Developer Reference for Intel® Integrated Performance Primitives Cryptography 2019

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 + Ax + B

where

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).

You can use standard elliptic curves by calling GFpECInitStd or GFpECBindGxyTblStd. The following table contains the supported standard elliptic curves:

Standard Elliptic Curves

Name of the Curve

Reference

secp128r1

[SEC2]

secp128r2

[SEC2]

secp160r1

[SEC2]

secp160r2

[SEC2]

secp192r1

[SEC2]

secp224r1

[SEC2]

secp256r1

[SEC2]

secp384r1

[SEC2]

secp521r1

[SEC2]

SM2

[SM2]

BN256

[ISO/IEC 11889-4]

For more information on parameters of the standard elliptic curves, see [SEC2], [SM2], and [ISO/IEC 11889-4].

Note

In this table, the name BN256 corresponds to the Barreto-Naehrig Prime 256-bit elliptic curve.

Important

To provide minimum security of the elliptic curve cryptosystem over a prime finite field, the length of the underlying prime must be equal to or greater than 160 bits.