ID 768738
Date 12/16/2022
Public

## 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

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