Diff: wolfcrypt/src/ge_low_mem.c

Revision:

13:f67a6c6013ca

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/wolfcrypt/src/ge_low_mem.c	Tue Aug 22 10:48:22 2017 +0000
@@ -0,0 +1,564 @@
+/* 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>
+
+#ifdef HAVE_ED25519
+#ifdef ED25519_SMALL /* use slower code that takes less memory */
+
+#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;
+
+    lm_copy(tmp, xIn);
+    parity = (tmp[0] & 1) << 7;
+
+    lm_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) */
+    lm_sub(c, p1->Y, p1->X);
+    lm_sub(d, p2->Y, p2->X);
+    fe_mul__distinct(a, c, d);
+
+    /* B = (Y1+X1)(Y2+X2) */
+    lm_add(c, p1->Y, p1->X);
+    lm_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);
+    lm_add(d, d, d);
+
+    /* E = B - A */
+    lm_sub(e, b, a);
+
+    /* F = D - C */
+    lm_sub(f, d, c);
+
+    /* G = D + C */
+    lm_add(g, d, c);
+
+    /* H = B + A */
+    lm_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);
+    lm_add(c, c, c);
+
+    /* D = a A (alter sign) */
+    /* E = (X1+Y1)^2-A-B */
+    lm_add(f, p->X, p->Y);
+    fe_mul__distinct(e, f, f);
+    lm_sub(e, e, a);
+    lm_sub(e, e, b);
+
+    /* G = D + B */
+    lm_sub(g, b, a);
+
+    /* F = G - C */
+    lm_sub(f, g, c);
+
+    /* H = D - B */
+    lm_neg(h, b);
+    lm_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;
+    lm_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;
+    lm_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;
+    lm_copy(y, s);
+    y[31] &= 127;
+
+    fe_mul__distinct(c, y, y);
+    fe_mul__distinct(b, c, ed25519_d);
+    lm_add(a, b, f25519_one);
+    fe_inv__distinct(b, a);
+    lm_sub(a, c, f25519_one);
+    fe_mul__distinct(c, a, b);
+    fe_sqrt(a, c);
+    lm_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 */
+    lm_copy(p->X, x);
+    lm_copy(p->Y, y);
+    fe_load(p->Z, 1);
+    fe_mul__distinct(p->T, x, y);
+
+    /* negate, the point becomes (-X,Y,Z,-T) */
+    lm_neg(p->X,p->X);
+    lm_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);
+
+    lm_copy(R->X, A.X);
+    lm_copy(R->Y, A.Y);
+    lm_copy(R->Z, A.Z);
+
+    return ret;
+}
+
+#endif /* ED25519_SMALL */
+#endif /* HAVE_ED25519 */
+