Diff: wolfcrypt/src/fe_low_mem.c

Revision:

13:f67a6c6013ca

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/wolfcrypt/src/fe_low_mem.c	Tue Aug 22 10:48:22 2017 +0000
@@ -0,0 +1,603 @@
+/* fe_low_mem.c
+ *
+ * Copyright (C) 2006-2016 wolfSSL Inc.
+ *
+ * This file is part of wolfSSL.
+ *
+ * wolfSSL is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * wolfSSL 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 General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
+ */
+
+
+/* Based from Daniel Beer's public domain work. */
+
+#ifdef HAVE_CONFIG_H
+    #include <config.h>
+#endif
+
+#include <wolfssl/wolfcrypt/settings.h>
+
+#if defined(HAVE_CURVE25519) || defined(HAVE_ED25519)
+#if defined(CURVE25519_SMALL) || defined(ED25519_SMALL) /* use slower code that takes less memory */
+
+#include <wolfssl/wolfcrypt/fe_operations.h>
+
+#ifdef NO_INLINE
+    #include <wolfssl/wolfcrypt/misc.h>
+#else
+    #define WOLFSSL_MISC_INCLUDED
+    #include <wolfcrypt/src/misc.c>
+#endif
+
+
+void fprime_copy(byte *x, const byte *a)
+{
+    int i;
+    for (i = 0; i < F25519_SIZE; i++)
+        x[i] = a[i];
+}
+
+
+void lm_copy(byte* x, const byte* a)
+{
+    int i;
+    for (i = 0; i < F25519_SIZE; i++)
+        x[i] = a[i];
+}
+
+
+#ifdef CURVE25519_SMALL
+/* Double an X-coordinate */
+static void xc_double(byte *x3, byte *z3,
+		      const byte *x1, const byte *z1)
+{
+	/* Explicit formulas database: dbl-1987-m
+	 *
+	 * source 1987 Montgomery "Speeding the Pollard and elliptic
+	 *   curve methods of factorization", page 261, fourth display
+	 * compute X3 = (X1^2-Z1^2)^2
+	 * compute Z3 = 4 X1 Z1 (X1^2 + a X1 Z1 + Z1^2)
+	 */
+	byte x1sq[F25519_SIZE];
+	byte z1sq[F25519_SIZE];
+	byte x1z1[F25519_SIZE];
+	byte a[F25519_SIZE];
+
+	fe_mul__distinct(x1sq, x1, x1);
+	fe_mul__distinct(z1sq, z1, z1);
+	fe_mul__distinct(x1z1, x1, z1);
+
+	lm_sub(a, x1sq, z1sq);
+	fe_mul__distinct(x3, a, a);
+
+	fe_mul_c(a, x1z1, 486662);
+	lm_add(a, x1sq, a);
+	lm_add(a, z1sq, a);
+	fe_mul__distinct(x1sq, x1z1, a);
+	fe_mul_c(z3, x1sq, 4);
+}
+
+
+/* Differential addition */
+static void xc_diffadd(byte *x5, byte *z5,
+		       const byte *x1, const byte *z1,
+		       const byte *x2, const byte *z2,
+		       const byte *x3, const byte *z3)
+{
+	/* Explicit formulas database: dbl-1987-m3
+	 *
+	 * source 1987 Montgomery "Speeding the Pollard and elliptic curve
+	 *   methods of factorization", page 261, fifth display, plus
+	 *   common-subexpression elimination
+	 * compute A = X2+Z2
+	 * compute B = X2-Z2
+	 * compute C = X3+Z3
+	 * compute D = X3-Z3
+	 * compute DA = D A
+	 * compute CB = C B
+	 * compute X5 = Z1(DA+CB)^2
+	 * compute Z5 = X1(DA-CB)^2
+	 */
+	byte da[F25519_SIZE];
+	byte cb[F25519_SIZE];
+	byte a[F25519_SIZE];
+	byte b[F25519_SIZE];
+
+	lm_add(a, x2, z2);
+	lm_sub(b, x3, z3); /* D */
+	fe_mul__distinct(da, a, b);
+
+	lm_sub(b, x2, z2);
+	lm_add(a, x3, z3); /* C */
+	fe_mul__distinct(cb, a, b);
+
+	lm_add(a, da, cb);
+	fe_mul__distinct(b, a, a);
+	fe_mul__distinct(x5, z1, b);
+
+	lm_sub(a, da, cb);
+	fe_mul__distinct(b, a, a);
+	fe_mul__distinct(z5, x1, b);
+}
+
+#ifndef FREESCALE_LTC_ECC
+int curve25519(byte *result, byte *e, byte *q)
+{
+	/* Current point: P_m */
+	byte xm[F25519_SIZE];
+	byte zm[F25519_SIZE] = {1};
+
+	/* Predecessor: P_(m-1) */
+	byte xm1[F25519_SIZE] = {1};
+	byte zm1[F25519_SIZE] = {0};
+
+	int i;
+
+	/* Note: bit 254 is assumed to be 1 */
+	lm_copy(xm, q);
+
+	for (i = 253; i >= 0; i--) {
+		const int bit = (e[i >> 3] >> (i & 7)) & 1;
+		byte xms[F25519_SIZE];
+		byte zms[F25519_SIZE];
+
+		/* From P_m and P_(m-1), compute P_(2m) and P_(2m-1) */
+		xc_diffadd(xm1, zm1, q, f25519_one, xm, zm, xm1, zm1);
+		xc_double(xm, zm, xm, zm);
+
+		/* Compute P_(2m+1) */
+		xc_diffadd(xms, zms, xm1, zm1, xm, zm, q, f25519_one);
+
+		/* Select:
+		 *   bit = 1 --> (P_(2m+1), P_(2m))
+		 *   bit = 0 --> (P_(2m), P_(2m-1))
+		 */
+		fe_select(xm1, xm1, xm, bit);
+		fe_select(zm1, zm1, zm, bit);
+		fe_select(xm, xm, xms, bit);
+		fe_select(zm, zm, zms, bit);
+	}
+
+	/* Freeze out of projective coordinates */
+	fe_inv__distinct(zm1, zm);
+	fe_mul__distinct(result, zm1, xm);
+	fe_normalize(result);
+    return 0;
+}
+#endif /* !FREESCALE_LTC_ECC */
+#endif /* CURVE25519_SMALL */
+
+
+static void raw_add(byte *x, const byte *p)
+{
+	word16 c = 0;
+	int i;
+
+	for (i = 0; i < F25519_SIZE; i++) {
+		c += ((word16)x[i]) + ((word16)p[i]);
+		x[i] = (byte)c;
+		c >>= 8;
+	}
+}
+
+
+static void raw_try_sub(byte *x, const byte *p)
+{
+	byte minusp[F25519_SIZE];
+	word16 c = 0;
+	int i;
+
+	for (i = 0; i < F25519_SIZE; i++) {
+		c = ((word16)x[i]) - ((word16)p[i]) - c;
+		minusp[i] = (byte)c;
+		c = (c >> 8) & 1;
+	}
+
+	fprime_select(x, minusp, x, (byte)c);
+}
+
+
+static int prime_msb(const byte *p)
+{
+    int i;
+    byte x;
+    int shift = 1;
+    int z     = F25519_SIZE - 1;
+
+   /*
+       Test for any hot bits.
+       As soon as one instance is encountered set shift to 0.
+    */
+	for (i = F25519_SIZE - 1; i >= 0; i--) {
+        shift &= ((shift ^ ((-p[i] | p[i]) >> 7)) & 1);
+        z -= shift;
+    }
+	x = p[z];
+	z <<= 3;
+    shift = 1;
+    for (i = 0; i < 8; i++) {
+        shift &= ((-(x >> i) | (x >> i)) >> (7 - i) & 1);
+        z += shift;
+    }
+
+	return z - 1;
+}
+
+
+void fprime_select(byte *dst, const byte *zero, const byte *one, byte condition)
+{
+	const byte mask = -condition;
+	int i;
+
+	for (i = 0; i < F25519_SIZE; i++)
+		dst[i] = zero[i] ^ (mask & (one[i] ^ zero[i]));
+}
+
+
+void fprime_add(byte *r, const byte *a, const byte *modulus)
+{
+	raw_add(r, a);
+	raw_try_sub(r, modulus);
+}
+
+
+void fprime_sub(byte *r, const byte *a, const byte *modulus)
+{
+	raw_add(r, modulus);
+	raw_try_sub(r, a);
+	raw_try_sub(r, modulus);
+}
+
+
+void fprime_mul(byte *r, const byte *a, const byte *b,
+		const byte *modulus)
+{
+	word16 c = 0;
+	int i,j;
+
+	XMEMSET(r, 0, F25519_SIZE);
+
+	for (i = prime_msb(modulus); i >= 0; i--) {
+		const byte bit = (b[i >> 3] >> (i & 7)) & 1;
+		byte plusa[F25519_SIZE];
+
+	    for (j = 0; j < F25519_SIZE; j++) {
+		    c |= ((word16)r[j]) << 1;
+		    r[j] = (byte)c;
+		    c >>= 8;
+	    }
+		raw_try_sub(r, modulus);
+
+		fprime_copy(plusa, r);
+		fprime_add(plusa, a, modulus);
+
+		fprime_select(r, r, plusa, bit);
+	}
+}
+
+
+void fe_load(byte *x, word32 c)
+{
+	word32 i;
+
+	for (i = 0; i < sizeof(c); i++) {
+		x[i] = c;
+		c >>= 8;
+	}
+
+	for (; i < F25519_SIZE; i++)
+		x[i] = 0;
+}
+
+
+void fe_normalize(byte *x)
+{
+	byte minusp[F25519_SIZE];
+	word16 c;
+	int i;
+
+	/* Reduce using 2^255 = 19 mod p */
+	c = (x[31] >> 7) * 19;
+	x[31] &= 127;
+
+	for (i = 0; i < F25519_SIZE; i++) {
+		c += x[i];
+		x[i] = (byte)c;
+		c >>= 8;
+	}
+
+	/* The number is now less than 2^255 + 18, and therefore less than
+	 * 2p. Try subtracting p, and conditionally load the subtracted
+	 * value if underflow did not occur.
+	 */
+	c = 19;
+
+	for (i = 0; i + 1 < F25519_SIZE; i++) {
+		c += x[i];
+		minusp[i] = (byte)c;
+		c >>= 8;
+	}
+
+	c += ((word16)x[i]) - 128;
+	minusp[31] = (byte)c;
+
+	/* Load x-p if no underflow */
+	fe_select(x, minusp, x, (c >> 15) & 1);
+}
+
+
+void fe_select(byte *dst,
+		   const byte *zero, const byte *one,
+		   byte condition)
+{
+	const byte mask = -condition;
+	int i;
+
+	for (i = 0; i < F25519_SIZE; i++)
+		dst[i] = zero[i] ^ (mask & (one[i] ^ zero[i]));
+}
+
+
+void lm_add(byte* r, const byte* a, const byte* b)
+{
+	word16 c = 0;
+	int i;
+
+	/* Add */
+	for (i = 0; i < F25519_SIZE; i++) {
+		c >>= 8;
+		c += ((word16)a[i]) + ((word16)b[i]);
+		r[i] = (byte)c;
+	}
+
+	/* Reduce with 2^255 = 19 mod p */
+	r[31] &= 127;
+	c = (c >> 7) * 19;
+
+	for (i = 0; i < F25519_SIZE; i++) {
+		c += r[i];
+		r[i] = (byte)c;
+		c >>= 8;
+	}
+}
+
+
+void lm_sub(byte* r, const byte* a, const byte* b)
+{
+	word32 c = 0;
+	int i;
+
+	/* Calculate a + 2p - b, to avoid underflow */
+	c = 218;
+	for (i = 0; i + 1 < F25519_SIZE; i++) {
+		c += 65280 + ((word32)a[i]) - ((word32)b[i]);
+		r[i] = c;
+		c >>= 8;
+	}
+
+	c += ((word32)a[31]) - ((word32)b[31]);
+	r[31] = c & 127;
+	c = (c >> 7) * 19;
+
+	for (i = 0; i < F25519_SIZE; i++) {
+		c += r[i];
+		r[i] = c;
+		c >>= 8;
+	}
+}
+
+
+void lm_neg(byte* r, const byte* a)
+{
+	word32 c = 0;
+	int i;
+
+	/* Calculate 2p - a, to avoid underflow */
+	c = 218;
+	for (i = 0; i + 1 < F25519_SIZE; i++) {
+		c += 65280 - ((word32)a[i]);
+		r[i] = c;
+		c >>= 8;
+	}
+
+	c -= ((word32)a[31]);
+	r[31] = c & 127;
+	c = (c >> 7) * 19;
+
+	for (i = 0; i < F25519_SIZE; i++) {
+		c += r[i];
+		r[i] = c;
+		c >>= 8;
+	}
+}
+
+
+void fe_mul__distinct(byte *r, const byte *a, const byte *b)
+{
+	word32 c = 0;
+	int i;
+
+	for (i = 0; i < F25519_SIZE; i++) {
+		int j;
+
+		c >>= 8;
+		for (j = 0; j <= i; j++)
+			c += ((word32)a[j]) * ((word32)b[i - j]);
+
+		for (; j < F25519_SIZE; j++)
+			c += ((word32)a[j]) *
+			     ((word32)b[i + F25519_SIZE - j]) * 38;
+
+		r[i] = c;
+	}
+
+	r[31] &= 127;
+	c = (c >> 7) * 19;
+
+	for (i = 0; i < F25519_SIZE; i++) {
+		c += r[i];
+		r[i] = c;
+		c >>= 8;
+	}
+}
+
+
+void lm_mul(byte *r, const byte* a, const byte *b)
+{
+	byte tmp[F25519_SIZE];
+
+	fe_mul__distinct(tmp, a, b);
+	lm_copy(r, tmp);
+}
+
+
+void fe_mul_c(byte *r, const byte *a, word32 b)
+{
+	word32 c = 0;
+	int i;
+
+	for (i = 0; i < F25519_SIZE; i++) {
+		c >>= 8;
+		c += b * ((word32)a[i]);
+		r[i] = c;
+	}
+
+	r[31] &= 127;
+	c >>= 7;
+	c *= 19;
+
+	for (i = 0; i < F25519_SIZE; i++) {
+		c += r[i];
+		r[i] = c;
+		c >>= 8;
+	}
+}
+
+
+void fe_inv__distinct(byte *r, const byte *x)
+{
+	byte s[F25519_SIZE];
+	int i;
+
+	/* This is a prime field, so by Fermat's little theorem:
+	 *
+	 *     x^(p-1) = 1 mod p
+	 *
+	 * Therefore, raise to (p-2) = 2^255-21 to get a multiplicative
+	 * inverse.
+	 *
+	 * This is a 255-bit binary number with the digits:
+	 *
+	 *     11111111... 01011
+	 *
+	 * We compute the result by the usual binary chain, but
+	 * alternate between keeping the accumulator in r and s, so as
+	 * to avoid copying temporaries.
+	 */
+
+	/* 1 1 */
+	fe_mul__distinct(s, x, x);
+	fe_mul__distinct(r, s, x);
+
+	/* 1 x 248 */
+	for (i = 0; i < 248; i++) {
+		fe_mul__distinct(s, r, r);
+		fe_mul__distinct(r, s, x);
+	}
+
+	/* 0 */
+	fe_mul__distinct(s, r, r);
+
+	/* 1 */
+	fe_mul__distinct(r, s, s);
+	fe_mul__distinct(s, r, x);
+
+	/* 0 */
+	fe_mul__distinct(r, s, s);
+
+	/* 1 */
+	fe_mul__distinct(s, r, r);
+	fe_mul__distinct(r, s, x);
+
+	/* 1 */
+	fe_mul__distinct(s, r, r);
+	fe_mul__distinct(r, s, x);
+}
+
+
+void lm_invert(byte *r, const byte *x)
+{
+	byte tmp[F25519_SIZE];
+
+	fe_inv__distinct(tmp, x);
+	lm_copy(r, tmp);
+}
+
+
+/* Raise x to the power of (p-5)/8 = 2^252-3, using s for temporary
+ * storage.
+ */
+static void exp2523(byte *r, const byte *x, byte *s)
+{
+	int i;
+
+	/* This number is a 252-bit number with the binary expansion:
+	 *
+	 *     111111... 01
+	 */
+
+	/* 1 1 */
+	fe_mul__distinct(r, x, x);
+	fe_mul__distinct(s, r, x);
+
+	/* 1 x 248 */
+	for (i = 0; i < 248; i++) {
+		fe_mul__distinct(r, s, s);
+		fe_mul__distinct(s, r, x);
+	}
+
+	/* 0 */
+	fe_mul__distinct(r, s, s);
+
+	/* 1 */
+	fe_mul__distinct(s, r, r);
+	fe_mul__distinct(r, s, x);
+}
+
+
+void fe_sqrt(byte *r, const byte *a)
+{
+	byte v[F25519_SIZE];
+	byte i[F25519_SIZE];
+	byte x[F25519_SIZE];
+	byte y[F25519_SIZE];
+
+	/* v = (2a)^((p-5)/8) [x = 2a] */
+	fe_mul_c(x, a, 2);
+	exp2523(v, x, y);
+
+	/* i = 2av^2 - 1 */
+	fe_mul__distinct(y, v, v);
+	fe_mul__distinct(i, x, y);
+	fe_load(y, 1);
+	lm_sub(i, i, y);
+
+	/* r = avi */
+	fe_mul__distinct(x, v, a);
+	fe_mul__distinct(r, x, i);
+}
+
+#endif /* CURVE25519_SMALL || ED25519_SMALL */
+#endif /* HAVE_CURVE25519 || HAVE_ED25519 */
+