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-rw-r--r--networking/tls_fe.c601
1 files changed, 601 insertions, 0 deletions
diff --git a/networking/tls_fe.c b/networking/tls_fe.c
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+++ b/networking/tls_fe.c
@@ -0,0 +1,601 @@
+/*
+ * Copyright (C) 2018 Denys Vlasenko
+ *
+ * Licensed under GPLv2, see file LICENSE in this source tree.
+ */
+#include "tls.h"
+
+typedef uint8_t byte;
+typedef uint16_t word16;
+typedef uint32_t word32;
+#define XMEMSET memset
+
+#define F25519_SIZE CURVE25519_KEYSIZE
+
+/* The code below is taken from wolfssl-3.15.3/wolfcrypt/src/fe_low_mem.c
+ * Header comment is kept intact:
+ */
+
+/* fe_low_mem.c
+ *
+ * Copyright (C) 2006-2017 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. */
+
+#if 0 //UNUSED
+static void fprime_copy(byte *x, const byte *a)
+{
+ int i;
+ for (i = 0; i < F25519_SIZE; i++)
+ x[i] = a[i];
+}
+#endif
+
+static void lm_copy(byte* x, const byte* a)
+{
+ int i;
+ for (i = 0; i < F25519_SIZE; i++)
+ x[i] = a[i];
+}
+
+#if 0 //UNUSED
+static 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]));
+}
+#endif
+
+static 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]));
+}
+
+#if 0 //UNUSED
+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;
+ }
+}
+#endif
+
+#if 0 //UNUSED
+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);
+}
+#endif
+
+#if 0 //UNUSED
+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;
+}
+#endif
+
+#if 0 //UNUSED
+static void fprime_add(byte *r, const byte *a, const byte *modulus)
+{
+ raw_add(r, a);
+ raw_try_sub(r, modulus);
+}
+#endif
+
+#if 0 //UNUSED
+static 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);
+}
+#endif
+
+#if 0 //UNUSED
+static 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);
+ }
+}
+#endif
+
+#if 0 //UNUSED
+static 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;
+}
+#endif
+
+static 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);
+}
+
+static 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;
+ }
+}
+
+static 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;
+ }
+}
+
+#if 0 //UNUSED
+static 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;
+ }
+}
+#endif
+
+static 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;
+ }
+}
+
+#if 0 //UNUSED
+static 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);
+}
+#endif
+
+static 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;
+ }
+}
+
+static 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);
+}
+
+#if 0 //UNUSED
+static void lm_invert(byte *r, const byte *x)
+{
+ byte tmp[F25519_SIZE];
+
+ fe_inv__distinct(tmp, x);
+ lm_copy(r, tmp);
+}
+#endif
+
+#if 0 //UNUSED
+/* 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);
+}
+#endif
+
+#if 0 //UNUSED
+static 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
+
+/* 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);
+}
+
+/* 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);
+}
+
+void curve25519(byte *result, const byte *e, const byte *q)
+{
+ /* from wolfssl-3.15.3/wolfssl/wolfcrypt/fe_operations.h */
+ static const byte f25519_one[F25519_SIZE] = {1};
+
+ /* 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);
+}
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