Visible to Intel only — GUID: GUID-B8291BF2-1D2B-4B51-90B8-798A12CC96AE
Visible to Intel only — GUID: GUID-B8291BF2-1D2B-4B51-90B8-798A12CC96AE
Arithmetic of the Group of Elliptic Curve Points
This section describes the Intel IPP functions that implement arithmetic operations with points of elliptic curves [EC]. The elliptic curve is defined by the following equation:
y2 = x3 + A ⋅ x + B
where
- A and B are the parameters of the curve
- x and y are the coordinates of a point on the curve
This document considers elliptic curves constructed over the finite field GF(p) (prime or its extension), therefore the arithmetic of elliptic curves is based on the arithmetic of the underlying finite field. In the equation above, A, B, x, and y belong to the underlying field GF(p).
- GFpECGetSize
Gets the size of an elliptic curve over the finite field. - GFpECInit
Initializes the context of an elliptic curve over a finite field. - GFpECSet
Sets up the parameters of an elliptic curve over a finite field. - GFpECSetSubgroup
Sets up the parameters defining an elliptic curve points subgroup. - GFpECInitStd
Initializes the context for the cryptosystem based on a standard elliptic curve. - GFpECGet
Extracts the parameters of an elliptic curve over a finite field from the context. - GFpECGetSubgroup
Extracts the parameters (base point and its order) that define an elliptic curve point subgroup. - GFpECScratchBufferSize
Gets the size of the scratch buffer. - GFpECVerify
Verifies the parameters of an elliptic curve. - GFpECPointGetSize
Gets the size of the IppsGFpECPoint context of a point on an elliptic curve. - GFpECPointInit
Initializes the context of a point on an elliptic curve. - GFpECSetPointAtInfinity
Sets a point on an elliptic curve as a point at infinity. - GFpECSetPoint, GFpECSetPointREgular
Sets up the coordinates of a point on an elliptic curve. - GFpECSetPointOctString
Sets the coordinates of a point on an elliptic curve defined over GF(p). - GFpECSetPointRandom
Sets the coordinates of a point on an elliptic curve to random values. - GFpECMakePoint
Constructs the coordinates of a point on an elliptic curve based on the X-coordinate. - GFpECSetPointHash, GFpECSetPointHashBackCompatible, GFpECSetPointHash_rmf, GFpECSetPointHashBackCompatible_rmf
Constructs a point on an elliptic curve based on the hash of the input message. - GFpECGetPoint , GFpECGetPointRegular
Retrieves coordinates of a point on an elliptic curve. - GFpECGetPointOctString
Retrieves coordinates of a point on an elliptic curve defined over GF(p). - GFpECTstPoint
Checks if a point belongs to an elliptic curve. - GFpECTstPointInSubgroup
Checks if a point belongs to a specified subgroup. - GFpECCpyPoint
Copies one point to another. - GFpECCmpPoint
Compares two points. - GFpECNegPoint
Computes the inverse of a point. - GFpECAddPoint
Computes the sum of two points on an elliptic curve. - GFpECMulPoint
Multiplies a point on an elliptic curve by a scalar. - GFpECPrivateKey, GFpECPublicKey, GFpECTstKeyPair
Generates a private key of the elliptic curve cryptosystem over GF(p). - GFpECPublicKey
Computes a public key from the given private key of the elliptic curve cryptosystem over GF(p). - GFpECTstKeyPair
Tests private and public keys of the elliptic curve cryptosystem over GF(p). - GFpECPSharedSecretDH, GFpECPSharedSecretDHC
Computes a shared secret field element by using the Diffie-Hellman scheme. - GFpECSharedSecretDHC
Computes a shared secret field element by using the Diffie-Hellman scheme and the elliptic curve cofactor. - GFpECPSignDSA, GFpECPSignNR, GFpECPSignSM2
Computes a digital signature over a message digest. - GFpECPVerifyDSA, GFpECPVerifyNR, GFpECPVerifySM2
Verifies authenticity of the digital signature over a message digest (ECDSA). - GFpECSignNR
Computes the digital signature over a message digest (the Nyberg-Rueppel scheme). - GFpECVerifyNR
Verifies authenticity of the digital signature over a message digest (the Nyberg-Rueppel scheme). - GFpECSignSM2
Computes a digital signature over a message digest using the SM2 scheme. - GFpECVerifySM2
Verifies authenticity of a digital signature over a message digest using the SM2 scheme.
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