ECP group structure. More...

#include <ecp.h>

Data Fields
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

ECP group structure.

We consider two types of curves equations: 1. Short Weierstrass y^2 = x^3 + A x + B mod P (SEC1 + RFC 4492) 2. Montgomery, y^2 = x^3 + A x^2 + x mod P (Curve25519 + draft) In both cases, a generator G for a prime-order subgroup is fixed. In the short weierstrass, this subgroup is actually the whole curve, and its cardinal is denoted by N.

In the case of Short Weierstrass curves, our code requires that N is an odd prime. (Use odd in mbedtls_ecp_mul() and prime in mbedtls_ecdsa_sign() for blinding.)

In the case of Montgomery curves, we don't store A but (A + 2) / 4 which is the quantity actually used in the formulas. Also, 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, it must point to a function that takes an mbedtls_mpi in the range 0..2^(2*pbits)-1 and transforms it in-place in an integer of little more than pbits, so that the integer may be efficiently brought in the 0..P-1 range by a few additions or substractions. It must return 0 on success and non-zero on failure.

Definition at line 129 of file ecp.h.