Algorithm Identifiers for Ed25519, Ed25519ph, Ed448, Ed448ph, X25519 and X448 for use in the Internet X.509 Public Key Infrastructure
draft-ietf-curdle-pkix-01

Abstract

This document specify algorithm identifiers and ASN.1 encoding formats for Elliptical Curve constructs using the Curve25519 and Curve448 curves. The signature algorithms covered are Ed25519, Ed25519ph, Ed448 and Ed448ph. The key agreement algorithm covered are X25519 and X448. The Encoding for Public Key, Private Key and EdDSA digital signature structures is provided.

Status of This Memo

This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79.

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This Internet-Draft will expire on February 20, 2017.

Copyright Notice

Copyright (c) 2016 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 (http://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 Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License.

Table of Contents

• 1. Introduction
• 2. Requirements Terminology
• 3. Curve25519 and Curve448 Algorithm Identifiers
• 4. Subject Public Key Fields
• 5. Key Usage Bits
• 6. EdDSA Signatures
• 7. Private Key Format
• 8. Human Readable Algorithm Names
• 9. ASN.1 Module
• 10. Examples
• 10.1. Example Ed25519 Public Key
• 10.2. Example X25519 Certificate
• 10.3. Example Ed25519 Private Key
• 11. Acknowledgements
• 12. IANA Considerations
• 13. Security Considerations
• 14. References
• 14.1. Normative References
• 14.2. Informative References
• Authors' Addresses

1. Introduction

In [RFC7748], the elliptic curves Curve25519 and Curve448 are described. They are designed with performance and security in mind. The curves may be used for Diffie-Hellman and Digital Signature operations. A convention has developed that when these two curves are used with the Diffie-Hellman operation, they are referred to as X25519 and X448.

In [I-D.irtf-cfrg-eddsa] the elliptic curve signature system EdDSA is described and the recommended choice of curves Ed25519/Ed448 are chosen. EdDSA has defined two modes, the PureEdDSA mode without pre-hashing, and the HashEdDSA mode with pre-hashing. Unlike other digital signature algorithms, the Ed25519ph and Ed448ph algorithm definitions specify the one-way hash function that is used. Attacks have been described when the same key is used with and without pre-hashing for Ed25519, so a single key MUST NOT be used for both modes. The convention used for identifying the algorithm/curve combinations are to use the Ed25519 and Ed448 for the PureEdDSA mode and Ed25519ph and Ed448ph for the HashEdDSA mode.

This RFC defines ASN.1 object identifiers for EdDSA for use in the Internet X.509 PKI [RFC5280], and parameters for Ed25519, Ed25519ph, Ed448 and Ed448ph. This document serves a similar role as [RFC3279] does for RSA (and more), [RFC4055] for RSA-OAEP/PSS, and [RFC5758] for SHA2-based (EC)DSA. This document also specify ASN.1 "named curve" object identifiers for Curve25519 and Curve448, similar to what is done in [RFC5639]. This allows the curves to be used and referenced in PKIX standards and software, in particular enabling re-use of existing constructs already defined for ECDSA/ECDH but for the new curves. Similar to [RFC5639], this document does not describe the cryptographic algorithms to be used with the specified parameters nor their application in other standards.

2. Requirements Terminology

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119].

3. Curve25519 and Curve448 Algorithm Identifiers

Certificates conforming to [RFC5280] can convey a public key for any public key algorithm. The certificate indicates the algorithm through an algorithm identifier. This algorithm identifier is an OID and optionally associated parameters.

The AlgorithmIdentifier type, which is included for convenience, is defined as follows:

AlgorithmIdentifier  ::=  SEQUENCE  {
    algorithm   OBJECT IDENTIFIER,
    parameters  ANY DEFINED BY algorithm OPTIONAL
}

The fields in AlgorithmIdentifier have the following meanings:

• algorithm identifies the cryptographic algorithm with an object identifier. This is one of the OIDs defined below.
• parameters, which are optional, are the associated parameters for the algorithm identifier in the algorithm field. When the 1997 syntax for AlgorithmIdentifier was initially defined, it omitted the OPTIONAL key word. The optionality of the parameters field was later recovered via a defect report, but by then many people thought that the field was mandatory. For this reason, a small number of implementations may still require the field to be present.

In this document we defined six new OIDs for identifying the different curve/algorithm pairs. The curves being Curve25519 and Curve448. The algorithms being ECDH, EdDSA in pure mode and EdDSA in pre-hash mode. For all of the OIDs, the parameters MUST be absent. Implementations SHOULD NOT accept a parameters value of NULL.

The same algorithm identifiers are used for identifying a public key, identifying a private key and identifying a signature (for the four EdDSA related OIDs). Additional encoding information is provided below for each of these locations.

id-X25519    OBJECT IDENTIFIER ::= { 1.3.101.110 }
id-X448      OBJECT IDENTIFIER ::= { 1.3.101.111 }
id-Ed25519   OBJECT IDENTIFIER ::= { 1.3.101.112 }
id-Ed448     OBJECT IDENTIFIER ::= { 1.3.101.113 }
id-Ed25519ph OBJECT IDENTIFIER ::= { 1.3.101.114 }
id-Ed448ph   OBJECT IDENTIFIER ::= { 1.3.101.115 }

4. Subject Public Key Fields

In the X.509 certificate, the subjectPublicKeyInfo field has the SubjectPublicKeyInfo type, which has the following ASN.1 syntax:

SubjectPublicKeyInfo  ::=  SEQUENCE  {
    algorithm         AlgorithmIdentifier,
    subjectPublicKey  BIT STRING
}

The fields in SubjectPublicKeyInfo have the following meanings:

• algorithm is the algorithm identifier and parameters for the public key (see above).
• subjectPublicKey contains the byte stream of the public key. While the encoded public keys for the current algorithms are all an even number of octets, future curves could change that.

Both [RFC7748] and [I-D.irtf-cfrg-eddsa] define the public key value as being a byte string. It should be noted that the public key is computed differently for each of these documents, thus the same private key will not produce the same public key.

The following is an example of a public key encoded using the textual encoding defined in [RFC7468].

-----BEGIN PUBLIC KEY-----
MCowBQYDK2VwAyEAGb9ECWmEzf6FQbrBZ9w7lshQhqowtrbLDFw4rXAxZmE=
-----END PUBLIC KEY-----      

5. Key Usage Bits

The intended application for the key is indicated in the keyUsage certificate extension.

If the keyUsage extension is present in a certificate that indicates id-X25119 or id-X448 in SubjectPublicKeyInfo, then the following MUST be present:

        keyAgreement;
      

one of the following MAY also be present:

          encipherOnly; or
          decipherOnly.
          

If the keyUsage extension is present in an end-entity certificate that indicates id-EdDSA25519, id-EdDSA25519ph, id-EdDSA448 or id-EdDSA448ph , then the keyUsage extension MUST contain one or both of the following values:

nonRepudiation; and
digitalSignature.

If the keyUsage extension is present in a certification authority certificate that indicates id-EdDSA25519 or id-EdDSA448, then the keyUsage extension MUST contain one or more of the following values:

       nonRepudiation;
       digitalSignature;
       keyCertSign; and
       cRLSign.
       

CAs MUST NOT use the pre-hash versions of the EdDSA algorithms for the creation of certificates or CRLs. This is implied by the fact that those algorithms are not listed in the previous paragraph. Additionally OCSP responders SHOULD NOT use the pre-hash versions of the EdDSA algorithms when generating OCSP responses. No restriction is placed on generation of OCSP requests.

AAs MUST NOT use the pre-hash versions of the EdDSA algorithms for the creation of attribute certificates or attribute CRLs [RFC5755].

6. EdDSA Signatures

Signatures can be placed in a number of different ASN.1 structures. The top level structure for a certificate is given below as being illustrative of how signatures are frequently encoded with an algorithm identifier and a location for the signature.

   Certificate  ::=  SEQUENCE  {
        tbsCertificate       TBSCertificate,
        signatureAlgorithm   AlgorithmIdentifier,
        signatureValue       BIT STRING  }

The same algorithm identifiers are used for signatures as are used for public keys. When used to identify signature algorithms, the parameters MUST be absent.

The data to be signed is prepared for EdDSA. Then, a private key operation is performed to generate the signature value. This value is the opaque value ENC(R) || ENC(S) described in section 3.3 of [I-D.irtf-cfrg-eddsa]. The octet string representing the signature is encoded directly in the BIT STRING without adding any additional ASN.1 wrapping. For the Certificate structure, the signature value is wrapped in the 'signatureValue' BIT STRING field.

When the pre-hash versions of the EdDSA signature algorithms are used, the hash function used for the pre-hash is defined by the algorithm. This means that the pre-hash function is implicitly included in the algorithm identifier rather than being explicit as done in [RFC3279].

7. Private Key Format

Asymmetric Key Packages [RFC5958] describes how encode a private key in a structure that both identifies what algorithm the private key is for, but allows for the public key and additional attributes about the key to be included as well. For illustration, the ASN.1 structure OneAsymmetricKey is replicated below. The algorithm specific details of how a private key is encoded is left for the document describing the algorithm itself.

OneAsymmetricKey ::= SEQUENCE {
   version Version,
   privateKeyAlgorithm PrivateKeyAlgorithmIdentifier,
   privateKey PrivateKey,
   attributes [0] Attributes OPTIONAL,
   ...,
   [[2: publicKey [1] PublicKey OPTIONAL ]],
   ...
}

PrivateKey ::= OCTET STRING

PublicKey ::= OCTET STRING

For the keys defined in this document, the private key is always an opaque byte sequence. The ASN.1 type EdPrivateKey is defined in this document to hold the byte sequence. Thus when encoding a OneAsymmetricKey object, the private key is wrapped in an EdPrivateKey object and then placed in the 'privateKey' field.

EdPrivateKey ::= OCTET STRING

To encode a EdDSA, X25519 or X448 private key, the "privateKey" field will hold the encoded private key. The "privateKeyAlgorithm" field uses the AlgorithmIdentifier structure. The structure is encoded as defined above. If present, the "publicKey" field will hold the encoded key as defined in [RFC7748] and [I-D.irtf-cfrg-eddsa]. public key.

The following is an example of a private key encoded using the textual encoding defined in [RFC7468].

-----BEGIN PRIVATE KEY-----
MC4CAQAwBQYDK2VwBCIEINTuctv5E1hK1bbY8fdp+K06/nwoy/HU++CXqI9EdVhC
-----END PRIVATE KEY-----

8. Human Readable Algorithm Names

For the purpose of consistent cross-implementation naming this section establishes human readable names for the algorithms specified in this document. Implementations SHOULD use these names when referring to the algorithms. If there is a strong reason to deviate from these names -- for example, if the implementation has a different naming convention and wants to maintain internal consistency -- it is encouraged to deviate as little as possible from the names given here.

Use the string "ECDH" when referring to a public key of type X25519 or X448 when the curve is not known or relevant.

When the curve is known, use the more specific string of X25519 or X448.

Use the string "EdDSA" when referring to a signing public key or signature when the curve is not known or relevant.

When the curve is known, use a more specific string. For the id-EdDSA25519 value use the string "Ed25519". For the id-EdDSA25519ph value use the string "Ed25519ph". For id-EdDSA448 use "Ed448". For id-EdDSA448ph use "Ed448ph".

9. ASN.1 Module

For reference purposes, the ASN.1 syntax is presented as an ASN.1 module here.

-- ASN.1 Module

Safecurves-pkix-0 {1 3 101 120}

DEFINITIONS EXPLICIT TAGS ::=
BEGIN

IMPORTS
  SIGNATURE-ALGORITHM, KEY-AGREE, PUBLIC-KEY, KEY-WRAP,
  KeyUsage, AlgorithmIdentifier
  FROM AlgorithmInformation-2009 
    {iso(1) identified-organization(3) dod(6) internet(1) security(5)
    mechanisms(5) pkix(7) id-mod(0)
    id-mod-algorithmInformation-02(58)}

  mda-sha512
  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) }

  kwa-aes128-wrap, kwa-aes256-wrap
  FROM CMSAesRsaesOaep-2009
    { iso(1) member-body(2) us(840) rsadsi(113549) pkcs(1) pkcs-9(9)
      smime(16) modules(0) id-mod-cms-aes-02(38) }
  ;
    

id-edwards-curve-algs OBJECT IDENTIFIER ::= { 1 3 101 }

id-X25519        OBJECT IDENTIFIER ::= { id-edwards-curve-algs 110 }
id-X448          OBJECT IDENTIFIER ::= { id-edwards-curve-algs 111 }
id-EdDSA25519    OBJECT IDENTIFIER ::= { id-edwards-curve-algs 112 }
id-EdDSA25519-ph OBJECT IDENTIFIER ::= { id-edwards-curve-algs 114 }
id-EdDSA448      OBJECT IDENTIFIER ::= { id-edwards-curve-algs 113 }
id-EdDSA448-ph   OBJECT IDENTIFIER ::= { id-edwards-curve-algs 115 }


 sa-EdDSA25519 SIGNATURE-ALGORITHM ::= {
    IDENTIFIER id-EdDSA25519
     PARAMS ARE absent
     PUBLIC-KEYS {pk-EdDSA25519}
     SMIME-CAPS { IDENTIFIED BY id-EdDSA25519 }
 }

 pk-EdDSA25519 PUBLIC-KEY ::= {
     IDENTIFIER id-EdDSA25519
     -- KEY no ASN.1 wrapping --
     PARAMS ARE absent
     CERT-KEY-USAGE {digitalSignature, nonRepudiation,
                     keyCertSign, cRLSign}
     PRIVATE-KEY EdPrivateKey
 }

 sa-EdDSA25519-ph SIGNATURE-ALGORITHM ::= {
     IDENTIFIER id-EdDSA25519-ph
     PARAMS ARE absent
     HASHES { mda-sha512 }
     PUBLIC-KEYS {pk-EdDSA25519-ph}
     SMIME-CAPS { IDENTIFIED BY id-EdDSA25519-ph }
 }

 pk-EdDSA25519-ph PUBLIC-KEY ::= {
     IDENTIFIER id-EdDSA25519-ph
     -- KEY no ASN.1 wrapping --
     PARAMS ARE absent
     CERT-KEY-USAGE {digitalSignature, nonRepudiation}
     PRIVATE-KEY EdPrivateKey
 }

 kaa-X25519 KEY-AGREE ::= {
     IDENTIFIER id-X25519
     PARAMS ARE absent
     PUBLIC-KEYS {pk-X25519}
     UKM -- TYPE no ASN.1 wrapping -- ARE preferredPresent
     SMIME-CAPS {
        TYPE AlgorithmIdentifier{KEY-WRAP, {KeyWrapAlgorithms}}
        IDENTIFIED BY id-X25519 }
 }

 pk-X25519 PUBLIC-KEY ::= {
     IDENTIFIER id-X25519
     -- KEY no ASN.1 wrapping --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyAgreement }
     PRIVATE-KEY EdPrivateKey
 }

 KeyWrapAlgorithms KEY-WRAP ::= {
     kwa-aes128-wrap | kwa-aes256-wrap,
     ...
 }
     
 kaa-X488 KEY-AGREE ::= {
     IDENTIFIER id-X448
     PARAMS ARE absent
     PUBLIC-KEYS {pk-X448}
     UKM -- TYPE no ASN.1 wrapping  -- ARE preferredPresent
     SMIME-CAPS {
        TYPE AlgorithmIdentifier{KEY-WRAP, {KeyWrapAlgorithms}}
        IDENTIFIED BY id-X448 }
 }

 pk-X448 PUBLIC-KEY ::= {
     IDENTIFIER id-X448
     -- KEY no ASN.1 wrapping --
     PARAMS ARE absent
     CERT-KEY-USAGE { keyAgreement }
     PRIVATE-KEY EdPrivateKey
 }

EdPrivateKey ::= OCTET STRING
    
                                 
END

10. Examples

This section contains illustrations of EdDSA public keys and certificates, illustrating parameter choices.

10.1. Example Ed25519 Public Key

An example of a Ed25519 public key:

      Public Key Information:
          Public Key Algorithm: EdDSA25519
          Algorithm Security Level: High

      Public Key Usage:
      
      Public Key ID: 9b1f5eeded043385e4f7bc623c5975b90bc8bb3b
      
      -----BEGIN PUBLIC KEY-----
      MCowBQYDK2VwAyEAGb9ECWmEzf6FQbrBZ9w7lshQhqowtrbLDFw4rXAxZmE=
      -----END PUBLIC KEY-----

10.2. Example X25519 Certificate

An example of a PKIX certificate using Ed25519 to sign X25519 would be:

   0 30  300: SEQUENCE {
   4 30  223:   SEQUENCE {
   7 A0    3:     [0] {
   9 02    1:       INTEGER 2
            :       }
  12 02    8:     INTEGER
            :       56 01 47 4A 2A 8D C3 30
  22 30    5:     SEQUENCE {
  24 06    3:       OBJECT IDENTIFIER
            :         EdDSA 25519 signature algorithm { 1 3 101 112 }
            :       }
  29 30   25:     SEQUENCE {
  31 31   23:       SET {
  33 30   21:         SEQUENCE {
  35 06    3:           OBJECT IDENTIFIER commonName (2 5 4 3)
  40 0C   14:           UTF8String (1997) 'IETF Test Demo'
            :           }
            :         }
            :       }
  56 30   30:     SEQUENCE {
  58 17   13:       UTCTime '160801121924Z'
  73 17   13:       UTCTime '401231235959Z'
            :       }
  88 30   25:     SEQUENCE {
  90 31   23:       SET {
  92 30   21:         SEQUENCE {
  94 06    3:           OBJECT IDENTIFIER commonName (2 5 4 3)
  99 0C   14:           UTF8String (1997) 'IETF Test Demo'
            :           }
            :         }
            :       }
 115 30   42:     SEQUENCE {
 117 30    5:       SEQUENCE {
 119 06    3:         OBJECT IDENTIFIER
            :           ECDH 25519 key agreement { 1 3 101 110 }
            :         }
 124 03   33:       BIT STRING 0 unused bits
            :         85 20 F0 09 89 30 A7 54 74 8B 7D DC B4 3E F7 5A
            :         0D BF 3A 0D 26 38 1A F4 EB A4 A9 8E AA 9B 4E 6A
            :       }
 159 A3   69:     [3] {
 161 30   67:       SEQUENCE {
 163 30   15:         SEQUENCE {
 165 06    3:           OBJECT IDENTIFIER basicConstraints (2 5 29 19)
 170 01    1:           BOOLEAN TRUE
 173 04    5:           OCTET STRING, encapsulates {
 175 30    3:               SEQUENCE {
 177 01    1:                 BOOLEAN FALSE
            :                 }
            :               }
            :           }
 180 30   14:         SEQUENCE {
 182 06    3:           OBJECT IDENTIFIER keyUsage (2 5 29 15)
 187 01    1:           BOOLEAN FALSE
 190 04    4:           OCTET STRING, encapsulates {
 192 03    2:               BIT STRING 7 unused bits
            :                 '1'B
            :               }
            :           }
 196 30   32:         SEQUENCE {
 198 06    3:           OBJECT IDENTIFIER subjectKeyIdentifier (2 5 29 14)
 203 01    1:           BOOLEAN FALSE
 206 04   22:           OCTET STRING
            :             04 14 9B 1F 5E ED ED 04 33 85 E4 F7 BC 62 3C 59
            :             75 B9 0B C8 BB 3B
            :           }
            :         }
            :       }
            :     }
 230 30    5:   SEQUENCE {
 232 06    3:     OBJECT IDENTIFIER
            :       EdDSA 25519 signature algorithm { 1 3 101 112 }
            :     }
 237 03   65:   BIT STRING 0 unused bits
            :     D1 EE DF 10 15 68 CA C2 4A C2 13 7F 45 C6 B7 6E
            :     7C 11 E8 B3 AC D5 67 D3 1A 6E 90 EA 0F 8B F6 50
            :     0F 91 66 BB EF BE 10 DE FA 37 7B 61 FC D7 C5 C6
            :     AB CF 3F 89 01 F9 BD 80 E8 1B 9D 21 DD 32 73 0A
            :   }
      
-----BEGIN CERTIFICATE-----
MIIBLDCB36ADAgECAghWAUdKKo3DMDAFBgMrZXAwGTEXMBUGA1UEAwwOSUVURiBUZXN0IERlbW8wHhcN
MTYwODAxMTIxOTI0WhcNNDAxMjMxMjM1OTU5WjAZMRcwFQYDVQQDDA5JRVRGIFRlc3QgRGVtbzAqMAUG
AytlbgMhAIUg8AmJMKdUdIt93LQ+91oNvzoNJjga9OukqY6qm05qo0UwQzAPBgNVHRMBAf8EBTADAQEA
MA4GA1UdDwEBAAQEAwIHgDAgBgNVHQ4BAQAEFgQUmx9e7e0EM4Xk97xiPFl1uQvIuzswBQYDK2VwA0EA
0e7fEBVoysJKwhN/Rca3bnwR6LOs1WfTGm6Q6g+L9lAPkWa7774Q3vo3e2H818XGq88/iQH5vYDoG50h
3TJzCg==
-----END CERTIFICATE-----

10.3. Example Ed25519 Private Key

An example of an Ed25519 private key:

-----BEGIN PRIVATE KEY-----
MC4CAQAwBQYDK2VwBCIEINTuctv5E1hK1bbY8fdp+K06/nwoy/HU++CXqI9EdVhC
-----END PRIVATE KEY-----

11. Acknowledgements

Text and/or inspiration were drawn from [RFC5280], [RFC3279], [RFC4055], [RFC5480], and [RFC5639].

The following people discussed the document and provided feedback: Klaus Hartke, Ilari Liusvaara, Erwann Abalea, Rick Andrews, Rob Stradling, James Manger, Nikos Mavrogiannopoulos, Russ Housley, and Alex Wilson.

A big thank you to Symantec for kindly donating the OIDs used in this draft.

12. IANA Considerations

None.

13. Security Considerations

The security considerations of [RFC5280], [RFC7748], and [I-D.irtf-cfrg-eddsa] apply accordingly.

A common misconception may be that a Ed25519 public key can be used to create Ed25519ph signatures, or vice versa. This leads to cross-key attacks, and is not permitted.

14. References

14.1. Normative References

14.2. Informative References

Authors' Addresses