mbedtls_ecp_group Struct Reference

The ECP group structure. More...

#include <ecp.h>

Collaboration diagram for mbedtls_ecp_group:

Public Attributes
mbedtls_ecp_group_id	id
mbedtls_mpi	P
mbedtls_mpi	A
mbedtls_mpi	B
mbedtls_ecp_point	G
mbedtls_mpi	N
size_t	pbits
size_t	nbits
unsigned int	h
int(*	modp )(mbedtls_mpi *)
int(*	t_pre )(mbedtls_ecp_point *, void *)
int(*	t_post )(mbedtls_ecp_point *, void *)
void *	t_data
mbedtls_ecp_point *	T
size_t	T_size

Detailed Description

The ECP group structure.

We consider two types of curve equations:

• Short Weierstrass: y^2 = x^3 + A x + B mod P (SEC1 + RFC-4492)
• Montgomery: y^2 = x^3 + A x^2 + x mod P (Curve25519, Curve448)

In both cases, the generator (G) for a prime-order subgroup is fixed.

For Short Weierstrass, this subgroup is the whole curve, and its cardinality is denoted by N. Our code requires that N is an odd prime as mbedtls_ecp_mul() requires an odd number, and mbedtls_ecdsa_sign() requires that it is prime for blinding purposes.

For Montgomery curves, we do not store A, but (A + 2) / 4, which is the quantity used in the formulas. Additionally, nbits is not the size of N but the required size for private keys.

If modp is NULL, reduction modulo P is done using a generic algorithm. Otherwise, modp must point to a function that takes an mbedtls_mpi in the range of 0..2^(2*pbits)-1, and transforms it in-place to an integer which is congruent mod P to the given MPI, and is close enough to pbits in size, so that it may be efficiently brought in the 0..P-1 range by a few additions or subtractions. Therefore, it is only an approximative modular reduction. It must return 0 on success and non-zero on failure.

Note

Alternative implementations must keep the group IDs distinct. If two group structures have the same ID, then they must be identical.

Member Data Documentation

A

mbedtls_mpi mbedtls_ecp_group::A

For Short Weierstrass: A in the equation. For Montgomery curves: (A + 2) / 4.

B

mbedtls_mpi mbedtls_ecp_group::B

For Short Weierstrass: B in the equation. For Montgomery curves: unused.

G

mbedtls_ecp_point mbedtls_ecp_group::G

The generator of the subgroup used.

h

unsigned int mbedtls_ecp_group::h

id

mbedtls_ecp_group_id mbedtls_ecp_group::id

An internal group identifier.

modp

int(* mbedtls_ecp_group::modp) (mbedtls_mpi *)

The function for fast pseudo-reduction mod P (see above).

N

mbedtls_mpi mbedtls_ecp_group::N

The order of G.

nbits

size_t mbedtls_ecp_group::nbits

For Short Weierstrass: The number of bits in P. For Montgomery curves: the number of bits in the private keys.

P

mbedtls_mpi mbedtls_ecp_group::P

The prime modulus of the base field.

pbits

size_t mbedtls_ecp_group::pbits

The number of bits in P.

T

mbedtls_ecp_point* mbedtls_ecp_group::T

Pre-computed points for ecp_mul_comb().

t_data

void* mbedtls_ecp_group::t_data

Unused.

t_post

int(* mbedtls_ecp_group::t_post) (mbedtls_ecp_point *, void *)

Unused.

t_pre

int(* mbedtls_ecp_group::t_pre) (mbedtls_ecp_point *, void *)

Unused.

T_size

size_t mbedtls_ecp_group::T_size

The number of pre-computed points.

---

The documentation for this struct was generated from the following file:

• C:/Users/Enriquez/Documents/Arduino/libraries/arduino-optiga-trust-m/src/mbedtls/ecp.h