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Diffstat (limited to 'src/ltc/pk/ecc/ltc_ecc_projective_dbl_point.c')
-rw-r--r--src/ltc/pk/ecc/ltc_ecc_projective_dbl_point.c200
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diff --git a/src/ltc/pk/ecc/ltc_ecc_projective_dbl_point.c b/src/ltc/pk/ecc/ltc_ecc_projective_dbl_point.c
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index 00000000..f954a597
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+++ b/src/ltc/pk/ecc/ltc_ecc_projective_dbl_point.c
@@ -0,0 +1,200 @@
+/* LibTomCrypt, modular cryptographic library -- Tom St Denis
+ *
+ * LibTomCrypt is a library that provides various cryptographic
+ * algorithms in a highly modular and flexible manner.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ */
+
+/* Implements ECC over Z/pZ for curve y^2 = x^3 + a*x + b
+ *
+ */
+#include "tomcrypt.h"
+
+/* ### Point doubling in Jacobian coordinate system ###
+ *
+ * let us have a curve: y^2 = x^3 + a*x + b
+ * in Jacobian coordinates it becomes: y^2 = x^3 + a*x*z^4 + b*z^6
+ *
+ * The doubling of P = (Xp, Yp, Zp) is given by R = (Xr, Yr, Zr) where:
+ * Xr = M^2 - 2*S
+ * Yr = M * (S - Xr) - 8*T
+ * Zr = 2 * Yp * Zp
+ *
+ * M = 3 * Xp^2 + a*Zp^4
+ * T = Yp^4
+ * S = 4 * Xp * Yp^2
+ *
+ * SPECIAL CASE: when a == -3 we can compute M as
+ * M = 3 * (Xp^2 - Zp^4) = 3 * (Xp + Zp^2) * (Xp - Zp^2)
+ */
+
+/**
+ @file ltc_ecc_projective_dbl_point.c
+ ECC Crypto, Tom St Denis
+*/
+
+#if defined(LTC_MECC) && (!defined(LTC_MECC_ACCEL) || defined(LTM_DESC))
+
+/**
+ Double an ECC point
+ @param P The point to double
+ @param R [out] The destination of the double
+ @param ma ECC curve parameter a in montgomery form (if NULL we assume a == -3)
+ @param modulus The modulus of the field the ECC curve is in
+ @param mp The "b" value from montgomery_setup()
+ @return CRYPT_OK on success
+*/
+int ltc_ecc_projective_dbl_point(ecc_point *P, ecc_point *R, void *ma, void *modulus, void *mp)
+{
+ void *t1, *t2;
+ int err;
+
+ LTC_ARGCHK(P != NULL);
+ LTC_ARGCHK(R != NULL);
+ LTC_ARGCHK(modulus != NULL);
+ LTC_ARGCHK(mp != NULL);
+
+ if ((err = mp_init_multi(&t1, &t2, NULL)) != CRYPT_OK) {
+ return err;
+ }
+
+ if (P != R) {
+ if ((err = mp_copy(P->x, R->x)) != CRYPT_OK) { goto done; }
+ if ((err = mp_copy(P->y, R->y)) != CRYPT_OK) { goto done; }
+ if ((err = mp_copy(P->z, R->z)) != CRYPT_OK) { goto done; }
+ }
+
+ if (ltc_ecc_is_point_at_infinity(P, modulus)) {
+ /* if P is point at infinity >> Result = point at infinity */
+ if ((err = ltc_mp.set_int(R->x, 1)) != CRYPT_OK) { goto done; }
+ if ((err = ltc_mp.set_int(R->y, 1)) != CRYPT_OK) { goto done; }
+ if ((err = ltc_mp.set_int(R->z, 0)) != CRYPT_OK) { goto done; }
+ goto done; /* CRYPT_OK */
+ }
+
+ /* t1 = Z * Z */
+ if ((err = mp_sqr(R->z, t1)) != CRYPT_OK) { goto done; }
+ if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK) { goto done; }
+ /* Z = Y * Z */
+ if ((err = mp_mul(R->z, R->y, R->z)) != CRYPT_OK) { goto done; }
+ if ((err = mp_montgomery_reduce(R->z, modulus, mp)) != CRYPT_OK) { goto done; }
+ /* Z = 2Z */
+ if ((err = mp_add(R->z, R->z, R->z)) != CRYPT_OK) { goto done; }
+ if (mp_cmp(R->z, modulus) != LTC_MP_LT) {
+ if ((err = mp_sub(R->z, modulus, R->z)) != CRYPT_OK) { goto done; }
+ }
+
+ if (ma == NULL) { /* special case for ma == -3 (slightly faster than general case) */
+ /* T2 = X - T1 */
+ if ((err = mp_sub(R->x, t1, t2)) != CRYPT_OK) { goto done; }
+ if (mp_cmp_d(t2, 0) == LTC_MP_LT) {
+ if ((err = mp_add(t2, modulus, t2)) != CRYPT_OK) { goto done; }
+ }
+ /* T1 = X + T1 */
+ if ((err = mp_add(t1, R->x, t1)) != CRYPT_OK) { goto done; }
+ if (mp_cmp(t1, modulus) != LTC_MP_LT) {
+ if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK) { goto done; }
+ }
+ /* T2 = T1 * T2 */
+ if ((err = mp_mul(t1, t2, t2)) != CRYPT_OK) { goto done; }
+ if ((err = mp_montgomery_reduce(t2, modulus, mp)) != CRYPT_OK) { goto done; }
+ /* T1 = 2T2 */
+ if ((err = mp_add(t2, t2, t1)) != CRYPT_OK) { goto done; }
+ if (mp_cmp(t1, modulus) != LTC_MP_LT) {
+ if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK) { goto done; }
+ }
+ /* T1 = T1 + T2 */
+ if ((err = mp_add(t1, t2, t1)) != CRYPT_OK) { goto done; }
+ if (mp_cmp(t1, modulus) != LTC_MP_LT) {
+ if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK) { goto done; }
+ }
+ }
+ else {
+ /* T2 = T1 * T1 */
+ if ((err = mp_sqr(t1, t2)) != CRYPT_OK) { goto done; }
+ if ((err = mp_montgomery_reduce(t2, modulus, mp)) != CRYPT_OK) { goto done; }
+ /* T1 = T2 * a */
+ if ((err = mp_mul(t2, ma, t1)) != CRYPT_OK) { goto done; }
+ if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK) { goto done; }
+ /* T2 = X * X */
+ if ((err = mp_sqr(R->x, t2)) != CRYPT_OK) { goto done; }
+ if ((err = mp_montgomery_reduce(t2, modulus, mp)) != CRYPT_OK) { goto done; }
+ /* T1 = T2 + T1 */
+ if ((err = mp_add(t1, t2, t1)) != CRYPT_OK) { goto done; }
+ if (mp_cmp(t1, modulus) != LTC_MP_LT) {
+ if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK) { goto done; }
+ }
+ /* T1 = T2 + T1 */
+ if ((err = mp_add(t1, t2, t1)) != CRYPT_OK) { goto done; }
+ if (mp_cmp(t1, modulus) != LTC_MP_LT) {
+ if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK) { goto done; }
+ }
+ /* T1 = T2 + T1 */
+ if ((err = mp_add(t1, t2, t1)) != CRYPT_OK) { goto done; }
+ if (mp_cmp(t1, modulus) != LTC_MP_LT) {
+ if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK) { goto done; }
+ }
+ }
+
+ /* Y = 2Y */
+ if ((err = mp_add(R->y, R->y, R->y)) != CRYPT_OK) { goto done; }
+ if (mp_cmp(R->y, modulus) != LTC_MP_LT) {
+ if ((err = mp_sub(R->y, modulus, R->y)) != CRYPT_OK) { goto done; }
+ }
+ /* Y = Y * Y */
+ if ((err = mp_sqr(R->y, R->y)) != CRYPT_OK) { goto done; }
+ if ((err = mp_montgomery_reduce(R->y, modulus, mp)) != CRYPT_OK) { goto done; }
+ /* T2 = Y * Y */
+ if ((err = mp_sqr(R->y, t2)) != CRYPT_OK) { goto done; }
+ if ((err = mp_montgomery_reduce(t2, modulus, mp)) != CRYPT_OK) { goto done; }
+ /* T2 = T2/2 */
+ if (mp_isodd(t2)) {
+ if ((err = mp_add(t2, modulus, t2)) != CRYPT_OK) { goto done; }
+ }
+ if ((err = mp_div_2(t2, t2)) != CRYPT_OK) { goto done; }
+ /* Y = Y * X */
+ if ((err = mp_mul(R->y, R->x, R->y)) != CRYPT_OK) { goto done; }
+ if ((err = mp_montgomery_reduce(R->y, modulus, mp)) != CRYPT_OK) { goto done; }
+
+ /* X = T1 * T1 */
+ if ((err = mp_sqr(t1, R->x)) != CRYPT_OK) { goto done; }
+ if ((err = mp_montgomery_reduce(R->x, modulus, mp)) != CRYPT_OK) { goto done; }
+ /* X = X - Y */
+ if ((err = mp_sub(R->x, R->y, R->x)) != CRYPT_OK) { goto done; }
+ if (mp_cmp_d(R->x, 0) == LTC_MP_LT) {
+ if ((err = mp_add(R->x, modulus, R->x)) != CRYPT_OK) { goto done; }
+ }
+ /* X = X - Y */
+ if ((err = mp_sub(R->x, R->y, R->x)) != CRYPT_OK) { goto done; }
+ if (mp_cmp_d(R->x, 0) == LTC_MP_LT) {
+ if ((err = mp_add(R->x, modulus, R->x)) != CRYPT_OK) { goto done; }
+ }
+
+ /* Y = Y - X */
+ if ((err = mp_sub(R->y, R->x, R->y)) != CRYPT_OK) { goto done; }
+ if (mp_cmp_d(R->y, 0) == LTC_MP_LT) {
+ if ((err = mp_add(R->y, modulus, R->y)) != CRYPT_OK) { goto done; }
+ }
+ /* Y = Y * T1 */
+ if ((err = mp_mul(R->y, t1, R->y)) != CRYPT_OK) { goto done; }
+ if ((err = mp_montgomery_reduce(R->y, modulus, mp)) != CRYPT_OK) { goto done; }
+ /* Y = Y - T2 */
+ if ((err = mp_sub(R->y, t2, R->y)) != CRYPT_OK) { goto done; }
+ if (mp_cmp_d(R->y, 0) == LTC_MP_LT) {
+ if ((err = mp_add(R->y, modulus, R->y)) != CRYPT_OK) { goto done; }
+ }
+
+ err = CRYPT_OK;
+done:
+ mp_clear_multi(t1, t2, NULL);
+ return err;
+}
+#endif
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
+
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