wolf SSL
wolfSSL 3.11.1 for TLS1.3 beta
Diff: wolfcrypt/src/ge_low_mem.c
- Revision:
- 13:80fb167dafdf
- Parent:
- 11:cee25a834751
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/wolfcrypt/src/ge_low_mem.c Tue May 30 06:16:19 2017 +0000
@@ -0,0 +1,565 @@
+/* ge_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(CURVED25519_SMALL) /* use slower code that takes less memory */
+#if defined(HAVE_ED25519)
+
+#include <wolfssl/wolfcrypt/ge_operations.h>
+#include <wolfssl/wolfcrypt/error-crypt.h>
+#ifdef NO_INLINE
+ #include <wolfssl/wolfcrypt/misc.h>
+#else
+ #define WOLFSSL_MISC_INCLUDED
+ #include <wolfcrypt/src/misc.c>
+#endif
+
+void ed25519_smult(ge_p3 *r, const ge_p3 *a, const byte *e);
+void ed25519_add(ge_p3 *r, const ge_p3 *a, const ge_p3 *b);
+void ed25519_double(ge_p3 *r, const ge_p3 *a);
+
+
+static const byte ed25519_order[F25519_SIZE] = {
+ 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58,
+ 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10
+};
+
+/*Arithmetic modulo the group order m = 2^252 +
+ 27742317777372353535851937790883648493 =
+ 7237005577332262213973186563042994240857116359379907606001950938285454250989 */
+
+static const word32 m[32] = {
+ 0xED,0xD3,0xF5,0x5C,0x1A,0x63,0x12,0x58,0xD6,0x9C,0xF7,0xA2,0xDE,0xF9,
+ 0xDE,0x14,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+ 0x00,0x00,0x00,0x10
+};
+
+static const word32 mu[33] = {
+ 0x1B,0x13,0x2C,0x0A,0xA3,0xE5,0x9C,0xED,0xA7,0x29,0x63,0x08,0x5D,0x21,
+ 0x06,0x21,0xEB,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+ 0xFF,0xFF,0xFF,0xFF,0x0F
+};
+
+
+int ge_compress_key(byte* out, const byte* xIn, const byte* yIn,
+ word32 keySz)
+{
+ byte tmp[F25519_SIZE];
+ byte parity;
+ byte pt[32];
+ int i;
+
+ fe_copy(tmp, xIn);
+ parity = (tmp[0] & 1) << 7;
+
+ fe_copy(pt, yIn);
+ pt[31] |= parity;
+
+ for(i = 0; i < 32; i++) {
+ out[32-i-1] = pt[i];
+ }
+ (void)keySz;
+ return 0;
+}
+
+
+static word32 lt(word32 a,word32 b) /* 16-bit inputs */
+{
+ unsigned int x = a;
+ x -= (unsigned int) b; /* 0..65535: no; 4294901761..4294967295: yes */
+ x >>= 31; /* 0: no; 1: yes */
+ return x;
+}
+
+
+/* Reduce coefficients of r before calling reduce_add_sub */
+static void reduce_add_sub(word32 *r)
+{
+ word32 pb = 0;
+ word32 b;
+ word32 mask;
+ int i;
+ unsigned char t[32];
+
+ for(i=0;i<32;i++)
+ {
+ pb += m[i];
+ b = lt(r[i],pb);
+ t[i] = r[i]-pb+(b<<8);
+ pb = b;
+ }
+ mask = b - 1;
+ for(i=0;i<32;i++)
+ r[i] ^= mask & (r[i] ^ t[i]);
+}
+
+
+/* Reduce coefficients of x before calling barrett_reduce */
+static void barrett_reduce(word32* r, word32 x[64])
+{
+ /* See HAC, Alg. 14.42 */
+ int i,j;
+ word32 q2[66];
+ word32 *q3 = q2 + 33;
+ word32 r1[33];
+ word32 r2[33];
+ word32 carry;
+ word32 pb = 0;
+ word32 b;
+
+ for (i = 0;i < 66;++i) q2[i] = 0;
+ for (i = 0;i < 33;++i) r2[i] = 0;
+
+ for(i=0;i<33;i++)
+ for(j=0;j<33;j++)
+ if(i+j >= 31) q2[i+j] += mu[i]*x[j+31];
+ carry = q2[31] >> 8;
+ q2[32] += carry;
+ carry = q2[32] >> 8;
+ q2[33] += carry;
+
+ for(i=0;i<33;i++)r1[i] = x[i];
+ for(i=0;i<32;i++)
+ for(j=0;j<33;j++)
+ if(i+j < 33) r2[i+j] += m[i]*q3[j];
+
+ for(i=0;i<32;i++)
+ {
+ carry = r2[i] >> 8;
+ r2[i+1] += carry;
+ r2[i] &= 0xff;
+ }
+
+ for(i=0;i<32;i++)
+ {
+ pb += r2[i];
+ b = lt(r1[i],pb);
+ r[i] = r1[i]-pb+(b<<8);
+ pb = b;
+ }
+
+ /* XXX: Can it really happen that r<0?, See HAC, Alg 14.42, Step 3
+ * r is an unsigned type.
+ * If so: Handle it here!
+ */
+
+ reduce_add_sub(r);
+ reduce_add_sub(r);
+}
+
+
+void sc_reduce(unsigned char x[64])
+{
+ int i;
+ word32 t[64];
+ word32 r[32];
+ for(i=0;i<64;i++) t[i] = x[i];
+ barrett_reduce(r, t);
+ for(i=0;i<32;i++) x[i] = (r[i] & 0xFF);
+}
+
+
+void sc_muladd(byte* out, const byte* a, const byte* b, const byte* c)
+{
+
+ byte s[32];
+ byte e[64];
+
+ XMEMSET(e, 0, sizeof(e));
+ XMEMCPY(e, b, 32);
+
+ /* Obtain e */
+ sc_reduce(e);
+
+ /* Compute s = ze + k */
+ fprime_mul(s, a, e, ed25519_order);
+ fprime_add(s, c, ed25519_order);
+
+ XMEMCPY(out, s, 32);
+}
+
+
+/* Base point is (numbers wrapped):
+ *
+ * x = 151122213495354007725011514095885315114
+ * 54012693041857206046113283949847762202
+ * y = 463168356949264781694283940034751631413
+ * 07993866256225615783033603165251855960
+ *
+ * y is derived by transforming the original Montgomery base (u=9). x
+ * is the corresponding positive coordinate for the new curve equation.
+ * t is x*y.
+ */
+const ge_p3 ed25519_base = {
+ {
+ 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, 0},
+ {
+ 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 ge_p3 ed25519_neutral = {
+ {0},
+ {1, 0},
+ {1, 0},
+ {0},
+
+};
+
+
+static const byte ed25519_d[F25519_SIZE] = {
+ 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
+};
+
+
+/* k = 2d */
+static const byte ed25519_k[F25519_SIZE] = {
+ 0x59, 0xf1, 0xb2, 0x26, 0x94, 0x9b, 0xd6, 0xeb,
+ 0x56, 0xb1, 0x83, 0x82, 0x9a, 0x14, 0xe0, 0x00,
+ 0x30, 0xd1, 0xf3, 0xee, 0xf2, 0x80, 0x8e, 0x19,
+ 0xe7, 0xfc, 0xdf, 0x56, 0xdc, 0xd9, 0x06, 0x24
+};
+
+
+void ed25519_add(ge_p3 *r,
+ const ge_p3 *p1, const ge_p3 *p2)
+{
+ /* Explicit formulas database: add-2008-hwcd-3
+ *
+ * source 2008 Hisil--Wong--Carter--Dawson,
+ * http://eprint.iacr.org/2008/522, Section 3.1
+ * appliesto extended-1
+ * parameter k
+ * assume k = 2 d
+ * compute A = (Y1-X1)(Y2-X2)
+ * compute B = (Y1+X1)(Y2+X2)
+ * compute C = T1 k T2
+ * compute D = Z1 2 Z2
+ * compute E = B - A
+ * compute F = D - C
+ * compute G = D + C
+ * compute H = B + A
+ * compute X3 = E F
+ * compute Y3 = G H
+ * compute T3 = E H
+ * compute Z3 = F G
+ */
+ byte a[F25519_SIZE];
+ byte b[F25519_SIZE];
+ byte c[F25519_SIZE];
+ byte d[F25519_SIZE];
+ byte e[F25519_SIZE];
+ byte f[F25519_SIZE];
+ byte g[F25519_SIZE];
+ byte h[F25519_SIZE];
+
+ /* A = (Y1-X1)(Y2-X2) */
+ fe_sub(c, p1->Y, p1->X);
+ fe_sub(d, p2->Y, p2->X);
+ fe_mul__distinct(a, c, d);
+
+ /* B = (Y1+X1)(Y2+X2) */
+ fe_add(c, p1->Y, p1->X);
+ fe_add(d, p2->Y, p2->X);
+ fe_mul__distinct(b, c, d);
+
+ /* C = T1 k T2 */
+ fe_mul__distinct(d, p1->T, p2->T);
+ fe_mul__distinct(c, d, ed25519_k);
+
+ /* D = Z1 2 Z2 */
+ fe_mul__distinct(d, p1->Z, p2->Z);
+ fe_add(d, d, d);
+
+ /* E = B - A */
+ fe_sub(e, b, a);
+
+ /* F = D - C */
+ fe_sub(f, d, c);
+
+ /* G = D + C */
+ fe_add(g, d, c);
+
+ /* H = B + A */
+ fe_add(h, b, a);
+
+ /* X3 = E F */
+ fe_mul__distinct(r->X, e, f);
+
+ /* Y3 = G H */
+ fe_mul__distinct(r->Y, g, h);
+
+ /* T3 = E H */
+ fe_mul__distinct(r->T, e, h);
+
+ /* Z3 = F G */
+ fe_mul__distinct(r->Z, f, g);
+}
+
+
+void ed25519_double(ge_p3 *r, const ge_p3 *p)
+{
+ /* Explicit formulas database: dbl-2008-hwcd
+ *
+ * source 2008 Hisil--Wong--Carter--Dawson,
+ * http://eprint.iacr.org/2008/522, Section 3.3
+ * compute A = X1^2
+ * compute B = Y1^2
+ * compute C = 2 Z1^2
+ * compute D = a A
+ * compute E = (X1+Y1)^2-A-B
+ * compute G = D + B
+ * compute F = G - C
+ * compute H = D - B
+ * compute X3 = E F
+ * compute Y3 = G H
+ * compute T3 = E H
+ * compute Z3 = F G
+ */
+ byte a[F25519_SIZE];
+ byte b[F25519_SIZE];
+ byte c[F25519_SIZE];
+ byte e[F25519_SIZE];
+ byte f[F25519_SIZE];
+ byte g[F25519_SIZE];
+ byte h[F25519_SIZE];
+
+ /* A = X1^2 */
+ fe_mul__distinct(a, p->X, p->X);
+
+ /* B = Y1^2 */
+ fe_mul__distinct(b, p->Y, p->Y);
+
+ /* C = 2 Z1^2 */
+ fe_mul__distinct(c, p->Z, p->Z);
+ fe_add(c, c, c);
+
+ /* D = a A (alter sign) */
+ /* E = (X1+Y1)^2-A-B */
+ fe_add(f, p->X, p->Y);
+ fe_mul__distinct(e, f, f);
+ fe_sub(e, e, a);
+ fe_sub(e, e, b);
+
+ /* G = D + B */
+ fe_sub(g, b, a);
+
+ /* F = G - C */
+ fe_sub(f, g, c);
+
+ /* H = D - B */
+ fe_neg(h, b);
+ fe_sub(h, h, a);
+
+ /* X3 = E F */
+ fe_mul__distinct(r->X, e, f);
+
+ /* Y3 = G H */
+ fe_mul__distinct(r->Y, g, h);
+
+ /* T3 = E H */
+ fe_mul__distinct(r->T, e, h);
+
+ /* Z3 = F G */
+ fe_mul__distinct(r->Z, f, g);
+}
+
+
+void ed25519_smult(ge_p3 *r_out, const ge_p3 *p, const byte *e)
+{
+ ge_p3 r;
+ int i;
+
+ XMEMCPY(&r, &ed25519_neutral, sizeof(r));
+
+ for (i = 255; i >= 0; i--) {
+ const byte bit = (e[i >> 3] >> (i & 7)) & 1;
+ ge_p3 s;
+
+ ed25519_double(&r, &r);
+ ed25519_add(&s, &r, p);
+
+ fe_select(r.X, r.X, s.X, bit);
+ fe_select(r.Y, r.Y, s.Y, bit);
+ fe_select(r.Z, r.Z, s.Z, bit);
+ fe_select(r.T, r.T, s.T, bit);
+ }
+ XMEMCPY(r_out, &r, sizeof(r));
+}
+
+
+void ge_scalarmult_base(ge_p3 *R,const unsigned char *nonce)
+{
+ ed25519_smult(R, &ed25519_base, nonce);
+}
+
+
+/* pack the point h into array s */
+void ge_p3_tobytes(unsigned char *s,const ge_p3 *h)
+{
+ byte x[F25519_SIZE];
+ byte y[F25519_SIZE];
+ byte z1[F25519_SIZE];
+ byte parity;
+
+ fe_inv__distinct(z1, h->Z);
+ fe_mul__distinct(x, h->X, z1);
+ fe_mul__distinct(y, h->Y, z1);
+
+ fe_normalize(x);
+ fe_normalize(y);
+
+ parity = (x[0] & 1) << 7;
+ fe_copy(s, y);
+ fe_normalize(s);
+ s[31] |= parity;
+}
+
+
+/* pack the point h into array s */
+void ge_tobytes(unsigned char *s,const ge_p2 *h)
+{
+ byte x[F25519_SIZE];
+ byte y[F25519_SIZE];
+ byte z1[F25519_SIZE];
+ byte parity;
+
+ fe_inv__distinct(z1, h->Z);
+ fe_mul__distinct(x, h->X, z1);
+ fe_mul__distinct(y, h->Y, z1);
+
+ fe_normalize(x);
+ fe_normalize(y);
+
+ parity = (x[0] & 1) << 7;
+ fe_copy(s, y);
+ fe_normalize(s);
+ s[31] |= parity;
+}
+
+
+/*
+ Test if the public key can be uncompressed and negate it (-X,Y,Z,-T)
+ return 0 on success
+ */
+int ge_frombytes_negate_vartime(ge_p3 *p,const unsigned char *s)
+{
+
+ byte parity;
+ byte x[F25519_SIZE];
+ byte y[F25519_SIZE];
+ byte a[F25519_SIZE];
+ byte b[F25519_SIZE];
+ byte c[F25519_SIZE];
+ int ret = 0;
+
+ /* unpack the key s */
+ parity = s[31] >> 7;
+ fe_copy(y, s);
+ y[31] &= 127;
+
+ fe_mul__distinct(c, y, y);
+ fe_mul__distinct(b, c, ed25519_d);
+ fe_add(a, b, f25519_one);
+ fe_inv__distinct(b, a);
+ fe_sub(a, c, f25519_one);
+ fe_mul__distinct(c, a, b);
+ fe_sqrt(a, c);
+ fe_neg(b, a);
+ fe_select(x, a, b, (a[0] ^ parity) & 1);
+
+ /* test that x^2 is equal to c */
+ fe_mul__distinct(a, x, x);
+ fe_normalize(a);
+ fe_normalize(c);
+ ret |= ConstantCompare(a, c, F25519_SIZE);
+
+ /* project the key s onto p */
+ fe_copy(p->X, x);
+ fe_copy(p->Y, y);
+ fe_load(p->Z, 1);
+ fe_mul__distinct(p->T, x, y);
+
+ /* negate, the point becomes (-X,Y,Z,-T) */
+ fe_neg(p->X,p->X);
+ fe_neg(p->T,p->T);
+
+ return ret;
+}
+
+
+int ge_double_scalarmult_vartime(ge_p2* R, const unsigned char *h,
+ const ge_p3 *inA,const unsigned char *sig)
+{
+ ge_p3 p, A;
+ int ret = 0;
+
+ XMEMCPY(&A, inA, sizeof(ge_p3));
+
+ /* find SB */
+ ed25519_smult(&p, &ed25519_base, sig);
+
+ /* find H(R,A,M) * -A */
+ ed25519_smult(&A, &A, h);
+
+ /* SB + -H(R,A,M)A */
+ ed25519_add(&A, &p, &A);
+
+ fe_copy(R->X, A.X);
+ fe_copy(R->Y, A.Y);
+ fe_copy(R->Z, A.Z);
+
+ return ret;
+}
+
+#endif /* HAVE_ED25519 */
+#endif /* CURVED25519_SMALL */
+
+