ecp_group Struct Reference

ECP group structure. More...

#include <ecp.h>

Collaboration diagram for ecp_group:

Data Fields
ecp_group_id	id
mpi	P
mpi	A
mpi	B
ecp_point	G
mpi	N
size_t	pbits
size_t	nbits
unsigned int	h
int(*	modp )(mpi *)
int(*	t_pre )(ecp_point *, void *)
int(*	t_post )(ecp_point *, void *)
void *	t_data
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 (M255 + 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 ecp_mul() and prime in 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 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 136 of file ecp.h.

Field Documentation

A

mpi ecp_group::A

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

Definition at line 140 of file ecp.h.

B

mpi ecp_group::B

1. B in the equation, or 2. unused
   

Definition at line 141 of file ecp.h.

G

ecp_point ecp_group::G

generator of the (sub)group used

Definition at line 142 of file ecp.h.

h

unsigned int ecp_group::h

internal: 1 if the constants are static

Definition at line 146 of file ecp.h.

id

ecp_group_id ecp_group::id

internal group identifier

Definition at line 138 of file ecp.h.

modp

int(* ecp_group::modp) (mpi *)

function for fast reduction mod P

Definition at line 147 of file ecp.h.

N

mpi ecp_group::N

1. the order of G, or 2. unused
   

Definition at line 143 of file ecp.h.

nbits

size_t ecp_group::nbits

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

Definition at line 145 of file ecp.h.

P

mpi ecp_group::P

prime modulus of the base field

Definition at line 139 of file ecp.h.

pbits

size_t ecp_group::pbits

number of bits in P

Definition at line 144 of file ecp.h.

T

ecp_point* ecp_group::T

pre-computed points for ecp_mul_comb()

Definition at line 151 of file ecp.h.

t_data

void* ecp_group::t_data

unused

Definition at line 150 of file ecp.h.

t_post

int(* ecp_group::t_post) (ecp_point *, void *)

unused

Definition at line 149 of file ecp.h.

t_pre

int(* ecp_group::t_pre) (ecp_point *, void *)

unused

Definition at line 148 of file ecp.h.

T_size

size_t ecp_group::T_size

number for pre-computed points

Definition at line 152 of file ecp.h.

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

• ecp.h