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Composite Signatures For Use In Internet PKI
draft-ounsworth-pq-composite-sigs-08

Document Type Active Internet-Draft (individual)
Authors Mike Ounsworth , John Gray , Massimiliano Pala
Last updated 2023-03-13
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draft-ounsworth-pq-composite-sigs-08
LAMPS                                                       M. Ounsworth
Internet-Draft                                                   J. Gray
Intended status: Standards Track                                 Entrust
Expires: 14 September 2023                                       M. Pala
                                                               CableLabs
                                                           13 March 2023

              Composite Signatures For Use In Internet PKI
                  draft-ounsworth-pq-composite-sigs-08

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 cryptanalysis, 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 CompositeSignatureValue, and
   CompositeSignatureParams, which are sequences of the respective
   structure for each component algorithm.  The explicit variant is
   defined which allows for a set of signature algorithm identifier OIDs
   to be registered together as an explicit composite signature
   algorithm and assigned an OID.  The generic composite variant is also
   defined which allows arbitrary combinations of signature algorithms
   to be used in the CompositeSignatureValue and
   CompositeSignatureParams structures without needing the combination
   to be pre-registered or pre-agreed.

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   This document is intended to be coupled with corresponding documents
   that define the structure and semantics of composite public and
   private keys and encryption [I-D.ounsworth-pq-composite-keys],
   however may also be used with non-composite keys, such as when a
   protocol combines multiple certificates into a single cryptographic
   operation.

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.

Table of Contents

   1.  Changes in version -08  . . . . . . . . . . . . . . . . . . .   3
   2.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   4
     2.1.  Algorithm Selection Criteria  . . . . . . . . . . . . . .   4
     2.2.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   5
   3.  Composite Signature Structures  . . . . . . . . . . . . . . .   6
     3.1.  Composite Keys  . . . . . . . . . . . . . . . . . . . . .   7
       3.1.1.  Key Usage Bits  . . . . . . . . . . . . . . . . . . .   7
     3.2.  sa-CompositeSignature . . . . . . . . . . . . . . . . . .   7

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     3.3.  CompositeSignatureValue . . . . . . . . . . . . . . . . .   8
     3.4.  CompositeSignatureParameters  . . . . . . . . . . . . . .   8
     3.5.  Encoding Rules  . . . . . . . . . . . . . . . . . . . . .   9
   4.  Algorithm Identifiers . . . . . . . . . . . . . . . . . . . .   9
     4.1.  Notes on id-Dilithium3-RSA-PSS  . . . . . . . . . . . . .  12
     4.2.  Notes on Generic Composite  . . . . . . . . . . . . . . .  12
       4.2.1.  Pre-Hashed Generic Composite Signatures . . . . . . .  13
   5.  Composite Signature Processes . . . . . . . . . . . . . . . .  14
     5.1.  Composite Signature Generation Process  . . . . . . . . .  14
     5.2.  Composite Signature Verification Process  . . . . . . . .  16
   6.  ASN.1 Module  . . . . . . . . . . . . . . . . . . . . . . . .  18
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  23
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  23
     8.1.  Policy for Deprecated and Acceptable Algorithms . . . . .  23
     8.2.  K-of-N Validation Mode  . . . . . . . . . . . . . . . . .  23
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  24
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  24
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  26
   Appendix A.  Work in Progress . . . . . . . . . . . . . . . . . .  28
     A.1.  Combiner modes (KofN) . . . . . . . . . . . . . . . . . .  28
   Appendix B.  Samples  . . . . . . . . . . . . . . . . . . . . . .  28
     B.1.  Generic Composite Signature Examples  . . . . . . . . . .  28
     B.2.  Explicit Composite Signature Examples . . . . . . . . . .  28
   Appendix C.  Implementation Considerations  . . . . . . . . . . .  28
     C.1.  Backwards Compatibility . . . . . . . . . . . . . . . . .  29
       C.1.1.  Composite K-of-N (OR modes) . . . . . . . . . . . . .  29
       C.1.2.  Parallel PKIs . . . . . . . . . . . . . . . . . . . .  30
       C.1.3.  Hybrid Extensions (Keys and Signatures) . . . . . . .  31
   Appendix D.  Intellectual Property Considerations . . . . . . . .  31
   Appendix E.  Contributors and Acknowledgements  . . . . . . . . .  31
     E.1.  Making contributions  . . . . . . . . . . . . . . . . . .  32
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  32

1.  Changes in version -08

   *  explicit composite combinations defined and ASN.1 module updated

   *  Added new OIDs and considerations for the hash-then-sign paradigm
      for generic composite signatures

   *  Removed the OR modes of operation and replaced with K-of-N I-D
      reference

   *  Added considerations for external hashing

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2.  Introduction

   During the transition to post-quantum cryptography, 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 will also not
   fully trust their post-quantum replacements until they have had
   sufficient scrutiny and time to discover and fix 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.

   The deployment of composite signatures using post-quantum algorithms
   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.

   *  _Backwards compatibility_: During the transition period, post-
      quantum algorithms will not be supported by all clients.

   This document provides a mechanism to address algorithm strength
   uncertainty concerns by building on [I-D.ounsworth-pq-composite-keys]
   by providing formats for encoding multiple signature values into
   existing public signature fields, as well as the process for
   validating a composite signature.  Backwards compatibility is
   addressed via using composite in conjunction with a non-composite
   hybrid mode such as that described in
   [I-D.becker-guthrie-noncomposite-hybrid-auth].

   This document is intended for general applicability anywhere that
   digital signatures are used within PKIX and 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.

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   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 keys
   [I-D.ounsworth-pq-composite-keys] 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
   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 BCP
   14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

   The following terms are used in this document:

   ALGORITHM: A standardized cryptographic primitive, as well as any
   ASN.1 structures needed for encoding data and metadata needed to use
   the algorithm.  This document is primarily concerned with algorithms
   for producing digital signatures.

   BER: Basic Encoding Rules (BER) as defined in [X.690].

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   CLIENT: Any software that is making use of a cryptographic key.  This
   includes a signer, verifier, encrypter, decrypter.

   COMPONENT ALGORITHM: A single basic algorithm which is contained
   within a composite algorithm.

   COMPOSITE ALGORITHM: An algorithm which is a sequence of two or more
   component algorithms, as defined in Section 3.

   DER: Distinguished Encoding Rules as defined in [X.690].

   LEGACY: For the purposes of this document, a legacy algorithm is any
   cryptographic algorithm currently is use which is not believe to be
   resistant to quantum cryptanalysis.

   PKI: Public Key Infrastructure, as defined in [RFC5280].

   POST-QUANTUM ALGORITHM: Any cryptographic algorithm which is believed
   to be resistant to classical and quantum cryptanalysis, such as the
   algorithms being considered for standardization by NIST.

   PUBLIC / PRIVATE KEY: The public and private portion of an asymmetric
   cryptographic key, making no assumptions about which algorithm.

   SIGNATURE: A digital cryptographic signature, making no assumptions
   about which algorithm.

   STRIPPING ATTACK: An attack in which the attacker is able to
   downgrade the cryptographic object to an attacker-chosen subset of
   original set of component algorithms in such a way that it is not
   detectable by the receiver.  For example, substituting a composite
   public key or signature for a version with fewer components.

3.  Composite Signature Structures

   In order for signatures to be composed of multiple algorithms, we
   define encodings consisting of a sequence of signature primitives
   (aka "component algorithms") such that these structures can be used
   as a drop-in replacement for existing signature fields such as those
   found in PKCS#10 [RFC2986], CMP [RFC4210], X.509 [RFC5280], CMS
   [RFC5652].

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3.1.  Composite Keys

   A composite signature MAY be associated with a composite public key
   as defined in [I-D.ounsworth-pq-composite-keys], but MAY also be
   associated with multiple public keys from different sources, for
   example multiple X.509 certificates, or multiple cryptographic
   modules.  In the latter case, composite signatures MAY be used as the
   mechanism for carrying multiple signatures in a non-composite hybrid
   authentication mechanism such as those described in
   [I-D.becker-guthrie-noncomposite-hybrid-auth].

3.1.1.  Key Usage Bits

   For protocols such as X.509 [RFC5280] that specify key usage along
   with the public key, then the composite public key associated with a
   composite signature MUST have a signing-type key usage.

   If the keyUsage extension is present in a Certification Authority
   (CA) certificate that indicates a composite key, then any combination
   of the following values MAY be present:

   digitalSignature;
   nonRepudiation;
   keyCertSign; and
   cRLSign.

   If the keyUsage extension is present in an End Entity (EE)
   certificate that indicates a composite key, then any combination of
   the following values MAY be present:

   digitalSignature; and
   nonRepudiation;

3.2.  sa-CompositeSignature

   The ASN.1 algorithm object for a composite signature is:

   sa-CompositeSignature SIGNATURE-ALGORITHM ::= {
       IDENTIFIER TYPE OBJECT IDENTIFIER
       VALUE CompositeSignatureValue
       PARAMS ANY DEFINED BY ALGORITHM
       PUBLIC-KEYS { pk-Composite }
       SMIME-CAPS ANY DEFINED BY ALGORITHM }

   The following is an explanation how SIGNATURE-ALGORITHM elements are
   used to create Composite Signatures:

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   +=====================+=============================================+
   | SIGNATURE-ALGORITHM | Definition                                  |
   | element             |                                             |
   +=====================+=============================================+
   | IDENTIFIER          | The Object ID used to identify              |
   |                     | the composite Signature Algorithm           |
   +---------------------+---------------------------------------------+
   | VALUE               | The Sequence of BIT STRINGS for             |
   |                     | each component signature value              |
   +---------------------+---------------------------------------------+
   | PARAMS              | Signature parameters either                 |
   |                     | declared ABSENT, or defined with            |
   |                     | a type and encoding                         |
   +---------------------+---------------------------------------------+
   | PUBLIC-KEYS         | The composite key required to               |
   |                     | produce the composite signature             |
   +---------------------+---------------------------------------------+
   | SMIME_CAPS          | Not needed for composite                    |
   +---------------------+---------------------------------------------+

                                  Table 1

3.3.  CompositeSignatureValue

   The output of the composite signature algorithm is the DER encoding
   of the following structure:

   CompositeSignatureValue ::= SEQUENCE SIZE (2..MAX) OF BIT STRING

   Where each BIT STRING within the SEQUENCE is a signature value
   produced by one of the component keys.  It MUST contain one signature
   value produced by each component algorithm, and in the same order as
   in the associated CompositeSignatureParams object.

   A CompositeSignatureValue MUST contain the same number of component
   signatures as the corresponding public and private keys, and the
   order of component signature values MUST correspond to the component
   public keys.

   The choice of SEQUENCE OF BIT STRING, rather than for example a
   single BIT STRING containing the concatenated signature values, is to
   gracefully handle variable-length signature values by taking
   advantage of ASN.1's built-in length fields.

3.4.  CompositeSignatureParameters

   Composite signature parameters are defined as follows and MAY be used
   when a composite signature is used with an AlgorithmIdentifier:

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   CompositeSignatureParams ::= SEQUENCE SIZE (2..MAX) OF
        AlgorithmIdentifier{SIGNATURE-ALGORITHM, {SignatureAlgSet}}

   The signature's CompositeSignatureParams sequence MUST contain the
   same component algorithms listed in the same order as in the
   associated CompositePublicKey.

   For explicit algorithms, it is not strictly necessary to carry a
   CompositeSignatureParams with the list of component algorithms in the
   signature algorithm parameters because clients can infer the expected
   component algorithms from the algorithm identifier.  The PARAMS is
   left optional because some types of component algorithms will require
   parameters to be carried, such as RSASSA-PSS-params as defined in
   [RFC8017].  Section 3.2 defines PARAMS ANY DEFINED BY ALGORITHM so
   that explicit algorithms may define params as ABSENT, or use
   CompositeSignatureParams as defined in ASN.1 module.  For generic
   compsite algorithms, CompositeSignatureParams MUST be included.

3.5.  Encoding Rules

   Many protocol specifications will require that composite signature
   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.

   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.

   In the interests of simplicity and avoiding compatibility issues,
   implementations that parse these structures MAY accept both BER and
   DER.

4.  Algorithm Identifiers

   This section defines the algorithm identifiers for explicit
   combinations.  For simplicity and prototyping purposes, the signature
   algorithm object identifiers specified in this document are the same
   as the composite key object Identifiers specified in {draft-
   ounsworth-pq-composite-keys}.  A proper implementation should not
   presume that the object ID of a composite key will be the same as its
   composite signature algorithm.

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   This section is not intended to be exhaustive and other authors may
   define others composite signature algorithms so long as they are
   compatible with the structures and processes defined in this and
   companion public and private key documents.

   Some use-cases desire the flexibility for clients to use any
   combination of supported algorithms, while others desire the rigidity
   of explicitly-specified combinations of algorithms.

   The following table summarizes the details for each explicit
   composite signature algorithms:

   The OID referenced are TBD for prototyping only, and 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

   replace <SPHINCS> with the String "SPHINCSplusSHA256128sSimple"

   Signature public key types:

   +============================+=======================+==========+=======================+
   |Composite Signature         |OID                    |First     |Second Algorithm       |
   |AlgorithmID                 |                       |Algorithm |                       |
   +============================+=======================+==========+=======================+
   |id-Dilithium3-RSA-PSS       |<CompSig>.14           |Dilithium3|SHA256WithRSAPSS       |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-Dilithium3-RSA-          |<CompSig>.1            |Dilithium3|SHA256WithRSAEncryption|
   |PKCS15-SHA256               |                       |          |                       |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-Dilithium3-ECDSA-        |<CompSig>.2            |Dilithium3|SHA256withECDSA        |
   |P256-SHA256                 |                       |          |                       |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-Dilithium3-ECDSA-        |<CompSig>.3            |Dilithium3|SHA256withECDSA        |
   |brainpoolP256r1-SHA256      |                       |          |                       |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-Dilithium3-Ed25519       |<CompSig>.4            |Dilithium3|Ed25519                |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-Dilithium5-ECDSA-        |<CompSig>.5            |Dilithium5|SHA384withECDSA        |
   |P384-SHA384                 |                       |          |                       |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-Dilithium5-ECDSA-        |<CompSig>.6            |Dilithium5|SHA384withECDSA        |
   |brainpoolP384r1-SHA384      |                       |          |                       |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-Dilithium5-Ed448         |<CompSig>.7            |Dilithium5|Ed448                  |
   +----------------------------+-----------------------+----------+-----------------------+

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   |id-Falcon512-ECDSA-         |<CompSig>.8            |Falcon512 |SHA256withECDSA        |
   |P256-SHA256                 |                       |          |                       |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-Falcon512-ECDSA-         |<CompSig>.9            |Falcon512 |SHA256withECDSA        |
   |brainpoolP256r1-SHA256      |                       |          |                       |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-Falcon512-Ed25519        |<CompSig>.10           |Falcon512 |Ed25519                |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-                         |<CompSig>.11           |<SPHINCS> |SHA256withECDSA        |
   |SPHINCSplusSHA256128sSimple-|                       |          |                       |
   |ECDSA-P256-SHA256           |                       |          |                       |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-                         |<CompSig>.12           |<SPHINCS> |SHA256withECDSA        |
   |SPHINCSplusSHA256128sSimple-|                       |          |                       |
   |ECDSA-brainpoolP256r1-SHA256|                       |          |                       |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-                         |<CompSig>.13           |<SPHINCS> |Ed25519                |
   |SPHINCSplusSHA256128sSimple-|                       |          |                       |
   |Ed25519                     |                       |          |                       |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-                         |<CompSig>.13           |<SPHINCS> |Ed25519                |
   |SPHINCSplusSHA256128sSimple-|                       |          |                       |
   |Ed25519                     |                       |          |                       |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-alg-composite            |1.3.6.1.4.1.18227.2.1  |Any       |Any                    |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-alg-composite-sha256     |1.3.6.1.4.1.18227.2.1.2|Any       |Any                    |
   +----------------------------+-----------------------+----------+-----------------------+
   |id-alg-composite-sha512     |1.3.6.1.4.1.18227.2.1.4|Any       |Any                    |
   +----------------------------+-----------------------+----------+-----------------------+

              Table 2: Explicit Composite Signature Algorithms

   The table above contains everything needed to implement the listed
   explicit composite algorithms.  See the ASN.1 module in section
   Section 6 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]

   *  _ECDSA_: [RFC5480]

   *  _Ed25519 / Ed448_: [RFC8410]

   *  _Falcon_: TBD

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   *  _RSAES-PKCS-v1_5_: [RFC8017]

   *  _RSASSA-PSS_: [RFC8017]

   *  _SPHICNCSplus_: [I-D.ietf-lamps-cms-sphincs-plus]

   *  id-alg-composite: [I-D.ounsworth-pq-composite-keys]

4.1.  Notes on id-Dilithium3-RSA-PSS

   Use of RSA-PSS [RFC8017] deserves a special explanation.

   When the id-Dilithium3-RSA-PSS object identifier is used with an
   AlgorithmIdentifier, the AlgorithmIdentifier.parameters MUST be of
   type `CompositeSignatureParams as follows:

   SEQUENCE {
       AlgorithmIdentifier {
           id-Dilithium3TBD
       },
       AlgorithmIdentifier {
           id-RSASSA-PSS,
           RSASSA-PSS-params
       }
   }

   EDNOTE: We probably should pick concrete crypto for the RSASSA-PSS-
   params.  Once the crypto is fixed, we could omit the parameters
   entirely and expect implementations to re-constitute the params
   structures as necessary in order to call into lower-level crypto
   libraries.

   TODO: there must be a way to put all this the ASN.1 Module rather
   than just specifying it as text?

4.2.  Notes on Generic Composite

   This draft remains backwards compatible with the previous version of
   composite signatures.  Explicit Composite keys are a rigid subset of
   generic composite keys.  In previous versions, the composite
   signature algorihtm Identifier and the composite key identifier used
   different Object Identifiers.  The generic composite signature
   algorithm identifier is:

   id-alg-composite OBJECT IDENTIFIER ::= {
       iso(1)  identified-organization(3) dod(6) internet(1) private(4)
       enterprise(1) opencA(18227) algorithms(2) id-alg-composite(1) }

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   As defined in [I-D.ounsworth-pq-composite-keys], a generic composite
   key uses the following identifier:

   id-composite-key OBJECT IDENTIFIER ::= {
       joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
       algorithm(80) composite(4) compositekey(1) }

   See the ASN.1 module in section Section 6 for the definitions of
   Generic Composite algorithms

4.2.1.  Pre-Hashed Generic Composite Signatures

   The id-alg-composite-sha256 and id-alg-composite-sha512 object
   identifiers are used for identifying a pre-hashed generic composite
   signature that uses SHA-256 or SHA-512.  These algorithms allow
   arbitrary combinations of component signature algorithms to be used
   in the CompositeSignatureValue and CompositeSignatureParams
   structures without needing the combination to be pre-registered or
   standardized.

   When the id-alg-composite-sha256 and id-alg-composite-sha512 are
   used, the signature is calculated over the digest of the message
   rather than the message itself.  This mode can be used to generate
   signatures with any type of key (i.e., classic, post-quantum, or
   post-post-quantum, etc...) by signing the SHA256 or SHA512 value
   calculated over the message.

   This identifier MAY be used in sa-CompositeSignature.identifier.

   id-alg-composite-sha256 OBJECT IDENTIFIER ::= {
       iso(1)  identified-organization(3) dod(6) internet(1) private(4)
       enterprise(1) openCA(18227) algorithms(2) id-alg-composite(1)
       id-alg-composite-sha256(2) }

   EDNOTE: this is a temporary OID for the purposes of prototyping.  We
   are requesting IANA to assign a permanent OID, see Section 7.

   id-alg-composite-sha512 OBJECT IDENTIFIER ::= {
       iso(1)  identified-organization(3) dod(6) internet(1) private(4)
       enterprise(1) openCA(18227) algorithms(2) id-alg-composite(1)
       id-alg-composite-sha512(4) }

   EDNOTE: this is a temporary OID for the purposes of prototyping.  We
   are requesting IANA to assign a permanent OID, see Section 7.

   The following algorithm parameters MUST be included:

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   CompositeSignatureParams ::= SEQUENCE SIZE (2..MAX) OF
        AlgorithmIdentifier{SIGNATURE-ALGORITHM, {SignatureAlgSet}}

   The signature's CompositeSignatureParams sequence MUST contain the
   same component algorithms listed in the same order as in the
   associated CompositePublicKey.

5.  Composite Signature Processes

   This section specifies the processes for generating and verifying
   composite signatures.

   This process addresses algorithm strength uncertainty by providing
   the verifier with parallel signatures from all the component
   signature algorithms; thus forging the composite signature would
   require forging all of the component signatures.

5.1.  Composite Signature Generation Process

   Generation of a composite signature involves applying each component
   algorithm's signature process to the input message according to its
   specification, and then placing each component signature value into
   the CompositeSignatureValue structure defined in Section 3.2.

   The following process is used to generate composite signature values.

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Input:
     K1, K2, .., Kn     Signing private keys. See note below on
                        composite inputs.

     A1, A2, ... An     Component signature algorithms. See note below on
                        composite inputs.

     M                  Message to be signed, an octet string

Output:
     S                  The signatures, a CompositeSignatureValue

Signature Generation Process:
   1. Generate the n component signatures independently,
      according to their algorithm specifications.

        for i := 1 to n
            Si := Sign( Ki, Ai, M )

   2. Encode each component signature S1, S2, .., Sn into a BIT STRING
      according to its algorithm specification.

        S ::= Sequence { S1, S2, .., Sn }

   3. Output S

   Note on composite inputs: the method of providing the list of
   component keys and algorithms is flexible and beyond the scope of
   this pseudo-code, for example they may be carried in
   CompositePrivateKey and CompositeSignatureParams structures.  It is
   also possible to generate a composite signature that combines
   signatures from distinct keys stored in separate software or hardware
   keystores.  Variations in the process to accommodate particular
   private key storage mechanisms are considered to be conformant to
   this document so long as it produces the same output as the process
   sketched above.

   Since recursive composite public keys are disallowed in
   [I-D.ounsworth-pq-composite-keys], no component signature may itself
   be a composite; ie the signature generation process MUST fail if one
   of the private keys K1, K2, .., Kn is a composite with the OID id-
   alg-composite or an explicit composite OID.

   A composite signature MUST produce, and include in the output, a
   signature value for every component key in and include in the output,
   a signature value for every component key in the corresponding
   CompositePublicKey, and they MUST be in the same order; ie in the
   output, S1 MUST correspond to K1, S2 to K2, etc.

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   For security when using a generic composite signature algorithm, the
   list of component signature algorithms A1, A2, .., An, which may be
   carried in a CompositeSignatureParams object, SHOULD be included in
   the signed message M to prevent an attacker from substituting a
   weaker algorithm which is compatible with the same public key.  This
   attack is not unique or new to the composite format.

5.2.  Composite Signature Verification Process

   Verification of a composite signature involves applying each
   component algorithm's verification process according to its
   specification.

   In the absence of an application profile specifying otherwise,
   compliant applications MUST output "Valid signature" (true) if and
   only if all component signatures were successfully validated, and
   "Invalid signature" (false) otherwise.

   The following process is used to perform this verification.

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  Input:
       P1, P2, .., Pn     Public verification keys. See note below on
                          composite inputs.

       M                  Message whose signature is to be verified,
                          an octet string

       S1, S2, .., Sn    Component signature values to be verified.
                         See note below on composite inputs.

       A1, A2, ... An     Component signature algorithms. See note
                          below on composite inputs.

  Output:
      Validity (bool)    "Valid signature" (true) if the composite
                          signature is valid, "Invalid signature"
                          (false) otherwise.

  Signature Verification Procedure::
     1. Check keys, signatures, and algorithms lists for consistency.

        If Error during Desequencing, or the three sequences have
        different numbers of elements, or any of the public keys
        P1, P2, .., Pn or algorithm identifiers A1, A2, .., An are
        composite with the OID id-alg-composite or an explicit composite
        OID then output "Invalid signature" and stop.

     2. Check each component signature individually, according to its
         algorithm specification.
         If any fail, then the entire signature validation fails.

       for i := 1 to n
            if not verify( Pi, M, Si, Ai ), then
              output "Invalid signature"

        if all succeeded, then
          output "Valid signature"

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   Note on composite inputs: the method of providing the list of
   component keys, algorithms and signatures is flexible and beyond the
   scope of this pseudo-code, for example they may be carried in
   CompositePublicKey, CompositeSignatureParams, and
   compositesignaturevalue structures.  It is also possible to verify a
   composite signature where the component public verification keys
   belong, for example, to separate X.509 certificates or cryptographic
   modules.  Variations in the process to accommodate particular public
   verification key storage mechanisms are considered to be conformant
   to this document so long as it produces the same output as the
   process sketched above.

   Since recursive composite public keys are disallowed in
   [I-D.ounsworth-pq-composite-keys], no component signature may be
   composite; ie the signature verification procedure MUST fail if any
   of the public keys P1, P2, .., Pn or algorithm identifiers A1, A2,
   .., An are composite with OID id-alg-composite or an explicit
   composite OID.

   Some verification clients may include a policy mechanism for
   specifying acceptable subsets of algorithms.  In these cases,
   implementer MAY, in the interest of performance of compatibility,
   modify the above process to skip one or more signature validations as
   per their local client policy.  See
   [I-D.pala-klaussner-composite-kofn] for a discussion of
   implementation and associated risks.

6.  ASN.1 Module

   <CODE STARTS>

      Composite-Signatures-2023
        { joint-iso-itu-t(2) country(16) us(840) organization(1) entrust(114027)
          algorithm(80) id-composite-signatures-2023 (TBD) }

   DEFINITIONS IMPLICIT TAGS ::= BEGIN

   EXPORTS ALL;

   IMPORTS
     PUBLIC-KEY, SIGNATURE-ALGORITHM, 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

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       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) }

     sa-rsaSSA-PSS
       FROM PKIX1-PSS-OAEP-Algorithms-2009
          {iso(1) identified-organization(3) dod(6) internet(1) security(5)
          mechanisms(5) pkix(7) id-mod(0) id-mod-pkix1-rsa-pkalgs-02(54)}

     pk-Dilithium3-RSA-PSS, id-Dilithium3-RSA-PSS,
     pk-Dilithium3-RSA-PKCS15-SHA256, id-Dilithium3-RSA-PKCS15-SHA256,
     pk-Dilithium3-ECDSA-P256-SHA256, id-Dilithium3-ECDSA-P256-SHA256,
     pk-Dilithium3-ECDSA-brainpoolP256r1, id-Dilithium3-ECDSA-brainpoolP256r1,
     pk-Dilithium3-Ed25519, id-Dilithium3-Ed25519,
     pk-Dilithium5-ECDSA-P384, id-Dilithium5-ECDSA-P384,
     pk-Dilithium5-ECDSA-brainpoolP384r1-SHA384,
     id-Dilithium5-ECDSA-brainpoolP384r1-SHA384,
     pk-Dilithium5-Ed448, id-Dilithium5-Ed448,
     pk-Falcon512-ECDSA-P256-SHA256, id-Falcon512-ECDSA-P256-SHA256,
     pk-Falcon512-ECDSA-brainpoolP256r1-SHA256,
     id-Falcon512-ECDSA-brainpoolP256r1-SHA256,
     pk-Falcon512-Ed25519, id-Falcon512-Ed25519,
     pk-SPHINCSplusSHA256128sSimple-ECDSA-P256-SHA256,
     id-SPHINCSplusSHA256128sSimple-ECDSA-P256-SHA256,
     pk-SPHINCSplusSHA256128sSimple-ECDSA-brainpoolP256r1-SHA256,
     id-SPHINCSplusSHA256128sSimple-ECDSA-brainpoolP256r1-SHA256,
     pk-SPHINCSplusSHA256128sSimple-Ed25519,
     id-SPHINCSplusSHA256128sSimple-Ed25519
       FROM CompositeKeys-2023
              {iso(1) identified-organization(3) dod(6) internet(1) security(5)
          mechanisms(5) pkix(7) id-mod(0) id-mod-composite-keys(TBD)};

   --
   -- Signature Algorithm
   --

   -- Composite Signature Value is just a sequence of OCTET STRINGS

      CompositeSignaturePair{FirstSignatureValue, SecondSignatureValue} ::=
        SEQUENCE {
         signaturevalue1 FirstSignatureValue,

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         signaturevalue2 SecondSignatureValue }

      -- An Explicit Compsite Signature is a set of Signatures which
      -- are composed of OCTET STRINGS
      ExplicitCompositeSignatureValue ::= CompositeSignaturePair {
          OCTET STRING,OCTET STRING}

   ExplicitSignatureParameters{SIGNATURE-ALGORITHM:FirstSignatureAlg,
      SIGNATURE-ALGORITHM:SecondSignatureAlg}  ::=
         SEQUENCE {
             signatureAlgorithm1   AlgorithmIdentifier
                           { SIGNATURE-ALGORITHM, {FirstSignatureAlg}},
                   signatureAlgorithm2   AlgorithmIdentifier
                           { SIGNATURE-ALGORITHM, {SecondSignatureAlg}} }

   sa-explicitCompositeSignature{OBJECT IDENTIFIER:id,
      PUBLIC-KEY:publicKeyObject, ExplicitCompositeParams}
         SIGNATURE-ALGORITHM ::=  {
            IDENTIFIER id
            VALUE ExplicitCompositeSignatureValue
            PARAMS TYPE ExplicitCompositeParams ARE required
            PUBLIC-KEYS {publicKeyObject} }

   sa-Dilithium3-RSA-PSS-SHA256 SIGNATURE-ALGORITHM ::=
      sa-explicitCompositeSignature{id-Dilithium3-RSA-PSS-SHA256,
      pk-Dilithium3-RSA-PSS-SHA256,
      ExplicitSignatureParameters{{sa-Dilithium3TBD},{sa-rsaSSA-PSS}} }

   sa-Dilithium3-RSA-PKCS15-SHA256 SIGNATURE-ALGORITHM ::=
       sa-explicitCompositeSignature{ id-Dilithium3-RSA-PKCS15-SHA256,
       pk-Dilithium3-RSA-PKCS15-SHA256,
       ExplicitSignatureParameters{{sa-Dilithium3TBD},{sa-rsaWithSHA256}} }

   sa-Dilithium3-ECDSA-P256-SHA256 SIGNATURE-ALGORITHM ::=
       sa-explicitCompositeSignature{id-Dilithium3-ECDSA-P256-SHA256,
       pk-Dilithium3-ECDSA-P256-SHA256,
       ExplicitSignatureParameters{{sa-Dilithium3TBD},{sa-ecdsaWithSHA256}} }

   sa-Dilithium3-ECDSA-brainpoolP256r1-SHA256 SIGNATURE-ALGORITHM ::=
       sa-explicitCompositeSignature{id-Dilithium3-ECDSA-brainpoolP256r1-SHA256,
       pk-Dilithium3-ECDSA-brainpoolP256r1-SHA256,
       ExplicitSignatureParameters{{sa-Dilithium3TBD},{sa-ecdsaWithSHA256}} }

   sa-Dilithium3-Ed25519 SIGNATURE-ALGORITHM ::=

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       sa-explicitCompositeSignature{id-Dilithium3-Ed25519,pk-Dilithium3-Ed25519,
       ExplicitSignatureParameters{{sa-Dilithium3TBD},{sa-Ed25519}} }

   sa-Dilithium5-ECDSA-P384-SHA384 SIGNATURE-ALGORITHM ::=
       sa-explicitCompositeSignature{ id-Dilithium5-ECDSA-P384-SHA384,
       pk-Dilithium5-ECDSA-P384-SHA384,
       ExplicitSignatureParameters{{sa-Dilithium5TBD},{sa-ecdsaWithSHA384}} }

   sa-Dilithium5-ECDSA-brainpoolP384r1-SHA384 SIGNATURE-ALGORITHM ::=
       sa-explicitCompositeSignature{id-Dilithium5-ECDSA-brainpoolP384r1-SHA384,
       pk-Dilithium5-ECDSA-brainpoolP384r1-SHA384,
       ExplicitSignatureParameters{{sa-Dilithium5TBD},{sa-ecdsaWithSHA384}} }

   sa-Dilithium5-Ed448 SIGNATURE-ALGORITHM ::=
       sa-explicitCompositeSignature{id-Dilithium5-Ed448,pk-Dilithium5-Ed448,
       ExplicitSignatureParameters{{sa-Dilithium5TBD},{sa-ed448}} }

   sa-Falcon512-ECDSA-P256-SHA256 SIGNATURE-ALGORITHM ::=
       sa-explicitCompositeSignature{id-Falcon512-ECDSA-P256-SHA256,
       pk-Falcon512-ECDSA-P256-SHA256,
       ExplicitSignatureParameters{{sa-Falcon512TBD},{sa-ecdsaWithSHA256}} }

   sa-Falcon512-ECDSA-brainpoolP256r1-SHA256 SIGNATURE-ALGORITHM ::=
       sa-explicitCompositeSignature{id-Falcon512-ECDSA-brainpoolP256r1-SHA256,
       pk-Falcon512-ECDSA-brainpoolP256r1-SHA256,
       ExplicitSignatureParameters{{sa-Falcon512TBD},{sa-ecdsaWithSHA256}} }

   sa-Falcon512-Ed25519 SIGNATURE-ALGORITHM ::=
       sa-explicitCompositeSignature{id-Falcon512-Ed25519,pk-Falcon512-Ed25519,
       ExplicitSignatureParameters{{sa-Falcon512TBD},{sa-Ed25519}} }

   sa-SPHINCSplusSHA256128sSimple-ECDSA-P256-SHA256 SIGNATURE-ALGORITHM ::=
       sa-explicitCompositeSignature{
       id-SPHINCSplusSHA256128sSimple-ECDSA-P256-SHA256,
       pk-SPHINCSplusSHA256128sSimple-ECDSA-P256-SHA256,
       ExplicitSignatureParameters{{sa-SPHINCSTBD},{sa-ecdsaWithSHA256}} }

   sa-SPHINCSplusSHA256128sSimple-ECDSA-brainpoolP256r1-SHA256
      SIGNATURE-ALGORITHM ::= sa-explicitCompositeSignature {
       id-SPHINCSplusSHA256128sSimple-ECDSA-brainpoolP256r1-SHA256,
       pk-SPHINCSplusSHA256128sSimple-ECDSA-brainpoolP256r1-SHA256,
         ExplicitSignatureParameters{{sa-SPHINCSTBD},
             {sa-ecdsaWithSHA256}} }

   sa-SPHINCSplusSHA256128sSimple-Ed25519 SIGNATURE-ALGORITHM ::=
      sa-explicitCompositeSignature{id-SPHINCSplusSHA256128sSimple-Ed25519,
         pk-SPHINCSplusSHA256128sSimple-Ed25519,
            ExplicitSignatureParameters{{sa-SPHINCSTBD},{sa-Ed25519}} }

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   -- Generic Composite definition

   --
   -- Object Identifiers
   --

   id-alg-composite OBJECT IDENTIFIER ::= {
     iso(1)  identified-organization(3) dod(6) internet(1) private(4)
     enterprise(1) opencA(18227) algorithms(2) id-alg-composite(1) }

   id-alg-composite-sha256 OBJECT IDENTIFIER ::= {
       iso(1)  identified-organization(3) dod(6) internet(1) private(4)
       enterprise(1) openCA(18227) algorithms(2) id-alg-composite(1)
       id-alg-composite-sha256(2) }

   id-alg-composite-sha512 OBJECT IDENTIFIER ::= {
       iso(1)  identified-organization(3) dod(6) internet(1) private(4)
       enterprise(1) openCA(18227) algorithms(2) id-alg-composite(1)
       id-alg-composite-sha512(4) }

   sa-CompositeSignature SIGNATURE-ALGORITHM ::= {
       IDENTIFIER id-alg-composite
       VALUE CompositeSignatureValue
       PARAMS TYPE CompositeSignatureParams ARE required
       PUBLIC-KEYS { pk-Composite }
    }

   sa-CompositeSignature-SHA256 SIGNATURE-ALGORITHM ::= {
       IDENTIFIER id-alg-composite-sha256
       VALUE CompositeSignatureValue
       PARAMS TYPE CompositeSignatureParams ARE required
       PUBLIC-KEYS { pk-Composite }
    }

   sa-CompositeSignature-SHA512 SIGNATURE-ALGORITHM ::= {
       IDENTIFIER id-alg-composite-sha512
       VALUE CompositeSignatureValue
       PARAMS TYPE CompositeSignatureParams ARE required
       PUBLIC-KEYS { pk-Composite }
    }

    CompositeSignatureValue ::= SEQUENCE SIZE (2..MAX) OF BIT STRING

    CompositeSignatureParams ::= SEQUENCE SIZE (2..MAX) OF
        AlgorithmIdentifier{SIGNATURE-ALGORITHM, {SignatureAlgSet}}

   END

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   <CODE ENDS>

7.  IANA Considerations

   This document registers the following in the SMI "Security for PKIX
   Algorithms (1.3.6.1.5.5.7.6)" registry:

   id-alg-composite OBJECT IDENTIFIER ::= {
       iso(1) identified-organization(3) dod(6) internet(1) security(5)
       mechanisms(5) pkix(7) algorithms(6) composite(??) }

   Plus the ASN.1 Module OID for Composite-Signatures-2023.

8.  Security Considerations

8.1.  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), then clients performing
   signatures or verifications should be updated to adhere to
   appropriate policies.

   In the composite model this is less obvious since a single public
   key, certificate, or signature may contain a mixture of deprecated
   and non-deprecated algorithms.  Moreover, implementers may decide
   that certain cryptographic algorithms have complementary security
   properties and are acceptable in combination even though neither
   algorithm is acceptable by itself.

   Specifying a modified verification algorithm to handle these
   situations is beyond the scope of this draft, but could be desirable
   as the subject of an application profile document, or to be up to the
   discretion of implementers.

   2. Check policy to see whether A1, A2, ..., An constitutes a valid
      combination of algorithms.

      if not checkPolicy(A1, A2, ..., An), then
        output "Invalid signature"

8.2.  K-of-N Validation Mode

   This document defines a composite signature verification process in
   Section 5.2 where the verifier verifies all component signatures and
   fails if any component fails.

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   The authors recognize that there will be scenarios where the verifier
   considers a single component algorithm -- or subset of component
   algorithms -- to provide sufficient security, and therefore for
   performance, or other practical reasons, wishes to skip the
   verification of one or more component signatures.  For example, it
   might be the case where the signer (whether it be a CA or an end
   entity) needs to be able to specify how its signatures are to be
   interpreted and verified.  Another use-case is where one of the
   composite algorithms' implementation might not be stable yet,
   possibly causing signature validation or generation issues across
   different providers or vendors.

   A detailed description of a K of N validation mode that address all
   these use-cases is described in [I-D.pala-klaussner-composite-kofn].

9.  References

9.1.  Normative References

   [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-
              01, 6 February 2023,
              <https://datatracker.ietf.org/doc/html/draft-ietf-lamps-
              dilithium-certificates-01>.

   [I-D.massimo-lamps-pq-sig-certificates]
              Massimo, J., Kampanakis, P., Turner, S., and B.
              Westerbaan, "Algorithms and Identifiers for Post-Quantum
              Algorithms", Work in Progress, Internet-Draft, draft-
              massimo-lamps-pq-sig-certificates-00, 8 July 2022,
              <https://datatracker.ietf.org/doc/html/draft-massimo-
              lamps-pq-sig-certificates-00>.

   [I-D.ounsworth-pq-composite-keys]
              Ounsworth, M., Gray, J., Pala, M., and J. Klaussner,
              "Composite Public and Private Keys For Use In Internet
              PKI", Work in Progress, Internet-Draft, draft-ounsworth-

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              pq-composite-keys-04, 13 March 2023,
              <https://datatracker.ietf.org/api/v1/doc/document/draft-
              ounsworth-pq-composite-keys/>.

   [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>.

   [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>.

   [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>.

   [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>.

   [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>.

   [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>.

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   [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.

9.2.  Informative References

   [Bindel2017]
              Bindel, N., Herath, U., McKague, M., and D. Stebila,
              "Transitioning to a quantum-resistant public key
              infrastructure", 2017, <https://link.springer.com/
              chapter/10.1007/978-3-319-59879-6_22>.

   [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.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>.

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   [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.pala-klaussner-composite-kofn]
              Pala, M. and J. Klau├čner, "K-threshold Composite
              Signatures for the Internet PKI", Work in Progress,
              Internet-Draft, draft-pala-klaussner-composite-kofn-00, 15
              November 2022, <https://datatracker.ietf.org/doc/html/
              draft-pala-klaussner-composite-kofn-00>.

   [I-D.truskovsky-lamps-pq-hybrid-x509]
              Truskovsky, A., Van Geest, D., Fluhrer, S., Kampanakis,
              P., Ounsworth, M., and S. Mister, "Multiple Public-Key
              Algorithm X.509 Certificates", Work in Progress, Internet-
              Draft, draft-truskovsky-lamps-pq-hybrid-x509-01, 29 August
              2018, <https://datatracker.ietf.org/doc/html/draft-
              truskovsky-lamps-pq-hybrid-x509-01>.

   [RFC3279]  Bassham, L., Polk, W., and R. Housley, "Algorithms and
              Identifiers for the Internet X.509 Public Key
              Infrastructure Certificate and Certificate Revocation List
              (CRL) Profile", RFC 3279, DOI 10.17487/RFC3279, April
              2002, <https://www.rfc-editor.org/info/rfc3279>.

   [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>.

   [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>.

   [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>.

   [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>.

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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

B.1.  Generic Composite Signature Examples

   TODO

B.2.  Explicit Composite Signature Examples

   TODO

Appendix C.  Implementation Considerations

   This section addresses practical issues of how this draft affects
   other protocols and standards.

   ~~~ BEGIN EDNOTE 10~~~

   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.

   *  We could talk about overhead (size and processing).

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   *  We could also discuss backwards compatibility.

   *  We could include a subsection about implementation considerations.

   ~~~ END EDNOTE 10~~~

C.1.  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.

   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 digital signature objects, from
   online negotiated protocols such as TLS 1.3 [RFC8446] and IKEv2
   [RFC7296], to non-negotiated asynchronous protocols such as S/MIME
   signed 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 structures.

C.1.1.  Composite K-of-N (OR modes)

   Section 5.1 and Section 5.2 make reference to subset signature
   generation and verification modes to achieve an OR relation between
   component signatures, 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 signature
   algorithm for which it does not posses a compatible implementation
   but wishes to proceed with the signature verification using the
   subset of component signatures 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.

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   It is important to notice that although Composite Crypto 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), upgrading today's systems to be able to handle
   composite keys and signatures will also provide the tool for the next
   generation of migration.  In other words, the work to support
   Composite Crypto will also provide crypto agility options for
   subsequent crypto-migration in a truly crypto-agile fashion (i.e.,
   entities will always able to process composite signatures independent
   from the individual cryptographic algorithms that are supported
   today).

   Please refer to [I-D.pala-klaussner-composite-kofn] for more
   information.

C.1.2.  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 identity (name), 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
   algorithms (legacy and post-quantum).

   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 signature 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 algorithms defined in Section 4 as a way to carry
   the multiple signature values generated by one of the 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.

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   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 objects is often
   already treated as an OR relationship, so including one for each of
   the signer'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.

C.1.3.  Hybrid Extensions (Keys and Signatures)

   The use of Composite Crypto provides the possibility to process
   multiple algorithms without changing the logic of applications, but
   updating the cryptographic libraries: one-time change across the
   whole system.  However, when it is not possible to upgrade the crypto
   engines/libraries, it is possible to leverage X.509 extensions to
   encode the additional keys and signatures.  When the custom
   extensions are not marked critical, although this approach provides
   the most backward-compatible approach where clients can simply ignore
   the post-quantum (or extra) keys and signatures, it also requires all
   applications to be updated for correctly processing multiple
   algorithms together.

   Please refer to [I-D.truskovsky-lamps-pq-hybrid-x509] for more
   information.

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:

   Serge Mister (Entrust), Scott Fluhrer (Cisco Systems), Panos
   Kampanakis (Cisco Systems), Daniel Van Geest (ISARA), Tim Hollebeek
   (Digicert), and Francois Rousseau.

   We are grateful to all, including any contributors who may have been
   inadvertently omitted from this list.

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   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-composite-sigs

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
   858 Coal Creek Circle
   Louisville, Colorado,  80027
   United States of America
   Email: director@openca.org

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