37.3.7 Elliptic Curves Over GF(2ⁿ) Services

This section provides a complete description of the currently available elliptic curve over Polynomials in GF(2ⁿ) services.

These services process Polynomials in GF(2ⁿ) only.

The offered services cover the basic operations over elliptic curves such as:

• Adding two points over a curve
• Doubling a point over a curve
• Multiplying a point by an integral constant
• Converting a point’s projective coordinates (resulting from a doubling or an addition) to the affine coordinates, and oppositely converting a point’s affine coordinates to the projective coordinates.
• Testing the point presence on the curve.

Additionally, some higher level services covering the needs for signature generation and verification are offered:

• Generating an ECDSA signature (compliant with FIPS186-2)
• Verifying an ECDSA signature (compliant with FIPS 186-2) The supported curves use the following curve equation in GF(2ⁿ):

Y² + XY = X³ + aX + b