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Public key accelerator (PKA) RM0453

714/1454 RM0453 Rev 2

24.5 Example of configurations and processing times

24.5.1 Supported elliptic curves

The PKA supports all non-singular elliptic curves defined over prime fields. Those

curvescan be described with a short Weierstrass equation y

= x

+ ax + b (mod p).

Note: Binary curves, Edwards curves and Curve25519 are not supported by the PKA.

The maximum supported operand size for ECC operations is 640 bits.

When publishing the ECC domain parameters of those elliptic curves, standard bodies

define the following parameters:

• the prime integer p, used as the modulus for all point arithmetic in the finite field GF(p)

• the (usually prime) integer n, the order of the group generated by G, defined below

• the base point of the curve G, defined by its coordinates (Gx, Gy)

• the integers a and b, coefficients of the short Weierstrass equation.

For the last bullet, when standard bodies define a as negative, PKA supports two

representations:

1. a defined as p-|a| in the finite field GF(p), for example p-3:

Curve coefficient p = 0xFFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF

00000000 FFFFFFFF FFFFFFFF

Curve coefficient a sign= 0x0 (positive)

Curve coefficient a = 0xFFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF

00000000 FFFFFFFF FFFFFFFC

2. a defined as negative, for example -3:

Curve coefficient p = 0xFFFFFFFE FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF

00000000 FFFFFFFF FFFFFFFF

Curve coefficient a sign= 0x1 (negative)

Curve coefficient a = 0x00000000 00000000 00000000 00000000 00000000 00000000

00000000 00000003

Table 167 summarizes the family of curves supported by PKA for ECC operations.

Table 167. Family of supported curves for ECC operations

Curve name Standard Reference

P-192

NIST Digital Signature Standard (DSS), NIST FIPS 186-4

P-224

P-256

P-384

P-521

ST STM32WL55JC User Manual

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