Algorithm Identifiers for Ed25519, Ed25519ph, Ed448, Ed448ph, X25519 and X448 for use in the Internet X.509 Public Key Infrastructure

In , 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. describes the operations on these curves for the Diffie-Hellman operation. A convention has developed that when these two curves are used with the Diffie-Hellman operation, they are referred to as X25519 and X448. This RFC defines the ASN.1 Object Identifiers (OIDs) for the operations X25519 and X448 along with the parameters. The use of these OIDs is described for public and private keys. In the elliptic curve signature system Edwards-curve Digital Signature Algorithm (EdDSA) is described along with a recommendation for the use of the Curve25519 and Curve448. EdDSA has defined two modes, the PureEdDSA mode without pre-hashing, and the HashEdDSA mode with pre-hashing. The Ed25519ph and Ed448ph algorithm definitions specify the one-way hash function that is used for pre-hashing. The convention used for identifying the algorithm/curve combinations are to use the Ed25519 and Ed448 for the PureEdDSA mode, with Ed25519ph and Ed448ph for the HashEdDSA mode. The use of the OIDs is described for public keys, private keys and signatures.

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 .

Certificates conforming to 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:

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.

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

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 and 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 .

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:

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:

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 .

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.

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 . 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 . In , a parameter was defined for a context value, specific to an application, to be provided to the signing operation. This value is used to force different signatures to be generated for different applications. Along with the defintion of the context comes a recommendation that contexts only be used if all of the signature algorithms used for an application have the ability to accept a context string. For this reason, applications MUST NOT define the use a context value with the signatures created for these OIDs. New OIDs would be defined in the event that context values appear to provide additional value.

Asymmetric Key Packages 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.

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.

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 and . public key. The following is an example of a private key encoded using the textual encoding defined in .

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".

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

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

An example of a Ed25519 public key:

An example of a self issued PKIX certificate using Ed25519 to sign a X25519 public key would be:

An example of an Ed25519 private key:

Text and/or inspiration were drawn from , , , , and . 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, David Benjamin, and Alex Wilson. A big thank you to Symantec for kindly donating the OIDs used in this draft.

None.

The security considerations of , , and apply accordingly. The procedures for going from a private key to a public key is different for when used with Diffie-Helman and when used with Edwards Signatures. This means that the same public key cannot be used for both ECDH and EdDSA. In the original design of Ed25519 signatures, there was a known attack between the pure and the pre-hash version of the signatures. This has sense been corrected in the final version of the design. The initial problem meant that there was a known attack, and therefore a known reason to forbid the use of Ed25519 keys with the Ed25519ph signature scheme and visa versa. With the change in the design this attack has been prevented. This does not mean that the same Ed25519 key should be used with both schemes, there still may be attacks where collisions can be found. For this reason, the same keys are not to be used for the pure and pre-hash versions of the scheme. This applies to both curve 25519 and curve 448.