Table 167. Family Of Supported Curves For Ecc Operations - STMicroelectronics STM32WL5 Series Reference Manual

RM0453
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
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

Table 167. Family of supported curves for ECC operations

Curve name
P-192
P-224
P-256
P-384
P-521
summarizes the family of curves supported by PKA for ECC operations.
Standard
NIST Digital Signature Standard (DSS), NIST FIPS 186-4
Reference
RM0453 Rev 5
Public key accelerator (PKA)
2 3
= x + ax + b (mod p).
713/1450
720