tls: implement secp256r1 elliptic curve (aka P256)

function                                             old     new   delta
sp_256_mod_mul_norm_10                                 -    1439   +1439
sp_256_ecc_mulmod_10                                   -    1363   +1363
sp_256_proj_point_dbl_10                               -     490    +490
p256_base                                              -     244    +244
static.sp_256_mont_sqr_10                              -     234    +234
static.sp_256_mont_mul_10                              -     214    +214
curve_P256_compute_pubkey_and_premaster                -     197    +197
static.sp_256_mont_reduce_10                           -     176    +176
static.sp_256_from_bin                                 -     149    +149
sp_256_to_bin                                          -     148    +148
tls_handshake                                       2046    2146    +100
static.sp_256_mul_add_10                               -      82     +82
.rodata                                           103275  103336     +61
static.sp_256_mont_sub_10                              -      52     +52
static.sp_256_mont_dbl_10                              -      52     +52
static.sp_256_cmp_10                                   -      43     +43
p256_mod                                               -      40     +40
static.sp_256_cond_sub_10                              -      32     +32
p256_mod_2                                             -      32     +32
sp_256_norm_10                                         -      31     +31
sp_256_cmp_equal_10                                    -      30     +30
sp_256_add_10                                          -      22     +22
addr_mask                                              -       8      +8
------------------------------------------------------------------------------
(add/remove: 22/0 grow/shrink: 2/0 up/down: 5239/0)          Total: 5239 bytes
   text	   data	    bss	    dec	    hex	filename
1018192	    559	   5020	1023771	  f9f1b	busybox_old
1023431	    559	   5020	1029010	  fb392	busybox_unstripped

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>

1 files changed, 1052 insertions, 0 deletions

diff --git a/networking/tls_sp_c32.c b/networking/tls_sp_c32.c
new file mode 100644
index 000000000..e7667de73
--- /dev/null
+++ b/networking/tls_sp_c32.c
@@ -0,0 +1,1052 @@
+/*
+ * Copyright (C) 2021 Denys Vlasenko
+ *
+ * Licensed under GPLv2, see file LICENSE in this source tree.
+ */
+#include "tls.h"
+
+#define SP_DEBUG          0
+#define FIXED_SECRET      0
+#define FIXED_PEER_PUBKEY 0
+
+#if SP_DEBUG
+# define dbg(...) fprintf(stderr, __VA_ARGS__)
+static void dump_hex(const char *fmt, const void *vp, int len)
+{
+	char hexbuf[32 * 1024 + 4];
+	const uint8_t *p = vp;
+
+	bin2hex(hexbuf, (void*)p, len)[0] = '\0';
+	dbg(fmt, hexbuf);
+}
+#else
+# define dbg(...) ((void)0)
+# define dump_hex(...) ((void)0)
+#endif
+
+#undef DIGIT_BIT
+#define DIGIT_BIT  32
+typedef int32_t sp_digit;
+
+/* The code below is taken from parts of
+ *  wolfssl-3.15.3/wolfcrypt/src/sp_c32.c
+ * and heavily modified.
+ * Header comment is kept intact:
+ */
+
+/* sp.c
+ *
+ * Copyright (C) 2006-2018 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
+ */
+
+/* Implementation by Sean Parkinson. */
+
+/* Point structure to use. */
+typedef struct sp_point {
+	sp_digit x[2 * 10];
+	sp_digit y[2 * 10];
+	sp_digit z[2 * 10];
+	int infinity;
+} sp_point;
+
+/* The modulus (prime) of the curve P256. */
+static const sp_digit p256_mod[10] = {
+	0x3ffffff,0x3ffffff,0x3ffffff,0x003ffff,0x0000000,
+	0x0000000,0x0000000,0x0000400,0x3ff0000,0x03fffff,
+};
+
+#define p256_mp_mod ((sp_digit)0x000001)
+
+/* Mask for address to obfuscate which of the two address will be used. */
+static const size_t addr_mask[2] = { 0, (size_t)-1 };
+
+/* The base point of curve P256. */
+static const sp_point p256_base = {
+	/* X ordinate */
+	{ 0x098c296,0x04e5176,0x33a0f4a,0x204b7ac,0x277037d,0x0e9103c,0x3ce6e56,0x1091fe2,0x1f2e12c,0x01ac5f4 },
+	/* Y ordinate */
+	{ 0x3bf51f5,0x1901a0d,0x1ececbb,0x15dacc5,0x22bce33,0x303e785,0x27eb4a7,0x1fe6e3b,0x2e2fe1a,0x013f8d0 },
+	/* Z ordinate */
+	{ 0x0000001,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000,0x0000000 },
+	/* infinity */
+	0
+};
+
+/* Write r as big endian to byte aray.
+ * Fixed length number of bytes written: 32
+ *
+ * r  A single precision integer.
+ * a  Byte array.
+ */
+static void sp_256_to_bin(sp_digit* r, uint8_t* a)
+{
+    int i, j, s = 0, b;
+
+    for (i = 0; i < 9; i++) {
+        r[i+1] += r[i] >> 26;
+        r[i] &= 0x3ffffff;
+    }
+    j = 256 / 8 - 1;
+    a[j] = 0;
+    for (i=0; i<10 && j>=0; i++) {
+        b = 0;
+        a[j--] |= r[i] << s; b += 8 - s;
+        if (j < 0)
+            break;
+        while (b < 26) {
+            a[j--] = r[i] >> b; b += 8;
+            if (j < 0)
+                break;
+        }
+        s = 8 - (b - 26);
+        if (j >= 0)
+            a[j] = 0;
+        if (s != 0)
+            j++;
+    }
+}
+
+/* Read big endian unsigned byte aray into r.
+ *
+ * r  A single precision integer.
+ * a  Byte array.
+ * n  Number of bytes in array to read.
+ */
+static void sp_256_from_bin(sp_digit* r, int max, const uint8_t* a, int n)
+{
+    int i, j = 0, s = 0;
+
+    r[0] = 0;
+    for (i = n-1; i >= 0; i--) {
+        r[j] |= ((sp_digit)a[i]) << s;
+        if (s >= 18) {
+            r[j] &= 0x3ffffff;
+            s = 26 - s;
+            if (j + 1 >= max)
+                break;
+            r[++j] = a[i] >> s;
+            s = 8 - s;
+        }
+        else
+            s += 8;
+    }
+
+    for (j++; j < max; j++)
+        r[j] = 0;
+}
+
+/* Convert a point of big-endian 32-byte x,y pair to type sp_point. */
+static void sp_256_point_from_bin2x32(sp_point* p, const uint8_t *bin2x32)
+{
+    memset(p, 0, sizeof(*p));
+    /*p->infinity = 0;*/
+    sp_256_from_bin(p->x, 2 * 10, bin2x32, 32);
+    sp_256_from_bin(p->y, 2 * 10, bin2x32 + 32, 32);
+    //static const uint8_t one[1] = { 1 };
+    //sp_256_from_bin(p->z, 2 * 10, one, 1);
+    p->z[0] = 1;
+}
+
+/* Compare a with b in constant time.
+ *
+ * a  A single precision integer.
+ * b  A single precision integer.
+ * return -ve, 0 or +ve if a is less than, equal to or greater than b
+ * respectively.
+ */
+static sp_digit sp_256_cmp_10(const sp_digit* a, const sp_digit* b)
+{
+    sp_digit r = 0;
+    int i;
+    for (i = 9; i >= 0; i--)
+        r |= (a[i] - b[i]) & (0 - !r);
+    return r;
+}
+
+/* Compare two numbers to determine if they are equal.
+ *
+ * a  First number to compare.
+ * b  Second number to compare.
+ * return 1 when equal and 0 otherwise.
+ */
+static int sp_256_cmp_equal_10(const sp_digit* a, const sp_digit* b)
+{
+#if 1
+    sp_digit r = 0;
+    int i;
+    for (i = 0; i < 10; i++)
+        r |= (a[i] ^ b[i]);
+    return r == 0;
+#else
+    return sp_256_cmp_10(a, b) == 0;
+#endif
+}
+
+/* Normalize the values in each word to 26.
+ *
+ * a  Array of sp_digit to normalize.
+ */
+static void sp_256_norm_10(sp_digit* a)
+{
+    int i;
+    for (i = 0; i < 9; i++) {
+        a[i+1] += a[i] >> 26;
+        a[i] &= 0x3ffffff;
+    }
+}
+
+/* Add b to a into r. (r = a + b)
+ *
+ * r  A single precision integer.
+ * a  A single precision integer.
+ * b  A single precision integer.
+ */
+static void sp_256_add_10(sp_digit* r, const sp_digit* a, const sp_digit* b)
+{
+    int i;
+    for (i = 0; i < 10; i++)
+        r[i] = a[i] + b[i];
+}
+
+/* Conditionally add a and b using the mask m.
+ * m is -1 to add and 0 when not.
+ *
+ * r  A single precision number representing conditional add result.
+ * a  A single precision number to add with.
+ * b  A single precision number to add.
+ * m  Mask value to apply.
+ */
+static void sp_256_cond_add_10(sp_digit* r, const sp_digit* a,
+        const sp_digit* b, const sp_digit m)
+{
+    int i;
+    for (i = 0; i < 10; i++)
+        r[i] = a[i] + (b[i] & m);
+}
+
+/* Conditionally subtract b from a using the mask m.
+ * m is -1 to subtract and 0 when not.
+ *
+ * r  A single precision number representing condition subtract result.
+ * a  A single precision number to subtract from.
+ * b  A single precision number to subtract.
+ * m  Mask value to apply.
+ */
+static void sp_256_cond_sub_10(sp_digit* r, const sp_digit* a,
+        const sp_digit* b, const sp_digit m)
+{
+    int i;
+    for (i = 0; i < 10; i++)
+        r[i] = a[i] - (b[i] & m);
+}
+
+/* Add 1 to a. (a = a + 1)
+ *
+ * r  A single precision integer.
+ * a  A single precision integer.
+ */
+static void sp_256_add_one_10(sp_digit* a)
+{
+    a[0]++;
+    sp_256_norm_10(a);
+}
+
+/* Shift number left one bit.
+ * Bottom bit is lost.
+ *
+ * r  Result of shift.
+ * a  Number to shift.
+ */
+static void sp_256_rshift1_10(sp_digit* r, sp_digit* a)
+{
+    int i;
+    for (i = 0; i < 9; i++)
+        r[i] = ((a[i] >> 1) | (a[i + 1] << 25)) & 0x3ffffff;
+    r[9] = a[9] >> 1;
+}
+
+/* Multiply a number by Montogmery normalizer mod modulus (prime).
+ *
+ * r  The resulting Montgomery form number.
+ * a  The number to convert.
+ */
+static void sp_256_mod_mul_norm_10(sp_digit* r, const sp_digit* a)
+{
+    int64_t t[8];
+    int64_t a32[8];
+    int64_t o;
+
+    a32[0] = a[0];
+    a32[0] |= a[1] << 26;
+    a32[0] &= 0xffffffff;
+    a32[1] = (sp_digit)(a[1] >> 6);
+    a32[1] |= a[2] << 20;
+    a32[1] &= 0xffffffff;
+    a32[2] = (sp_digit)(a[2] >> 12);
+    a32[2] |= a[3] << 14;
+    a32[2] &= 0xffffffff;
+    a32[3] = (sp_digit)(a[3] >> 18);
+    a32[3] |= a[4] << 8;
+    a32[3] &= 0xffffffff;
+    a32[4] = (sp_digit)(a[4] >> 24);
+    a32[4] |= a[5] << 2;
+    a32[4] |= a[6] << 28;
+    a32[4] &= 0xffffffff;
+    a32[5] = (sp_digit)(a[6] >> 4);
+    a32[5] |= a[7] << 22;
+    a32[5] &= 0xffffffff;
+    a32[6] = (sp_digit)(a[7] >> 10);
+    a32[6] |= a[8] << 16;
+    a32[6] &= 0xffffffff;
+    a32[7] = (sp_digit)(a[8] >> 16);
+    a32[7] |= a[9] << 10;
+    a32[7] &= 0xffffffff;
+
+    /*  1  1  0 -1 -1 -1 -1  0 */
+    t[0] = 0 + a32[0] + a32[1] - a32[3] - a32[4] - a32[5] - a32[6];
+    /*  0  1  1  0 -1 -1 -1 -1 */
+    t[1] = 0 + a32[1] + a32[2] - a32[4] - a32[5] - a32[6] - a32[7];
+    /*  0  0  1  1  0 -1 -1 -1 */
+    t[2] = 0 + a32[2] + a32[3] - a32[5] - a32[6] - a32[7];
+    /* -1 -1  0  2  2  1  0 -1 */
+    t[3] = 0 - a32[0] - a32[1] + 2 * a32[3] + 2 * a32[4] + a32[5] - a32[7];
+    /*  0 -1 -1  0  2  2  1  0 */
+    t[4] = 0 - a32[1] - a32[2] + 2 * a32[4] + 2 * a32[5] + a32[6];
+    /*  0  0 -1 -1  0  2  2  1 */
+    t[5] = 0 - a32[2] - a32[3] + 2 * a32[5] + 2 * a32[6] + a32[7];
+    /* -1 -1  0  0  0  1  3  2 */
+    t[6] = 0 - a32[0] - a32[1] + a32[5] + 3 * a32[6] + 2 * a32[7];
+    /*  1  0 -1 -1 -1 -1  0  3 */
+    t[7] = 0 + a32[0] - a32[2] - a32[3] - a32[4] - a32[5] + 3 * a32[7];
+
+    t[1] += t[0] >> 32; t[0] &= 0xffffffff;
+    t[2] += t[1] >> 32; t[1] &= 0xffffffff;
+    t[3] += t[2] >> 32; t[2] &= 0xffffffff;
+    t[4] += t[3] >> 32; t[3] &= 0xffffffff;
+    t[5] += t[4] >> 32; t[4] &= 0xffffffff;
+    t[6] += t[5] >> 32; t[5] &= 0xffffffff;
+    t[7] += t[6] >> 32; t[6] &= 0xffffffff;
+    o     = t[7] >> 32; t[7] &= 0xffffffff;
+    t[0] += o;
+    t[3] -= o;
+    t[6] -= o;
+    t[7] += o;
+    t[1] += t[0] >> 32; t[0] &= 0xffffffff;
+    t[2] += t[1] >> 32; t[1] &= 0xffffffff;
+    t[3] += t[2] >> 32; t[2] &= 0xffffffff;
+    t[4] += t[3] >> 32; t[3] &= 0xffffffff;
+    t[5] += t[4] >> 32; t[4] &= 0xffffffff;
+    t[6] += t[5] >> 32; t[5] &= 0xffffffff;
+    t[7] += t[6] >> 32; t[6] &= 0xffffffff;
+
+    r[0] = (sp_digit)(t[0]) & 0x3ffffff;
+    r[1] = (sp_digit)(t[0] >> 26);
+    r[1] |= t[1] << 6;
+    r[1] &= 0x3ffffff;
+    r[2] = (sp_digit)(t[1] >> 20);
+    r[2] |= t[2] << 12;
+    r[2] &= 0x3ffffff;
+    r[3] = (sp_digit)(t[2] >> 14);
+    r[3] |= t[3] << 18;
+    r[3] &= 0x3ffffff;
+    r[4] = (sp_digit)(t[3] >> 8);
+    r[4] |= t[4] << 24;
+    r[4] &= 0x3ffffff;
+    r[5] = (sp_digit)(t[4] >> 2) & 0x3ffffff;
+    r[6] = (sp_digit)(t[4] >> 28);
+    r[6] |= t[5] << 4;
+    r[6] &= 0x3ffffff;
+    r[7] = (sp_digit)(t[5] >> 22);
+    r[7] |= t[6] << 10;
+    r[7] &= 0x3ffffff;
+    r[8] = (sp_digit)(t[6] >> 16);
+    r[8] |= t[7] << 16;
+    r[8] &= 0x3ffffff;
+    r[9] = (sp_digit)(t[7] >> 10);
+}
+
+/* Mul a by scalar b and add into r. (r += a * b)
+ *
+ * r  A single precision integer.
+ * a  A single precision integer.
+ * b  A scalar.
+ */
+static void sp_256_mul_add_10(sp_digit* r, const sp_digit* a,
+        const sp_digit b)
+{
+    int64_t tb = b;
+    int64_t t = 0;
+    int i;
+
+    for (i = 0; i < 10; i++) {
+        t += (tb * a[i]) + r[i];
+        r[i] = t & 0x3ffffff;
+        t >>= 26;
+    }
+    r[10] += t;
+}
+
+/* Divide the number by 2 mod the modulus (prime). (r = a / 2 % m)
+ *
+ * r  Result of division by 2.
+ * a  Number to divide.
+ * m  Modulus (prime).
+ */
+static void sp_256_div2_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
+{
+    sp_256_cond_add_10(r, a, m, 0 - (a[0] & 1));
+    sp_256_norm_10(r);
+    sp_256_rshift1_10(r, r);
+}
+
+/* Shift the result in the high 256 bits down to the bottom.
+ *
+ * r  A single precision number.
+ * a  A single precision number.
+ */
+static void sp_256_mont_shift_10(sp_digit* r, const sp_digit* a)
+{
+    int i;
+    sp_digit n, s;
+
+    s = a[10];
+    n = a[9] >> 22;
+    for (i = 0; i < 9; i++) {
+        n += (s & 0x3ffffff) << 4;
+        r[i] = n & 0x3ffffff;
+        n >>= 26;
+        s = a[11 + i] + (s >> 26);
+    }
+    n += s << 4;
+    r[9] = n;
+    memset(&r[10], 0, sizeof(*r) * 10);
+}
+
+/* Add two Montgomery form numbers (r = a + b % m).
+ *
+ * r   Result of addition.
+ * a   First number to add in Montogmery form.
+ * b   Second number to add in Montogmery form.
+ * m   Modulus (prime).
+ */
+static void sp_256_mont_add_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
+        const sp_digit* m)
+{
+    sp_256_add_10(r, a, b);
+    sp_256_norm_10(r);
+    sp_256_cond_sub_10(r, r, m, 0 - ((r[9] >> 22) > 0));
+    sp_256_norm_10(r);
+}
+
+/* Double a Montgomery form number (r = a + a % m).
+ *
+ * r   Result of doubling.
+ * a   Number to double in Montogmery form.
+ * m   Modulus (prime).
+ */
+static void sp_256_mont_dbl_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
+{
+    sp_256_add_10(r, a, a);
+    sp_256_norm_10(r);
+    sp_256_cond_sub_10(r, r, m, 0 - ((r[9] >> 22) > 0));
+    sp_256_norm_10(r);
+}
+
+/* Triple a Montgomery form number (r = a + a + a % m).
+ *
+ * r   Result of Tripling.
+ * a   Number to triple in Montogmery form.
+ * m   Modulus (prime).
+ */
+static void sp_256_mont_tpl_10(sp_digit* r, const sp_digit* a, const sp_digit* m)
+{
+    sp_256_add_10(r, a, a);
+    sp_256_norm_10(r);
+    sp_256_cond_sub_10(r, r, m, 0 - ((r[9] >> 22) > 0));
+    sp_256_norm_10(r);
+    sp_256_add_10(r, r, a);
+    sp_256_norm_10(r);
+    sp_256_cond_sub_10(r, r, m, 0 - ((r[9] >> 22) > 0));
+    sp_256_norm_10(r);
+}
+
+/* Sub b from a into r. (r = a - b)
+ *
+ * r  A single precision integer.
+ * a  A single precision integer.
+ * b  A single precision integer.
+ */
+static void sp_256_sub_10(sp_digit* r, const sp_digit* a,
+        const sp_digit* b)
+{
+    int i;
+    for (i = 0; i < 10; i++)
+        r[i] = a[i] - b[i];
+}
+
+/* Subtract two Montgomery form numbers (r = a - b % m).
+ *
+ * r   Result of subtration.
+ * a   Number to subtract from in Montogmery form.
+ * b   Number to subtract with in Montogmery form.
+ * m   Modulus (prime).
+ */
+static void sp_256_mont_sub_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
+        const sp_digit* m)
+{
+    sp_256_sub_10(r, a, b);
+    sp_256_cond_add_10(r, r, m, r[9] >> 22);
+    sp_256_norm_10(r);
+}
+
+/* Reduce the number back to 256 bits using Montgomery reduction.
+ *
+ * a   A single precision number to reduce in place.
+ * m   The single precision number representing the modulus.
+ * mp  The digit representing the negative inverse of m mod 2^n.
+ */
+static void sp_256_mont_reduce_10(sp_digit* a, const sp_digit* m, sp_digit mp)
+{
+    int i;
+    sp_digit mu;
+
+    if (mp != 1) {
+        for (i = 0; i < 9; i++) {
+            mu = (a[i] * mp) & 0x3ffffff;
+            sp_256_mul_add_10(a+i, m, mu);
+            a[i+1] += a[i] >> 26;
+        }
+        mu = (a[i] * mp) & 0x3fffffl;
+        sp_256_mul_add_10(a+i, m, mu);
+        a[i+1] += a[i] >> 26;
+        a[i] &= 0x3ffffff;
+    }
+    else {
+        for (i = 0; i < 9; i++) {
+            mu = a[i] & 0x3ffffff;
+            sp_256_mul_add_10(a+i, p256_mod, mu);
+            a[i+1] += a[i] >> 26;
+        }
+        mu = a[i] & 0x3fffffl;
+        sp_256_mul_add_10(a+i, p256_mod, mu);
+        a[i+1] += a[i] >> 26;
+        a[i] &= 0x3ffffff;
+    }
+
+    sp_256_mont_shift_10(a, a);
+    sp_256_cond_sub_10(a, a, m, 0 - ((a[9] >> 22) > 0));
+    sp_256_norm_10(a);
+}
+
+/* Multiply a and b into r. (r = a * b)
+ *
+ * r  A single precision integer.
+ * a  A single precision integer.
+ * b  A single precision integer.
+ */
+static void sp_256_mul_10(sp_digit* r, const sp_digit* a, const sp_digit* b)
+{
+    int i, j, k;
+    int64_t c;
+
+    c = ((int64_t)a[9]) * b[9];
+    r[19] = (sp_digit)(c >> 26);
+    c = (c & 0x3ffffff) << 26;
+    for (k = 17; k >= 0; k--) {
+        for (i = 9; i >= 0; i--) {
+            j = k - i;
+            if (j >= 10)
+                break;
+            if (j < 0)
+                continue;
+            c += ((int64_t)a[i]) * b[j];
+        }
+        r[k + 2] += c >> 52;
+        r[k + 1] = (c >> 26) & 0x3ffffff;
+        c = (c & 0x3ffffff) << 26;
+    }
+    r[0] = (sp_digit)(c >> 26);
+}
+
+/* Multiply two Montogmery form numbers mod the modulus (prime).
+ * (r = a * b mod m)
+ *
+ * r   Result of multiplication.
+ * a   First number to multiply in Montogmery form.
+ * b   Second number to multiply in Montogmery form.
+ * m   Modulus (prime).
+ * mp  Montogmery mulitplier.
+ */
+static void sp_256_mont_mul_10(sp_digit* r, const sp_digit* a, const sp_digit* b,
+        const sp_digit* m, sp_digit mp)
+{
+    sp_256_mul_10(r, a, b);
+    sp_256_mont_reduce_10(r, m, mp);
+}
+
+/* Square a and put result in r. (r = a * a)
+ *
+ * r  A single precision integer.
+ * a  A single precision integer.
+ */
+static void sp_256_sqr_10(sp_digit* r, const sp_digit* a)
+{
+    int i, j, k;
+    int64_t c;
+
+    c = ((int64_t)a[9]) * a[9];
+    r[19] = (sp_digit)(c >> 26);
+    c = (c & 0x3ffffff) << 26;
+    for (k = 17; k >= 0; k--) {
+        for (i = 9; i >= 0; i--) {
+            j = k - i;
+            if (j >= 10 || i <= j)
+                break;
+            if (j < 0)
+                continue;
+
+            c += ((int64_t)a[i]) * a[j] * 2;
+        }
+        if (i == j)
+           c += ((int64_t)a[i]) * a[i];
+
+        r[k + 2] += c >> 52;
+        r[k + 1] = (c >> 26) & 0x3ffffff;
+        c = (c & 0x3ffffff) << 26;
+    }
+    r[0] = (sp_digit)(c >> 26);
+}
+
+/* Square the Montgomery form number. (r = a * a mod m)
+ *
+ * r   Result of squaring.
+ * a   Number to square in Montogmery form.
+ * m   Modulus (prime).
+ * mp  Montogmery mulitplier.
+ */
+static void sp_256_mont_sqr_10(sp_digit* r, const sp_digit* a, const sp_digit* m,
+        sp_digit mp)
+{
+    sp_256_sqr_10(r, a);
+    sp_256_mont_reduce_10(r, m, mp);
+}
+
+/* Invert the number, in Montgomery form, modulo the modulus (prime) of the
+ * P256 curve. (r = 1 / a mod m)
+ *
+ * r   Inverse result.
+ * a   Number to invert.
+ * td  Temporary data.
+ */
+/* Mod-2 for the P256 curve. */
+static const uint32_t p256_mod_2[8] = {
+	0xfffffffd,0xffffffff,0xffffffff,0x00000000,
+	0x00000000,0x00000000,0x00000001,0xffffffff,
+};
+static void sp_256_mont_inv_10(sp_digit* r, sp_digit* a, sp_digit* td)
+{
+    sp_digit* t = td;
+    int i;
+
+    memcpy(t, a, sizeof(sp_digit) * 10);
+    for (i = 254; i >= 0; i--) {
+        sp_256_mont_sqr_10(t, t, p256_mod, p256_mp_mod);
+        if (p256_mod_2[i / 32] & ((sp_digit)1 << (i % 32)))
+            sp_256_mont_mul_10(t, t, a, p256_mod, p256_mp_mod);
+    }
+    memcpy(r, t, sizeof(sp_digit) * 10);
+}
+
+/* Map the Montgomery form projective co-ordinate point to an affine point.
+ *
+ * r  Resulting affine co-ordinate point.
+ * p  Montgomery form projective co-ordinate point.
+ * t  Temporary ordinate data.
+ */
+static void sp_256_map_10(sp_point* r, sp_point* p, sp_digit* t)
+{
+    sp_digit* t1 = t;
+    sp_digit* t2 = t + 2*10;
+    int32_t n;
+
+    sp_256_mont_inv_10(t1, p->z, t + 2*10);
+
+    sp_256_mont_sqr_10(t2, t1, p256_mod, p256_mp_mod);
+    sp_256_mont_mul_10(t1, t2, t1, p256_mod, p256_mp_mod);
+
+    /* x /= z^2 */
+    sp_256_mont_mul_10(r->x, p->x, t2, p256_mod, p256_mp_mod);
+    memset(r->x + 10, 0, sizeof(r->x) / 2);
+    sp_256_mont_reduce_10(r->x, p256_mod, p256_mp_mod);
+    /* Reduce x to less than modulus */
+    n = sp_256_cmp_10(r->x, p256_mod);
+    sp_256_cond_sub_10(r->x, r->x, p256_mod, 0 - (n >= 0));
+    sp_256_norm_10(r->x);
+
+    /* y /= z^3 */
+    sp_256_mont_mul_10(r->y, p->y, t1, p256_mod, p256_mp_mod);
+    memset(r->y + 10, 0, sizeof(r->y) / 2);
+    sp_256_mont_reduce_10(r->y, p256_mod, p256_mp_mod);
+    /* Reduce y to less than modulus */
+    n = sp_256_cmp_10(r->y, p256_mod);
+    sp_256_cond_sub_10(r->y, r->y, p256_mod, 0 - (n >= 0));
+    sp_256_norm_10(r->y);
+
+    memset(r->z, 0, sizeof(r->z));
+    r->z[0] = 1;
+}
+
+/* Double the Montgomery form projective point p.
+ *
+ * r  Result of doubling point.
+ * p  Point to double.
+ * t  Temporary ordinate data.
+ */
+static void sp_256_proj_point_dbl_10(sp_point* r, sp_point* p, sp_digit* t)
+{
+    sp_point *rp[2];
+    sp_point tp;
+    sp_digit* t1 = t;
+    sp_digit* t2 = t + 2*10;
+    sp_digit* x;
+    sp_digit* y;
+    sp_digit* z;
+    int i;
+
+    /* When infinity don't double point passed in - constant time. */
+    rp[0] = r;
+    rp[1] = &tp;
+    x = rp[p->infinity]->x;
+    y = rp[p->infinity]->y;
+    z = rp[p->infinity]->z;
+    /* Put point to double into result - good for infinity. */
+    if (r != p) {
+        for (i = 0; i < 10; i++)
+            r->x[i] = p->x[i];
+        for (i = 0; i < 10; i++)
+            r->y[i] = p->y[i];
+        for (i = 0; i < 10; i++)
+            r->z[i] = p->z[i];
+        r->infinity = p->infinity;
+    }
+
+    /* T1 = Z * Z */
+    sp_256_mont_sqr_10(t1, z, p256_mod, p256_mp_mod);
+    /* Z = Y * Z */
+    sp_256_mont_mul_10(z, y, z, p256_mod, p256_mp_mod);
+    /* Z = 2Z */
+    sp_256_mont_dbl_10(z, z, p256_mod);
+    /* T2 = X - T1 */
+    sp_256_mont_sub_10(t2, x, t1, p256_mod);
+    /* T1 = X + T1 */
+    sp_256_mont_add_10(t1, x, t1, p256_mod);
+    /* T2 = T1 * T2 */
+    sp_256_mont_mul_10(t2, t1, t2, p256_mod, p256_mp_mod);
+    /* T1 = 3T2 */
+    sp_256_mont_tpl_10(t1, t2, p256_mod);
+    /* Y = 2Y */
+    sp_256_mont_dbl_10(y, y, p256_mod);
+    /* Y = Y * Y */
+    sp_256_mont_sqr_10(y, y, p256_mod, p256_mp_mod);
+    /* T2 = Y * Y */
+    sp_256_mont_sqr_10(t2, y, p256_mod, p256_mp_mod);
+    /* T2 = T2/2 */
+    sp_256_div2_10(t2, t2, p256_mod);
+    /* Y = Y * X */
+    sp_256_mont_mul_10(y, y, x, p256_mod, p256_mp_mod);
+    /* X = T1 * T1 */
+    sp_256_mont_mul_10(x, t1, t1, p256_mod, p256_mp_mod);
+    /* X = X - Y */
+    sp_256_mont_sub_10(x, x, y, p256_mod);
+    /* X = X - Y */
+    sp_256_mont_sub_10(x, x, y, p256_mod);
+    /* Y = Y - X */
+    sp_256_mont_sub_10(y, y, x, p256_mod);
+    /* Y = Y * T1 */
+    sp_256_mont_mul_10(y, y, t1, p256_mod, p256_mp_mod);
+    /* Y = Y - T2 */
+    sp_256_mont_sub_10(y, y, t2, p256_mod);
+}
+
+/* Add two Montgomery form projective points.
+ *
+ * r  Result of addition.
+ * p  Frist point to add.
+ * q  Second point to add.
+ * t  Temporary ordinate data.
+ */
+static void sp_256_proj_point_add_10(sp_point* r, sp_point* p, sp_point* q,
+        sp_digit* t)
+{
+    sp_point *ap[2];
+    sp_point *rp[2];
+    sp_point tp;
+    sp_digit* t1 = t;
+    sp_digit* t2 = t + 2*10;
+    sp_digit* t3 = t + 4*10;
+    sp_digit* t4 = t + 6*10;
+    sp_digit* t5 = t + 8*10;
+    sp_digit* x;
+    sp_digit* y;
+    sp_digit* z;
+    int i;
+
+    /* Ensure only the first point is the same as the result. */
+    if (q == r) {
+        sp_point* a = p;
+        p = q;
+        q = a;
+    }
+
+    /* Check double */
+    sp_256_sub_10(t1, p256_mod, q->y);
+    sp_256_norm_10(t1);
+    if (sp_256_cmp_equal_10(p->x, q->x)
+     & sp_256_cmp_equal_10(p->z, q->z)
+     & (sp_256_cmp_equal_10(p->y, q->y) | sp_256_cmp_equal_10(p->y, t1))
+    ) {
+        sp_256_proj_point_dbl_10(r, p, t);
+    }
+    else {
+        rp[0] = r;
+        rp[1] = &tp;
+        memset(&tp, 0, sizeof(tp));
+        x = rp[p->infinity | q->infinity]->x;
+        y = rp[p->infinity | q->infinity]->y;
+        z = rp[p->infinity | q->infinity]->z;
+
+        ap[0] = p;
+        ap[1] = q;
+        for (i=0; i<10; i++)
+            r->x[i] = ap[p->infinity]->x[i];
+        for (i=0; i<10; i++)
+            r->y[i] = ap[p->infinity]->y[i];
+        for (i=0; i<10; i++)
+            r->z[i] = ap[p->infinity]->z[i];
+        r->infinity = ap[p->infinity]->infinity;
+
+        /* U1 = X1*Z2^2 */
+        sp_256_mont_sqr_10(t1, q->z, p256_mod, p256_mp_mod);
+        sp_256_mont_mul_10(t3, t1, q->z, p256_mod, p256_mp_mod);
+        sp_256_mont_mul_10(t1, t1, x, p256_mod, p256_mp_mod);
+        /* U2 = X2*Z1^2 */
+        sp_256_mont_sqr_10(t2, z, p256_mod, p256_mp_mod);
+        sp_256_mont_mul_10(t4, t2, z, p256_mod, p256_mp_mod);
+        sp_256_mont_mul_10(t2, t2, q->x, p256_mod, p256_mp_mod);
+        /* S1 = Y1*Z2^3 */
+        sp_256_mont_mul_10(t3, t3, y, p256_mod, p256_mp_mod);
+        /* S2 = Y2*Z1^3 */
+        sp_256_mont_mul_10(t4, t4, q->y, p256_mod, p256_mp_mod);
+        /* H = U2 - U1 */
+        sp_256_mont_sub_10(t2, t2, t1, p256_mod);
+        /* R = S2 - S1 */
+        sp_256_mont_sub_10(t4, t4, t3, p256_mod);
+        /* Z3 = H*Z1*Z2 */
+        sp_256_mont_mul_10(z, z, q->z, p256_mod, p256_mp_mod);
+        sp_256_mont_mul_10(z, z, t2, p256_mod, p256_mp_mod);
+        /* X3 = R^2 - H^3 - 2*U1*H^2 */
+        sp_256_mont_sqr_10(x, t4, p256_mod, p256_mp_mod);
+        sp_256_mont_sqr_10(t5, t2, p256_mod, p256_mp_mod);
+        sp_256_mont_mul_10(y, t1, t5, p256_mod, p256_mp_mod);
+        sp_256_mont_mul_10(t5, t5, t2, p256_mod, p256_mp_mod);
+        sp_256_mont_sub_10(x, x, t5, p256_mod);
+        sp_256_mont_dbl_10(t1, y, p256_mod);
+        sp_256_mont_sub_10(x, x, t1, p256_mod);
+        /* Y3 = R*(U1*H^2 - X3) - S1*H^3 */
+        sp_256_mont_sub_10(y, y, x, p256_mod);
+        sp_256_mont_mul_10(y, y, t4, p256_mod, p256_mp_mod);
+        sp_256_mont_mul_10(t5, t5, t3, p256_mod, p256_mp_mod);
+        sp_256_mont_sub_10(y, y, t5, p256_mod);
+    }
+}
+
+/* Multiply the point by the scalar and return the result.
+ * If map is true then convert result to affine co-ordinates.
+ *
+ * r     Resulting point.
+ * g     Point to multiply.
+ * k     Scalar to multiply by.
+ */
+static void sp_256_ecc_mulmod_10(sp_point* r, const sp_point* g, const sp_digit* k /*, int map*/)
+{
+    enum { map = 1 }; /* we always convert result to affine coordinates */
+    sp_point td[3];
+    sp_point* t[3];
+    sp_digit tmp[2 * 10 * 5];
+    sp_digit n;
+    int i;
+    int c, y;
+
+    memset(td, 0, sizeof(td));
+
+    t[0] = &td[0];
+    t[1] = &td[1];
+    t[2] = &td[2];
+
+    /* t[0] = {0, 0, 1} * norm */
+    t[0]->infinity = 1;
+    /* t[1] = {g->x, g->y, g->z} * norm */
+    sp_256_mod_mul_norm_10(t[1]->x, g->x);
+    sp_256_mod_mul_norm_10(t[1]->y, g->y);
+    sp_256_mod_mul_norm_10(t[1]->z, g->z);
+
+    i = 9;
+    c = 22;
+    n = k[i--] << (26 - c);
+    for (; ; c--) {
+        if (c == 0) {
+            if (i == -1)
+                break;
+
+            n = k[i--];
+            c = 26;
+        }
+
+        y = (n >> 25) & 1;
+        n <<= 1;
+
+        sp_256_proj_point_add_10(t[y^1], t[0], t[1], tmp);
+///FIXME type (or rewrite - get rid of t[] array)
+        memcpy(t[2], (void*)(((size_t)t[0] & addr_mask[y^1]) +
+                              ((size_t)t[1] & addr_mask[y])),
+                sizeof(sp_point));
+        sp_256_proj_point_dbl_10(t[2], t[2], tmp);
+        memcpy((void*)(((size_t)t[0] & addr_mask[y^1]) +
+                        ((size_t)t[1] & addr_mask[y])), t[2],
+                sizeof(sp_point));
+    }
+
+    if (map)
+        sp_256_map_10(r, t[0], tmp);
+    else
+        memcpy(r, t[0], sizeof(sp_point));
+
+    memset(tmp, 0, sizeof(tmp));
+    memset(td, 0, sizeof(td));
+}
+
+/* Multiply the base point of P256 by the scalar and return the result.
+ * If map is true then convert result to affine co-ordinates.
+ *
+ * r     Resulting point.
+ * k     Scalar to multiply by.
+ */
+static void sp_256_ecc_mulmod_base_10(sp_point* r, sp_digit* k /*, int map*/)
+{
+	sp_256_ecc_mulmod_10(r, &p256_base, k /*, map*/);
+}
+
+/* Multiply the point by the scalar and serialize the X ordinate.
+ * The number is 0 padded to maximum size on output.
+ *
+ * priv    Scalar to multiply the point by.
+ * peerkey2x32   Point to multiply.
+ * out     Buffer to hold X ordinate.
+ */
+static void sp_ecc_secret_gen_256(sp_digit priv[10], const uint8_t *peerkey2x32, uint8_t* out32)
+{
+    sp_point point[1];
+
+#if FIXED_PEER_PUBKEY
+    memset((void*)peerkey32, 0x55, 64);
+#endif
+    dump_hex("peerkey32 %s\n", peerkey2x32, 32);
+    dump_hex("          %s\n", peerkey2x32 + 32, 32);
+
+    sp_256_point_from_bin2x32(point, peerkey2x32);
+    dump_hex("point->x %s\n", point->x, sizeof(point->x));
+    dump_hex("point->y %s\n", point->y, sizeof(point->y));
+
+    sp_256_ecc_mulmod_10(point, point, priv);
+
+    sp_256_to_bin(point->x, out32);
+    dump_hex("out32: %s\n", out32, 32);
+}
+
+/* Generates a scalar that is in the range 1..order-1.
+ *
+ * rng  Random number generator.
+ * k    Scalar value.
+ */
+static void sp_256_ecc_gen_k_10(sp_digit k[10])
+{
+#define SIMPLIFY 1
+#if !SIMPLIFY
+	/* The order of the curve P256 minus 2. */
+	static const sp_digit p256_order2[10] = {
+		0x063254f,0x272b0bf,0x1e84f3b,0x2b69c5e,0x3bce6fa,
+		0x3ffffff,0x3ffffff,0x00003ff,0x3ff0000,0x03fffff,
+	};
+#endif
+	uint8_t buf[32];
+
+	for (;;) {
+		tls_get_random(buf, sizeof(buf));
+#if FIXED_SECRET
+		memset(buf, 0x77, sizeof(buf));
+#endif
+		sp_256_from_bin(k, 10, buf, sizeof(buf));
+#if !SIMPLIFY
+		if (sp_256_cmp_10(k, p256_order2) < 0)
+			break;
+#else
+		/* non-loopy version (and not needing p256_order2[]):
+		 * if most-significant word seems that it can be larger
+		 * than p256_order2, fix it up:
+		 */
+		if (k[9] >= 0x03fffff)
+			k[9] = 0x03ffffe;
+		break;
+#endif
+	}
+	sp_256_add_one_10(k);
+#undef SIMPLIFY
+}
+
+/* Makes a random EC key pair.
+ *
+ * priv   Generated private value.
+ * pubkey Generated public point.
+ */
+static void sp_ecc_make_key_256(sp_digit k[10], uint8_t *pubkey)
+{
+	sp_point point[1];
+
+	sp_256_ecc_gen_k_10(k);
+	sp_256_ecc_mulmod_base_10(point, k);
+	sp_256_to_bin(point->x, pubkey);
+	sp_256_to_bin(point->y, pubkey + 32);
+
+	memset(point, 0, sizeof(point)); //paranoia
+}
+
+void FAST_FUNC curve_P256_compute_pubkey_and_premaster(
+		uint8_t *pubkey, uint8_t *premaster32,
+		const uint8_t *peerkey2x32)
+{
+	sp_digit privkey[10];
+
+	sp_ecc_make_key_256(privkey, pubkey);
+	dump_hex("pubkey: %s\n", pubkey, 32);
+	dump_hex("        %s\n", pubkey + 32, 32);
+
+	/* Combine our privkey and peerkey32 to generate premaster */
+	sp_ecc_secret_gen_256(privkey, /*x,y:*/peerkey2x32, premaster32);
+	dump_hex("premaster: %s\n", premaster32, 32);
+}