Cryptography for Intel® Integrated Performance Primitives Developer Reference

Developer Reference

Contents

SM2 Elliptic Curve Functions

Elliptic Curve Notation

There are several ways of defining equation for elliptic curves, but this section deals with Weierstrass equations. For the prime finite field
GF(p), p>3
, the Weierstrass equation is
E : y = x + a*x + b
, where
a
 and
b
 are integers modulo
p
. The number of points on the elliptic curve
E
 is denoted by
#E
.
For purpose of cryptography some additional parameters are presented:
  • n
     - prime divisor of
    #E
     and the order of point
    G
  • G
     - the point on curve
    E
     generated subgroup of the order
    n
The set of
p, a, b, n
, and
G
 parameters are Elliptic Curve (EC) domain parameter.

Elliptic Curve Key Pair

Private key is a positive integer
u
 in the range
[1, n-1]
. Public key
V
, which is the point on elliptic curve
E
, where
V = [u] * G
. In cryptography, there are two types of keypairs: regular (long-term) and ephemeral (nonce - number that can only be used once). From the math point of view, they are similar.

Supported Algorithms:

  • Public key generation
  • ECDHE generation of shared secret
  • SM2 ECDSA signature generation
  • SM2 ECDSA signature verification

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.