Functions Based on GF(p)

This section describes functions designed to specify the elliptic curve cryptosystem and perform various operations on the elliptic curve defined over a prime finite field. The examples of the operations are shown below:

• Setting up operations: ECCPSet sets up elliptic curve domain parameters. ECCPSetKeyPair sets a pair of public and private keys for the given cryptosystem.
• Computation operations: ECCPAddPoint adds two points on the elliptic curve. ECCPMulPointScalar performs the scalar multiplication of a point on the elliptic curve. ECCPSignDSA computes the digital signature of a message.
• Validation operations: ECCPValidate checks validity of the elliptic curve domain parameters. ECCPValidateKeyPair validates correctness of the public and private keys.
• Generation operations: ECCPGenKeyPair generates a private key and computes a public key for the given elliptic cryptosystem.
• Retrieval operations: ECCPGet retrieves elliptic curve domain parameters. ECCPGetOrderBitSize retrieves the size of a base point in bytes.

All functions described in this section employ a context IppsECCPState that catches several auxiliary components specifying operations performed on the elliptic curve or entire elliptic cryptosystem. ECCP stands for Elliptic Curve Cryptography Prime and means that all functions whose name include this abbreviation perform operations over a prime finite field GF( p).

The IppECCType enumerator lists standard elliptic curves supported. You can select a particular type in a call to ECCPSetStd.

The table below associates each value of IppECCType with parameters of the elliptic curve and provides a reference to the appropriate specification.

For more information on parameters recommended for the functions, see [SEC2] and [SM2].

• ECCPGetSize
  Gets the size of the IppsECCPState context.
• ECCPGetSizeStd
  Gets the size of the IppsECCPState context for a standard elliptic curve.
• ECCPInit
  Initializes the context for the elliptic curve cryptosystem over GF(p).
• ECCPInitStd
  Initializes the context for the cryptosystem based on a standard elliptic curve.
• ECCPBindGxyTblStd
  Enable the use of base point-based pre-computed tables of standard elliptic curves.
• ECCPSet
  Sets up elliptic curve domain parameters over GF(p).
• ECCPSetStd
  Sets up a recommended set of domain parameters for an elliptic curve over GF(p).
• ECCPGet
  Retrieves elliptic curve domain parameters over GF(p).
• ECCPGetOrderBitSize
  Retrieves order size of the elliptic curve base point over GF(p) in bits.
• ECCPValidate
  Checks validity of the elliptic curve domain parameters over GF(p).
• ECCPPointGetSize
  Gets the size of the IppsECCPPoint context in bytes for a point on the elliptic curve point defined over GF(p).
• ECCPPointInit
  Initializes the context for a point on the elliptic curve defined over GF(p).
• ECCPSetPoint
  Sets coordinates of a point on the elliptic curve defined over GF(p).
• ECCPSetPointAtInfinity
  Sets the point at infinity.
• ECCPGetPoint
  Retrieves coordinates of the point on the elliptic curve defined over GF(p).
• ECCPCheckPoint
  Checks correctness of the point on the elliptic curve defined over GF(p).
• ECCPComparePoint
  Compares two points on the elliptic curve defined over GF(p).
• ECCPNegativePoint
  Finds an elliptic curve point which is an additive inverse for the given point over GF(p).
• ECCPAddPoint
  Computes the addition of two elliptic curve points over GF(p).
• ECCPMulPointScalar
  Performs scalar multiplication of a point on the elliptic curve defined over GF(p).
• ECCPGenKeyPair
  Generates a private key and computes public keys of the elliptic cryptosystem over GF(p).
• ECCPPublicKey
  Computes a public key from the given private key of the elliptic cryptosystem over GF(p).
• ECCPValidateKeyPair
  Validates private and public keys of the elliptic cryptosystem over GF(p).
• ECCPSetKeyPair
  Sets private and/or public keys of the elliptic cryptosystem over GF(p).
• ECCPSharedSecretDH
  Computes a shared secret field element by using the Diffie-Hellman scheme.
• ECCPSharedSecretDHC
  Computes a shared secret field element by using the Diffie-Hellman scheme and the elliptic curve cofactor.
• ECCPSignDSA
  Computes a digital signature over a message digest.
• ECCPVerifyDSA
  Verifies authenticity of the digital signature over a message digest (ECDSA).
• ECCPSignNR
  Computes the digital signature over a message digest (the Nyberg-Rueppel scheme).
• ECCPVerifyNR
  Verifies authenticity of the digital signature over a message digest (the Nyberg-Rueppel scheme).
• ECCPSignSM2
  Computes a digital signature over a message digest using the SM2 scheme.
• ECCPVerifySM2
  Verifies authenticity of a digital signature over a message digest using the SM2 scheme.
• Signing/Verification Using the Elliptic Curve Cryptography Functions over a Prime Finite Field