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ec_inits.c
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ec_inits.c
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/*
* ec.c
*
* Created on: Sep 9, 2015
* Author: tslld
*/
#include "ecdsa.h"
#include "ec.h"
#include "ec_point.h"
#include "utils.h"
struct curve_params {
char* name;
const char *p, *a, *b, *Gx, *Gy, *order, *cofactor;
};
static const struct curve_params curves_params[] = {
{
/* Certicom recommendations P-224 */
"secp224k1",
/* p */
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D",
/* a */
"00000000000000000000000000000000000000000000000000000000",
/* b */
"00000000000000000000000000000000000000000000000000000005",
/* Gx */
"A1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C",
/* Gy */
"7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5",
/* order */
"010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7",
/* cofactor */
"01",
},
{
/* NIST P-224 */
"secp224r1",
/* p */
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
/* a */
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
/* b */
"B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
/* Gx */
"B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
/* Gy */
"BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
/* order */
"FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
/* cofactor */
"01",
},
{
/* Certicom 256 bits curve */
"secp256k1",
/* p */
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F",
/* a */
"0000000000000000000000000000000000000000000000000000000000000000",
/* b */
"0000000000000000000000000000000000000000000000000000000000000007",
/* Gx */
"79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798",
/* Gy */
"483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8",
/* order */
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141",
/* cofactor */
"01",
},
{
/* NIST P-256 */
"secp256r1",
/* p */
"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF",
/* a */
"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC",
/* b */
"5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B",
/* Gx */
"6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296",
/* Gy */
"4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5",
/* order */
"FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",
/* cofactor */
"01",
},
};
/** Allocates and initialize a ec_group structure
* \return pointer to a ec_group structure or NULL if an error occurred
*/
ec_group ec_group_init() {
ec_group ec;
ec = malloc(sizeof(struct ec_group_st));
assert(ec != NULL);
mpz_init(ec->A);
mpz_init(ec->B);
mpz_init(ec->field);
mpz_init(ec->order);
mpz_init(ec->cofactor);
ec->generator = ec_point_init();
return ec;
}
ec_group ec_group_init_by_curve_name(const char* name) {
ec_group ret = ec_group_init();
int ok = 0;
unsigned int i;
int no_curves = sizeof(curves_params) / sizeof(struct curve_params);
for (i = 0; i < no_curves; i++) {
if (strcmp(curves_params[i].name, name) == 0) {
ec_group_set_str_hex(ret, name, curves_params[i].p, curves_params[i].a, curves_params[i].b, curves_params[i].Gx,
curves_params[i].Gy, curves_params[i].order, curves_params[i].cofactor);
ok = 1;
break;
}
}
if (ok == 0) {
return NULL;
}
return ret;
}
/** Set up parameters for a ec_group from Big number mpz_t
* \param ec pointer to the ec_group structure
* \param name pointer to a constant string
* \param field mpz_t big number, the characteristic of the finite field
* \param a, b mpz_t big number, the curve parameters of the Weierstrass form
* \param Gx, Gy coordinates of the generator
* \param order the order of subgroup of points used on the curve
* \param cofactor the cofactor of the curve
*
* \return pointer to a ec_group structure or NULL if an error occurred
*
*/
void ec_group_set_mpz(ec_group ret, const char* name, mpz_t field, mpz_t a, mpz_t b, mpz_t Gx, mpz_t Gy, mpz_t order, mpz_t cofactor) {
int length = strlen(name);
ret->curve_name = (char*)malloc(sizeof(char) * (length + 1));
assert(ret->curve_name != NULL);
ret->curve_name[length] = '\0';
strcpy(ret->curve_name, name);
mpz_init_set(ret->field, field);
mpz_init_set(ret->A, a);
mpz_init_set(ret->B, b);
mpz_init_set(ret->order, order);
mpz_init_set(ret->cofactor, cofactor);
ret->generator = ec_point_init_set_mpz(Gx, Gy);
gmp_printf("\n We work on curve E: y^2 = x^3 + %Zd x + %Zd over finite field F_p: %Zd \n", a, b, field);
printf("The size of the finite field F_p = %d bits \n", bitlength(field));
gmp_printf("The order of the curve E = %Zd \n", order);
}
/** Initialize and assign an elliptic curve from big integers
* \param ec pointer to the ec_group structure
* \param name pointer to a constant string
* \param field mpz_t big number, the characteristic of the finite field
* \param a, b mpz_t big number, the curve parameters of the Weierstrass form
* \param Gx, Gy coordinates of the generator
* \param order the order of subgroup of points used on the curve
* \param cofactor the cofactor of the curve
*
* \return pointer to a ec_group structure or NULL if an error occurred
*/
ec_group ec_group_init_set_mpz(const char* name, mpz_t field, mpz_t a, mpz_t b, mpz_t Gx, mpz_t Gy, mpz_t order, mpz_t cofactor) {
ec_group ret;
ret = malloc(sizeof(struct ec_group_st));
assert(ret != NULL);
int length = strlen(name);
ret->curve_name = (char*)malloc(sizeof(char) * (length + 1));
assert(ret->curve_name != NULL);
ret->curve_name[length] = '\0';
strcpy(ret->curve_name, name);
mpz_init_set(ret->field, field);
mpz_init_set(ret->A, a);
mpz_init_set(ret->B, b);
mpz_init_set(ret->order, order);
mpz_init_set(ret->cofactor, cofactor);
ret->generator = ec_point_init_set_mpz(Gx, Gy);
gmp_printf("\n We work on curve E: y^2 = x^3 + %Zd x + %Zd over finite field F_p: %Zd \n", a, b, field);
printf("The size of the finite field F_p = %d bits \n", bitlength(field));
gmp_printf("The order of the curve E = %Zd \n", order);
return ret;
}
/*
* Initialize and set parameters of a curve from strings
*
* \param ec pointer to the ec_group structure
* \param name pointer to a constant string
* \param field mpz_t big number, the characteristic of the finite field
* \param a, b mpz_t big number, the curve parameters of the Weierstrass form
* \param Gx, Gy coordinates of the generator
* \param order the order of subgroup of points used on the curve
* \param cofactor the cofactor of the curve
*
* \return pointer to a ec_group structure or NULL if an error occurred
*/
ec_group ec_group_init_set_str(const char* name, const char* field, const char* a, const char* b,
const char* Gx, const char* Gy, const char* order, const char* cofactor,
int base) {
ec_group ret;
ret = malloc(sizeof(struct ec_group_st));
assert(ret != NULL);
int len = strlen(name);
ret->curve_name = (char*)malloc(sizeof(char) * (len + 1));
assert(ret->curve_name != NULL);
ret->curve_name[len] = '\0';
strcpy(ret->curve_name, name);
mpz_init_set_str(ret->field, field, base);
mpz_init_set_str(ret->A, a, base);
mpz_init_set_str(ret->B, b, base);
ret->generator = ec_point_init_set_str(Gx, Gy, base);
mpz_init_set_str(ret->order, order, base);
mpz_init_set_str(ret->cofactor, cofactor, base);
return ret;
}
/*
* Assign parameters of a curve from strings
*
* \param ec pointer to the ec_group structure
* \param name pointer to a constant string
* \param field mpz_t big number, the characteristic of the finite field
* \param a, b mpz_t big number, the curve parameters of the Weierstrass form
* \param Gx, Gy coordinates of the generator
* \param order the order of subgroup of points used on the curve
* \param cofactor the cofactor of the curve
*
* \return pointer to a ec_group structure or NULL if an error occurred
*/
void ec_group_set_str(ec_group ret, const char* name, const char* field, const char* a, const char* b,
const char* Gx, const char* Gy, const char* order, const char* cofactor,
int base) {
int len = strlen(name);
ret->curve_name = (char*)malloc(sizeof(char) * (len + 1));
assert(ret->curve_name != NULL);
ret->curve_name[len] = '\0';
strcpy(ret->curve_name, name);
mpz_init_set_str(ret->field, field, base);
mpz_init_set_str(ret->A, a, base);
mpz_init_set_str(ret->B, b, base);
ret->generator = ec_point_init_set_str(Gx, Gy, base);
mpz_init_set_str(ret->order, order, base);
mpz_init_set_str(ret->cofactor, cofactor, base);
}
/*
* Initialize and assign parameters of a curve from strings in hex
*
* \param ec pointer to the ec_group structure
* \param name pointer to a constant string
* \param field mpz_t big number, the characteristic of the finite field
* \param a, b mpz_t big number, the curve parameters of the Weierstrass form
* \param Gx, Gy coordinates of the generator
* \param order the order of subgroup of points used on the curve
* \param cofactor the cofactor of the curve
*
* \return pointer to a ec_group structure or NULL if an error occurred
*/
ec_group ec_group_init_set_str_hex(const char* name, const char* field, const char* a, const char* b,
const char* Gx, const char* Gy, const char* order, const char* cofactor) {
return ec_group_init_set_str(name, field, a, b, Gx, Gy, order, cofactor, 16);
}
/*
* Assign parameters of a curve from strings in hex
*
* \param ec pointer to the ec_group structure
* \param name pointer to a constant string
* \param field mpz_t big number, the characteristic of the finite field
* \param a, b mpz_t big number, the curve parameters of the Weierstrass form
* \param Gx, Gy coordinates of the generator
* \param order the order of subgroup of points used on the curve
* \param cofactor the cofactor of the curve
*
* \return pointer to a ec_group structure or NULL if an error occurred
*/
void ec_group_set_str_hex(ec_group ret, const char* name, const char* field, const char* a, const char* b,
const char* Gx, const char* Gy, const char* order, const char* cofactor) {
ec_group_set_str(ret, name, field, a, b, Gx, Gy, order, cofactor, 16);
}