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.