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Implemented support for secp256k1 (issue #4).

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This commit is contained in:
Ken MacKay
2014-01-26 22:00:01 -08:00
parent ed3f5967cc
commit 7bb1ccc4c9
3 changed files with 173 additions and 42 deletions
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ecc.c
+145 -30
View File
@@ -4,49 +4,60 @@
typedef unsigned int uint;
#define CONCAT1(a, b) a##b
#define CONCAT(a, b) CONCAT1(a, b)
#define Curve_P_4 {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFD}
#define Curve_P_6 {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_P_8 {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0x00000000, 0x00000000, 0x00000001, 0xFFFFFFFF}
#define Curve_P_12 {0xFFFFFFFF, 0x00000000, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, \
#define Curve_P_secp128r1 {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFD}
#define Curve_P_secp192r1 {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_P_secp256r1 {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0x00000000, 0x00000000, 0x00000001, 0xFFFFFFFF}
#define Curve_P_secp384r1 {0xFFFFFFFF, 0x00000000, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, \
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_P_secp256k1 {0xFFFFFC2F, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_B_4 {0x2CEE5ED3, 0xD824993C, 0x1079F43D, 0xE87579C1}
#define Curve_B_6 {0xC146B9B1, 0xFEB8DEEC, 0x72243049, 0x0FA7E9AB, 0xE59C80E7, 0x64210519}
#define Curve_B_8 {0x27D2604B, 0x3BCE3C3E, 0xCC53B0F6, 0x651D06B0, 0x769886BC, 0xB3EBBD55, 0xAA3A93E7, 0x5AC635D8}
#define Curve_B_12 {0xD3EC2AEF, 0x2A85C8ED, 0x8A2ED19D, 0xC656398D, 0x5013875A, 0x0314088F, 0xFE814112, 0x181D9C6E, \
#define Curve_B_secp128r1 {0x2CEE5ED3, 0xD824993C, 0x1079F43D, 0xE87579C1}
#define Curve_B_secp192r1 {0xC146B9B1, 0xFEB8DEEC, 0x72243049, 0x0FA7E9AB, 0xE59C80E7, 0x64210519}
#define Curve_B_secp256r1 {0x27D2604B, 0x3BCE3C3E, 0xCC53B0F6, 0x651D06B0, 0x769886BC, 0xB3EBBD55, 0xAA3A93E7, 0x5AC635D8}
#define Curve_B_secp384r1 {0xD3EC2AEF, 0x2A85C8ED, 0x8A2ED19D, 0xC656398D, 0x5013875A, 0x0314088F, 0xFE814112, 0x181D9C6E, \
0xE3F82D19, 0x988E056B, 0xE23EE7E4, 0xB3312FA7}
#define Curve_B_secp256k1 {0x00000007, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000}
#define Curve_G_4 { \
#define Curve_G_secp128r1 { \
{0xA52C5B86, 0x0C28607C, 0x8B899B2D, 0x161FF752}, \
{0xDDED7A83, 0xC02DA292, 0x5BAFEB13, 0xCF5AC839}}
#define Curve_G_6 { \
#define Curve_G_secp192r1 { \
{0x82FF1012, 0xF4FF0AFD, 0x43A18800, 0x7CBF20EB, 0xB03090F6, 0x188DA80E}, \
{0x1E794811, 0x73F977A1, 0x6B24CDD5, 0x631011ED, 0xFFC8DA78, 0x07192B95}}
#define Curve_G_8 { \
#define Curve_G_secp256r1 { \
{0xD898C296, 0xF4A13945, 0x2DEB33A0, 0x77037D81, 0x63A440F2, 0xF8BCE6E5, 0xE12C4247, 0x6B17D1F2}, \
{0x37BF51F5, 0xCBB64068, 0x6B315ECE, 0x2BCE3357, 0x7C0F9E16, 0x8EE7EB4A, 0xFE1A7F9B, 0x4FE342E2}}
#define Curve_G_12 { \
#define Curve_G_secp384r1 { \
{0x72760AB7, 0x3A545E38, 0xBF55296C, 0x5502F25D, 0x82542A38, 0x59F741E0, 0x8BA79B98, 0x6E1D3B62, \
0xF320AD74, 0x8EB1C71E, 0xBE8B0537, 0xAA87CA22}, \
{0x90EA0E5F, 0x7A431D7C, 0x1D7E819D, 0x0A60B1CE, 0xB5F0B8C0, 0xE9DA3113, 0x289A147C, 0xF8F41DBD, \
0x9292DC29, 0x5D9E98BF, 0x96262C6F, 0x3617DE4A}}
#define Curve_N_4 {0x9038A115, 0x75A30D1B, 0x00000000, 0xFFFFFFFE}
#define Curve_N_6 {0xB4D22831, 0x146BC9B1, 0x99DEF836, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_N_8 {0xFC632551, 0xF3B9CAC2, 0xA7179E84, 0xBCE6FAAD, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0xFFFFFFFF}
#define Curve_N_12 {0xCCC52973, 0xECEC196A, 0x48B0A77A, 0x581A0DB2, 0xF4372DDF, 0xC7634D81, 0xFFFFFFFF, 0xFFFFFFFF, \
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_G_secp256k1 { \
{0x16F81798, 0x59F2815B, 0x2DCE28D9, 0x029BFCDB, 0xCE870B07, 0x55A06295, 0xF9DCBBAC, 0x79BE667E}, \
{0xFB10D4B8, 0x9C47D08F, 0xA6855419, 0xFD17B448, 0x0E1108A8, 0x5DA4FBFC, 0x26A3C465, 0x483ADA77}}
static uint32_t curve_p[NUM_ECC_DIGITS] = CONCAT(Curve_P_, ECC_CURVE);
static uint32_t curve_b[NUM_ECC_DIGITS] = CONCAT(Curve_B_, ECC_CURVE);
static EccPoint curve_G = CONCAT(Curve_G_, ECC_CURVE);
static uint32_t curve_n[NUM_ECC_DIGITS] = CONCAT(Curve_N_, ECC_CURVE);
#define Curve_N_secp128r1 {0x9038A115, 0x75A30D1B, 0x00000000, 0xFFFFFFFE}
#define Curve_N_secp192r1 {0xB4D22831, 0x146BC9B1, 0x99DEF836, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_N_secp256r1 {0xFC632551, 0xF3B9CAC2, 0xA7179E84, 0xBCE6FAAD, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0xFFFFFFFF}
#define Curve_N_secp384r1 {0xCCC52973, 0xECEC196A, 0x48B0A77A, 0x581A0DB2, 0xF4372DDF, 0xC7634D81, 0xFFFFFFFF, 0xFFFFFFFF, \
0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define Curve_N_secp256k1 {0xD0364141, 0xBFD25E8C, 0xAF48A03B, 0xBAAEDCE6, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
#define secp128r1_id 1
#define secp192r1_id 2
#define secp256r1_id 3
#define secp384r1_id 4
#define secp256k1_id 5
#define ECC_ALG ECC_CONCAT(ECC_CURVE, _id)
static uint32_t curve_p[NUM_ECC_DIGITS] = ECC_CONCAT(Curve_P_, ECC_CURVE);
static uint32_t curve_b[NUM_ECC_DIGITS] = ECC_CONCAT(Curve_B_, ECC_CURVE);
static EccPoint curve_G = ECC_CONCAT(Curve_G_, ECC_CURVE);
static uint32_t curve_n[NUM_ECC_DIGITS] = ECC_CONCAT(Curve_N_, ECC_CURVE);
static void vli_clear(uint32_t *p_vli)
{
@@ -472,7 +483,7 @@ static void vli_modSub(uint32_t *p_result, uint32_t *p_left, uint32_t *p_right,
}
}
#if ECC_CURVE == secp128r1
#if ECC_ALG == secp128r1_id
/* Computes p_result = p_product % curve_p.
See algorithm 5 and 6 from http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf */
@@ -525,7 +536,7 @@ static void vli_mmod_fast(uint32_t *p_result, uint32_t *p_product)
}
}
#elif ECC_CURVE == secp192r1
#elif ECC_ALG == secp192r1_id
/* Computes p_result = p_product % curve_p.
See algorithm 5 and 6 from http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf */
@@ -557,7 +568,7 @@ static void vli_mmod_fast(uint32_t *p_result, uint32_t *p_product)
}
}
#elif ECC_CURVE == secp256r1
#elif ECC_ALG == secp256r1_id
/* Computes p_result = p_product % curve_p
from http://www.nsa.gov/ia/_files/nist-routines.pdf */
@@ -665,7 +676,7 @@ static void vli_mmod_fast(uint32_t *p_result, uint32_t *p_product)
}
}
#elif ECC_CURVE == secp384r1
#elif ECC_ALG == secp384r1_id
static void omega_mult(uint32_t *p_result, uint32_t *p_right)
{
@@ -723,6 +734,59 @@ static void vli_mmod_fast(uint32_t *p_result, uint32_t *p_product)
vli_set(p_result, p_product);
}
#elif ECC_ALG == secp256k1_id
static void omega_mult(uint32_t *p_result, uint32_t *p_right)
{
/* Multiply by (2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
uint64_t l_mult = 0x3D1; /* everything except 2^32 */
uint32_t l_carry = 0;
uint i;
for(i=0; i<NUM_ECC_DIGITS; ++i)
{
uint64_t p = l_mult * p_right[i] + l_carry;
p_result[i] = (p & 0xffffffff);
l_carry = p >> 32;
}
p_result[NUM_ECC_DIGITS] = l_carry;
p_result[1 + NUM_ECC_DIGITS] = vli_add(p_result + 1, p_result + 1, p_right); /* add the 2^32 multiple */
}
/* Computes p_result = p_product % curve_p */
static void vli_mmod_fast(uint32_t *p_result, uint32_t *p_product)
{
uint32_t l_tmp[2*NUM_ECC_DIGITS];
while(!vli_isZero(p_product + NUM_ECC_DIGITS)) /* While c1 != 0 */
{
uint32_t l_carry = 0;
uint i;
vli_clear(l_tmp);
vli_clear(l_tmp + NUM_ECC_DIGITS);
omega_mult(l_tmp, p_product + NUM_ECC_DIGITS); /* tmp = w * c1 */
vli_clear(p_product + NUM_ECC_DIGITS); /* p = c0 */
/* (c1, c0) = c0 + w * c1 */
for(i=0; i<NUM_ECC_DIGITS+2; ++i)
{
uint32_t l_sum = p_product[i] + l_tmp[i] + l_carry;
if(l_sum != p_product[i])
{
l_carry = (l_sum < p_product[i]);
}
p_product[i] = l_sum;
}
}
while(vli_cmp(p_product, curve_p) > 0)
{
vli_sub(p_product, p_product, curve_p);
}
vli_set(p_result, p_product);
}
#endif
/* Computes p_result = (p_left * p_right) % curve_p. */
@@ -1055,12 +1119,52 @@ From http://eprint.iacr.org/2011/338.pdf
*/
/* Double in place */
#if ECC_ALG == secp256k1_id
static void EccPoint_double_jacobian(uint32_t *X1, uint32_t *Y1, uint32_t *Z1)
{
/* t1 = X, t2 = Y, t3 = Z */
uint32_t t4[NUM_ECC_DIGITS];
uint32_t t5[NUM_ECC_DIGITS];
if(vli_isZero(Z1))
{
return;
}
vli_modSquare_fast(t5, Y1); /* t5 = y1^2 */
vli_modMult_fast(t4, X1, t5); /* t4 = x1*y1^2 = A */
vli_modSquare_fast(X1, X1); /* t1 = x1^2 */
vli_modSquare_fast(t5, t5); /* t5 = y1^4 */
vli_modMult_fast(Z1, Y1, Z1); /* t3 = y1*z1 = z3 */
vli_modAdd(Y1, X1, X1, curve_p); /* t2 = 2*x1^2 */
vli_modAdd(Y1, Y1, X1, curve_p); /* t2 = 3*x1^2 */
if(vli_testBit(Y1, 0))
{
uint32_t l_carry = vli_add(Y1, Y1, curve_p);
vli_rshift1(Y1);
Y1[NUM_ECC_DIGITS-1] |= l_carry << 31;
}
else
{
vli_rshift1(Y1);
}
/* t2 = 3/2*(x1^2) = B */
vli_modSquare_fast(X1, Y1); /* t1 = B^2 */
vli_modSub(X1, X1, t4, curve_p); /* t1 = B^2 - A */
vli_modSub(X1, X1, t4, curve_p); /* t1 = B^2 - 2A = x3 */
vli_modSub(t4, t4, X1, curve_p); /* t4 = A - x3 */
vli_modMult_fast(Y1, Y1, t4); /* t2 = B * (A - x3) */
vli_modSub(Y1, Y1, t5, curve_p); /* t2 = B * (A - x3) - y1^4 = y3 */
}
#else
static void EccPoint_double_jacobian(uint32_t *X1, uint32_t *Y1, uint32_t *Z1)
{
/* t1 = X, t2 = Y, t3 = Z */
uint32_t t4[NUM_ECC_DIGITS];
uint32_t t5[NUM_ECC_DIGITS];
uint32_t t9[NUM_ECC_DIGITS];
if(vli_isZero(Z1))
{
@@ -1090,7 +1194,7 @@ static void EccPoint_double_jacobian(uint32_t *X1, uint32_t *Y1, uint32_t *Z1)
{
vli_rshift1(X1);
}
/* t1 = 3/2*(x1^2 - z1^4) = B */
/* t1 = 3/2*(x1^2 - z1^4) = B */
vli_modSquare_fast(Z1, X1); /* t3 = B^2 */
vli_modSub(Z1, Z1, t5, curve_p); /* t3 = B^2 - A */
@@ -1103,6 +1207,7 @@ static void EccPoint_double_jacobian(uint32_t *X1, uint32_t *Y1, uint32_t *Z1)
vli_set(Z1, Y1);
vli_set(Y1, t4);
}
#endif
/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
static void apply_z(uint32_t *X1, uint32_t *Y1, uint32_t *Z)
@@ -1260,6 +1365,15 @@ int ecc_make_key(EccPoint *p_publicKey, uint32_t p_privateKey[NUM_ECC_DIGITS], u
return 1;
}
#if ECC_ALG == secp256k1_id
/* Compute p_result = x^3 + b */
static void curve_x_side(uint32_t p_result[NUM_ECC_DIGITS], uint32_t x[NUM_ECC_DIGITS])
{
vli_modSquare_fast(p_result, x); /* r = x^2 */
vli_modMult_fast(p_result, p_result, x); /* r = x^3 */
vli_modAdd(p_result, p_result, curve_b, curve_p); /* r = x^3 + b */
}
#else
/* Compute p_result = x^3 - 3x + b */
static void curve_x_side(uint32_t p_result[NUM_ECC_DIGITS], uint32_t x[NUM_ECC_DIGITS])
{
@@ -1270,6 +1384,7 @@ static void curve_x_side(uint32_t p_result[NUM_ECC_DIGITS], uint32_t x[NUM_ECC_D
vli_modMult_fast(p_result, p_result, x); /* r = x^3 - 3x */
vli_modAdd(p_result, p_result, curve_b, curve_p); /* r = x^3 - 3x + b */
}
#endif
int ecc_valid_public_key(EccPoint *p_publicKey)
{
ecc.h
+15 -8
View File
@@ -24,20 +24,27 @@ with strange assembler messages.
#define ECC_ASM ecc_asm_none
#endif
#define ECC_CONCAT1(a, b) a##b
#define ECC_CONCAT(a, b) ECC_CONCAT1(a, b)
/* Curve selection options. */
#define secp128r1 4
#define secp192r1 6
#define secp256r1 8
#define secp384r1 12
#define secp128r1 secp128r1
#define secp192r1 secp192r1
#define secp256r1 secp256r1
#define secp384r1 secp384r1
#define secp256k1 secp256k1
#ifndef ECC_CURVE
#define ECC_CURVE secp256r1
#endif
#if (ECC_CURVE != secp128r1 && ECC_CURVE != secp192r1 && ECC_CURVE != secp256r1 && ECC_CURVE != secp384r1)
#error "Must define ECC_CURVE to one of the available curves"
#endif
#define secp128r1_size 4
#define secp192r1_size 6
#define secp256r1_size 8
#define secp384r1_size 12
#define secp256k1_size 8
#define NUM_ECC_DIGITS ECC_CURVE
#define NUM_ECC_DIGITS ECC_CONCAT(ECC_CURVE, _size)
typedef struct EccPoint
{
test/speedtest.c
+13 -4
View File
@@ -25,6 +25,13 @@ uint64_t getTimeMs(void)
#include <stdio.h>
#define secp128r1_id 1
#define secp192r1_id 2
#define secp256r1_id 3
#define secp384r1_id 4
#define secp256k1_id 5
#define ECC_ALG ECC_CONCAT(ECC_CURVE, _id)
void vli_print(uint32_t *p_vli)
{
unsigned i;
@@ -34,7 +41,7 @@ void vli_print(uint32_t *p_vli)
}
}
#if (ECC_CURVE == secp128r1)
#if (ECC_ALG == secp128r1_id)
uint32_t g_private[10][NUM_ECC_DIGITS] = {
{0xB66C17D0, 0xD21CD12E, 0x1885B2F7, 0x71D40584},
{0x6C99B53A, 0x86686357, 0x3E34C5C4, 0x5314DFA3},
@@ -133,7 +140,7 @@ uint32_t g_dsa_s[10][NUM_ECC_DIGITS] = {
{0x7A19D7C2, 0x51AE91C0, 0x318DBAD9, 0xE520A100}
};
#elif (ECC_CURVE == secp192r1)
#elif (ECC_ALG == secp192r1_id)
uint32_t g_private[10][NUM_ECC_DIGITS] = {
{0x8A8590BC, 0xF8FC6B96, 0x216D16F6, 0x5D471999, 0x77B54115, 0xA1C40C96},
{0x60867073, 0xC781509C, 0x36ACD71C, 0x58F5AD9E, 0xC2DB7360, 0x33BD208D},
@@ -233,7 +240,7 @@ uint32_t g_dsa_s[10][NUM_ECC_DIGITS] = {
};
#elif (ECC_CURVE == secp256r1)
#elif (ECC_ALG == secp256r1_id)
uint32_t g_private[10][NUM_ECC_DIGITS] = {
{0x9399E0FA, 0xEB887947, 0xFACC412E, 0xC7AFD411, 0x735EE1E8, 0x2B8AFAF4, 0x986E3E7F, 0x742B1953},
@@ -333,7 +340,7 @@ uint32_t g_dsa_s[10][NUM_ECC_DIGITS] = {
{0xAFC08C0C, 0x949EF819, 0xB80751E5, 0x9E77D36C, 0x2338ADBF, 0xD3F84E20, 0x10E30B97, 0x617F0EF3}
};
#elif (ECC_CURVE == secp384r1)
#elif (ECC_ALG == secp384r1_id)
uint32_t g_private[10][NUM_ECC_DIGITS] = {
{0x32D5EFC6, 0x0A6E70F1, 0x6CAE9125, 0x78D74ECF, 0x33E423FB, 0x2B9F9991, 0x188E04C0, 0x6FEA1C8E, 0x2B2634A3, 0xDC5C521A, 0xDBF7265D, 0xB2975791},
@@ -438,6 +445,7 @@ uint32_t g_dsa_s[10][NUM_ECC_DIGITS] = {
int main()
{
#if (ECC_ALG != secp256k1_id)
uartInit(BAUD_115200);
initTime();
@@ -472,6 +480,7 @@ int main()
}
printf("Total ECDSA time: %llu\n", l_total);
#endif
return 0;
}