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ecc: Remove remaining ECC/ECDH files 

ECC primitives have now been fully converted / moved to ell.
This commit is contained in:
Denis Kenzior 2019-01-10 14:30:41 -06:00
parent e5cf66ddb2
commit 9b722197ba
6 changed files with 2 additions and 1389 deletions
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1
.gitignore vendored
View File

@ -48,7 +48,6 @@ unit/test-sae
unit/test-eap-mschapv2
unit/test-eap-sim
unit/test-client
unit/test-ecc
unit/test-ecdh
test-suite.log
src/builtin.h

9
Makefile.am
View File

@ -157,7 +157,6 @@ eap_sources = src/eap.c src/eap.h src/eap-private.h \
src/eap-pwd.c \
src/util.h src/util.c \
src/crypto.h src/crypto.c \
src/ecc.h src/ecc.c \
src/wscutil.h src/wscutil.c \
src/simutil.h src/simutil.c \
src/simauth.h src/simauth.c \
@ -309,7 +308,7 @@ unit_tests = unit/test-cmac-aes \
unit/test-crypto unit/test-eapol unit/test-mpdu \
unit/test-ie unit/test-ssid-to-utf8 unit/test-ssid-security \
unit/test-arc4 unit/test-wsc unit/test-eap-mschapv2 \
unit/test-eap-sim unit/test-ecc unit/test-sae
unit/test-eap-sim unit/test-sae
if CLIENT
unit_tests += unit/test-client
@ -432,16 +431,12 @@ unit_test_client_SOURCES = unit/test-client.c \
unit_test_client_LDADD = $(ell_ldadd) -lreadline
endif
unit_test_ecc_SOURCES = unit/test-ecc.c src/ecc.c src/ecc.h
unit_test_ecc_LDADD = $(ell_ldadd)
unit_test_sae_SOURCES = unit/test-sae.c \
src/sae.h src/sae.c \
src/crypto.h src/crypto.c \
src/ie.h src/ie.c \
src/handshake.h src/handshake.c \
src/util.h src/util.c \
src/ecc.h src/ecc.c
src/util.h src/util.c
unit_test_sae_LDADD = $(ell_ldadd)
TESTS = $(unit_tests)

936
src/ecc.c
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@ -1,936 +0,0 @@
/*
* Copyright (c) 2013, Kenneth MacKay
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <fcntl.h>
#include <unistd.h>
#include <sys/types.h>
#include <string.h>
#include "src/ecc.h"
#define MAX_TRIES 16
typedef struct {
uint64_t m_low;
uint64_t m_high;
} uint128_t;
static uint64_t curve_p[NUM_ECC_DIGITS] = CURVE_P_32;
static uint64_t curve_b[NUM_ECC_DIGITS] = CURVE_B_32;
static void vli_clear(uint64_t *vli)
{
int i;
for (i = 0; i < NUM_ECC_DIGITS; i++)
vli[i] = 0;
}
/* Returns true if vli == 0, false otherwise. */
static bool vli_is_zero(const uint64_t *vli)
{
int i;
for (i = 0; i < NUM_ECC_DIGITS; i++) {
if (vli[i])
return false;
}
return true;
}
/* Returns nonzero if bit bit of vli is set. */
static uint64_t vli_test_bit(const uint64_t *vli, unsigned int bit)
{
return (vli[bit / 64] & ((uint64_t) 1 << (bit % 64)));
}
/* Counts the number of 64-bit "digits" in vli. */
static unsigned int vli_num_digits(const uint64_t *vli)
{
int i;
/* Search from the end until we find a non-zero digit.
* We do it in reverse because we expect that most digits will
* be nonzero.
*/
for (i = NUM_ECC_DIGITS - 1; i >= 0 && vli[i] == 0; i--);
return (i + 1);
}
/* Counts the number of bits required for vli. */
unsigned int vli_num_bits(const uint64_t *vli)
{
unsigned int i, num_digits;
uint64_t digit;
num_digits = vli_num_digits(vli);
if (num_digits == 0)
return 0;
digit = vli[num_digits - 1];
for (i = 0; digit; i++)
digit >>= 1;
return ((num_digits - 1) * 64 + i);
}
/* Sets dest = src. */
static void vli_set(uint64_t *dest, const uint64_t *src)
{
int i;
for (i = 0; i < NUM_ECC_DIGITS; i++)
dest[i] = src[i];
}
/* Returns sign of left - right. */
int vli_cmp(const uint64_t *left, const uint64_t *right)
{
int i;
for (i = NUM_ECC_DIGITS - 1; i >= 0; i--) {
if (left[i] > right[i])
return 1;
else if (left[i] < right[i])
return -1;
}
return 0;
}
/* Constant-time comparison function - secure way to compare long integers */
/* Returns one if left == right, zero otherwise. */
static bool vli_equal(const uint64_t *left, const uint64_t *right)
{
uint64_t diff = 0;
int i;
for (i = NUM_ECC_DIGITS - 1; i >= 0; --i)
diff |= (left[i] ^ right[i]);
return (diff == 0);
}
/* Computes result = in << c, returning carry. Can modify in place
* (if result == in). 0 < shift < 64.
*/
static uint64_t vli_lshift(uint64_t *result, const uint64_t *in,
unsigned int shift)
{
uint64_t carry = 0;
int i;
for (i = 0; i < NUM_ECC_DIGITS; i++) {
uint64_t temp = in[i];
result[i] = (temp << shift) | carry;
carry = temp >> (64 - shift);
}
return carry;
}
/* Computes vli = vli >> 1. */
static void vli_rshift1(uint64_t *vli)
{
uint64_t *end = vli;
uint64_t carry = 0;
vli += NUM_ECC_DIGITS;
while (vli-- > end) {
uint64_t temp = *vli;
*vli = (temp >> 1) | carry;
carry = temp << 63;
}
}
/* Computes result = left + right, returning carry. Can modify in place. */
static uint64_t vli_add(uint64_t *result, const uint64_t *left,
const uint64_t *right)
{
uint64_t carry = 0;
int i;
for (i = 0; i < NUM_ECC_DIGITS; i++) {
uint64_t sum;
sum = left[i] + right[i] + carry;
if (sum != left[i])
carry = (sum < left[i]);
result[i] = sum;
}
return carry;
}
/* Computes result = left - right, returning borrow. Can modify in place. */
uint64_t vli_sub(uint64_t *result, const uint64_t *left,
const uint64_t *right)
{
uint64_t borrow = 0;
int i;
for (i = 0; i < NUM_ECC_DIGITS; i++) {
uint64_t diff;
diff = left[i] - right[i] - borrow;
if (diff != left[i])
borrow = (diff > left[i]);
result[i] = diff;
}
return borrow;
}
static uint128_t mul_64_64(uint64_t left, uint64_t right)
{
uint64_t a0 = left & 0xffffffffull;
uint64_t a1 = left >> 32;
uint64_t b0 = right & 0xffffffffull;
uint64_t b1 = right >> 32;
uint64_t m0 = a0 * b0;
uint64_t m1 = a0 * b1;
uint64_t m2 = a1 * b0;
uint64_t m3 = a1 * b1;
uint128_t result;
m2 += (m0 >> 32);
m2 += m1;
/* Overflow */
if (m2 < m1)
m3 += 0x100000000ull;
result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
result.m_high = m3 + (m2 >> 32);
return result;
}
static uint128_t add_128_128(uint128_t a, uint128_t b)
{
uint128_t result;
result.m_low = a.m_low + b.m_low;
result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);
return result;
}
static void vli_mult(uint64_t *result, const uint64_t *left,
const uint64_t *right)
{
uint128_t r01 = { 0, 0 };
uint64_t r2 = 0;
unsigned int i, k;
/* Compute each digit of result in sequence, maintaining the
* carries.
*/
for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; k++) {
unsigned int min;
if (k < NUM_ECC_DIGITS)
min = 0;
else
min = (k + 1) - NUM_ECC_DIGITS;
for (i = min; i <= k && i < NUM_ECC_DIGITS; i++) {
uint128_t product;
product = mul_64_64(left[i], right[k - i]);
r01 = add_128_128(r01, product);
r2 += (r01.m_high < product.m_high);
}
result[k] = r01.m_low;
r01.m_low = r01.m_high;
r01.m_high = r2;
r2 = 0;
}
result[NUM_ECC_DIGITS * 2 - 1] = r01.m_low;
}
static void vli_square(uint64_t *result, const uint64_t *left)
{
uint128_t r01 = { 0, 0 };
uint64_t r2 = 0;
int i, k;
for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; k++) {
unsigned int min;
if (k < NUM_ECC_DIGITS)
min = 0;
else
min = (k + 1) - NUM_ECC_DIGITS;
for (i = min; i <= k && i <= k - i; i++) {
uint128_t product;
product = mul_64_64(left[i], left[k - i]);
if (i < k - i) {
r2 += product.m_high >> 63;
product.m_high = (product.m_high << 1) |
(product.m_low >> 63);
product.m_low <<= 1;
}
r01 = add_128_128(r01, product);
r2 += (r01.m_high < product.m_high);
}
result[k] = r01.m_low;
r01.m_low = r01.m_high;
r01.m_high = r2;
r2 = 0;
}
result[NUM_ECC_DIGITS * 2 - 1] = r01.m_low;
}
/* Computes result = (left + right) % mod.
* Assumes that left < mod and right < mod, result != mod.
*/
void vli_mod_add(uint64_t *result, const uint64_t *left,
const uint64_t *right, const uint64_t *mod)
{
uint64_t carry;
carry = vli_add(result, left, right);
/* result > mod (result = mod + remainder), so subtract mod to
* get remainder.
*/
if (carry || vli_cmp(result, mod) >= 0)
vli_sub(result, result, mod);
}
/* Computes result = (left - right) % mod.
* Assumes that left < mod and right < mod, result != mod.
*/
void vli_mod_sub(uint64_t *result, const uint64_t *left,
const uint64_t *right, const uint64_t *mod)
{
uint64_t borrow = vli_sub(result, left, right);
/* In this case, p_result == -diff == (max int) - diff.
* Since -x % d == d - x, we can get the correct result from
* result + mod (with overflow).
*/
if (borrow)
vli_add(result, result, mod);
}
/* Computes result = product % curve_p
from http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void vli_mmod_fast(uint64_t *result, const uint64_t *product)
{
uint64_t tmp[NUM_ECC_DIGITS];
int carry;
/* t */
vli_set(result, product);
/* s1 */
tmp[0] = 0;
tmp[1] = product[5] & 0xffffffff00000000ull;
tmp[2] = product[6];
tmp[3] = product[7];
carry = vli_lshift(tmp, tmp, 1);
carry += vli_add(result, result, tmp);
/* s2 */
tmp[1] = product[6] << 32;
tmp[2] = (product[6] >> 32) | (product[7] << 32);
tmp[3] = product[7] >> 32;
carry += vli_lshift(tmp, tmp, 1);
carry += vli_add(result, result, tmp);
/* s3 */
tmp[0] = product[4];
tmp[1] = product[5] & 0xffffffff;
tmp[2] = 0;
tmp[3] = product[7];
carry += vli_add(result, result, tmp);
/* s4 */
tmp[0] = (product[4] >> 32) | (product[5] << 32);
tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
tmp[2] = product[7];
tmp[3] = (product[6] >> 32) | (product[4] << 32);
carry += vli_add(result, result, tmp);
/* d1 */
tmp[0] = (product[5] >> 32) | (product[6] << 32);
tmp[1] = (product[6] >> 32);
tmp[2] = 0;
tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
carry -= vli_sub(result, result, tmp);
/* d2 */
tmp[0] = product[6];
tmp[1] = product[7];
tmp[2] = 0;
tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
carry -= vli_sub(result, result, tmp);
/* d3 */
tmp[0] = (product[6] >> 32) | (product[7] << 32);
tmp[1] = (product[7] >> 32) | (product[4] << 32);
tmp[2] = (product[4] >> 32) | (product[5] << 32);
tmp[3] = (product[6] << 32);
carry -= vli_sub(result, result, tmp);
/* d4 */
tmp[0] = product[7];
tmp[1] = product[4] & 0xffffffff00000000ull;
tmp[2] = product[5];
tmp[3] = product[6] & 0xffffffff00000000ull;
carry -= vli_sub(result, result, tmp);
if (carry < 0) {
do {
carry += vli_add(result, result, curve_p);
} while (carry < 0);
} else {
while (carry || vli_cmp(curve_p, result) != 1)
carry -= vli_sub(result, result, curve_p);
}
}
/* Computes result = (left * right) % curve_p. */
void vli_mod_mult_fast(uint64_t *result, const uint64_t *left,
const uint64_t *right)
{
uint64_t product[2 * NUM_ECC_DIGITS];
vli_mult(product, left, right);
vli_mmod_fast(result, product);
}
/* Computes result = left^2 % curve_p. */
static void vli_mod_square_fast(uint64_t *result, const uint64_t *left)
{
uint64_t product[2 * NUM_ECC_DIGITS];
vli_square(product, left);
vli_mmod_fast(result, product);
}
#define EVEN(vli) (!(vli[0] & 1))
/* Computes result = (1 / p_input) % mod. All VLIs are the same size.
* See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
* https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
*/
void vli_mod_inv(uint64_t *result, const uint64_t *input,
const uint64_t *mod)
{
uint64_t a[NUM_ECC_DIGITS], b[NUM_ECC_DIGITS];
uint64_t u[NUM_ECC_DIGITS], v[NUM_ECC_DIGITS];
uint64_t carry;
int cmp_result;
if (vli_is_zero(input)) {
vli_clear(result);
return;
}
vli_set(a, input);
vli_set(b, mod);
vli_clear(u);
u[0] = 1;
vli_clear(v);
while ((cmp_result = vli_cmp(a, b)) != 0) {
carry = 0;
if (EVEN(a)) {
vli_rshift1(a);
if (!EVEN(u))
carry = vli_add(u, u, mod);
vli_rshift1(u);
if (carry)
u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
} else if (EVEN(b)) {
vli_rshift1(b);
if (!EVEN(v))
carry = vli_add(v, v, mod);
vli_rshift1(v);
if (carry)
v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
} else if (cmp_result > 0) {
vli_sub(a, a, b);
vli_rshift1(a);
if (vli_cmp(u, v) < 0)
vli_add(u, u, mod);
vli_sub(u, u, v);
if (!EVEN(u))
carry = vli_add(u, u, mod);
vli_rshift1(u);
if (carry)
u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
} else {
vli_sub(b, b, a);
vli_rshift1(b);
if (vli_cmp(v, u) < 0)
vli_add(v, v, mod);
vli_sub(v, v, u);
if (!EVEN(v))
carry = vli_add(v, v, mod);
vli_rshift1(v);
if (carry)
v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
}
}
vli_set(result, u);
}
/* ------ Point operations ------ */
/* Returns true if p_point is the point at infinity, false otherwise. */
static bool ecc_point_is_zero(const struct ecc_point *point)
{
return (vli_is_zero(point->x) && vli_is_zero(point->y));
}
/* Point multiplication algorithm using Montgomery's ladder with co-Z
* coordinates. From http://eprint.iacr.org/2011/338.pdf
*/
/* Double in place */
static void ecc_point_double_jacobian(uint64_t *x1, uint64_t *y1, uint64_t *z1)
{
/* t1 = x, t2 = y, t3 = z */
uint64_t t4[NUM_ECC_DIGITS];
uint64_t t5[NUM_ECC_DIGITS];
if (vli_is_zero(z1))
return;
vli_mod_square_fast(t4, y1); /* t4 = y1^2 */
vli_mod_mult_fast(t5, x1, t4); /* t5 = x1*y1^2 = A */
vli_mod_square_fast(t4, t4); /* t4 = y1^4 */
vli_mod_mult_fast(y1, y1, z1); /* t2 = y1*z1 = z3 */
vli_mod_square_fast(z1, z1); /* t3 = z1^2 */
vli_mod_add(x1, x1, z1, curve_p); /* t1 = x1 + z1^2 */
vli_mod_add(z1, z1, z1, curve_p); /* t3 = 2*z1^2 */
vli_mod_sub(z1, x1, z1, curve_p); /* t3 = x1 - z1^2 */
vli_mod_mult_fast(x1, x1, z1); /* t1 = x1^2 - z1^4 */
vli_mod_add(z1, x1, x1, curve_p); /* t3 = 2*(x1^2 - z1^4) */
vli_mod_add(x1, x1, z1, curve_p); /* t1 = 3*(x1^2 - z1^4) */
if (vli_test_bit(x1, 0)) {
uint64_t carry = vli_add(x1, x1, curve_p);
vli_rshift1(x1);
x1[NUM_ECC_DIGITS - 1] |= carry << 63;
} else {
vli_rshift1(x1);
}
/* t1 = 3/2*(x1^2 - z1^4) = B */
vli_mod_square_fast(z1, x1); /* t3 = B^2 */
vli_mod_sub(z1, z1, t5, curve_p); /* t3 = B^2 - A */
vli_mod_sub(z1, z1, t5, curve_p); /* t3 = B^2 - 2A = x3 */
vli_mod_sub(t5, t5, z1, curve_p); /* t5 = A - x3 */
vli_mod_mult_fast(x1, x1, t5); /* t1 = B * (A - x3) */
vli_mod_sub(t4, x1, t4, curve_p); /* t4 = B * (A - x3) - y1^4 = y3 */
vli_set(x1, z1);
vli_set(z1, y1);
vli_set(y1, t4);
}
/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
static void apply_z(uint64_t *x1, uint64_t *y1, uint64_t *z)
{
uint64_t t1[NUM_ECC_DIGITS];
vli_mod_square_fast(t1, z); /* z^2 */
vli_mod_mult_fast(x1, x1, t1); /* x1 * z^2 */
vli_mod_mult_fast(t1, t1, z); /* z^3 */
vli_mod_mult_fast(y1, y1, t1); /* y1 * z^3 */
}
/* P = (x1, y1) => 2P, (x2, y2) => P' */
static void xycz_initial_double(uint64_t *x1, uint64_t *y1, uint64_t *x2,
uint64_t *y2, uint64_t *p_initial_z)
{
uint64_t z[NUM_ECC_DIGITS];
vli_set(x2, x1);
vli_set(y2, y1);
vli_clear(z);
z[0] = 1;
if (p_initial_z)
vli_set(z, p_initial_z);
apply_z(x1, y1, z);
ecc_point_double_jacobian(x1, y1, z);
apply_z(x2, y2, z);
}
/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
* Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
* or P => P', Q => P + Q
*/
static void xycz_add(uint64_t *x1, uint64_t *y1, uint64_t *x2, uint64_t *y2)
{
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
uint64_t t5[NUM_ECC_DIGITS];
vli_mod_sub(t5, x2, x1, curve_p); /* t5 = x2 - x1 */
vli_mod_square_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */
vli_mod_mult_fast(x1, x1, t5); /* t1 = x1*A = B */
vli_mod_mult_fast(x2, x2, t5); /* t3 = x2*A = C */
vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y2 - y1 */
vli_mod_square_fast(t5, y2); /* t5 = (y2 - y1)^2 = D */
vli_mod_sub(t5, t5, x1, curve_p); /* t5 = D - B */
vli_mod_sub(t5, t5, x2, curve_p); /* t5 = D - B - C = x3 */
vli_mod_sub(x2, x2, x1, curve_p); /* t3 = C - B */
vli_mod_mult_fast(y1, y1, x2); /* t2 = y1*(C - B) */
vli_mod_sub(x2, x1, t5, curve_p); /* t3 = B - x3 */
vli_mod_mult_fast(y2, y2, x2); /* t4 = (y2 - y1)*(B - x3) */
vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y3 */
vli_set(x2, t5);
}
/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
* Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
* or P => P - Q, Q => P + Q
*/
static void xycz_add_c(uint64_t *x1, uint64_t *y1, uint64_t *x2, uint64_t *y2)
{
/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
uint64_t t5[NUM_ECC_DIGITS];
uint64_t t6[NUM_ECC_DIGITS];
uint64_t t7[NUM_ECC_DIGITS];
vli_mod_sub(t5, x2, x1, curve_p); /* t5 = x2 - x1 */
vli_mod_square_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */
vli_mod_mult_fast(x1, x1, t5); /* t1 = x1*A = B */
vli_mod_mult_fast(x2, x2, t5); /* t3 = x2*A = C */
vli_mod_add(t5, y2, y1, curve_p); /* t4 = y2 + y1 */
vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y2 - y1 */
vli_mod_sub(t6, x2, x1, curve_p); /* t6 = C - B */
vli_mod_mult_fast(y1, y1, t6); /* t2 = y1 * (C - B) */
vli_mod_add(t6, x1, x2, curve_p); /* t6 = B + C */
vli_mod_square_fast(x2, y2); /* t3 = (y2 - y1)^2 */
vli_mod_sub(x2, x2, t6, curve_p); /* t3 = x3 */
vli_mod_sub(t7, x1, x2, curve_p); /* t7 = B - x3 */
vli_mod_mult_fast(y2, y2, t7); /* t4 = (y2 - y1)*(B - x3) */
vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y3 */
vli_mod_square_fast(t7, t5); /* t7 = (y2 + y1)^2 = F */
vli_mod_sub(t7, t7, t6, curve_p); /* t7 = x3' */
vli_mod_sub(t6, t7, x1, curve_p); /* t6 = x3' - B */
vli_mod_mult_fast(t6, t6, t5); /* t6 = (y2 + y1)*(x3' - B) */
vli_mod_sub(y1, t6, y1, curve_p); /* t2 = y3' */
vli_set(x1, t7);
}
void ecc_point_mult(struct ecc_point *result,
const struct ecc_point *point,
uint64_t *scalar, uint64_t *initial_z,
int num_bits)
{
/* R0 and R1 */
uint64_t rx[2][NUM_ECC_DIGITS];
uint64_t ry[2][NUM_ECC_DIGITS];
uint64_t z[NUM_ECC_DIGITS];
int i, nb;
vli_set(rx[1], point->x);
vli_set(ry[1], point->y);
xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z);
for (i = num_bits - 2; i > 0; i--) {
nb = !vli_test_bit(scalar, i);
xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb]);
xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb]);
}
nb = !vli_test_bit(scalar, 0);
xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb]);
/* Find final 1/Z value. */
vli_mod_sub(z, rx[1], rx[0], curve_p); /* X1 - X0 */
vli_mod_mult_fast(z, z, ry[1 - nb]); /* Yb * (X1 - X0) */
vli_mod_mult_fast(z, z, point->x); /* xP * Yb * (X1 - X0) */
vli_mod_inv(z, z, curve_p); /* 1 / (xP * Yb * (X1 - X0)) */
vli_mod_mult_fast(z, z, point->y); /* yP / (xP * Yb * (X1 - X0)) */
vli_mod_mult_fast(z, z, rx[1 - nb]); /* Xb * yP / (xP * Yb * (X1 - X0)) */
/* End 1/Z calculation */
xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb]);
apply_z(rx[0], ry[0], z);
vli_set(result->x, rx[0]);
vli_set(result->y, ry[0]);
}
bool ecc_valid_point(struct ecc_point *point)
{
uint64_t tmp1[NUM_ECC_DIGITS];
uint64_t tmp2[NUM_ECC_DIGITS];
uint64_t _3[NUM_ECC_DIGITS] = { 3 }; /* -a = 3 */
/* The point at infinity is invalid. */
if (ecc_point_is_zero(point))
return false;
/* x and y must be smaller than p. */
if (vli_cmp(curve_p, point->x) != 1 ||
vli_cmp(curve_p, point->y) != 1)
return false;
/* Computes result = y^2. */
vli_mod_square_fast(tmp1, point->y);
/* Computes result = x^3 + ax + b. result must not overlap x. */
vli_mod_square_fast(tmp2, point->x); /* r = x^2 */
vli_mod_sub(tmp2, tmp2, _3, curve_p); /* r = x^2 - 3 */
vli_mod_mult_fast(tmp2, tmp2, point->x); /* r = x^3 - 3x */
vli_mod_add(tmp2, tmp2, curve_b, curve_p); /* r = x^3 - 3x + b */
/* Make sure that y^2 == x^3 + ax + b */
return vli_equal(tmp1, tmp2);
}
/*
* These two byte conversion functions were modified to allow for conversion
* to and from both BE and LE architectures.
*/
/* Big endian byte-array to native conversion */
void ecc_be2native(uint64_t bytes[NUM_ECC_DIGITS])
{
int i;
uint64_t tmp[NUM_ECC_DIGITS];
for (i = 0; i < NUM_ECC_DIGITS; i++)
tmp[NUM_ECC_DIGITS - 1 - i] = l_get_be64(&bytes[i]);
memcpy(bytes, tmp, 32);
}
/* Native to big endian byte-array conversion */
void ecc_native2be(uint64_t native[NUM_ECC_DIGITS])
{
int i;
uint64_t tmp[NUM_ECC_DIGITS];
for (i = 0; i < NUM_ECC_DIGITS; i++)
l_put_be64(native[NUM_ECC_DIGITS - 1 - i], &tmp[i]);
memcpy(native, tmp, 32);
}
/*
* The code below was not in the original file and was added to support EAP-PWD.
* The above ECC implementation did not include functionality for point
* addition or the ability to solve for Y value given some X.
*/
/* (rx, ry) = (px, py) + (qx, qy) */
void ecc_point_add(struct ecc_point *ret, struct ecc_point *p,
struct ecc_point *q)
{
/*
* s = (py - qy)/(px - qx)
*
* rx = s^2 - px - qx
* ry = s(px - rx) - py
*/
uint64_t s[NUM_ECC_DIGITS];
uint64_t kp1[NUM_ECC_DIGITS];
uint64_t kp2[NUM_ECC_DIGITS];
uint64_t resx[NUM_ECC_DIGITS];
uint64_t resy[NUM_ECC_DIGITS];
vli_clear(s);
/* kp1 = py - qy */
vli_mod_sub(kp1, q->y, p->y, curve_p);
/* kp2 = px - qx */
vli_mod_sub(kp2, q->x, p->x, curve_p);
/* s = kp1/kp2 */
vli_mod_inv(kp2, kp2, curve_p);
vli_mod_mult_fast(s, kp1, kp2);
/* rx = s^2 - px - qx */
vli_mod_mult_fast(kp1, s, s);
vli_mod_sub(kp1, kp1, p->x, curve_p);
vli_mod_sub(resx, kp1, q->x, curve_p);
/* ry = s(px - rx) - py */
vli_mod_sub(kp1, p->x, resx, curve_p);
vli_mod_mult_fast(kp1, s, kp1);
vli_mod_sub(resy, kp1, p->y, curve_p);
vli_set(ret->x, resx);
vli_set(ret->y, resy);
}
/* result = (base ^ exp) % p */
void vli_mod_exp(uint64_t *result, uint64_t *base, uint64_t *exp,
const uint64_t *mod)
{
int i;
int bit;
uint64_t n[NUM_ECC_DIGITS];
uint64_t r[NUM_ECC_DIGITS] = { 1 };
vli_set(n, base);
for (i = 0; i < NUM_ECC_DIGITS; i++) {
for (bit = 0; bit < 64; bit++) {
uint64_t tmp[NUM_ECC_DIGITS];
if (exp[i] & (1ull << bit)) {
vli_mod_mult_fast(tmp, r, n);
memcpy(r, tmp, 32);
}
vli_mod_mult_fast(tmp, n, n);
memcpy(n, tmp, 32);
}
}
memcpy(result, r, 32);
}
bool ecc_compute_y(uint64_t *y, uint64_t *x)
{
/*
* y = sqrt(x^3 + ax + b) (mod p)
*
* Since our prime p satisfies p = 3 (mod 4), we can say:
*
* y = (x^3 - 3x + b)^((p + 1) / 4)
*
* This avoids the need for a square root function.
*/
uint64_t sum[NUM_ECC_DIGITS] = { 0 };
uint64_t expo[NUM_ECC_DIGITS] = { 0 };
uint64_t one[NUM_ECC_DIGITS] = { 1ull };
uint64_t check[NUM_ECC_DIGITS] = { 0 };
uint64_t _3[NUM_ECC_DIGITS] = { 3ull }; /* -a = 3 */
uint64_t tmp[NUM_ECC_DIGITS] = { 0 };
vli_set(expo, curve_p);
vli_mod_square_fast(sum, x);
vli_mod_mult_fast(sum, sum, x); /* x^3 */
vli_mod_mult_fast(tmp, _3, x);
vli_mod_sub(sum, sum, tmp, curve_p); /* x^3 - ax */
vli_mod_add(sum, sum, curve_b, curve_p); /* x^3 - ax + b */
/* (p + 1) / 4 == (p >> 2) + 1 */
vli_rshift1(expo);
vli_rshift1(expo);
vli_mod_add(expo, expo, one, curve_p);
/* sum ^ ((p + 1) / 4) */
vli_mod_exp(y, sum, expo, curve_p);
/* square y to ensure we have a correct value */
vli_mod_mult_fast(check, y, y);
if (vli_cmp(check, sum) != 0)
return false;
return true;
}
void ecc_compute_y_sqr(uint64_t *y_sqr, uint64_t *x)
{
uint64_t sum[NUM_ECC_DIGITS] = { 0 };
uint64_t tmp[NUM_ECC_DIGITS] = { 0 };
uint64_t _3[NUM_ECC_DIGITS] = { 3ull }; /* -a = 3 */
vli_mod_square_fast(sum, x);
vli_mod_mult_fast(sum, sum, x); /* x^3 */
vli_mod_mult_fast(tmp, _3, x);
vli_mod_sub(sum, sum, tmp, curve_p); /* x^3 - ax */
vli_mod_add(sum, sum, curve_b, curve_p); /* x^3 - ax + b */
memcpy(y_sqr, sum, 32);
}
int vli_legendre(uint64_t *val, const uint64_t *p)
{
uint64_t tmp[NUM_ECC_DIGITS];
uint64_t exp[NUM_ECC_DIGITS];
uint64_t _1[NUM_ECC_DIGITS] = { 1ull };
uint64_t _0[NUM_ECC_DIGITS] = { 0 };
/* check that val ^ ((p - 1) / 2) == [1, 0 or -1] */
vli_sub(exp, p, _1);
vli_rshift1(exp);
vli_mod_exp(tmp, val, exp, p);
if (vli_cmp(tmp, _1) == 0)
return 1;
else if (vli_cmp(tmp, _0) == 0)
return 0;
else
return -1;
}

93
src/ecc.h
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@ -1,93 +0,0 @@
/*
*
* Wireless daemon for Linux
*
* Copyright (C) 2018 Intel Corporation. All rights reserved.
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <stdio.h>
#include <ell/ell.h>
/* 256-bit curve */
#define ECC_BYTES 32
/* Number of uint64_t's needed */
#define NUM_ECC_DIGITS (ECC_BYTES / 8)
#define CURVE_P_32 { 0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull, \
0x0000000000000000ull, 0xFFFFFFFF00000001ull }
#define CURVE_G_32 { \
{ 0xF4A13945D898C296ull, 0x77037D812DEB33A0ull, \
0xF8BCE6E563A440F2ull, 0x6B17D1F2E12C4247ull }, \
{ 0xCBB6406837BF51F5ull, 0x2BCE33576B315ECEull, \
0x8EE7EB4A7C0F9E16ull, 0x4FE342E2FE1A7F9Bull } \
}
#define CURVE_N_32 { 0xF3B9CAC2FC632551ull, 0xBCE6FAADA7179E84ull, \
0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFF00000000ull }
#define CURVE_B_32 { 0x3BCE3C3E27D2604Bull, 0x651D06B0CC53B0F6ull, \
0xB3EBBD55769886BCull, 0x5AC635D8AA3A93E7ull }
struct ecc_point {
uint64_t x[NUM_ECC_DIGITS];
uint64_t y[NUM_ECC_DIGITS];
};
void ecc_point_mult(struct ecc_point *result, const struct ecc_point *point,
uint64_t *scalar, uint64_t *initial_z, int num_bits);
void ecc_point_add(struct ecc_point *ret, struct ecc_point *p,
struct ecc_point *q);
bool ecc_valid_point(struct ecc_point *point);
void ecc_be2native(uint64_t bytes[NUM_ECC_DIGITS]);
void ecc_native2be(uint64_t native[NUM_ECC_DIGITS]);
bool ecc_compute_y(uint64_t *y, uint64_t *x);
void vli_mod_inv(uint64_t *result, const uint64_t *input, const uint64_t *mod);
void vli_mod_sub(uint64_t *result, const uint64_t *left, const uint64_t *right,
const uint64_t *mod);
void vli_mod_add(uint64_t *result, const uint64_t *left, const uint64_t *right,
const uint64_t *mod);
uint64_t vli_sub(uint64_t *result, const uint64_t *left, const uint64_t *right);
void vli_mod_mult_fast(uint64_t *result, const uint64_t *left,
const uint64_t *right);
void vli_mod_exp(uint64_t *result, uint64_t *base, uint64_t *exp,
const uint64_t *mod);
int vli_cmp(const uint64_t *left, const uint64_t *right);
unsigned int vli_num_bits(const uint64_t *vli);
int vli_legendre(uint64_t *val, const uint64_t *p);
void ecc_compute_y_sqr(uint64_t *y_sqr, uint64_t *x);

34
src/ecdh.h
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@ -1,34 +0,0 @@
/*
*
* Wireless daemon for Linux
*
* Copyright (C) 2018 Intel Corporation. All rights reserved.
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*
*/
/*
* Generate a private/public key pair. All inputs are expected in little-endian.
*/
bool ecdh_generate_key_pair(void *private, size_t priv_len,
void *public, size_t pub_len);
/*
* Generate a shared secret from a private/public key. All inputs are expected
* in little-endian.
*/
bool ecdh_generate_shared_secret(const void *private, const void *other_public,
size_t pub_len, void *secret,
size_t secret_len);

318
unit/test-ecc.c
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@ -1,318 +0,0 @@
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <string.h>
#include <assert.h>
#include <ell/ell.h>
#include "src/ecc.h"
#define HEX2BUF(s, buf) { \
unsigned char *tmp = l_util_from_hexstring(s, NULL); \
memcpy(buf, tmp, 32); \
l_free(tmp); \
}
#define CURVE_P_32_STR "ffffffffffffffffffffffff00000000"\
"000000000000000001000000ffffffff"
enum ecc_test_type {
TEST_ADD = 0,
TEST_SUB,
TEST_MULT,
TEST_INV,
TEST_EXP,
TEST_POINT_ADD,
TEST_SCALAR_MULT,
TEST_LEGENDRE,
};
struct ecc_test_data {
enum ecc_test_type type;
/* basic math arguments/result */
char *a;
char *b;
char *qr;
char *qnr;
char *r;
bool is_residue;
char *mod;
char *result;
int lres;
/* point operations */
char *scalar;
char *ax, *ay;
char *bx, *by;
char *rx, *ry;
};
/* (a + b) mod c */
struct ecc_test_data add_test = {
.type = TEST_ADD,
.a = "cae1d5624344984073fd955a72d4ebacedc084679333e4beebff94869e9f6ca8",
.b = "93a02ae89d15e38a33bf3fea4c99937825b279fa8fa81dded1ccb687cec88461",
.mod = CURVE_P_32_STR,
.result = "5e82004ae05a7bcaa7bcd545bf6e7f25"
"1372fe6222dc029dbccc4b0d6d67f10a"
};
/* (a - b) mod c */
struct ecc_test_data sub_test = {
.type = TEST_SUB,
.a = "cae1d5624344984073fd955a72d4ebacedc084679333e4beebff94869e9f6ca8",
.b = "93a02ae89d15e38a33bf3fea4c99937825b279fa8fa81dded1ccb687cec88461",
.mod = CURVE_P_32_STR,
.result = "3741aa79a62eb4b6403e5570263b5834"
"c80e0a6d038bc6e01a32ddfecfd6e847"
};
/* (a * b) mod c */
struct ecc_test_data mult_test = {
.type = TEST_MULT,
.a = "cae1d5624344984073fd955a72d4ebacedc084679333e4beebff94869e9f6ca8",
.b = "93a02ae89d15e38a33bf3fea4c99937825b279fa8fa81dded1ccb687cec88461",
.mod = CURVE_P_32_STR,
.result = "a31ff5c7d65d8bd806b0407f27d1f1bc"
"2c072e28c19720f6a654a75efc2faab5"
};
/* (a^-1) mod c */
struct ecc_test_data inv_test = {
.type = TEST_INV,
.a = "cae1d5624344984073fd955a72d4ebacedc084679333e4beebff94869e9f6ca8",
.mod = CURVE_P_32_STR,
.result = "48faaac115571047ead565911fc334fd"
"633c986755e87ab10fd79a4453a60bc5"
};
/* (a^-1) mod c */
struct ecc_test_data inv_test2 = {
.type = TEST_INV,
.a = "698e5c10b63a9c79a9720b3f7f4d2f5c9fbb31daf93ac0f8fa8ca5cde8234418",
.mod = CURVE_P_32_STR,
.result = "5fd113c3b6053c38e54e5917826c8520"
"c5a0708a8a47345edbb7fc1d67d9b42b"
};
/* (a ^ b) mod c */
struct ecc_test_data exp_test = {
.type = TEST_EXP,
.a = "cae1d5624344984073fd955a72d4ebacedc084679333e4beebff94869e9f6ca8",
.b = "93a02ae89d15e38a33bf3fea4c99937825b279fa8fa81dded1ccb687cec88461",
.mod = CURVE_P_32_STR,
.result = "415b2e00b2dfd0bf4889a64398c0fe6f"
"b4960df8e18c95799e08bfffb5814d5a"
};
struct ecc_test_data legendre_test1 = {
.type = TEST_LEGENDRE,
.a = "b59c0c366aa89ba229f857190497261d5a0a7a0a774caa72aef041ff00092447",
.mod = "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
.lres = -1
};
struct ecc_test_data legendre_test2 = {
.type = TEST_LEGENDRE,
.a = "1214f9607d348c998b3fba332d884d65945561fd007ff56d8bf603148d74d2e4",
.mod = "ffffffff000000010000000000000000"
"00000000ffffffffffffffffffffffff",
.lres = 1
};
struct ecc_test_data legendre_test3 = {
.type = TEST_LEGENDRE,
.a = "282d751c898bfc593b1d21b6812df48e3ec811f40349b30b7294575c47b871d8",
.mod = "ffffffff000000010000000000000000"
"00000000ffffffffffffffffffffffff",
.lres = 1
};
struct ecc_test_data legendre_test4 = {
.type = TEST_LEGENDRE,
.a = "0694ccde1db3d02faa26856678bd9358ecc0d82791405eb3892a8b4f07f1e5d6",
.mod = "ffffffff000000010000000000000000"
"00000000ffffffffffffffffffffffff",
.lres = -1
};
struct ecc_test_data legendre_test5 = {
.type = TEST_LEGENDRE,
.a = "92247f96df65a6d04af0c57318e999fd493c42864d156f7e5bba75c964f3c6b0",
.mod = "ffffffff000000010000000000000000"
"00000000ffffffffffffffffffffffff",
.lres = 1
};
struct ecc_test_data legendre_test6 = {
.type = TEST_LEGENDRE,
.a = "084f7eb6ed8021d095787fd401b0f19b13937dc23f7c84dfe69bb9a204bb3768",
.mod = "ffffffff000000010000000000000000"
"00000000ffffffffffffffffffffffff",
.lres = -1
};
struct ecc_test_data point_add_test = {
.type = TEST_POINT_ADD,
.ax = "d36b6768a3279fbe23a5bf5cc19b13354"
"fa2c6d6fd9de467d62db007c39452df",
.ay = "4d601e7be3efd7f357452de7584274c54"
"c18ddb0ef2f0f4cf43375152a9780c4",
.bx = "c833c5d3ab916ed37f16597ace5dcf41f"
"080891c0c41b6ce561705bd736a29e0",
.by = "9d266e5ba8ba3e8d9679238f44a376b05"
"133df0510a7b8e6e7dd3a654d40a04a",
.rx = "24c4ede340dbdd144ccaaea67e5b1fca"
"87b3aa26dc11114fcd12186318533101",
.ry = "1d96391fb2942bf286e9251c257b960e"
"7d23d4caff4b6fc898aff87e1f6f5514"
};
struct ecc_test_data point_mult_test = {
.type = TEST_SCALAR_MULT,
.ax = "768bc2f17fbf4e49282fbd4068994562b"
"fc7145306762c26a90be1e9c346ac67",
.ay = "93a02ae89d15e38a33bf3fea4c9993782"
"5b279fa8fa81dded1ccb687cec88461",
.scalar = "7521d940aa073c1675114ed27b866561"
"9c826cac8eaa341f70d61b43ad32058b",
.rx = "d4c80de349966df5542c984e80885d36"
"a965ceb74ffe6a0fdc8343184dedfe66",
.ry = "6d3a1ac3d1d392413286a0e00e94b01e"
"ae8423c7f53b9d39cc7fc9c3a5880f3b"
};
static void run_test(const void *arg)
{
const struct ecc_test_data *data = arg;
uint64_t a[NUM_ECC_DIGITS], b[NUM_ECC_DIGITS], mod[NUM_ECC_DIGITS],
scalar[NUM_ECC_DIGITS], result[NUM_ECC_DIGITS],
check[NUM_ECC_DIGITS];
struct ecc_point point1, point2, point_ret;
memset(result, 0, sizeof(result));
if (data->a) {
HEX2BUF(data->a, a);
ecc_be2native(a);
}
if (data->b) {
HEX2BUF(data->b, b);
ecc_be2native(b);
}
if (data->mod) {
HEX2BUF(data->mod, mod);
ecc_be2native(mod);
}
if (data->ax) {
HEX2BUF(data->ax, point1.x);
ecc_be2native(point1.x);
}
if (data->ay) {
HEX2BUF(data->ay, point1.y);
ecc_be2native(point1.y);
}
if (data->bx) {
HEX2BUF(data->bx, point2.x);
ecc_be2native(point2.x);
}
if (data->by) {
HEX2BUF(data->by, point2.y);
ecc_be2native(point2.y);
}
if (data->scalar) {
HEX2BUF(data->scalar, scalar);
ecc_be2native(scalar);
}
switch (data->type) {
case TEST_ADD:
vli_mod_add(result, a, b, mod);
break;
case TEST_SUB:
vli_mod_sub(result, a, b, mod);
break;
case TEST_MULT:
vli_mod_mult_fast(result, a, b);
break;
case TEST_INV:
vli_mod_inv(result, a, mod);
break;
case TEST_EXP:
vli_mod_exp(result, a, b, mod);
break;
case TEST_LEGENDRE:
{
int lres = vli_legendre(a, mod);
assert(data->lres == lres);
break;
}
case TEST_POINT_ADD:
assert(ecc_valid_point(&point1) == true);
assert(ecc_valid_point(&point2) == true);
ecc_point_add(&point_ret, &point1, &point2);
break;
case TEST_SCALAR_MULT:
assert(ecc_valid_point(&point1) == true);
ecc_point_mult(&point_ret, &point1, scalar, NULL,
vli_num_bits(scalar));
break;
}
if (data->type <= TEST_EXP) {
HEX2BUF(data->result, check);
ecc_native2be(check);
assert(memcmp(result, check, 32) == 0);
} else if (data->type <= TEST_SCALAR_MULT) {
uint64_t checkx[NUM_ECC_DIGITS];
uint64_t checky[NUM_ECC_DIGITS];
HEX2BUF(data->rx, checkx);
ecc_native2be(checkx);
HEX2BUF(data->ry, checky);
ecc_native2be(checky);
assert(memcmp(checkx, point_ret.x, 32) == 0);
assert(memcmp(checky, point_ret.y, 32) == 0);
assert(ecc_valid_point(&point_ret) == true);
}
}
int main(int argc, char *argv[])
{
l_test_init(&argc, &argv);
l_test_add("ECC add test", run_test, &add_test);
l_test_add("ECC sub test", run_test, &sub_test);
l_test_add("ECC mult test", run_test, &mult_test);
l_test_add("ECC inv test", run_test, &inv_test);
l_test_add("ECC inv test", run_test, &inv_test2);
l_test_add("ECC exp test", run_test, &exp_test);
l_test_add("ECC point add test", run_test, &point_add_test);
l_test_add("ECC point mult test", run_test, &point_mult_test);
l_test_add("ECC legendre", run_test, &legendre_test1);
l_test_add("ECC legendre", run_test, &legendre_test2);
l_test_add("ECC legendre", run_test, &legendre_test3);
l_test_add("ECC legendre", run_test, &legendre_test4);
l_test_add("ECC legendre", run_test, &legendre_test5);
l_test_add("ECC legendre", run_test, &legendre_test6);
return l_test_run();
}