1 files changed, 611 insertions, 0 deletions

diff --git a/networking/tls_fe.c b/networking/tls_fe.c
new file mode 100644
index 000000000..f235082f5
--- /dev/null
+++ b/networking/tls_fe.c
@@ -0,0 +1,611 @@
+/*
+ * 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 FAST_FUNC curve25519(byte *result, const byte *e, const byte *q)
+{
+        int i;
+
+        struct {
+                /* 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};
+        } z;
+#define f25519_one z.f25519_one
+#define xm         z.xm
+#define zm         z.zm
+#define xm1        z.xm1
+#define zm1        z.zm1
+        memset(&z, 0, sizeof(z));
+        f25519_one[0] = 1;
+        zm[0] = 1;
+        xm1[0] = 1;
+
+        /* 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);
+}