mbedtls_ecp_group Struct Reference

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

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.

Member Data Documentation

A

mbedtls_mpi mbedtls_ecp_group::A

1. A in the equation, or 2. (A + 2) / 4

B

mbedtls_mpi mbedtls_ecp_group::B

1. B in the equation, or 2. unused

G

mbedtls_ecp_point mbedtls_ecp_group::G

generator of the (sub)group used

h

unsigned int mbedtls_ecp_group::h

internal: 1 if the constants are static

id

mbedtls_ecp_group_id mbedtls_ecp_group::id

internal group identifier

modp

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

function for fast reduction mod P

N

mbedtls_mpi mbedtls_ecp_group::N

1. the order of G, or 2. unused

nbits

size_t mbedtls_ecp_group::nbits

number of bits in 1. P, or 2. private keys

P

mbedtls_mpi mbedtls_ecp_group::P

prime modulus of the base field

pbits

size_t mbedtls_ecp_group::pbits

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

number for pre-computed points

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

• deps/mbedtls/mbedtls/ecp.h