About Elliptic Curve

The EC cryptosystem (also related to ECDSA) in this document is the one described in the ANSI X9.62 standard and the ANSI X9.63 draft developed by the ANSI X9F1 working group.

In these standards, there are two different varieties of EC defined:

EC using a field with an odd prime number of elements (i.e. the finite field F_p ).
EC using a field of characteristic two (i.e. the finite field F _{2 m}).

An EC key in Cryptoki contains information about which variety of EC it is suited for. It is preferable that a Cryptoki library, which can perform EC mechanisms, be capable of performing operations with the two varieties of EC, however this is not required. The CK_MECHANISM_INFO structure CKF_EC_F_P flag identifies a Cryptoki library supporting EC keys over F_p whereas the CKF_EC_F_2M flag identifies a Cryptoki library supporting EC keys over F _{2 m}. A Cryptoki library that can perform EC mechanisms must set either or both of these flags for each EC mechanism.

In these specifications there are also three representation methods to define the domain parameters for an EC key. Only the ecParameters and the namedCurve choices are supported in Cryptoki. The CK_MECHANISM_INFO structure CKF_EC_ECPARAMETERS flag identifies a Cryptoki library supporting the ecParameters choice whereas the CKF_EC_NAMEDCURVE flag identifies a Cryptoki library supporting the namedCurve choice. A Cryptoki library that can perform EC mechanisms must set either or both of these flags for each EC mechanism.

In these specifications, an EC public key (i.e. EC point Q) or the base point G when the ecParameters choice is used can be represented as an octet string of the uncompressed form or the compressed form. The CK_MECHANISM_INFO structure CKF_EC_UNCOMPRESS flag identifies a Cryptoki library supporting the uncompressed form whereas the CKF_EC_COMPRESS flag identifies a Cryptoki library supporting the compressed form. A Cryptoki library that can perform EC mechanisms must set either or both of these flags for each EC mechanism.

Note that an implementation of a Cryptoki library supporting EC with only one variety, one representation of domain parameters or one form may encounter difficulties achieving interoperability with other implementations.

If an attempt to create, generate, derive, or unwrap an EC key of an unsupported variety (or of an unsupported size of a supported variety) is made, that attempt should fail with the error code CKR_TEMPLATE_INCONSISTENT. If an attempt to create, generate, derive, or unwrap an EC key with invalid or of an unsupported representation of domain parameters is made, that attempt should fail with the error code CKR_DOMAIN_PARAMS_INVALID. If an attempt to create, generate, derive, or unwrap an EC key of an unsupported form is made, that attempt should fail with the error code CKR_TEMPLATE_INCONSISTENT.

RSA Security Inc. Public-Key Cryptography Standards - PKCS#11 - v211