cases where it is needed (maybe a X.509 v3 extension, or a signature
algorithm param).
Appendix B. Samples
These samples are reproduced here for completeness, but are also
available in github:
https://github.com/EntrustCorporation/draft-ounsworth-pq-composite-
keys/tree/master/sampledata
TODO: move these to https://github.com/lamps-wg before publication
B.1. Generic Composite Public Key Samples
This is an example generic composite public key
-----BEGIN PUBLIC KEY-----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-----END PUBLIC KEY-----
which decodes as:
Ounsworth, et al. Expires 14 September 2023 [Page 33]
Internet-Draft PQ Composite Keys March 2023
algorithm: AlgorithmIdentifier{id-composite-key}
subjectPublicKey: CompositePublicKey {
SubjectPublicKeyInfo {
algorithm: AlgorithmIdentifier {
algorithm: ecPublicKey
parameters: prime256v1
}
subjectPublicKey: <ec key octet string>
},
SubjectPublicKeyInfo {
algorithm: AlgorithmIdentifier {
algorithm: rsaEncryption
parameters: NULL
}
subjectPublicKey: <rsa key octet string>
}
}
The corresponding explicit private key is as follows. Note that the
PQ key comes from OpenQuantumSafe-openssl and is in the
{privatekey || publickey} concatenated format. This may cause
interoperability issues with some clients, and also makes the private
keys appear larger than they would be if generated by a non-openssl
client.
Ounsworth, et al. Expires 14 September 2023 [Page 34]
Internet-Draft PQ Composite Keys March 2023
-----BEGIN PRIVATE KEY-----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-----END PRIVATE KEY-----
which decodes as:
Ounsworth, et al. Expires 14 September 2023 [Page 35]
Internet-Draft PQ Composite Keys March 2023
algorithm: AlgorithmIdentifier{id-composite-key}
SEQUENCE {
OneAsymmetricKey {
version: 0,
privateKeyAlgorithm: PrivateKeyAlgorithmIdentifier{
algorithm: ecPublicKey
parameters: prime256v1
}
privateKey: <ec key octet string>
},
OneAsymmetricKey {
version: 0,
privateKeyAlgorithm: PrivateKeyAlgorithmIdentifier{
algorithm: rsaEncryption
parameters: NULL
}
privateKey: <rsa key octet string>
}
}
B.2. Explicit Composite Public Key Samples
B.2.1. id-Dilithium3-ECDSA-P256
This example uses the following OID as defined in Open Quantum Safe,
which correspond to NIST Round3 candidates:
https://github.com/open-quantum-safe/oqs-provider/blob/main/
ALGORITHMS.md
id-dilithium3_aes 1.3.6.1.4.1.2.267.11.6.5
A Dilithium3-ECDSA-P256 public key:
Ounsworth, et al. Expires 14 September 2023 [Page 36]
Internet-Draft PQ Composite Keys March 2023
-----BEGIN PUBLIC KEY-----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-----END PUBLIC KEY-----
The corresponding explicit private key is as follows. Note that the
PQ key comes from OpenQuantumSafe-openssl and is in the
{privatekey || publickey} concatenated format. This may cause
interoperability issues with some clients, and also makes the private
keys appear larger than they would be if generated by a non-openssl
client.
Ounsworth, et al. Expires 14 September 2023 [Page 37]
Internet-Draft PQ Composite Keys March 2023
-----BEGIN PRIVATE KEY-----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, et al. Expires 14 September 2023 [Page 38]
Internet-Draft PQ Composite Keys March 2023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, et al. Expires 14 September 2023 [Page 39]
Internet-Draft PQ Composite Keys March 2023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-----END PRIVATE KEY-----
B.2.2. id-Dilithium3-RSA
This example uses the following OID as defined in Open Quantum Safe,
which correspond to NIST Round3 candidates:
https://github.com/open-quantum-safe/oqs-provider/blob/main/
ALGORITHMS.md
id-dilithium3_aes 1.3.6.1.4.1.2.267.11.6.5
A Dilithium3-RSA public key:
Ounsworth, et al. Expires 14 September 2023 [Page 40]
Internet-Draft PQ Composite Keys March 2023
-----BEGIN PUBLIC KEY-----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=
-----END PUBLIC KEY-----
Ounsworth, et al. Expires 14 September 2023 [Page 41]
Internet-Draft PQ Composite Keys March 2023
The corresponding explicit private key is as follows. Note that the
PQ key comes from OpenQuantumSafe-openssl and is in the
{privatekey || publickey} concatenated format. This may cause
interoperability issues with some clients, and also makes the private
keys appear larger than they would be if generated by a non-openssl
client.
-----BEGIN PRIVATE KEY-----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, et al. Expires 14 September 2023 [Page 42]
Internet-Draft PQ Composite Keys March 2023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, et al. Expires 14 September 2023 [Page 43]
Internet-Draft PQ Composite Keys March 2023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-----END PRIVATE KEY-----
B.2.3. id-Falcon512-ECDSA-P256
This example uses the following OID as definid in Open Quantum Safe,
which correspond to NIST Round3 candidates:
Ounsworth, et al. Expires 14 September 2023 [Page 44]
Internet-Draft PQ Composite Keys March 2023
https://github.com/open-quantum-safe/oqs-provider/blob/main/
ALGORITHMS.md
id-falcon512 1.3.9999.3.1
A Falcon512-ECDSA-P256 public key:
-----BEGIN PUBLIC KEY-----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-----END PUBLIC KEY-----
The corresponding explicit private key is as follows. Note that the
PQ key comes from OpenQuantumSafe-openssl and is in the
{privatekey || publickey} concatenated format. This may cause
interoperability issues with some clients, and also makes the private
keys appear larger than they would be if generated by a non-openssl
client.
Ounsworth, et al. Expires 14 September 2023 [Page 45]
Internet-Draft PQ Composite Keys March 2023
-----BEGIN PRIVATE KEY-----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-----END PRIVATE KEY-----
B.2.4. id-SPHINCSplusSHA256256frobust-ECDSA-P256
TODO: we switched to using a pub key identifier without the
signing mode, ie just id-SPHINCSplusSHA256-ECDSA-P256
Ounsworth, et al. Expires 14 September 2023 [Page 46]
Internet-Draft PQ Composite Keys March 2023
This example uses the following OID as definid in Open Quantum Safe:
https://github.com/open-quantum-safe/oqs-provider/blob/main/
ALGORITHMS.md
id-SPHINCSplusSHA256256frobust 1.3.9999.6.6.1
A SPHINCSplusSHA256256frobust-ECDSA-P256 public key:
-----BEGIN PUBLIC KEY-----
MIG/MAwGCmCGSAGG+mtQBQcDga4AMIGqME0wCAYGK84PBgYBA0EA6HRU4f2vmr2LV5vZVlaniti
Ly8ZCfheVqolJGrY5GxpNwvIt8fK6swNtftSgmrC+fCDE48/fbzX7a2U3F1/S3TBZMBMGByqGSM
49AgEGCCqGSM49AwEHA0IABFjKamMP3nn7Ua8Y8XEJtqnp7ya+Ino3UoxjMhhVKHx0fQxAz7lB7
Eytrtq3H7e59JYdkceK1h+T8jZFyUP5e0M=
-----END PUBLIC KEY-----
which decodes as:
algorithm: AlgorithmIdentifier{id-Dilithium3-ECDSA-P256}
subjectPublicKey: CompositePublicKey {
SubjectPublicKeyInfo {
algorithm: AlgorithmIdentifier {
algorithm: id-SPHINCSplusSHA256256frobust
}
subjectPublicKey: <sphincs key octet string>
},
SubjectPublicKeyInfo {
algorithm: AlgorithmIdentifier {
algorithm: ecPublicKey
parameters: prime256v1
}
subjectPublicKey: <ec octet string>
}
}
The corresponding explicit private key is as follows. Note that the
PQ key comes from OpenQuantumSafe-openssl and is in the
{privatekey || publickey} concatenated format. This may cause
interoperability issues with some clients, and also makes the private
keys appear larger than they would be if generated by a non-openssl
client.
Ounsworth, et al. Expires 14 September 2023 [Page 47]
Internet-Draft PQ Composite Keys March 2023
-----BEGIN PRIVATE KEY-----
MIIBMgIBADAMBgpghkgBhvprUAUHBIIBHTCCARkwgdMCAQAwCAYGK84PBgYBBIHDBIHA0PwPCww
Ulg3VLrZC7cGLqF0jRZrREj/l4kKF4JsLTjRR2P4RLqEm0qBa7ukb4ytHE6HDfM0h6dJ19F02hO
SO6Oh0VOH9r5q9i1eb2VZWp4rYi8vGQn4XlaqJSRq2ORsaTcLyLfHyurMDbX7UoJqwvnwgxOPP3
281+2tlNxdf0t3odFTh/a+avYtXm9lWVqeK2IvLxkJ+F5WqiUkatjkbGk3C8i3x8rqzA21+1KCa
sL58IMTjz99vNftrZTcXX9LdMEECAQAwEwYHKoZIzj0CAQYIKoZIzj0DAQcEJzAlAgEBBCAwCM4
KKsZbXlaZBph1ixcUhlNiZ1qp4LnA90Nm/rArZw==
-----END PRIVATE KEY-----
Appendix C. Implementation Considerations
This section addresses practical issues of how this draft affects
other protocols and standards.
EDNOTE 10: Possible topics to address:
* The size of these certs and cert chains.
* In particular, implications for (large) composite keys /
signatures / certs on the handshake stages of TLS and IKEv2.
* If a cert in the chain is a composite cert then does the whole
chain need to be of composite Certs?
* We could also explain that the root CA cert does not have to be of
the same algorithms. The root cert SHOULD NOT be transferred in
the authentication exchange to save transport overhead and thus it
can be different than the intermediate and leaf certs.
C.1. Textual encoding of Composite Private Keys
CompositePrivateKeys can be encoded to the Privacy-Enhanced Mail
(PEM) [RFC1421] format by placing a CompositePrivateKey into the
privateKey field of a PrivateKeyInfo (OneAsymmetricKey) object, and
then applying the PEM encoding rules as defined in [RFC7468] section
10 and 11 for plaintext and encrypted private keys, respectively.
C.2. Backwards Compatibility
As noted in the introduction, the post-quantum cryptographic
migration will face challenges in both ensuring cryptographic
strength against adversaries of unknown capabilities, as well as
providing ease of migration. The composite mechanisms defined in
this document primarily address cryptographic strength, however this
section contains notes on how backwards compatibility may be
obtained.
Ounsworth, et al. Expires 14 September 2023 [Page 48]
Internet-Draft PQ Composite Keys March 2023
The term "ease of migration" is used here to mean that existing
systems can be gracefully transitioned to the new technology without
requiring large service disruptions or expensive upgrades. The term
"backwards compatibility" is used here to mean something more
specific; that existing systems, as they are deployed today, can
interoperate with the upgraded systems of the future.
These migration and interoperability concerns need to be thought
about in the context of various types of protocols that make use of
X.509 and PKIX with relation to public key objects, from online
negotiated protocols such as TLS 1.3 [RFC8446] and IKEv2 [RFC7296],
to non-negotiated asynchronous protocols such as S/MIME signed and
encrypted email [RFC8551], document signing such as in the context of
the European eIDAS regulations [eIDAS2014], and publicly trusted code
signing [codeSigningBRsv2.8], as well as myriad other standardized
and proprietary protocols and applications that leverage CMS
[RFC5652] signed or encrypted structures.
C.2.1. OR modes
This document purposefully does not specify how clients are to
combine component keys together to form a single cryptographic
operation; this is left up to the specifications of signature and
encryption algorithms that make use of the composite key type. One
possible way to combine component keys is through an OR relation, or
OR-like client policies for acceptable algorithm combinations, where
senders and / or receivers are permitted to ignore some component
keys. Some envisioned uses of this include environments where the
client encounters a component key for which it does not possess a
compatible algorithm implementation but wishes to proceed with the
cryptographic operation using the subset of component keys for which
it does have compatible implementations. Such a mechanism could be
designed to provide ease of migration by allowing for composite keys
to be distributed and used before all clients in the environment are
fully upgraded, but it does not allow for full backwards
compatibility since clients would at least need to be upgraded from
their current state to be able to parse the composite structures.
C.2.2. Parallel PKIs
We present the term "Parallel PKI" to refer to the setup where a PKI
end entity possesses two or more distinct public keys or certificates
for the same key type (signature, key establishment, etc) for the
same identity (name, SAN), but containing keys for different
cryptographic algorithms. One could imagine a set of parallel PKIs
where an existing PKI using legacy algorithms (RSA, ECC) is left
operational during the post-quantum migration but is shadowed by one
or more parallel PKIs using pure post quantum algorithms or composite
Ounsworth, et al. Expires 14 September 2023 [Page 49]
Internet-Draft PQ Composite Keys March 2023
algorithms (legacy and post-quantum). This concept contains strong
overlap with other documented approaches, such as
[I-D.becker-guthrie-noncomposite-hybrid-auth] and highlights the
synergy between composite and non-composite hybrid approaches.
Equipped with a set of parallel public keys in this way, a client
would have the flexibility to choose which public key(s) or
certificate(s) to use in a given cryptographic operation.
For negotiated protocols, the client could choose which public key(s)
or certificate(s) to use based on the negotiated algorithms, or could
combine two of the public keys for example in a non-composite hybrid
method such as [I-D.becker-guthrie-noncomposite-hybrid-auth] or
[I-D.guthrie-ipsecme-ikev2-hybrid-auth]. Note that it is possible to
use the signature algorithm defined in
[I-D.ounsworth-pq-composite-sigs] as a way to carry the multiple
signature values generated by a non-composite public mechanism in
protocols where it is easier to support the composite signature
algorithms than to implement such a mechanism in the protocol itself.
There is also nothing precluding a composite public key from being
one of the components used within a non-composite authentication
operation; this may lead to greater convenience in setting up
parallel PKI hierarchies that need to service a range of clients
implementing different styles of post-quantum migration strategies.
For non-negotiated protocols, the details for obtaining backwards
compatibility will vary by protocol, but for example in CMS
[RFC5652], the inclusion of multiple SignerInfo or RecipientInfo
objects is often already treated as an OR relationship, so including
one for each of the end entity's parallel PKI public keys would, in
many cases, have the desired effect of allowing the receiver to
choose one they are compatible with and ignore the others, thus
achieving full backwards compatibility.
Appendix D. Intellectual Property Considerations
The following IPR Disclosure relates to this draft:
https://datatracker.ietf.org/ipr/3588/
Appendix E. Contributors and Acknowledgements
This document incorporates contributions and comments from a large
group of experts. The Editors would especially like to acknowledge
the expertise and tireless dedication of the following people, who
attended many long meetings and generated millions of bytes of
electronic mail and VOIP traffic over the past year in pursuit of
this document:
Ounsworth, et al. Expires 14 September 2023 [Page 50]
Internet-Draft PQ Composite Keys March 2023
John Gray (Entrust),
Serge Mister (Entrust),
Scott Fluhrer (Cisco Systems),
Panos Kampanakis (Cisco Systems),
Daniel Van Geest (ISARA),
Tim Hollebeek (Digicert),
Klaus-Dieter Wirth (D-Trust),
Patrick Kelsey (Not for Radio LLC),
Anthony Hu (wolfSSL), and
Francois Rousseau.
We are grateful to all, including any contributors who may have been
inadvertently omitted from this list.
This document borrows text from similar documents, including those
referenced below. Thanks go to the authors of those documents.
"Copying always makes things easier and less error prone" -
[RFC8411].
E.1. Making contributions
Additional contributions to this draft are welcome. Please see the
working copy of this draft at, as well as open issues at:
https://github.com/EntrustCorporation/draft-ounsworth-pq-composite-
keys
Authors' Addresses
Mike Ounsworth
Entrust Limited
2500 Solandt Road -- Suite 100
Ottawa, Ontario K2K 3G5
Canada
Email: mike.ounsworth@entrust.com
John Gray
Entrust Limited
2500 Solandt Road -- Suite 100
Ottawa, Ontario K2K 3G5
Canada
Email: john.gray@entrust.com
Massimiliano Pala
CableLabs
Email: director@openca.org
Ounsworth, et al. Expires 14 September 2023 [Page 51]
Internet-Draft PQ Composite Keys March 2023
Jan Klaussner
D-Trust GmbH
Kommandantenstr. 15
10969 Berlin
Germany
Email: jan.klaussner@d-trust.net
Ounsworth, et al. Expires 14 September 2023 [Page 52]
