libuecc v7

Update CHANGELOG
Improve ecc_25519_scalarmult_base documentation
2025-04-19 18:45:09 +02:00 · 2016-03-27 01:37:26 +01:00 · 2016-03-19 14:02:43 +01:00 · 2016-03-19 13:59:30 +01:00 · 2016-03-19 00:51:39 +01:00 · 2016-03-19 00:51:31 +01:00
4 changed files with 230 additions and 146 deletions
--- a/19
+++ b/19
@ -1,3 +1,22 @@
+libuecc v7 (2016/03/27)
+
+* Change conversion between Ed25519 and legacy representation. This should
+    not affect any operations unless Ed25519 and legacy load/store
+    functions are mixed when accessing a work structure. Doing so is now
+    officially supported, for example to convert a legacy public key to
+    Ed25519 format.
+* The changed representation allows to use the same
+    ecc_25519_work_default_base for both Ed25519 and legacy.
+    ecc_25519_work_default_base and ecc_25519_scalarmult_base have been
+    undeprecated, ecc_25519_work_base_ed25519 and
+    ecc_25519_work_base_legacy are deprecated now.
+* All points are now internally represented with Ed25519 coordinates, which
+    allows about 6% faster scalar multplication than the legacy
+    representation.
+* ecc_25519_scalarmult_base has been further optimized, making it another
+    6% faster than normal ecc_25519_scalarmult.
+
+
 libuecc v6 (2015/10/25)

 * Fixes a bug which might have caused a point's y coordinate to be negated
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@ -1,6 +1,6 @@
 cmake_minimum_required(VERSION 2.6)
 project(LIBUECC C)
-set(PROJECT_VERSION 6)
+set(PROJECT_VERSION 7)

 set(CMAKE_MODULE_PATH ${LIBUECC_SOURCE_DIR})

--- a/include/libuecc/ecc.h
+++ b/include/libuecc/ecc.h
@ -68,33 +68,27 @@ extern const ecc_25519_work_t ecc_25519_work_identity;


 /**
- * The generator point used by Ed25519
+ * The Ed25519 default generator point
 *
- * \ref ecc_25519_work_base_ed25519 is the inverse of \ref ecc_25519_work_base_legacy
+ * \deprecated Use the equivalent \ref ecc_25519_work_default_base instead.
 *
- * The order of the base point is \f$ 2^{252} + 27742317777372353535851937790883648493 \f$.
 **/
-extern const ecc_25519_work_t ecc_25519_work_base_ed25519;
+DEPRECATED extern const ecc_25519_work_t ecc_25519_work_base_ed25519;

 /**
- * The ec25519 legacy generator point ("default base" till libuecc v5)
+ * The Ed25519 default generator point
 *
- * In new software that doesn't need compablity with older libuecc releases, you should consider
- * using \ref ecc_25519_work_base_ed25519 instead.
- *
- * \ref ecc_25519_work_base_legacy is the inverse of \ref ecc_25519_work_base_ed25519
+ * \deprecated Use the equivalent \ref ecc_25519_work_default_base instead.
+ */
+DEPRECATED extern const ecc_25519_work_t ecc_25519_work_base_legacy;
+
+
+/**
+ * The Ed25519 default generator point
 *
 * The order of the base point is \f$ 2^{252} + 27742317777372353535851937790883648493 \f$.
 */
-extern const ecc_25519_work_t ecc_25519_work_base_legacy;
-
-
-/**
- * The ec25519 legacy generator point (provided for API/ABI compatiblity with older releases of libuecc)
- *
- * \deprecated Use \ref ecc_25519_work_base_legacy instead.
- */
-DEPRECATED extern const ecc_25519_work_t ecc_25519_work_default_base;
+extern const ecc_25519_work_t ecc_25519_work_default_base;


 /** Loads a point of the Ed25519 curve with given coordinates into its unpacked representation */
@ -255,20 +249,20 @@ void ecc_25519_scalarmult(ecc_25519_work_t *out, const ecc_int256_t *n, const ec
 *
 * The order of the base point is \f$ 2^{252} + 27742317777372353535851937790883648493 \f$.
 *
- * See the notes about \ref ecc_25519_scalarmult_bits before using this function.
+ * ecc_25519_scalarmult_base_bits(out, n, bits) is faster than ecc_25519_scalarmult_bits(out, n, &ecc_25519_work_default_base, bits).
 *
- * \deprecated Use \ref ecc_25519_scalarmult_bits and explicitly specify the base point.
+ * See the notes about \ref ecc_25519_scalarmult_bits before using this function.
 */
-DEPRECATED void ecc_25519_scalarmult_base_bits(ecc_25519_work_t *out, const ecc_int256_t *n, unsigned bits);
+void ecc_25519_scalarmult_base_bits(ecc_25519_work_t *out, const ecc_int256_t *n, unsigned bits);

 /**
 * Does a scalar multiplication of the default base point (generator element) of the Elliptic Curve with an integer
 *
 * The order of the base point is \f$ 2^{252} + 27742317777372353535851937790883648493 \f$.
 *
- * \deprecated Use \ref ecc_25519_scalarmult and explicitly specify the base point.
+ * ecc_25519_scalarmult_base(out, n) is faster than ecc_25519_scalarmult(out, n, &ecc_25519_work_default_base).
 */
-DEPRECATED void ecc_25519_scalarmult_base(ecc_25519_work_t *out, const ecc_int256_t *n);
+void ecc_25519_scalarmult_base(ecc_25519_work_t *out, const ecc_int256_t *n);

 /**@}*/

--- a/src/ec25519.c
+++ b/src/ec25519.c
@ -41,7 +41,7 @@
 * which is the curve used by the Ed25519 algorithm. The functions for this curve
 * have the suffix \em ed25519.
 *
- * Internally, libuecc always uses the former representation for its \em work structure.
+ * Internally, libuecc always uses the latter representation for its \em work structure.
 *
 * The curves are equivalent to the Montgomery Curve used in D. J. Bernstein's
 * Curve25519 Diffie-Hellman algorithm.
@ -62,73 +62,88 @@
 const ecc_25519_work_t ecc_25519_work_identity = {{0}, {1}, {1}, {0}};

 const ecc_25519_work_t ecc_25519_work_base_legacy = {
-	{0xd4, 0x6b, 0xfe, 0x7f, 0x39, 0xfa, 0x8c, 0x22,
-	 0xe1, 0x96, 0x23, 0xeb, 0x26, 0xb7, 0x8e, 0x6a,
-	 0x34, 0x74, 0x8b, 0x66, 0xd6, 0xa3, 0x26, 0xdd,
-	 0x19, 0x5e, 0x9f, 0x21, 0x50, 0x43, 0x7c, 0x54},
+	{0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9,
+	 0xb2, 0xa7, 0x25, 0x95, 0x60, 0xc7, 0x2c, 0x69,
+	 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
+	 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21},
 	{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
 	 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
 	 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
 	 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66},
 	{1},
-	{0x47, 0x56, 0x98, 0x99, 0xc7, 0x61, 0x0a, 0x82,
-	 0x1a, 0xdf, 0x82, 0x22, 0x1f, 0x2c, 0x72, 0x88,
-	 0xc3, 0x29, 0x09, 0x52, 0x78, 0xe9, 0x1e, 0xe4,
-	 0x47, 0x4b, 0x4c, 0x81, 0xa6, 0x02, 0xfd, 0x29}
+	{0xa3, 0xdd, 0xb7, 0xa5, 0xb3, 0x8a, 0xde, 0x6d,
+	 0xf5, 0x52, 0x51, 0x77, 0x80, 0x9f, 0xf0, 0x20,
+	 0x7d, 0xe3, 0xab, 0x64, 0x8e, 0x4e, 0xea, 0x66,
+	 0x65, 0x76, 0x8b, 0xd7, 0x0f, 0x5f, 0x87, 0x67},
 };

 const ecc_25519_work_t ecc_25519_work_default_base = {
-	{0xd4, 0x6b, 0xfe, 0x7f, 0x39, 0xfa, 0x8c, 0x22,
-	 0xe1, 0x96, 0x23, 0xeb, 0x26, 0xb7, 0x8e, 0x6a,
-	 0x34, 0x74, 0x8b, 0x66, 0xd6, 0xa3, 0x26, 0xdd,
-	 0x19, 0x5e, 0x9f, 0x21, 0x50, 0x43, 0x7c, 0x54},
+	{0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9,
+	 0xb2, 0xa7, 0x25, 0x95, 0x60, 0xc7, 0x2c, 0x69,
+	 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
+	 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21},
 	{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
 	 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
 	 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
 	 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66},
 	{1},
-	{0x47, 0x56, 0x98, 0x99, 0xc7, 0x61, 0x0a, 0x82,
-	 0x1a, 0xdf, 0x82, 0x22, 0x1f, 0x2c, 0x72, 0x88,
-	 0xc3, 0x29, 0x09, 0x52, 0x78, 0xe9, 0x1e, 0xe4,
-	 0x47, 0x4b, 0x4c, 0x81, 0xa6, 0x02, 0xfd, 0x29}
+	{0xa3, 0xdd, 0xb7, 0xa5, 0xb3, 0x8a, 0xde, 0x6d,
+	 0xf5, 0x52, 0x51, 0x77, 0x80, 0x9f, 0xf0, 0x20,
+	 0x7d, 0xe3, 0xab, 0x64, 0x8e, 0x4e, 0xea, 0x66,
+	 0x65, 0x76, 0x8b, 0xd7, 0x0f, 0x5f, 0x87, 0x67},
 };


 const ecc_25519_work_t ecc_25519_work_base_ed25519 = {
-	{0x19, 0x94, 0x01, 0x80, 0xc6, 0x05, 0x73, 0xdd,
-	 0x1e, 0x69, 0xdc, 0x14, 0xd9, 0x48, 0x71, 0x95,
-	 0xcb, 0x8b, 0x74, 0x99, 0x29, 0x5c, 0xd9, 0x22,
-	 0xe6, 0xa1, 0x60, 0xde, 0xaf, 0xbc, 0x83, 0x2b},
+	{0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9,
+	 0xb2, 0xa7, 0x25, 0x95, 0x60, 0xc7, 0x2c, 0x69,
+	 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
+	 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21},
 	{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
 	 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
 	 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
 	 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66},
 	{1},
-	{0xa6, 0xa9, 0x67, 0x66, 0x38, 0x9e, 0xf5, 0x7d,
-	 0xe5, 0x20, 0x7d, 0xdd, 0xe0, 0xd3, 0x8d, 0x77,
-	 0x3c, 0xd6, 0xf6, 0xad, 0x87, 0x16, 0xe1, 0x1b,
-	 0xb8, 0xb4, 0xb3, 0x7e, 0x59, 0xfd, 0x02, 0x56},
+	{0xa3, 0xdd, 0xb7, 0xa5, 0xb3, 0x8a, 0xde, 0x6d,
+	 0xf5, 0x52, 0x51, 0x77, 0x80, 0x9f, 0xf0, 0x20,
+	 0x7d, 0xe3, 0xab, 0x64, 0x8e, 0x4e, 0xea, 0x66,
+	 0x65, 0x76, 0x8b, 0xd7, 0x0f, 0x5f, 0x87, 0x67},
 };


 static const uint32_t zero[32] = {0};
 static const uint32_t one[32] = {1};

+static const uint32_t minus1[32] = {
+	0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f,
+};
+
+/** Ed25519 parameter -(121665/121666) */
+static const uint32_t d[32] = {
+	0xa3, 0x78, 0x59, 0x13, 0xca, 0x4d, 0xeb, 0x75,
+	0xab, 0xd8, 0x41, 0x41, 0x4d, 0x0a, 0x70, 0x00,
+	0x98, 0xe8, 0x79, 0x77, 0x79, 0x40, 0xc7, 0x8c,
+	0x73, 0xfe, 0x6f, 0x2b, 0xee, 0x6c, 0x03, 0x52,
+};
+

 /** Factor to multiply the X coordinate with to convert from the legacy to the Ed25519 curve */
 static const uint32_t legacy_to_ed25519[32] = {
-	0x06, 0x7e, 0x45, 0xff, 0xaa, 0x04, 0x6e, 0xcc,
-	0x82, 0x1a, 0x7d, 0x4b, 0xd1, 0xd3, 0xa1, 0xc5,
-	0x7e, 0x4f, 0xfc, 0x03, 0xdc, 0x08, 0x7b, 0xd2,
-	0xbb, 0x06, 0xa0, 0x60, 0xf4, 0xed, 0x26, 0x0f,
+	0xe7, 0x81, 0xba, 0x00, 0x55, 0xfb, 0x91, 0x33,
+	0x7d, 0xe5, 0x82, 0xb4, 0x2e, 0x2c, 0x5e, 0x3a,
+	0x81, 0xb0, 0x03, 0xfc, 0x23, 0xf7, 0x84, 0x2d,
+	0x44, 0xf9, 0x5f, 0x9f, 0x0b, 0x12, 0xd9, 0x70,
 };

 /** Factor to multiply the X coordinate with to convert from the Ed25519 to the legacy curve */
 static const uint32_t ed25519_to_legacy[32] = {
-	0x04, 0x97, 0xbd, 0x24, 0x50, 0xfb, 0x4b, 0xbf,
-	0x5e, 0x2a, 0xbc, 0x0d, 0x06, 0xc7, 0xce, 0xd7,
-	0xfe, 0xe8, 0xfa, 0x98, 0x64, 0x7e, 0x9e, 0x07,
-	0x56, 0xa4, 0xc1, 0x95, 0xdf, 0x98, 0xb4, 0x5b,
+	0xe9, 0x68, 0x42, 0xdb, 0xaf, 0x04, 0xb4, 0x40,
+	0xa1, 0xd5, 0x43, 0xf2, 0xf9, 0x38, 0x31, 0x28,
+	0x01, 0x17, 0x05, 0x67, 0x9b, 0x81, 0x61, 0xf8,
+	0xa9, 0x5b, 0x3e, 0x6a, 0x20, 0x67, 0x4b, 0x24,
 };


@ -233,7 +248,7 @@ static void freeze(uint32_t a[32]) {
 *
 * The input must be \em squeezed.
 */
-static int parity(uint32_t a[32]) {
+static int parity(const uint32_t a[32]) {
 	uint32_t b[32];

 	add(b, a, minusp);
@ -395,13 +410,6 @@ static void select(uint32_t out[32], const uint32_t r[32], const uint32_t s[32],
 * If the given integer has no square root, 0 is returned, 1 otherwise.
 */
 static int square_root(uint32_t out[32], const uint32_t z[32]) {
-	static const uint32_t minus1[32] = {
-		0xec, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-		0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f
-	};
-
 	static const uint32_t rho_s[32] = {
 		0xb0, 0xa0, 0x0e, 0x4a, 0x27, 0x1b, 0xee, 0xc4,
 		0x78, 0xe4, 0x2f, 0xad, 0x06, 0x18, 0x43, 0x2f,
@ -557,20 +565,22 @@ static void recip(uint32_t out[32], const uint32_t z[32]) {
 /**
 * Checks if the X and Y coordinates of a work structure represent a valid point of the curve
 *
- * Also fills out the T coordinate.
+ * Also fills in the T coordinate.
 */
 static int check_load_xy(ecc_25519_work_t *val) {
-	uint32_t X2[32], Y2[32], aX2[32], dX2[32], dX2Y2[32], aX2_Y2[32], _1_dX2Y2[32], r[32];
+	uint32_t X2[32], Y2[32], dX2[32], dX2Y2[32], Y2_X2[32], Y2_X2_1[32], r[32];

 	/* Check validity */
 	square(X2, val->X);
 	square(Y2, val->Y);
-	mult_int(aX2, UINT32_C(486664), X2);
-	mult_int(dX2, UINT32_C(486660), X2);
+
+	mult(dX2, d, X2);
 	mult(dX2Y2, dX2, Y2);
-	add(aX2_Y2, aX2, Y2);
-	add(_1_dX2Y2, one, dX2Y2);
-	sub(r, aX2_Y2, _1_dX2Y2);
+
+	sub(Y2_X2, Y2, X2);
+	sub(Y2_X2_1, Y2_X2, one);
+
+	sub(r, Y2_X2_1, dX2Y2);
 	squeeze(r);

 	if (!check_zero(r))
@ -583,21 +593,6 @@ static int check_load_xy(ecc_25519_work_t *val) {

 int ecc_25519_load_xy_ed25519(ecc_25519_work_t *out, const ecc_int256_t *x, const ecc_int256_t *y) {
 	int i;
-	uint32_t tmp[32];
-
-	for (i = 0; i < 32; i++) {
-		tmp[i] = x->p[i];
-		out->Y[i] = y->p[i];
-		out->Z[i] = (i == 0);
-	}
-
-	mult(out->X, tmp, ed25519_to_legacy);
-
-	return check_load_xy(out);
-}
-
-int ecc_25519_load_xy_legacy(ecc_25519_work_t *out, const ecc_int256_t *x, const ecc_int256_t *y) {
-	int i;

 	for (i = 0; i < 32; i++) {
 		out->X[i] = x->p[i];
@ -608,34 +603,27 @@ int ecc_25519_load_xy_legacy(ecc_25519_work_t *out, const ecc_int256_t *x, const
 	return check_load_xy(out);
 }

+int ecc_25519_load_xy_legacy(ecc_25519_work_t *out, const ecc_int256_t *x, const ecc_int256_t *y) {
+	int i;
+	uint32_t tmp[32];
+
+	for (i = 0; i < 32; i++) {
+		tmp[i] = x->p[i];
+		out->Y[i] = y->p[i];
+		out->Z[i] = (i == 0);
+	}
+
+	mult(out->X, tmp, legacy_to_ed25519);
+
+	return check_load_xy(out);
+}
+
 int ecc_25519_load_xy(ecc_25519_work_t *out, const ecc_int256_t *x, const ecc_int256_t *y) {
 	return ecc_25519_load_xy_legacy(out, x, y);
 }


 void ecc_25519_store_xy_ed25519(ecc_int256_t *x, ecc_int256_t *y, const ecc_25519_work_t *in) {
-	uint32_t X[32], tmp[32], Y[32], Z[32];
-	int i;
-
-	recip(Z, in->Z);
-
-	if (x) {
-		mult(tmp, Z, in->X);
-		mult(X, tmp, legacy_to_ed25519);
-		freeze(X);
-		for (i = 0; i < 32; i++)
-			x->p[i] = X[i];
-	}
-
-	if (y) {
-		mult(Y, Z, in->Y);
-		freeze(Y);
-		for (i = 0; i < 32; i++)
-			y->p[i] = Y[i];
-	}
-}
-
-void ecc_25519_store_xy_legacy(ecc_int256_t *x, ecc_int256_t *y, const ecc_25519_work_t *in) {
 	uint32_t X[32], Y[32], Z[32];
 	int i;

@ -656,16 +644,37 @@ void ecc_25519_store_xy_legacy(ecc_int256_t *x, ecc_int256_t *y, const ecc_25519
 	}
 }

+void ecc_25519_store_xy_legacy(ecc_int256_t *x, ecc_int256_t *y, const ecc_25519_work_t *in) {
+	uint32_t X[32], tmp[32], Y[32], Z[32];
+	int i;
+
+	recip(Z, in->Z);
+
+	if (x) {
+		mult(tmp, Z, in->X);
+		mult(X, tmp, ed25519_to_legacy);
+		freeze(X);
+		for (i = 0; i < 32; i++)
+			x->p[i] = X[i];
+	}
+
+	if (y) {
+		mult(Y, Z, in->Y);
+		freeze(Y);
+		for (i = 0; i < 32; i++)
+			y->p[i] = Y[i];
+	}
+}
+
 void ecc_25519_store_xy(ecc_int256_t *x, ecc_int256_t *y, const ecc_25519_work_t *in) {
 	ecc_25519_store_xy_legacy(x, y, in);
 }


 int ecc_25519_load_packed_ed25519(ecc_25519_work_t *out, const ecc_int256_t *in) {
-	static const uint32_t a[32] = {UINT32_C(486664)};
 	int i;
-	uint32_t Y2[32] /* Y^2 */, dY2[32] /* dY^2 */, _1_Y2[32] /* 1-Y^2 */, a_dY2[32] /* a-dY^2 */, _1_a_dY2[32] /* 1/(a-dY^2) */;
-	uint32_t X2[32] /* X^2 */, X[32], Xt[32], X_ed25519[32];
+	uint32_t Y2[32] /* Y^2 */, dY2[32] /* dY^2 */, Y2_1[32] /* Y^2-1 */, dY2_1[32] /* dY^2+1 */, _1_dY2_1[32] /* 1/(dY^2+1) */;
+	uint32_t X2[32] /* X^2 */, X[32], Xt[32];

 	for (i = 0; i < 32; i++) {
 		out->Y[i] = in->p[i];
@ -675,21 +684,19 @@ int ecc_25519_load_packed_ed25519(ecc_25519_work_t *out, const ecc_int256_t *in)
 	out->Y[31] &= 0x7f;

 	square(Y2, out->Y);
-	mult_int(dY2, UINT32_C(486660), Y2);
-	sub(_1_Y2, one, Y2);
-	sub(a_dY2, a, dY2);
-	recip(_1_a_dY2, a_dY2);
-	mult(X2, _1_Y2, _1_a_dY2);
+	mult(dY2, d, Y2);
+	sub(Y2_1, Y2, one);
+	add(dY2_1, dY2, one);
+	recip(_1_dY2_1, dY2_1);
+	mult(X2, Y2_1, _1_dY2_1);

 	if (!square_root(X, X2))
 		return 0;

-	mult(X_ed25519, X, legacy_to_ed25519);
-
 	/* No squeeze is necessary after subtractions from zero if the subtrahend is squeezed */
 	sub(Xt, zero, X);

-	select(out->X, X, Xt, (in->p[31] >> 7) ^ parity(X_ed25519));
+	select(out->X, X, Xt, (in->p[31] >> 7) ^ parity(X));

 	mult(out->T, out->X, out->Y);

@ -699,16 +706,16 @@ int ecc_25519_load_packed_ed25519(ecc_25519_work_t *out, const ecc_int256_t *in)
 int ecc_25519_load_packed_legacy(ecc_25519_work_t *out, const ecc_int256_t *in) {
 	int i;
 	uint32_t X2[32] /* X^2 */, aX2[32] /* aX^2 */, dX2[32] /* dX^2 */, _1_aX2[32] /* 1-aX^2 */, _1_dX2[32] /* 1-aX^2 */;
-	uint32_t _1_1_dX2[32]  /* 1/(1-aX^2) */, Y2[32] /* Y^2 */, Y[32], Yt[32];
+	uint32_t _1_1_dX2[32]  /* 1/(1-aX^2) */, Y2[32] /* Y^2 */, Y[32], Yt[32], X_legacy[32];

 	for (i = 0; i < 32; i++) {
-		out->X[i] = in->p[i];
+		X_legacy[i] = in->p[i];
 		out->Z[i] = (i == 0);
 	}

-	out->X[31] &= 0x7f;
+	X_legacy[31] &= 0x7f;

-	square(X2, out->X);
+	square(X2, X_legacy);
 	mult_int(aX2, UINT32_C(486664), X2);
 	mult_int(dX2, UINT32_C(486660), X2);
 	sub(_1_aX2, one, aX2);
@ -724,6 +731,7 @@ int ecc_25519_load_packed_legacy(ecc_25519_work_t *out, const ecc_int256_t *in)

 	select(out->Y, Y, Yt, (in->p[31] >> 7) ^ parity(Y));

+	mult(out->X, X_legacy, legacy_to_ed25519);
 	mult(out->T, out->X, out->Y);

 	return 1;
@ -776,20 +784,26 @@ void ecc_25519_negate(ecc_25519_work_t *out, const ecc_25519_work_t *in) {
 }

 void ecc_25519_double(ecc_25519_work_t *out, const ecc_25519_work_t *in) {
-	uint32_t A[32], B[32], C[32], D[32], E[32], F[32], G[32], H[32], t0[32], t1[32], t2[32], t3[32];
+	uint32_t A[32], B[32], C[32], D[32], E[32], F[32], G[32], H[32], t0[32], t1[32];

 	square(A, in->X);
+
 	square(B, in->Y);
+
 	square(t0, in->Z);
 	mult_int(C, 2, t0);
-	mult_int(D, UINT32_C(486664), A);
-	add(t1, in->X, in->Y);
-	square(t2, t1);
-	sub(t3, t2, A);
-	sub(E, t3, B);
+
+	sub(D, zero, A);
+
+	add(t0, in->X, in->Y);
+	square(t1, t0);
+	sub(t0, t1, A);
+	sub(E, t0, B);
+
 	add(G, D, B);
 	sub(F, G, C);
 	sub(H, D, B);
+
 	mult(out->X, E, F);
 	mult(out->Y, G, H);
 	mult(out->T, E, H);
@ -797,22 +811,63 @@ void ecc_25519_double(ecc_25519_work_t *out, const ecc_25519_work_t *in) {
 }

 void ecc_25519_add(ecc_25519_work_t *out, const ecc_25519_work_t *in1, const ecc_25519_work_t *in2) {
-	uint32_t A[32], B[32], C[32], D[32], E[32], F[32], G[32], H[32], t0[32], t1[32], t2[32], t3[32], t4[32], t5[32];
+	const uint32_t j = UINT32_C(60833);
+	const uint32_t k = UINT32_C(121665);
+	uint32_t A[32], B[32], C[32], D[32], E[32], F[32], G[32], H[32], t0[32], t1[32];

-	mult(A, in1->X, in2->X);
-	mult(B, in1->Y, in2->Y);
-	mult_int(t0, UINT32_C(486660), in2->T);
+	sub(t0, in1->Y, in1->X);
+	mult_int(t1, j, t0);
+	sub(t0, in2->Y, in2->X);
+	mult(A, t0, t1);
+
+	add(t0, in1->Y, in1->X);
+	mult_int(t1, j, t0);
+	add(t0, in2->Y, in2->X);
+	mult(B, t0, t1);
+
+	mult_int(t0, k, in2->T);
 	mult(C, in1->T, t0);
-	mult(D, in1->Z, in2->Z);
-	add(t1, in1->X, in1->Y);
-	add(t2, in2->X, in2->Y);
-	mult(t3, t1, t2);
-	sub(t4, t3, A);
-	sub(E, t4, B);
-	sub(F, D, C);
-	add(G, D, C);
-	mult_int(t5, UINT32_C(486664), A);
-	sub(H, B, t5);
+
+	mult_int(t0, 2*j, in2->Z);
+	mult(D, in1->Z, t0);
+
+	sub(E, B, A);
+	add(F, D, C);
+	sub(G, D, C);
+	add(H, B, A);
+
+	mult(out->X, E, F);
+	mult(out->Y, G, H);
+	mult(out->T, E, H);
+	mult(out->Z, F, G);
+}
+
+/** Adds two points of the Elliptic Curve, assuming that in2->Z == 1 */
+static void ecc_25519_add1(ecc_25519_work_t *out, const ecc_25519_work_t *in1, const ecc_25519_work_t *in2) {
+	const uint32_t j = UINT32_C(60833);
+	const uint32_t k = UINT32_C(121665);
+	uint32_t A[32], B[32], C[32], D[32], E[32], F[32], G[32], H[32], t0[32], t1[32];
+
+	sub(t0, in1->Y, in1->X);
+	mult_int(t1, j, t0);
+	sub(t0, in2->Y, in2->X);
+	mult(A, t0, t1);
+
+	add(t0, in1->Y, in1->X);
+	mult_int(t1, j, t0);
+	add(t0, in2->Y, in2->X);
+	mult(B, t0, t1);
+
+	mult_int(t0, k, in2->T);
+	mult(C, in1->T, t0);
+
+	mult_int(D, 2*j, in1->Z);
+
+	sub(E, B, A);
+	add(F, D, C);
+	sub(G, D, C);
+	add(H, B, A);
+
 	mult(out->X, E, F);
 	mult(out->Y, G, H);
 	mult(out->T, E, H);
@ -851,9 +906,25 @@ void ecc_25519_scalarmult(ecc_25519_work_t *out, const ecc_int256_t *n, const ec
 }

 void ecc_25519_scalarmult_base_bits(ecc_25519_work_t *out, const ecc_int256_t *n, unsigned bits) {
-	ecc_25519_scalarmult_bits(out, n, &ecc_25519_work_base_legacy, bits);
+	ecc_25519_work_t Q2, Q2p;
+	ecc_25519_work_t cur = ecc_25519_work_identity;
+	int b, pos;
+
+	if (bits > 256)
+		bits = 256;
+
+	for (pos = bits - 1; pos >= 0; --pos) {
+		b = n->p[pos / 8] >> (pos & 7);
+		b &= 1;
+
+		ecc_25519_double(&Q2, &cur);
+		ecc_25519_add1(&Q2p, &Q2, &ecc_25519_work_default_base);
+		selectw(&cur, &Q2, &Q2p, b);
+	}
+
+	*out = cur;
 }

 void ecc_25519_scalarmult_base(ecc_25519_work_t *out, const ecc_int256_t *n) {
-	ecc_25519_scalarmult(out, n, &ecc_25519_work_base_legacy);
+	ecc_25519_scalarmult_base_bits(out, n, 256);
 }
Author	SHA1	Message	Date
Matthias Schiffer	7c9a6f6af0	libuecc v7	2016-03-27 01:37:26 +01:00
Matthias Schiffer	3eb02ade40	Update CHANGELOG	2016-03-19 14:02:43 +01:00
Matthias Schiffer	b5b4697c1c	Improve ecc_25519_scalarmult_base documentation	2016-03-19 13:59:30 +01:00
Matthias Schiffer	bb87f7b0e8	Optimize ecc_25519_scalarmult_base We can elide one multiplication assuming that Z == 1 for the default base.	2016-03-19 00:51:39 +01:00
Matthias Schiffer	26cbc55f78	Switch internal point representation to the Ed25519 curve The Ed25519 curve allows slightly more efficient addition.	2016-03-19 00:51:31 +01:00
Matthias Schiffer	5ade164170	Deprecate ecc_25519_work_base_ed25519 and ecc_25519_work_base_legacy The deprecation of ecc_25519_work_default_base and ecc_25519_scalarmult_base{,_bits} is reverted, as the Ed25519 and legacy base points are represented in the same way now.	2016-03-18 15:12:46 +01:00
Matthias Schiffer	740355d5dd	Unify legacy and Ed25519 base point by negating conversion factors	2016-03-18 15:03:46 +01:00