Datasheet

Figure 43-14. The a parameter and Workspace {pu1AWorkBase, 9*u2ModLength + 48}
43.3.7 Elliptic Curves Over GF(2
n
) Services
This section provides a complete description of the currently available elliptic curve over Polynomials in
GF(2
n
) services.
These services process Polynomials in GF(2
n
) 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(2
n
):
Y
2
+ XY = X
3
+ aX + b
43.3.7.1 Parameters Format
43.3.7.1.1 Polynomials in GF(2
n
)
Polynomials in GF(2
n
) are binary polynomials reduced modulo the polynomial P[X]. This polynomial is
called the modulus and may be abbreviated to P in this document. The storage of these polynomials in
memory area is described in 43.3.3.4 Aligned Significant Length.
For notation simplicity the comparison signs “<“ or “>” may be used for polynomials, this is to be
interpreted as a comparison between the degree of the polynomials.
SAM D5x/E5x Family Data Sheet
Public Key Cryptography Controller (PUKCC)
© 2019 Microchip Technology Inc.
Datasheet
DS60001507E-page 1544