Removed wolfssl

1 files changed, 0 insertions, 2458 deletions

diff --git a/client/wolfssl/wolfcrypt/src/fe_448.c b/client/wolfssl/wolfcrypt/src/fe_448.c
deleted file mode 100644
index bc38c11..0000000
--- a/client/wolfssl/wolfcrypt/src/fe_448.c
+++ /dev/null
@@ -1,2458 +0,0 @@
-/* fe_448.c
- *
- * Copyright (C) 2006-2020 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 On Daniel J Bernstein's curve25519 Public Domain ref10 work.
- * Small implementation based on Daniel Beer's curve25519 public domain work.
- * Reworked for curve448 by Sean Parkinson.
- */
-
-#ifdef HAVE_CONFIG_H
-    #include <config.h>
-#endif
-
-#include <wolfssl/wolfcrypt/settings.h>
-
-#if defined(HAVE_CURVE448) || defined(HAVE_ED448)
-
-#include <wolfssl/wolfcrypt/fe_448.h>
-#include <stdint.h>
-
-#ifdef NO_INLINE
-    #include <wolfssl/wolfcrypt/misc.h>
-#else
-    #define WOLFSSL_MISC_INCLUDED
-    #include <wolfcrypt/src/misc.c>
-#endif
-
-#if defined(CURVE448_SMALL) || defined(ED448_SMALL)
-
-/* Initialize the field element operations.
- */
-void fe448_init(void)
-{
-}
-
-/* Normalize the field element.
- * Ensure result is in range: 0..2^448-2^224-2
- *
- * a  [in]  Field element in range 0..2^448-1.
- */
-void fe448_norm(uint8_t* a)
-{
-    int i;
-    int16_t c = 0;
-    int16_t o = 0;
-
-    for (i = 0; i < 56; i++) {
-        c += a[i];
-        if ((i == 0) || (i == 28))
-            c += 1;
-        c >>= 8;
-    }
-
-    for (i = 0; i < 56; i++) {
-        if ((i == 0) || (i == 28)) o += c;
-        o += a[i];
-        a[i] = (uint8_t)o;
-        o >>= 8;
-    }
-}
-
-/* Copy one field element into another: d = a.
- *
- * d  [in]  Destination field element.
- * a  [in]  Source field element.
- */
-void fe448_copy(uint8_t* d, const uint8_t* a)
-{
-    int i;
-    for (i = 0; i < 56; i++) {
-         d[i] = a[i];
-    }
-}
-
-/* Conditionally swap the elements.
- * Constant time implementation.
- *
- * a  [in]  First field element.
- * b  [in]  Second field element.
- * c  [in]  Swap when 1. Valid values: 0, 1.
- */
-static void fe448_cswap(uint8_t* a, uint8_t* b, int c)
-{
-    int i;
-    uint8_t mask = -(uint8_t)c;
-    uint8_t t[56];
-
-    for (i = 0; i < 56; i++)
-        t[i] = (a[i] ^ b[i]) & mask;
-    for (i = 0; i < 56; i++)
-        a[i] ^= t[i];
-    for (i = 0; i < 56; i++)
-        b[i] ^= t[i];
-}
-
-/* Add two field elements. r = (a + b) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold sum.
- * a  [in]  Field element to add.
- * b  [in]  Field element to add.
- */
-void fe448_add(uint8_t* r, const uint8_t* a, const uint8_t* b)
-{
-    int i;
-    int16_t c = 0;
-    int16_t o = 0;
-
-    for (i = 0; i < 56; i++) {
-        c += a[i];
-        c += b[i];
-        r[i] = (uint8_t)c;
-        c >>= 8;
-    }
-
-    for (i = 0; i < 56; i++) {
-        if ((i == 0) || (i == 28)) o += c;
-        o += r[i];
-        r[i] = (uint8_t)o;
-        o >>= 8;
-    }
-}
-
-/* Subtract a field element from another. r = (a - b) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold difference.
- * a  [in]  Field element to subtract from.
- * b  [in]  Field element to subtract.
- */
-void fe448_sub(uint8_t* r, const uint8_t* a, const uint8_t* b)
-{
-    int i;
-    int16_t c = 0;
-    int16_t o = 0;
-
-    for (i = 0; i < 56; i++) {
-        if (i == 28)
-            c += 0x1fc;
-        else
-            c += 0x1fe;
-        c += a[i];
-        c -= b[i];
-        r[i] = (uint8_t)c;
-        c >>= 8;
-    }
-
-    for (i = 0; i < 56; i++) {
-        if ((i == 0) || (i == 28)) o += c;
-        o += r[i];
-        r[i] = (uint8_t)o;
-        o >>= 8;
-    }
-}
-
-/* Mulitply a field element by 39081. r = (39081 * a) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to multiply.
- */
-void fe448_mul39081(uint8_t* r, const uint8_t* a)
-{
-    int i;
-    int32_t c = 0;
-    int32_t o = 0;
-
-    for (i = 0; i < 56; i++) {
-        c += a[i] * (int32_t)39081;
-        r[i] = (uint8_t)c;
-        c >>= 8;
-    }
-
-    for (i = 0; i < 56; i++) {
-        if ((i == 0) || (i == 28)) o += c;
-        o += r[i];
-        r[i] = (uint8_t)o;
-        o >>= 8;
-    }
-}
-
-/* Mulitply two field elements. r = (a * b) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to multiply.
- * b  [in]  Field element to multiply.
- */
-void fe448_mul(uint8_t* r, const uint8_t* a, const uint8_t* b)
-{
-    int i, k;
-    int32_t c = 0;
-    int16_t o = 0, cc = 0;
-    uint8_t t[112];
-
-    for (k = 0; k < 56; k++) {
-        i = 0;
-        for (; i <= k; i++) {
-            c += (int32_t)a[i] * b[k - i];
-        }
-        t[k] = (uint8_t)c;
-        c >>= 8;
-    }
-    for (; k < 111; k++) {
-        i = k - 55;
-        for (; i < 56; i++) {
-            c += (int32_t)a[i] * b[k - i];
-        }
-        t[k] = (uint8_t)c;
-        c >>= 8;
-    }
-    t[k] = (uint8_t)c;
-
-    for (i = 0; i < 28; i++) {
-        o += t[i];
-        o += t[i + 56];
-        o += t[i + 84];
-        r[i] = (uint8_t)o;
-        o >>= 8;
-    }
-    for (i = 28; i < 56; i++) {
-        o += t[i];
-        o += t[i + 56];
-        o += t[i + 28];
-        o += t[i + 56];
-        r[i] = (uint8_t)o;
-        o >>= 8;
-    }
-    for (i = 0; i < 56; i++) {
-        if ((i == 0) || (i == 28)) cc += o;
-        cc += r[i];
-        r[i] = (uint8_t)cc;
-        cc >>= 8;
-    }
-}
-
-/* Square a field element. r = (a * a) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to square.
- */
-void fe448_sqr(uint8_t* r, const uint8_t* a)
-{
-    int i, k;
-    int32_t c = 0;
-    int32_t p;
-    int16_t o = 0, cc = 0;
-    uint8_t t[112];
-
-    for (k = 0; k < 56; k++) {
-        i = 0;
-        for (; i <= k; i++) {
-            if (k - i < i)
-                break;
-            p = (int32_t)a[i] * a[k - i];
-            if (k - i != i)
-                p *= 2;
-            c += p;
-        }
-        t[k] = (uint8_t)c;
-        c >>= 8;
-    }
-    for (; k < 111; k++) {
-         i = k - 55;
-        for (; i < 56; i++) {
-            if (k - i < i)
-                break;
-            p = (int32_t)a[i] * a[k - i];
-            if (k - i != i)
-                p *= 2;
-            c += p;
-        }
-        t[k] = (uint8_t)c;
-        c >>= 8;
-    }
-    t[k] = (uint8_t)c;
-
-    for (i = 0; i < 28; i++) {
-        o += t[i];
-        o += t[i + 56];
-        o += t[i + 84];
-        r[i] = (uint8_t)o;
-        o >>= 8;
-    }
-    for (i = 28; i < 56; i++) {
-        o += t[i];
-        o += t[i + 56];
-        o += t[i + 28];
-        o += t[i + 56];
-        r[i] = (uint8_t)o;
-        o >>= 8;
-    }
-    for (i = 0; i < 56; i++) {
-        if ((i == 0) || (i == 28)) cc += o;
-        cc += r[i];
-        r[i] = (uint8_t)cc;
-        cc >>= 8;
-    }
-    fe448_norm(r);
-}
-
-/* Invert the field element. (r * a) mod (2^448 - 2^224 - 1) = 1
- * Constant time implementation - using Fermat's little theorem:
- *   a^(p-1) mod p = 1 => a^(p-2) mod p = 1/a
- * For curve448: p - 2 = 2^448 - 2^224 - 3
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to invert.
- */
-void fe448_invert(uint8_t* r, const uint8_t* a)
-{
-    int i;
-    uint8_t t[56];
-
-    fe448_sqr(t, a);
-    fe448_mul(t, t, a);
-    for (i = 0; i < 221; i++) {
-        fe448_sqr(t, t);
-        fe448_mul(t, t, a);
-    }
-    fe448_sqr(t, t);
-    for (i = 0; i < 222; i++) {
-        fe448_sqr(t, t);
-        fe448_mul(t, t, a);
-    }
-    fe448_sqr(t, t);
-    fe448_sqr(t, t);
-    fe448_mul(r, t, a);
-}
-
-/* Scalar multiply the point by a number. r = n.a
- * Uses Montogmery ladder and only requires the x-ordinate.
- *
- * r  [in]  Field element to hold result.
- * n  [in]  Scalar as an array of bytes.
- * a  [in]  Point to multiply - x-ordinate only.
- */
-int curve448(byte* r, const byte* n, const byte* a)
-{
-    uint8_t x1[56];
-    uint8_t x2[56] = {1};
-    uint8_t z2[56] = {0};
-    uint8_t x3[56];
-    uint8_t z3[56] = {1};
-    uint8_t t0[56];
-    uint8_t t1[56];
-    int i;
-    unsigned int swap;
-    unsigned int b;
-
-    fe448_copy(x1, a);
-    fe448_copy(x3, a);
-
-    swap = 0;
-    for (i = 447; i >= 0; --i) {
-        b = (n[i >> 3] >> (i & 7)) & 1;
-        swap ^= b;
-        fe448_cswap(x2, x3, swap);
-        fe448_cswap(z2, z3, swap);
-        swap = b;
-
-        /* Montgomery Ladder - double and add */
-        fe448_add(t0, x2, z2);
-        fe448_add(t1, x3, z3);
-        fe448_sub(x2, x2, z2);
-        fe448_sub(x3, x3, z3);
-        fe448_mul(t1, t1, x2);
-        fe448_mul(z3, x3, t0);
-        fe448_sqr(t0, t0);
-        fe448_sqr(x2, x2);
-        fe448_add(x3, z3, t1);
-        fe448_sqr(x3, x3);
-        fe448_sub(z3, z3, t1);
-        fe448_sqr(z3, z3);
-        fe448_mul(z3, z3, x1);
-        fe448_sub(t1, t0, x2);
-        fe448_mul(x2, t0, x2);
-        fe448_mul39081(z2, t1);
-        fe448_add(z2, t0, z2);
-        fe448_mul(z2, z2, t1);
-    }
-    fe448_cswap(x2, x3, swap);
-    fe448_cswap(z2, z3, swap);
-
-    fe448_invert(z2, z2);
-    fe448_mul(r, x2, z2);
-    fe448_norm(r);
-
-    return 0;
-}
-
-#ifdef HAVE_ED448
-/* Check whether field element is not 0.
- * Field element must have been normalized before call.
- *
- * a  [in]  Field element.
- * returns 0 when zero, and any other value otherwise.
- */
-int fe448_isnonzero(const uint8_t* a)
-{
-    int i;
-    uint8_t c = 0;
-    for (i = 0; i < 56; i++)
-        c |= a[i];
-    return c;
-}
-
-/* Negates the field element. r = -a mod (2^448 - 2^224 - 1)
- * Add 0x200 to each element and subtract 2 from next.
- * Top element overflow handled by subtracting 2 from index 0 and 28.
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element.
- */
-void fe448_neg(uint8_t* r, const uint8_t* a)
-{
-    int i;
-    int16_t c = 0;
-    int16_t o = 0;
-
-    for (i = 0; i < 56; i++) {
-        if (i == 28)
-            c += 0x1fc;
-        else
-            c += 0x1fe;
-        c -= a[i];
-        r[i] = (uint8_t)c;
-        c >>= 8;
-    }
-
-    for (i = 0; i < 56; i++) {
-        if ((i == 0) || (i == 28)) o += c;
-        o += r[i];
-        r[i] = (uint8_t)o;
-        o >>= 8;
-    }
-}
-
-/* Raise field element to (p-3) / 4: 2^446 - 2^222 - 1
- * Used for calcualting y-ordinate from x-ordinate for Ed448.
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to exponentiate.
- */
-void fe448_pow_2_446_222_1(uint8_t* r, const uint8_t* a)
-{
-    int i;
-    uint8_t t[56];
-
-    fe448_sqr(t, a);
-    fe448_mul(t, t, a);
-    for (i = 0; i < 221; i++) {
-        fe448_sqr(t, t);
-        fe448_mul(t, t, a);
-    }
-    fe448_sqr(t, t);
-    for (i = 0; i < 221; i++) {
-        fe448_sqr(t, t);
-        fe448_mul(t, t, a);
-    }
-    fe448_sqr(t, t);
-    fe448_mul(r, t, a);
-}
-
-/* Constant time, conditional move of b into a.
- * a is not changed if the condition is 0.
- *
- * a  A field element.
- * b  A field element.
- * c  If 1 then copy and if 0 then don't copy.
- */
-void fe448_cmov(uint8_t* a, const uint8_t* b, int c)
-{
-    int i;
-    uint8_t m = -(uint8_t)c;
-    uint8_t t[56];
-
-    for (i = 0; i < 56; i++)
-        t[i] = m & (a[i] ^ b[i]);
-    for (i = 0; i < 56; i++)
-        a[i] ^= t[i];
-}
-
-#endif /* HAVE_ED448 */
-#elif defined(CURVED448_128BIT)
-
-/* Initialize the field element operations.
- */
-void fe448_init(void)
-{
-}
-
-/* Convert the field element from a byte array to an array of 56-bits.
- *
- * r  [in]  Array to encode into.
- * b  [in]  Byte array.
- */
-void fe448_from_bytes(int64_t* r, const unsigned char* b)
-{
-    r[ 0] =  ((int64_t) (b[ 0]) <<  0)
-          |  ((int64_t) (b[ 1]) <<  8)
-          |  ((int64_t) (b[ 2]) << 16)
-          |  ((int64_t) (b[ 3]) << 24)
-          |  ((int64_t) (b[ 4]) << 32)
-          |  ((int64_t) (b[ 5]) << 40)
-          |  ((int64_t) (b[ 6]) << 48);
-    r[ 1] =  ((int64_t) (b[ 7]) <<  0)
-          |  ((int64_t) (b[ 8]) <<  8)
-          |  ((int64_t) (b[ 9]) << 16)
-          |  ((int64_t) (b[10]) << 24)
-          |  ((int64_t) (b[11]) << 32)
-          |  ((int64_t) (b[12]) << 40)
-          |  ((int64_t) (b[13]) << 48);
-    r[ 2] =  ((int64_t) (b[14]) <<  0)
-          |  ((int64_t) (b[15]) <<  8)
-          |  ((int64_t) (b[16]) << 16)
-          |  ((int64_t) (b[17]) << 24)
-          |  ((int64_t) (b[18]) << 32)
-          |  ((int64_t) (b[19]) << 40)
-          |  ((int64_t) (b[20]) << 48);
-    r[ 3] =  ((int64_t) (b[21]) <<  0)
-          |  ((int64_t) (b[22]) <<  8)
-          |  ((int64_t) (b[23]) << 16)
-          |  ((int64_t) (b[24]) << 24)
-          |  ((int64_t) (b[25]) << 32)
-          |  ((int64_t) (b[26]) << 40)
-          |  ((int64_t) (b[27]) << 48);
-    r[ 4] =  ((int64_t) (b[28]) <<  0)
-          |  ((int64_t) (b[29]) <<  8)
-          |  ((int64_t) (b[30]) << 16)
-          |  ((int64_t) (b[31]) << 24)
-          |  ((int64_t) (b[32]) << 32)
-          |  ((int64_t) (b[33]) << 40)
-          |  ((int64_t) (b[34]) << 48);
-    r[ 5] =  ((int64_t) (b[35]) <<  0)
-          |  ((int64_t) (b[36]) <<  8)
-          |  ((int64_t) (b[37]) << 16)
-          |  ((int64_t) (b[38]) << 24)
-          |  ((int64_t) (b[39]) << 32)
-          |  ((int64_t) (b[40]) << 40)
-          |  ((int64_t) (b[41]) << 48);
-    r[ 6] =  ((int64_t) (b[42]) <<  0)
-          |  ((int64_t) (b[43]) <<  8)
-          |  ((int64_t) (b[44]) << 16)
-          |  ((int64_t) (b[45]) << 24)
-          |  ((int64_t) (b[46]) << 32)
-          |  ((int64_t) (b[47]) << 40)
-          |  ((int64_t) (b[48]) << 48);
-    r[ 7] =  ((int64_t) (b[49]) <<  0)
-          |  ((int64_t) (b[50]) <<  8)
-          |  ((int64_t) (b[51]) << 16)
-          |  ((int64_t) (b[52]) << 24)
-          |  ((int64_t) (b[53]) << 32)
-          |  ((int64_t) (b[54]) << 40)
-          |  ((int64_t) (b[55]) << 48);
-}
-
-/* Convert the field element to a byte array from an array of 56-bits.
- *
- * b  [in]  Byte array.
- * a  [in]  Array to encode into.
- */
-void fe448_to_bytes(unsigned char* b, const int64_t* a)
-{
-    int128_t t;
-    /* Mod */
-    int64_t in0 = a[0];
-    int64_t in1 = a[1];
-    int64_t in2 = a[2];
-    int64_t in3 = a[3];
-    int64_t in4 = a[4];
-    int64_t in5 = a[5];
-    int64_t in6 = a[6];
-    int64_t in7 = a[7];
-    int64_t o = in7 >> 56;
-    in7 -= o << 56;
-    in0 += o;
-    in4 += o;
-    o = (in0 + 1) >> 56;
-    o = (o + in1) >> 56;
-    o = (o + in2) >> 56;
-    o = (o + in3) >> 56;
-    o = (o + in4 + 1) >> 56;
-    o = (o + in5) >> 56;
-    o = (o + in6) >> 56;
-    o = (o + in7) >> 56;
-    in0 += o;
-    in4 += o;
-    in7 -= o << 56;
-    o = in0  >> 56; in1  += o; t = o << 56; in0  -= t;
-    o = in1  >> 56; in2  += o; t = o << 56; in1  -= t;
-    o = in2  >> 56; in3  += o; t = o << 56; in2  -= t;
-    o = in3  >> 56; in4  += o; t = o << 56; in3  -= t;
-    o = in4  >> 56; in5  += o; t = o << 56; in4  -= t;
-    o = in5  >> 56; in6  += o; t = o << 56; in5  -= t;
-    o = in6  >> 56; in7  += o; t = o << 56; in6  -= t;
-    o = in7  >> 56; in0  += o;
-                    in4  += o; t = o << 56; in7  -= t;
-
-    /* Output as bytes */
-    b[ 0] = (in0  >>  0);
-    b[ 1] = (in0  >>  8);
-    b[ 2] = (in0  >> 16);
-    b[ 3] = (in0  >> 24);
-    b[ 4] = (in0  >> 32);
-    b[ 5] = (in0  >> 40);
-    b[ 6] = (in0  >> 48);
-    b[ 7] = (in1  >>  0);
-    b[ 8] = (in1  >>  8);
-    b[ 9] = (in1  >> 16);
-    b[10] = (in1  >> 24);
-    b[11] = (in1  >> 32);
-    b[12] = (in1  >> 40);
-    b[13] = (in1  >> 48);
-    b[14] = (in2  >>  0);
-    b[15] = (in2  >>  8);
-    b[16] = (in2  >> 16);
-    b[17] = (in2  >> 24);
-    b[18] = (in2  >> 32);
-    b[19] = (in2  >> 40);
-    b[20] = (in2  >> 48);
-    b[21] = (in3  >>  0);
-    b[22] = (in3  >>  8);
-    b[23] = (in3  >> 16);
-    b[24] = (in3  >> 24);
-    b[25] = (in3  >> 32);
-    b[26] = (in3  >> 40);
-    b[27] = (in3  >> 48);
-    b[28] = (in4  >>  0);
-    b[29] = (in4  >>  8);
-    b[30] = (in4  >> 16);
-    b[31] = (in4  >> 24);
-    b[32] = (in4  >> 32);
-    b[33] = (in4  >> 40);
-    b[34] = (in4  >> 48);
-    b[35] = (in5  >>  0);
-    b[36] = (in5  >>  8);
-    b[37] = (in5  >> 16);
-    b[38] = (in5  >> 24);
-    b[39] = (in5  >> 32);
-    b[40] = (in5  >> 40);
-    b[41] = (in5  >> 48);
-    b[42] = (in6  >>  0);
-    b[43] = (in6  >>  8);
-    b[44] = (in6  >> 16);
-    b[45] = (in6  >> 24);
-    b[46] = (in6  >> 32);
-    b[47] = (in6  >> 40);
-    b[48] = (in6  >> 48);
-    b[49] = (in7  >>  0);
-    b[50] = (in7  >>  8);
-    b[51] = (in7  >> 16);
-    b[52] = (in7  >> 24);
-    b[53] = (in7  >> 32);
-    b[54] = (in7  >> 40);
-    b[55] = (in7  >> 48);
-}
-
-/* Set the field element to 0.
- *
- * a  [in]  Field element.
- */
-void fe448_1(int64_t* a)
-{
-    a[0] = 1;
-    a[1] = 0;
-    a[2] = 0;
-    a[3] = 0;
-    a[4] = 0;
-    a[5] = 0;
-    a[6] = 0;
-    a[7] = 0;
-}
-
-/* Set the field element to 0.
- *
- * a  [in]  Field element.
- */
-void fe448_0(int64_t* a)
-{
-    a[0] = 0;
-    a[1] = 0;
-    a[2] = 0;
-    a[3] = 0;
-    a[4] = 0;
-    a[5] = 0;
-    a[6] = 0;
-    a[7] = 0;
-}
-
-/* Copy one field element into another: d = a.
- *
- * d  [in]  Destination field element.
- * a  [in]  Source field element.
- */
-void fe448_copy(int64_t* d, const int64_t* a)
-{
-    d[0] = a[0];
-    d[1] = a[1];
-    d[2] = a[2];
-    d[3] = a[3];
-    d[4] = a[4];
-    d[5] = a[5];
-    d[6] = a[6];
-    d[7] = a[7];
-}
-
-/* Conditionally swap the elements.
- * Constant time implementation.
- *
- * a  [in]  First field element.
- * b  [in]  Second field element.
- * c  [in]  Swap when 1. Valid values: 0, 1.
- */
-static void fe448_cswap(int64_t* a, int64_t* b, int c)
-{
-    int64_t mask = -(int64_t)c;
-    int64_t t0 = (a[0] ^ b[0]) & mask;
-    int64_t t1 = (a[1] ^ b[1]) & mask;
-    int64_t t2 = (a[2] ^ b[2]) & mask;
-    int64_t t3 = (a[3] ^ b[3]) & mask;
-    int64_t t4 = (a[4] ^ b[4]) & mask;
-    int64_t t5 = (a[5] ^ b[5]) & mask;
-    int64_t t6 = (a[6] ^ b[6]) & mask;
-    int64_t t7 = (a[7] ^ b[7]) & mask;
-    a[0] ^= t0;
-    a[1] ^= t1;
-    a[2] ^= t2;
-    a[3] ^= t3;
-    a[4] ^= t4;
-    a[5] ^= t5;
-    a[6] ^= t6;
-    a[7] ^= t7;
-    b[0] ^= t0;
-    b[1] ^= t1;
-    b[2] ^= t2;
-    b[3] ^= t3;
-    b[4] ^= t4;
-    b[5] ^= t5;
-    b[6] ^= t6;
-    b[7] ^= t7;
-}
-
-/* Add two field elements. r = (a + b) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold sum.
- * a  [in]  Field element to add.
- * b  [in]  Field element to add.
- */
-void fe448_add(int64_t* r, const int64_t* a, const int64_t* b)
-{
-    r[0] = a[0] + b[0];
-    r[1] = a[1] + b[1];
-    r[2] = a[2] + b[2];
-    r[3] = a[3] + b[3];
-    r[4] = a[4] + b[4];
-    r[5] = a[5] + b[5];
-    r[6] = a[6] + b[6];
-    r[7] = a[7] + b[7];
-}
-
-/* Subtract a field element from another. r = (a - b) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold difference.
- * a  [in]  Field element to subtract from.
- * b  [in]  Field element to subtract.
- */
-void fe448_sub(int64_t* r, const int64_t* a, const int64_t* b)
-{
-    r[0] = a[0] - b[0];
-    r[1] = a[1] - b[1];
-    r[2] = a[2] - b[2];
-    r[3] = a[3] - b[3];
-    r[4] = a[4] - b[4];
-    r[5] = a[5] - b[5];
-    r[6] = a[6] - b[6];
-    r[7] = a[7] - b[7];
-}
-
-/* Mulitply a field element by 39081. r = (39081 * a) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to multiply.
- */
-void fe448_mul39081(int64_t* r, const int64_t* a)
-{
-    int128_t t;
-    int64_t o;
-    int128_t t0 = a[0] * (int128_t)39081;
-    int128_t t1 = a[1] * (int128_t)39081;
-    int128_t t2 = a[2] * (int128_t)39081;
-    int128_t t3 = a[3] * (int128_t)39081;
-    int128_t t4 = a[4] * (int128_t)39081;
-    int128_t t5 = a[5] * (int128_t)39081;
-    int128_t t6 = a[6] * (int128_t)39081;
-    int128_t t7 = a[7] * (int128_t)39081;
-    o = t0  >> 56; t1  += o; t = (int128_t)o << 56; t0  -= t;
-    o = t1  >> 56; t2  += o; t = (int128_t)o << 56; t1  -= t;
-    o = t2  >> 56; t3  += o; t = (int128_t)o << 56; t2  -= t;
-    o = t3  >> 56; t4  += o; t = (int128_t)o << 56; t3  -= t;
-    o = t4  >> 56; t5  += o; t = (int128_t)o << 56; t4  -= t;
-    o = t5  >> 56; t6  += o; t = (int128_t)o << 56; t5  -= t;
-    o = t6  >> 56; t7  += o; t = (int128_t)o << 56; t6  -= t;
-    o = t7  >> 56; t0  += o;
-                   t4  += o; t = (int128_t)o << 56; t7  -= t;
-
-    /* Store */
-    r[0] = t0;
-    r[1] = t1;
-    r[2] = t2;
-    r[3] = t3;
-    r[4] = t4;
-    r[5] = t5;
-    r[6] = t6;
-    r[7] = t7;
-}
-
-/* Mulitply two field elements. r = (a * b) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to multiply.
- * b  [in]  Field element to multiply.
- */
-void fe448_mul(int64_t* r, const int64_t* a, const int64_t* b)
-{
-    int128_t t;
-    int64_t o;
-    int128_t t0   = (int128_t)a[ 0] * b[ 0];
-    int128_t t1   = (int128_t)a[ 0] * b[ 1];
-    int128_t t101 = (int128_t)a[ 1] * b[ 0];
-    int128_t t2   = (int128_t)a[ 0] * b[ 2];
-    int128_t t102 = (int128_t)a[ 1] * b[ 1];
-    int128_t t202 = (int128_t)a[ 2] * b[ 0];
-    int128_t t3   = (int128_t)a[ 0] * b[ 3];
-    int128_t t103 = (int128_t)a[ 1] * b[ 2];
-    int128_t t203 = (int128_t)a[ 2] * b[ 1];
-    int128_t t303 = (int128_t)a[ 3] * b[ 0];
-    int128_t t4   = (int128_t)a[ 0] * b[ 4];
-    int128_t t104 = (int128_t)a[ 1] * b[ 3];
-    int128_t t204 = (int128_t)a[ 2] * b[ 2];
-    int128_t t304 = (int128_t)a[ 3] * b[ 1];
-    int128_t t404 = (int128_t)a[ 4] * b[ 0];
-    int128_t t5   = (int128_t)a[ 0] * b[ 5];
-    int128_t t105 = (int128_t)a[ 1] * b[ 4];
-    int128_t t205 = (int128_t)a[ 2] * b[ 3];
-    int128_t t305 = (int128_t)a[ 3] * b[ 2];
-    int128_t t405 = (int128_t)a[ 4] * b[ 1];
-    int128_t t505 = (int128_t)a[ 5] * b[ 0];
-    int128_t t6   = (int128_t)a[ 0] * b[ 6];
-    int128_t t106 = (int128_t)a[ 1] * b[ 5];
-    int128_t t206 = (int128_t)a[ 2] * b[ 4];
-    int128_t t306 = (int128_t)a[ 3] * b[ 3];
-    int128_t t406 = (int128_t)a[ 4] * b[ 2];
-    int128_t t506 = (int128_t)a[ 5] * b[ 1];
-    int128_t t606 = (int128_t)a[ 6] * b[ 0];
-    int128_t t7   = (int128_t)a[ 0] * b[ 7];
-    int128_t t107 = (int128_t)a[ 1] * b[ 6];
-    int128_t t207 = (int128_t)a[ 2] * b[ 5];
-    int128_t t307 = (int128_t)a[ 3] * b[ 4];
-    int128_t t407 = (int128_t)a[ 4] * b[ 3];
-    int128_t t507 = (int128_t)a[ 5] * b[ 2];
-    int128_t t607 = (int128_t)a[ 6] * b[ 1];
-    int128_t t707 = (int128_t)a[ 7] * b[ 0];
-    int128_t t8   = (int128_t)a[ 1] * b[ 7];
-    int128_t t108 = (int128_t)a[ 2] * b[ 6];
-    int128_t t208 = (int128_t)a[ 3] * b[ 5];
-    int128_t t308 = (int128_t)a[ 4] * b[ 4];
-    int128_t t408 = (int128_t)a[ 5] * b[ 3];
-    int128_t t508 = (int128_t)a[ 6] * b[ 2];
-    int128_t t608 = (int128_t)a[ 7] * b[ 1];
-    int128_t t9   = (int128_t)a[ 2] * b[ 7];
-    int128_t t109 = (int128_t)a[ 3] * b[ 6];
-    int128_t t209 = (int128_t)a[ 4] * b[ 5];
-    int128_t t309 = (int128_t)a[ 5] * b[ 4];
-    int128_t t409 = (int128_t)a[ 6] * b[ 3];
-    int128_t t509 = (int128_t)a[ 7] * b[ 2];
-    int128_t t10  = (int128_t)a[ 3] * b[ 7];
-    int128_t t110 = (int128_t)a[ 4] * b[ 6];
-    int128_t t210 = (int128_t)a[ 5] * b[ 5];
-    int128_t t310 = (int128_t)a[ 6] * b[ 4];
-    int128_t t410 = (int128_t)a[ 7] * b[ 3];
-    int128_t t11  = (int128_t)a[ 4] * b[ 7];
-    int128_t t111 = (int128_t)a[ 5] * b[ 6];
-    int128_t t211 = (int128_t)a[ 6] * b[ 5];
-    int128_t t311 = (int128_t)a[ 7] * b[ 4];
-    int128_t t12  = (int128_t)a[ 5] * b[ 7];
-    int128_t t112 = (int128_t)a[ 6] * b[ 6];
-    int128_t t212 = (int128_t)a[ 7] * b[ 5];
-    int128_t t13  = (int128_t)a[ 6] * b[ 7];
-    int128_t t113 = (int128_t)a[ 7] * b[ 6];
-    int128_t t14  = (int128_t)a[ 7] * b[ 7];
-    t1  += t101;
-    t2  += t102; t2  += t202;
-    t3  += t103; t3  += t203; t3  += t303;
-    t4  += t104; t4  += t204; t4  += t304; t4  += t404;
-    t5  += t105; t5  += t205; t5  += t305; t5  += t405; t5  += t505;
-    t6  += t106; t6  += t206; t6  += t306; t6  += t406; t6  += t506;
-    t6  += t606;
-    t7  += t107; t7  += t207; t7  += t307; t7  += t407; t7  += t507;
-    t7  += t607;
-    t7  += t707;
-    t8  += t108; t8  += t208; t8  += t308; t8  += t408; t8  += t508;
-    t8  += t608;
-    t9  += t109; t9  += t209; t9  += t309; t9  += t409; t9  += t509;
-    t10 += t110; t10 += t210; t10 += t310; t10 += t410;
-    t11 += t111; t11 += t211; t11 += t311;
-    t12 += t112; t12 += t212;
-    t13 += t113;
-
-    /* Reduce */
-    t0  += t8  + t12;
-    t1  += t9  + t13;
-    t2  += t10 + t14;
-    t3  += t11;
-    t4  += t12 + t8  + t12;
-    t5  += t13 + t9  + t13;
-    t6  += t14 + t10 + t14;
-    t7  +=       t11;
-    o = t7  >> 56; t0  += o;
-                   t4  += o; t = (int128_t)o << 56; t7  -= t;
-    o = t0  >> 56; t1  += o; t = (int128_t)o << 56; t0  -= t;
-    o = t1  >> 56; t2  += o; t = (int128_t)o << 56; t1  -= t;
-    o = t2  >> 56; t3  += o; t = (int128_t)o << 56; t2  -= t;
-    o = t3  >> 56; t4  += o; t = (int128_t)o << 56; t3  -= t;
-    o = t4  >> 56; t5  += o; t = (int128_t)o << 56; t4  -= t;
-    o = t5  >> 56; t6  += o; t = (int128_t)o << 56; t5  -= t;
-    o = t6  >> 56; t7  += o; t = (int128_t)o << 56; t6  -= t;
-    o = t7  >> 56; t0  += o;
-                   t4  += o; t = (int128_t)o << 56; t7  -= t;
-
-    /* Store */
-    r[0] = t0;
-    r[1] = t1;
-    r[2] = t2;
-    r[3] = t3;
-    r[4] = t4;
-    r[5] = t5;
-    r[6] = t6;
-    r[7] = t7;
-}
-
-/* Square a field element. r = (a * a) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to square.
- */
-void fe448_sqr(int64_t* r, const int64_t* a)
-{
-    int128_t t;
-    int64_t o;
-    int128_t t0   =     (int128_t)a[ 0] * a[ 0];
-    int128_t t1   = 2 * (int128_t)a[ 0] * a[ 1];
-    int128_t t2   = 2 * (int128_t)a[ 0] * a[ 2];
-    int128_t t102 =     (int128_t)a[ 1] * a[ 1];
-    int128_t t3   = 2 * (int128_t)a[ 0] * a[ 3];
-    int128_t t103 = 2 * (int128_t)a[ 1] * a[ 2];
-    int128_t t4   = 2 * (int128_t)a[ 0] * a[ 4];
-    int128_t t104 = 2 * (int128_t)a[ 1] * a[ 3];
-    int128_t t204 =     (int128_t)a[ 2] * a[ 2];
-    int128_t t5   = 2 * (int128_t)a[ 0] * a[ 5];
-    int128_t t105 = 2 * (int128_t)a[ 1] * a[ 4];
-    int128_t t205 = 2 * (int128_t)a[ 2] * a[ 3];
-    int128_t t6   = 2 * (int128_t)a[ 0] * a[ 6];
-    int128_t t106 = 2 * (int128_t)a[ 1] * a[ 5];
-    int128_t t206 = 2 * (int128_t)a[ 2] * a[ 4];
-    int128_t t306 =     (int128_t)a[ 3] * a[ 3];
-    int128_t t7   = 2 * (int128_t)a[ 0] * a[ 7];
-    int128_t t107 = 2 * (int128_t)a[ 1] * a[ 6];
-    int128_t t207 = 2 * (int128_t)a[ 2] * a[ 5];
-    int128_t t307 = 2 * (int128_t)a[ 3] * a[ 4];
-    int128_t t8   = 2 * (int128_t)a[ 1] * a[ 7];
-    int128_t t108 = 2 * (int128_t)a[ 2] * a[ 6];
-    int128_t t208 = 2 * (int128_t)a[ 3] * a[ 5];
-    int128_t t308 =     (int128_t)a[ 4] * a[ 4];
-    int128_t t9   = 2 * (int128_t)a[ 2] * a[ 7];
-    int128_t t109 = 2 * (int128_t)a[ 3] * a[ 6];
-    int128_t t209 = 2 * (int128_t)a[ 4] * a[ 5];
-    int128_t t10  = 2 * (int128_t)a[ 3] * a[ 7];
-    int128_t t110 = 2 * (int128_t)a[ 4] * a[ 6];
-    int128_t t210 =     (int128_t)a[ 5] * a[ 5];
-    int128_t t11  = 2 * (int128_t)a[ 4] * a[ 7];
-    int128_t t111 = 2 * (int128_t)a[ 5] * a[ 6];
-    int128_t t12  = 2 * (int128_t)a[ 5] * a[ 7];
-    int128_t t112 =     (int128_t)a[ 6] * a[ 6];
-    int128_t t13  = 2 * (int128_t)a[ 6] * a[ 7];
-    int128_t t14  =     (int128_t)a[ 7] * a[ 7];
-    t2  += t102;
-    t3  += t103;
-    t4  += t104; t4  += t204;
-    t5  += t105; t5  += t205;
-    t6  += t106; t6  += t206; t6  += t306;
-    t7  += t107; t7  += t207; t7  += t307;
-    t8  += t108; t8  += t208; t8  += t308;
-    t9  += t109; t9  += t209;
-    t10 += t110; t10 += t210;
-    t11 += t111;
-    t12 += t112;
-
-    /* Reduce */
-    t0  += t8  + t12;
-    t1  += t9  + t13;
-    t2  += t10 + t14;
-    t3  += t11;
-    t4  += t12 + t8  + t12;
-    t5  += t13 + t9  + t13;
-    t6  += t14 + t10 + t14;
-    t7  +=       t11;
-    o = t7  >> 56; t0  += o;
-                   t4  += o; t = (int128_t)o << 56; t7  -= t;
-    o = t0  >> 56; t1  += o; t = (int128_t)o << 56; t0  -= t;
-    o = t1  >> 56; t2  += o; t = (int128_t)o << 56; t1  -= t;
-    o = t2  >> 56; t3  += o; t = (int128_t)o << 56; t2  -= t;
-    o = t3  >> 56; t4  += o; t = (int128_t)o << 56; t3  -= t;
-    o = t4  >> 56; t5  += o; t = (int128_t)o << 56; t4  -= t;
-    o = t5  >> 56; t6  += o; t = (int128_t)o << 56; t5  -= t;
-    o = t6  >> 56; t7  += o; t = (int128_t)o << 56; t6  -= t;
-    o = t7  >> 56; t0  += o;
-                   t4  += o; t = (int128_t)o << 56; t7  -= t;
-
-    /* Store */
-    r[0] = t0;
-    r[1] = t1;
-    r[2] = t2;
-    r[3] = t3;
-    r[4] = t4;
-    r[5] = t5;
-    r[6] = t6;
-    r[7] = t7;
-}
-
-/* Invert the field element. (r * a) mod (2^448 - 2^224 - 1) = 1
- * Constant time implementation - using Fermat's little theorem:
- *   a^(p-1) mod p = 1 => a^(p-2) mod p = 1/a
- * For curve448: p - 2 = 2^448 - 2^224 - 3
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to invert.
- */
-void fe448_invert(int64_t* r, const int64_t* a)
-{
-    int64_t t1[8];
-    int64_t t2[8];
-    int64_t t3[8];
-    int64_t t4[8];
-    int i;
-
-    fe448_sqr(t1, a);
-    /* t1 = 2 */
-    fe448_mul(t1, t1, a);
-    /* t1 = 3 */
-    fe448_sqr(t2, t1); for (i = 1; i < 2; ++i) fe448_sqr(t2, t2);
-    /* t2 = c */
-    fe448_mul(t3, t2, a);
-    /* t3 = d */
-    fe448_mul(t1, t2, t1);
-    /* t1 = f */
-    fe448_sqr(t2, t1);
-    /* t2 = 1e */
-    fe448_mul(t4, t2, a);
-    /* t4 = 1f */
-    fe448_sqr(t2, t4); for (i = 1; i < 5; ++i) fe448_sqr(t2, t2);
-    /* t2 = 3e0 */
-    fe448_mul(t1, t2, t4);
-    /* t1 = 3ff */
-    fe448_sqr(t2, t1); for (i = 1; i < 10; ++i) fe448_sqr(t2, t2);
-    /* t2 = ffc00 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = fffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 5; ++i) fe448_sqr(t2, t2);
-    /* t2 = 1ffffe0 */
-    fe448_mul(t1, t2, t4);
-    /* t1 = 1ffffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 25; ++i) fe448_sqr(t2, t2);
-    /* t2 = 3fffffe000000 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = 3ffffffffffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 5; ++i) fe448_sqr(t2, t2);
-    /* t2 = 7fffffffffffe0 */
-    fe448_mul(t1, t2, t4);
-    /* t1 = 7fffffffffffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 55; ++i) fe448_sqr(t2, t2);
-    /* t2 = 3fffffffffffff80000000000000 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = 3fffffffffffffffffffffffffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 110; ++i) fe448_sqr(t2, t2);
-    /* t2 = fffffffffffffffffffffffffffc000000000000000000000000000 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = fffffffffffffffffffffffffffffffffffffffffffffffffffffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 4; ++i) fe448_sqr(t2, t2);
-    /* t2 = fffffffffffffffffffffffffffffffffffffffffffffffffffffff0 */
-    fe448_mul(t3, t3, t2);
-    /* t3 = fffffffffffffffffffffffffffffffffffffffffffffffffffffffd */
-    fe448_mul(t1, t3, a);
-    /* t1 = fffffffffffffffffffffffffffffffffffffffffffffffffffffffe */
-    fe448_sqr(t1, t1); for (i = 1; i < 224; ++i) fe448_sqr(t1, t1);
-    /* t1 = fffffffffffffffffffffffffffffffffffffffffffffffffffffffe00000000000000000000000000000000000000000000000000000000 */
-    fe448_mul(r, t3, t1);
-    /* r = fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffffffffffffffffffffffffffffffffffffffffffffffffffffd */
-}
-
-/* Scalar multiply the point by a number. r = n.a
- * Uses Montogmery ladder and only requires the x-ordinate.
- *
- * r  [in]  Field element to hold result.
- * n  [in]  Scalar as an array of bytes.
- * a  [in]  Point to multiply - x-ordinate only.
- */
-int curve448(byte* r, const byte* n, const byte* a)
-{
-    int64_t x1[8];
-    int64_t x2[8];
-    int64_t z2[8];
-    int64_t x3[8];
-    int64_t z3[8];
-    int64_t t0[8];
-    int64_t t1[8];
-    int i;
-    unsigned int swap;
-    unsigned int b;
-
-    fe448_from_bytes(x1, a);
-    fe448_1(x2);
-    fe448_0(z2);
-    fe448_copy(x3, x1);
-    fe448_1(z3);
-
-    swap = 0;
-    for (i = 447; i >= 0; --i) {
-        b = (n[i >> 3] >> (i & 7)) & 1;
-        swap ^= b;
-        fe448_cswap(x2, x3, swap);
-        fe448_cswap(z2, z3, swap);
-        swap = b;
-
-        /* Montgomery Ladder - double and add */
-        fe448_add(t0, x2, z2);
-        fe448_reduce(t0);
-        fe448_add(t1, x3, z3);
-        fe448_reduce(t1);
-        fe448_sub(x2, x2, z2);
-        fe448_sub(x3, x3, z3);
-        fe448_mul(t1, t1, x2);
-        fe448_mul(z3, x3, t0);
-        fe448_sqr(t0, t0);
-        fe448_sqr(x2, x2);
-        fe448_add(x3, z3, t1);
-        fe448_reduce(x3);
-        fe448_sqr(x3, x3);
-        fe448_sub(z3, z3, t1);
-        fe448_sqr(z3, z3);
-        fe448_mul(z3, z3, x1);
-        fe448_sub(t1, t0, x2);
-        fe448_mul(x2, t0, x2);
-        fe448_mul39081(z2, t1);
-        fe448_add(z2, t0, z2);
-        fe448_mul(z2, z2, t1);
-    }
-    /* Last two bits are 0 - no final swap check required. */
-
-    fe448_invert(z2, z2);
-    fe448_mul(x2, x2, z2);
-    fe448_to_bytes(r, x2);
-
-    return 0;
-}
-
-#ifdef HAVE_ED448
-/* Check whether field element is not 0.
- * Must convert to a normalized form before checking.
- *
- * a  [in]  Field element.
- * returns 0 when zero, and any other value otherwise.
- */
-int fe448_isnonzero(const int64_t* a)
-{
-    uint8_t b[56];
-    int i;
-    uint8_t c = 0;
-    fe448_to_bytes(b, a);
-    for (i = 0; i < 56; i++)
-        c |= b[i];
-    return c;
-}
-
-/* Check whether field element is negative.
- * Must convert to a normalized form before checking.
- *
- * a  [in]  Field element.
- * returns 1 when negative, and 0 otherwise.
- */
-int fe448_isnegative(const int64_t* a)
-{
-    uint8_t b[56];
-    fe448_to_bytes(b, a);
-    return b[0] & 1;
-}
-
-/* Negates the field element. r = -a
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element.
- */
-void fe448_neg(int64_t* r, const int64_t* a)
-{
-    r[0] = -a[0];
-    r[1] = -a[1];
-    r[2] = -a[2];
-    r[3] = -a[3];
-    r[4] = -a[4];
-    r[5] = -a[5];
-    r[6] = -a[6];
-    r[7] = -a[7];
-}
-
-/* Raise field element to (p-3) / 4: 2^446 - 2^222 - 1
- * Used for calcualting y-ordinate from x-ordinate for Ed448.
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to exponentiate.
- */
-void fe448_pow_2_446_222_1(int64_t* r, const int64_t* a)
-{
-    int64_t t1[8];
-    int64_t t2[8];
-    int64_t t3[8];
-    int64_t t4[8];
-    int64_t t5[8];
-    int i;
-
-    fe448_sqr(t3, a);
-    /* t3 = 2 */
-    fe448_mul(t1, t3, a);
-    /* t1 = 3 */
-    fe448_sqr(t5, t1);
-    /* t5 = 6 */
-    fe448_mul(t5, t5, a);
-    /* t5 = 7 */
-    fe448_sqr(t2, t1); for (i = 1; i < 2; ++i) fe448_sqr(t2, t2);
-    /* t2 = c */
-    fe448_mul(t3, t2, t3);
-    /* t3 = e */
-    fe448_mul(t1, t2, t1);
-    /* t1 = f */
-    fe448_sqr(t2, t1); for (i = 1; i < 3; ++i) fe448_sqr(t2, t2);
-    /* t2 = 78 */
-    fe448_mul(t5, t2, t5);
-    /* t5 = 7f */
-    fe448_sqr(t2, t1); for (i = 1; i < 4; ++i) fe448_sqr(t2, t2);
-    /* t2 = f0 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = ff */
-    fe448_mul(t3, t3, t2);
-    /* t3 = fe */
-    fe448_sqr(t2, t1); for (i = 1; i < 7; ++i) fe448_sqr(t2, t2);
-    /* t2 = 7f80 */
-    fe448_mul(t5, t2, t5);
-    /* t5 = 7fff */
-    fe448_sqr(t2, t1); for (i = 1; i < 8; ++i) fe448_sqr(t2, t2);
-    /* t2 = ff00 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = ffff */
-    fe448_mul(t3, t3, t2);
-    /* t3 = fffe */
-    fe448_sqr(t2, t5); for (i = 1; i < 15; ++i) fe448_sqr(t2, t2);
-    /* t2 = 3fff8000 */
-    fe448_mul(t5, t2, t5);
-    /* t5 = 3fffffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 16; ++i) fe448_sqr(t2, t2);
-    /* t2 = ffff0000 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = ffffffff */
-    fe448_mul(t3, t3, t2);
-    /* t3 = fffffffe */
-    fe448_sqr(t2, t1); for (i = 1; i < 32; ++i) fe448_sqr(t2, t2);
-    /* t2 = ffffffff00000000 */
-    fe448_mul(t2, t2, t1);
-    /* t2 = ffffffffffffffff */
-    fe448_sqr(t1, t2); for (i = 1; i < 64; ++i) fe448_sqr(t1, t1);
-    /* t1 = ffffffffffffffff0000000000000000 */
-    fe448_mul(t1, t1, t2);
-    /* t1 = ffffffffffffffffffffffffffffffff */
-    fe448_sqr(t1, t1); for (i = 1; i < 64; ++i) fe448_sqr(t1, t1);
-    /* t1 = ffffffffffffffffffffffffffffffff0000000000000000 */
-    fe448_mul(t4, t1, t2);
-    /* t4 = ffffffffffffffffffffffffffffffffffffffffffffffff */
-    fe448_sqr(t2, t4); for (i = 1; i < 32; ++i) fe448_sqr(t2, t2);
-    /* t2 = ffffffffffffffffffffffffffffffffffffffffffffffff00000000 */
-    fe448_mul(t3, t3, t2);
-    /* t3 = fffffffffffffffffffffffffffffffffffffffffffffffffffffffe */
-    fe448_sqr(t1, t3); for (i = 1; i < 192; ++i) fe448_sqr(t1, t1);
-    /* t1 = fffffffffffffffffffffffffffffffffffffffffffffffffffffffe000000000000000000000000000000000000000000000000 */
-    fe448_mul(t1, t1, t4);
-    /* t1 = fffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffff */
-    fe448_sqr(t1, t1); for (i = 1; i < 30; ++i) fe448_sqr(t1, t1);
-    /* t1 = 3fffffffffffffffffffffffffffffffffffffffffffffffffffffffbfffffffffffffffffffffffffffffffffffffffffffffffc0000000 */
-    fe448_mul(r, t5, t1);
-    /* r = 3fffffffffffffffffffffffffffffffffffffffffffffffffffffffbfffffffffffffffffffffffffffffffffffffffffffffffffffffff */
-}
-
-/* Constant time, conditional move of b into a.
- * a is not changed if the condition is 0.
- *
- * a  A field element.
- * b  A field element.
- * c  If 1 then copy and if 0 then don't copy.
- */
-void fe448_cmov(int64_t* a, const int64_t* b, int c)
-{
-    int64_t m = -(int64_t)c;
-    int64_t t0 = m & (a[0] ^ b[0]);
-    int64_t t1 = m & (a[1] ^ b[1]);
-    int64_t t2 = m & (a[2] ^ b[2]);
-    int64_t t3 = m & (a[3] ^ b[3]);
-    int64_t t4 = m & (a[4] ^ b[4]);
-    int64_t t5 = m & (a[5] ^ b[5]);
-    int64_t t6 = m & (a[6] ^ b[6]);
-    int64_t t7 = m & (a[7] ^ b[7]);
-
-    a[0] ^= t0;
-    a[1] ^= t1;
-    a[2] ^= t2;
-    a[3] ^= t3;
-    a[4] ^= t4;
-    a[5] ^= t5;
-    a[6] ^= t6;
-    a[7] ^= t7;
-}
-
-#endif /* HAVE_ED448 */
-#else
-
-/* Initialize the field element operations.
- */
-void fe448_init(void)
-{
-}
-
-/* Convert the field element from a byte array to an array of 28-bits.
- *
- * r  [in]  Array to encode into.
- * b  [in]  Byte array.
- */
-void fe448_from_bytes(int32_t* r, const unsigned char* b)
-{
-    r[ 0] =  (((int32_t)((b[ 0]        ) >>  0)) <<  0)
-          |  (((int32_t)((b[ 1]        ) >>  0)) <<  8)
-          |  (((int32_t)((b[ 2]        ) >>  0)) << 16)
-          | ((((int32_t)((b[ 3] & 0xf )) >>  0)) << 24);
-    r[ 1] =  (((int32_t)((b[ 3]        ) >>  4)) <<  0)
-          |  (((int32_t)((b[ 4]        ) >>  0)) <<  4)
-          |  (((int32_t)((b[ 5]        ) >>  0)) << 12)
-          |  (((int32_t)((b[ 6]        ) >>  0)) << 20);
-    r[ 2] =  (((int32_t)((b[ 7]        ) >>  0)) <<  0)
-          |  (((int32_t)((b[ 8]        ) >>  0)) <<  8)
-          |  (((int32_t)((b[ 9]        ) >>  0)) << 16)
-          | ((((int32_t)((b[10] & 0xf )) >>  0)) << 24);
-    r[ 3] =  (((int32_t)((b[10]        ) >>  4)) <<  0)
-          |  (((int32_t)((b[11]        ) >>  0)) <<  4)
-          |  (((int32_t)((b[12]        ) >>  0)) << 12)
-          |  (((int32_t)((b[13]        ) >>  0)) << 20);
-    r[ 4] =  (((int32_t)((b[14]        ) >>  0)) <<  0)
-          |  (((int32_t)((b[15]        ) >>  0)) <<  8)
-          |  (((int32_t)((b[16]        ) >>  0)) << 16)
-          | ((((int32_t)((b[17] & 0xf )) >>  0)) << 24);
-    r[ 5] =  (((int32_t)((b[17]        ) >>  4)) <<  0)
-          |  (((int32_t)((b[18]        ) >>  0)) <<  4)
-          |  (((int32_t)((b[19]        ) >>  0)) << 12)
-          |  (((int32_t)((b[20]        ) >>  0)) << 20);
-    r[ 6] =  (((int32_t)((b[21]        ) >>  0)) <<  0)
-          |  (((int32_t)((b[22]        ) >>  0)) <<  8)
-          |  (((int32_t)((b[23]        ) >>  0)) << 16)
-          | ((((int32_t)((b[24] & 0xf )) >>  0)) << 24);
-    r[ 7] =  (((int32_t)((b[24]        ) >>  4)) <<  0)
-          |  (((int32_t)((b[25]        ) >>  0)) <<  4)
-          |  (((int32_t)((b[26]        ) >>  0)) << 12)
-          |  (((int32_t)((b[27]        ) >>  0)) << 20);
-    r[ 8] =  (((int32_t)((b[28]        ) >>  0)) <<  0)
-          |  (((int32_t)((b[29]        ) >>  0)) <<  8)
-          |  (((int32_t)((b[30]        ) >>  0)) << 16)
-          | ((((int32_t)((b[31] & 0xf )) >>  0)) << 24);
-    r[ 9] =  (((int32_t)((b[31]        ) >>  4)) <<  0)
-          |  (((int32_t)((b[32]        ) >>  0)) <<  4)
-          |  (((int32_t)((b[33]        ) >>  0)) << 12)
-          |  (((int32_t)((b[34]        ) >>  0)) << 20);
-    r[10] =  (((int32_t)((b[35]        ) >>  0)) <<  0)
-          |  (((int32_t)((b[36]        ) >>  0)) <<  8)
-          |  (((int32_t)((b[37]        ) >>  0)) << 16)
-          | ((((int32_t)((b[38] & 0xf )) >>  0)) << 24);
-    r[11] =  (((int32_t)((b[38]        ) >>  4)) <<  0)
-          |  (((int32_t)((b[39]        ) >>  0)) <<  4)
-          |  (((int32_t)((b[40]        ) >>  0)) << 12)
-          |  (((int32_t)((b[41]        ) >>  0)) << 20);
-    r[12] =  (((int32_t)((b[42]        ) >>  0)) <<  0)
-          |  (((int32_t)((b[43]        ) >>  0)) <<  8)
-          |  (((int32_t)((b[44]        ) >>  0)) << 16)
-          | ((((int32_t)((b[45] & 0xf )) >>  0)) << 24);
-    r[13] =  (((int32_t)((b[45]        ) >>  4)) <<  0)
-          |  (((int32_t)((b[46]        ) >>  0)) <<  4)
-          |  (((int32_t)((b[47]        ) >>  0)) << 12)
-          |  (((int32_t)((b[48]        ) >>  0)) << 20);
-    r[14] =  (((int32_t)((b[49]        ) >>  0)) <<  0)
-          |  (((int32_t)((b[50]        ) >>  0)) <<  8)
-          |  (((int32_t)((b[51]        ) >>  0)) << 16)
-          | ((((int32_t)((b[52] & 0xf )) >>  0)) << 24);
-    r[15] =  (((int32_t)((b[52]        ) >>  4)) <<  0)
-          |  (((int32_t)((b[53]        ) >>  0)) <<  4)
-          |  (((int32_t)((b[54]        ) >>  0)) << 12)
-          |  (((int32_t)((b[55]        ) >>  0)) << 20);
-}
-
-/* Convert the field element to a byte array from an array of 28-bits.
- *
- * b  [in]  Byte array.
- * a  [in]  Array to encode into.
- */
-void fe448_to_bytes(unsigned char* b, const int32_t* a)
-{
-    int64_t t;
-    /* Mod */
-    int32_t in0 = a[0];
-    int32_t in1 = a[1];
-    int32_t in2 = a[2];
-    int32_t in3 = a[3];
-    int32_t in4 = a[4];
-    int32_t in5 = a[5];
-    int32_t in6 = a[6];
-    int32_t in7 = a[7];
-    int32_t in8 = a[8];
-    int32_t in9 = a[9];
-    int32_t in10 = a[10];
-    int32_t in11 = a[11];
-    int32_t in12 = a[12];
-    int32_t in13 = a[13];
-    int32_t in14 = a[14];
-    int32_t in15 = a[15];
-    int32_t o = in15 >> 28;
-    in15 -= o << 28;
-    in0 += o;
-    in8 += o;
-    o = (in0 + 1) >> 28;
-    o = (o + in1) >> 28;
-    o = (o + in2) >> 28;
-    o = (o + in3) >> 28;
-    o = (o + in4) >> 28;
-    o = (o + in5) >> 28;
-    o = (o + in6) >> 28;
-    o = (o + in7) >> 28;
-    o = (o + in8 + 1) >> 28;
-    o = (o + in9) >> 28;
-    o = (o + in10) >> 28;
-    o = (o + in11) >> 28;
-    o = (o + in12) >> 28;
-    o = (o + in13) >> 28;
-    o = (o + in14) >> 28;
-    o = (o + in15) >> 28;
-    in0 += o;
-    in8 += o;
-    in15 -= o << 28;
-    o = in0  >> 28; in1  += o; t = o << 28; in0  -= t;
-    o = in1  >> 28; in2  += o; t = o << 28; in1  -= t;
-    o = in2  >> 28; in3  += o; t = o << 28; in2  -= t;
-    o = in3  >> 28; in4  += o; t = o << 28; in3  -= t;
-    o = in4  >> 28; in5  += o; t = o << 28; in4  -= t;
-    o = in5  >> 28; in6  += o; t = o << 28; in5  -= t;
-    o = in6  >> 28; in7  += o; t = o << 28; in6  -= t;
-    o = in7  >> 28; in8  += o; t = o << 28; in7  -= t;
-    o = in8  >> 28; in9  += o; t = o << 28; in8  -= t;
-    o = in9  >> 28; in10 += o; t = o << 28; in9  -= t;
-    o = in10 >> 28; in11 += o; t = o << 28; in10 -= t;
-    o = in11 >> 28; in12 += o; t = o << 28; in11 -= t;
-    o = in12 >> 28; in13 += o; t = o << 28; in12 -= t;
-    o = in13 >> 28; in14 += o; t = o << 28; in13 -= t;
-    o = in14 >> 28; in15 += o; t = o << 28; in14 -= t;
-    o = in15 >> 28; in0  += o;
-                    in8  += o; t = o << 28; in15 -= t;
-
-    /* Output as bytes */
-    b[ 0] = (in0  >>  0);
-    b[ 1] = (in0  >>  8);
-    b[ 2] = (in0  >> 16);
-    b[ 3] = (in0  >> 24) + ((in1  >>  0) <<  4);
-    b[ 4] = (in1  >>  4);
-    b[ 5] = (in1  >> 12);
-    b[ 6] = (in1  >> 20);
-    b[ 7] = (in2  >>  0);
-    b[ 8] = (in2  >>  8);
-    b[ 9] = (in2  >> 16);
-    b[10] = (in2  >> 24) + ((in3  >>  0) <<  4);
-    b[11] = (in3  >>  4);
-    b[12] = (in3  >> 12);
-    b[13] = (in3  >> 20);
-    b[14] = (in4  >>  0);
-    b[15] = (in4  >>  8);
-    b[16] = (in4  >> 16);
-    b[17] = (in4  >> 24) + ((in5  >>  0) <<  4);
-    b[18] = (in5  >>  4);
-    b[19] = (in5  >> 12);
-    b[20] = (in5  >> 20);
-    b[21] = (in6  >>  0);
-    b[22] = (in6  >>  8);
-    b[23] = (in6  >> 16);
-    b[24] = (in6  >> 24) + ((in7  >>  0) <<  4);
-    b[25] = (in7  >>  4);
-    b[26] = (in7  >> 12);
-    b[27] = (in7  >> 20);
-    b[28] = (in8  >>  0);
-    b[29] = (in8  >>  8);
-    b[30] = (in8  >> 16);
-    b[31] = (in8  >> 24) + ((in9  >>  0) <<  4);
-    b[32] = (in9  >>  4);
-    b[33] = (in9  >> 12);
-    b[34] = (in9  >> 20);
-    b[35] = (in10 >>  0);
-    b[36] = (in10 >>  8);
-    b[37] = (in10 >> 16);
-    b[38] = (in10 >> 24) + ((in11 >>  0) <<  4);
-    b[39] = (in11 >>  4);
-    b[40] = (in11 >> 12);
-    b[41] = (in11 >> 20);
-    b[42] = (in12 >>  0);
-    b[43] = (in12 >>  8);
-    b[44] = (in12 >> 16);
-    b[45] = (in12 >> 24) + ((in13 >>  0) <<  4);
-    b[46] = (in13 >>  4);
-    b[47] = (in13 >> 12);
-    b[48] = (in13 >> 20);
-    b[49] = (in14 >>  0);
-    b[50] = (in14 >>  8);
-    b[51] = (in14 >> 16);
-    b[52] = (in14 >> 24) + ((in15 >>  0) <<  4);
-    b[53] = (in15 >>  4);
-    b[54] = (in15 >> 12);
-    b[55] = (in15 >> 20);
-}
-
-/* Set the field element to 0.
- *
- * a  [in]  Field element.
- */
-void fe448_1(int32_t* a)
-{
-    a[0] = 1;
-    a[1] = 0;
-    a[2] = 0;
-    a[3] = 0;
-    a[4] = 0;
-    a[5] = 0;
-    a[6] = 0;
-    a[7] = 0;
-    a[8] = 0;
-    a[9] = 0;
-    a[10] = 0;
-    a[11] = 0;
-    a[12] = 0;
-    a[13] = 0;
-    a[14] = 0;
-    a[15] = 0;
-}
-
-/* Set the field element to 0.
- *
- * a  [in]  Field element.
- */
-void fe448_0(int32_t* a)
-{
-    a[0] = 0;
-    a[1] = 0;
-    a[2] = 0;
-    a[3] = 0;
-    a[4] = 0;
-    a[5] = 0;
-    a[6] = 0;
-    a[7] = 0;
-    a[8] = 0;
-    a[9] = 0;
-    a[10] = 0;
-    a[11] = 0;
-    a[12] = 0;
-    a[13] = 0;
-    a[14] = 0;
-    a[15] = 0;
-}
-
-/* Copy one field element into another: d = a.
- *
- * d  [in]  Destination field element.
- * a  [in]  Source field element.
- */
-void fe448_copy(int32_t* d, const int32_t* a)
-{
-    d[0] = a[0];
-    d[1] = a[1];
-    d[2] = a[2];
-    d[3] = a[3];
-    d[4] = a[4];
-    d[5] = a[5];
-    d[6] = a[6];
-    d[7] = a[7];
-    d[8] = a[8];
-    d[9] = a[9];
-    d[10] = a[10];
-    d[11] = a[11];
-    d[12] = a[12];
-    d[13] = a[13];
-    d[14] = a[14];
-    d[15] = a[15];
-}
-
-/* Conditionally swap the elements.
- * Constant time implementation.
- *
- * a  [in]  First field element.
- * b  [in]  Second field element.
- * c  [in]  Swap when 1. Valid values: 0, 1.
- */
-static void fe448_cswap(int32_t* a, int32_t* b, int c)
-{
-    int32_t mask = -(int32_t)c;
-    int32_t t0 = (a[0] ^ b[0]) & mask;
-    int32_t t1 = (a[1] ^ b[1]) & mask;
-    int32_t t2 = (a[2] ^ b[2]) & mask;
-    int32_t t3 = (a[3] ^ b[3]) & mask;
-    int32_t t4 = (a[4] ^ b[4]) & mask;
-    int32_t t5 = (a[5] ^ b[5]) & mask;
-    int32_t t6 = (a[6] ^ b[6]) & mask;
-    int32_t t7 = (a[7] ^ b[7]) & mask;
-    int32_t t8 = (a[8] ^ b[8]) & mask;
-    int32_t t9 = (a[9] ^ b[9]) & mask;
-    int32_t t10 = (a[10] ^ b[10]) & mask;
-    int32_t t11 = (a[11] ^ b[11]) & mask;
-    int32_t t12 = (a[12] ^ b[12]) & mask;
-    int32_t t13 = (a[13] ^ b[13]) & mask;
-    int32_t t14 = (a[14] ^ b[14]) & mask;
-    int32_t t15 = (a[15] ^ b[15]) & mask;
-    a[0] ^= t0;
-    a[1] ^= t1;
-    a[2] ^= t2;
-    a[3] ^= t3;
-    a[4] ^= t4;
-    a[5] ^= t5;
-    a[6] ^= t6;
-    a[7] ^= t7;
-    a[8] ^= t8;
-    a[9] ^= t9;
-    a[10] ^= t10;
-    a[11] ^= t11;
-    a[12] ^= t12;
-    a[13] ^= t13;
-    a[14] ^= t14;
-    a[15] ^= t15;
-    b[0] ^= t0;
-    b[1] ^= t1;
-    b[2] ^= t2;
-    b[3] ^= t3;
-    b[4] ^= t4;
-    b[5] ^= t5;
-    b[6] ^= t6;
-    b[7] ^= t7;
-    b[8] ^= t8;
-    b[9] ^= t9;
-    b[10] ^= t10;
-    b[11] ^= t11;
-    b[12] ^= t12;
-    b[13] ^= t13;
-    b[14] ^= t14;
-    b[15] ^= t15;
-}
-
-/* Add two field elements. r = (a + b) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold sum.
- * a  [in]  Field element to add.
- * b  [in]  Field element to add.
- */
-void fe448_add(int32_t* r, const int32_t* a, const int32_t* b)
-{
-    r[0] = a[0] + b[0];
-    r[1] = a[1] + b[1];
-    r[2] = a[2] + b[2];
-    r[3] = a[3] + b[3];
-    r[4] = a[4] + b[4];
-    r[5] = a[5] + b[5];
-    r[6] = a[6] + b[6];
-    r[7] = a[7] + b[7];
-    r[8] = a[8] + b[8];
-    r[9] = a[9] + b[9];
-    r[10] = a[10] + b[10];
-    r[11] = a[11] + b[11];
-    r[12] = a[12] + b[12];
-    r[13] = a[13] + b[13];
-    r[14] = a[14] + b[14];
-    r[15] = a[15] + b[15];
-}
-
-/* Subtract a field element from another. r = (a - b) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold difference.
- * a  [in]  Field element to subtract from.
- * b  [in]  Field element to subtract.
- */
-void fe448_sub(int32_t* r, const int32_t* a, const int32_t* b)
-{
-    r[0] = a[0] - b[0];
-    r[1] = a[1] - b[1];
-    r[2] = a[2] - b[2];
-    r[3] = a[3] - b[3];
-    r[4] = a[4] - b[4];
-    r[5] = a[5] - b[5];
-    r[6] = a[6] - b[6];
-    r[7] = a[7] - b[7];
-    r[8] = a[8] - b[8];
-    r[9] = a[9] - b[9];
-    r[10] = a[10] - b[10];
-    r[11] = a[11] - b[11];
-    r[12] = a[12] - b[12];
-    r[13] = a[13] - b[13];
-    r[14] = a[14] - b[14];
-    r[15] = a[15] - b[15];
-}
-
-void fe448_reduce(int32_t* a)
-{
-    int64_t o;
-
-    o = a[0 ] >> 28; a[1 ] += o; a[0 ] -= o << 28;
-    o = a[1 ] >> 28; a[2 ] += o; a[1 ] -= o << 28;
-    o = a[2 ] >> 28; a[3 ] += o; a[2 ] -= o << 28;
-    o = a[3 ] >> 28; a[4 ] += o; a[3 ] -= o << 28;
-    o = a[4 ] >> 28; a[5 ] += o; a[4 ] -= o << 28;
-    o = a[5 ] >> 28; a[6 ] += o; a[5 ] -= o << 28;
-    o = a[6 ] >> 28; a[7 ] += o; a[6 ] -= o << 28;
-    o = a[7 ] >> 28; a[8 ] += o; a[7 ] -= o << 28;
-    o = a[8 ] >> 28; a[9 ] += o; a[8 ] -= o << 28;
-    o = a[9 ] >> 28; a[10] += o; a[9 ] -= o << 28;
-    o = a[10] >> 28; a[11] += o; a[10] -= o << 28;
-    o = a[11] >> 28; a[12] += o; a[11] -= o << 28;
-    o = a[12] >> 28; a[13] += o; a[12] -= o << 28;
-    o = a[13] >> 28; a[14] += o; a[13] -= o << 28;
-    o = a[14] >> 28; a[15] += o; a[14] -= o << 28;
-    o = a[15] >> 28; a[0]  += o;
-                     a[8]  += o; a[15] -= o << 28;
-}
-/* Mulitply a field element by 39081. r = (39081 * a) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to multiply.
- */
-void fe448_mul39081(int32_t* r, const int32_t* a)
-{
-    int64_t t;
-    int32_t o;
-    int64_t t0 = a[0] * (int64_t)39081;
-    int64_t t1 = a[1] * (int64_t)39081;
-    int64_t t2 = a[2] * (int64_t)39081;
-    int64_t t3 = a[3] * (int64_t)39081;
-    int64_t t4 = a[4] * (int64_t)39081;
-    int64_t t5 = a[5] * (int64_t)39081;
-    int64_t t6 = a[6] * (int64_t)39081;
-    int64_t t7 = a[7] * (int64_t)39081;
-    int64_t t8 = a[8] * (int64_t)39081;
-    int64_t t9 = a[9] * (int64_t)39081;
-    int64_t t10 = a[10] * (int64_t)39081;
-    int64_t t11 = a[11] * (int64_t)39081;
-    int64_t t12 = a[12] * (int64_t)39081;
-    int64_t t13 = a[13] * (int64_t)39081;
-    int64_t t14 = a[14] * (int64_t)39081;
-    int64_t t15 = a[15] * (int64_t)39081;
-    o = t0  >> 28; t1  += o; t = (int64_t)o << 28; t0  -= t;
-    o = t1  >> 28; t2  += o; t = (int64_t)o << 28; t1  -= t;
-    o = t2  >> 28; t3  += o; t = (int64_t)o << 28; t2  -= t;
-    o = t3  >> 28; t4  += o; t = (int64_t)o << 28; t3  -= t;
-    o = t4  >> 28; t5  += o; t = (int64_t)o << 28; t4  -= t;
-    o = t5  >> 28; t6  += o; t = (int64_t)o << 28; t5  -= t;
-    o = t6  >> 28; t7  += o; t = (int64_t)o << 28; t6  -= t;
-    o = t7  >> 28; t8  += o; t = (int64_t)o << 28; t7  -= t;
-    o = t8  >> 28; t9  += o; t = (int64_t)o << 28; t8  -= t;
-    o = t9  >> 28; t10 += o; t = (int64_t)o << 28; t9  -= t;
-    o = t10 >> 28; t11 += o; t = (int64_t)o << 28; t10 -= t;
-    o = t11 >> 28; t12 += o; t = (int64_t)o << 28; t11 -= t;
-    o = t12 >> 28; t13 += o; t = (int64_t)o << 28; t12 -= t;
-    o = t13 >> 28; t14 += o; t = (int64_t)o << 28; t13 -= t;
-    o = t14 >> 28; t15 += o; t = (int64_t)o << 28; t14 -= t;
-    o = t15 >> 28; t0  += o;
-                   t8  += o; t = (int64_t)o << 28; t15 -= t;
-
-    /* Store */
-    r[0] = t0;
-    r[1] = t1;
-    r[2] = t2;
-    r[3] = t3;
-    r[4] = t4;
-    r[5] = t5;
-    r[6] = t6;
-    r[7] = t7;
-    r[8] = t8;
-    r[9] = t9;
-    r[10] = t10;
-    r[11] = t11;
-    r[12] = t12;
-    r[13] = t13;
-    r[14] = t14;
-    r[15] = t15;
-}
-
-/* Mulitply two field elements. r = a * b
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to multiply.
- * b  [in]  Field element to multiply.
- */
-static WC_INLINE void fe448_mul_8(int32_t* r, const int32_t* a, const int32_t* b)
-{
-    int64_t t;
-    int64_t t0   = (int64_t)a[ 0] * b[ 0];
-    int64_t t1   = (int64_t)a[ 0] * b[ 1];
-    int64_t t101 = (int64_t)a[ 1] * b[ 0];
-    int64_t t2   = (int64_t)a[ 0] * b[ 2];
-    int64_t t102 = (int64_t)a[ 1] * b[ 1];
-    int64_t t202 = (int64_t)a[ 2] * b[ 0];
-    int64_t t3   = (int64_t)a[ 0] * b[ 3];
-    int64_t t103 = (int64_t)a[ 1] * b[ 2];
-    int64_t t203 = (int64_t)a[ 2] * b[ 1];
-    int64_t t303 = (int64_t)a[ 3] * b[ 0];
-    int64_t t4   = (int64_t)a[ 0] * b[ 4];
-    int64_t t104 = (int64_t)a[ 1] * b[ 3];
-    int64_t t204 = (int64_t)a[ 2] * b[ 2];
-    int64_t t304 = (int64_t)a[ 3] * b[ 1];
-    int64_t t404 = (int64_t)a[ 4] * b[ 0];
-    int64_t t5   = (int64_t)a[ 0] * b[ 5];
-    int64_t t105 = (int64_t)a[ 1] * b[ 4];
-    int64_t t205 = (int64_t)a[ 2] * b[ 3];
-    int64_t t305 = (int64_t)a[ 3] * b[ 2];
-    int64_t t405 = (int64_t)a[ 4] * b[ 1];
-    int64_t t505 = (int64_t)a[ 5] * b[ 0];
-    int64_t t6   = (int64_t)a[ 0] * b[ 6];
-    int64_t t106 = (int64_t)a[ 1] * b[ 5];
-    int64_t t206 = (int64_t)a[ 2] * b[ 4];
-    int64_t t306 = (int64_t)a[ 3] * b[ 3];
-    int64_t t406 = (int64_t)a[ 4] * b[ 2];
-    int64_t t506 = (int64_t)a[ 5] * b[ 1];
-    int64_t t606 = (int64_t)a[ 6] * b[ 0];
-    int64_t t7   = (int64_t)a[ 0] * b[ 7];
-    int64_t t107 = (int64_t)a[ 1] * b[ 6];
-    int64_t t207 = (int64_t)a[ 2] * b[ 5];
-    int64_t t307 = (int64_t)a[ 3] * b[ 4];
-    int64_t t407 = (int64_t)a[ 4] * b[ 3];
-    int64_t t507 = (int64_t)a[ 5] * b[ 2];
-    int64_t t607 = (int64_t)a[ 6] * b[ 1];
-    int64_t t707 = (int64_t)a[ 7] * b[ 0];
-    int64_t t8   = (int64_t)a[ 1] * b[ 7];
-    int64_t t108 = (int64_t)a[ 2] * b[ 6];
-    int64_t t208 = (int64_t)a[ 3] * b[ 5];
-    int64_t t308 = (int64_t)a[ 4] * b[ 4];
-    int64_t t408 = (int64_t)a[ 5] * b[ 3];
-    int64_t t508 = (int64_t)a[ 6] * b[ 2];
-    int64_t t608 = (int64_t)a[ 7] * b[ 1];
-    int64_t t9   = (int64_t)a[ 2] * b[ 7];
-    int64_t t109 = (int64_t)a[ 3] * b[ 6];
-    int64_t t209 = (int64_t)a[ 4] * b[ 5];
-    int64_t t309 = (int64_t)a[ 5] * b[ 4];
-    int64_t t409 = (int64_t)a[ 6] * b[ 3];
-    int64_t t509 = (int64_t)a[ 7] * b[ 2];
-    int64_t t10  = (int64_t)a[ 3] * b[ 7];
-    int64_t t110 = (int64_t)a[ 4] * b[ 6];
-    int64_t t210 = (int64_t)a[ 5] * b[ 5];
-    int64_t t310 = (int64_t)a[ 6] * b[ 4];
-    int64_t t410 = (int64_t)a[ 7] * b[ 3];
-    int64_t t11  = (int64_t)a[ 4] * b[ 7];
-    int64_t t111 = (int64_t)a[ 5] * b[ 6];
-    int64_t t211 = (int64_t)a[ 6] * b[ 5];
-    int64_t t311 = (int64_t)a[ 7] * b[ 4];
-    int64_t t12  = (int64_t)a[ 5] * b[ 7];
-    int64_t t112 = (int64_t)a[ 6] * b[ 6];
-    int64_t t212 = (int64_t)a[ 7] * b[ 5];
-    int64_t t13  = (int64_t)a[ 6] * b[ 7];
-    int64_t t113 = (int64_t)a[ 7] * b[ 6];
-    int64_t t14  = (int64_t)a[ 7] * b[ 7];
-    t1  += t101;
-    t2  += t102; t2  += t202;
-    t3  += t103; t3  += t203; t3  += t303;
-    t4  += t104; t4  += t204; t4  += t304; t4  += t404;
-    t5  += t105; t5  += t205; t5  += t305; t5  += t405; t5  += t505;
-    t6  += t106; t6  += t206; t6  += t306; t6  += t406; t6  += t506;
-    t6  += t606;
-    t7  += t107; t7  += t207; t7  += t307; t7  += t407; t7  += t507;
-    t7  += t607;
-    t7  += t707;
-    t8  += t108; t8  += t208; t8  += t308; t8  += t408; t8  += t508;
-    t8  += t608;
-    t9  += t109; t9  += t209; t9  += t309; t9  += t409; t9  += t509;
-    t10 += t110; t10 += t210; t10 += t310; t10 += t410;
-    t11 += t111; t11 += t211; t11 += t311;
-    t12 += t112; t12 += t212;
-    t13 += t113;
-    int64_t o = t14 >> 28;
-    int64_t t15 = o;
-    t14 -= o << 28;
-    o = t0  >> 28; t1  += o; t = (int64_t)o << 28; t0  -= t;
-    o = t1  >> 28; t2  += o; t = (int64_t)o << 28; t1  -= t;
-    o = t2  >> 28; t3  += o; t = (int64_t)o << 28; t2  -= t;
-    o = t3  >> 28; t4  += o; t = (int64_t)o << 28; t3  -= t;
-    o = t4  >> 28; t5  += o; t = (int64_t)o << 28; t4  -= t;
-    o = t5  >> 28; t6  += o; t = (int64_t)o << 28; t5  -= t;
-    o = t6  >> 28; t7  += o; t = (int64_t)o << 28; t6  -= t;
-    o = t7  >> 28; t8  += o; t = (int64_t)o << 28; t7  -= t;
-    o = t8  >> 28; t9  += o; t = (int64_t)o << 28; t8  -= t;
-    o = t9  >> 28; t10 += o; t = (int64_t)o << 28; t9  -= t;
-    o = t10 >> 28; t11 += o; t = (int64_t)o << 28; t10 -= t;
-    o = t11 >> 28; t12 += o; t = (int64_t)o << 28; t11 -= t;
-    o = t12 >> 28; t13 += o; t = (int64_t)o << 28; t12 -= t;
-    o = t13 >> 28; t14 += o; t = (int64_t)o << 28; t13 -= t;
-    o = t14 >> 28; t15 += o; t = (int64_t)o << 28; t14 -= t;
-    o = t15 >> 28; t0  += o;
-                   t8  += o; t = (int64_t)o << 28; t15 -= t;
-
-    /* Store */
-    r[0] = t0;
-    r[1] = t1;
-    r[2] = t2;
-    r[3] = t3;
-    r[4] = t4;
-    r[5] = t5;
-    r[6] = t6;
-    r[7] = t7;
-    r[8] = t8;
-    r[9] = t9;
-    r[10] = t10;
-    r[11] = t11;
-    r[12] = t12;
-    r[13] = t13;
-    r[14] = t14;
-    r[15] = t15;
-}
-
-/* Mulitply two field elements. r = (a * b) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to multiply.
- * b  [in]  Field element to multiply.
- */
-void fe448_mul(int32_t* r, const int32_t* a, const int32_t* b)
-{
-    int32_t r0[16];
-    int32_t r1[16];
-    int32_t* a1 = r1;
-    int32_t b1[8];
-    int32_t r2[16];
-    a1[0] = a[0] + a[8];
-    a1[1] = a[1] + a[9];
-    a1[2] = a[2] + a[10];
-    a1[3] = a[3] + a[11];
-    a1[4] = a[4] + a[12];
-    a1[5] = a[5] + a[13];
-    a1[6] = a[6] + a[14];
-    a1[7] = a[7] + a[15];
-    b1[0] = b[0] + b[8];
-    b1[1] = b[1] + b[9];
-    b1[2] = b[2] + b[10];
-    b1[3] = b[3] + b[11];
-    b1[4] = b[4] + b[12];
-    b1[5] = b[5] + b[13];
-    b1[6] = b[6] + b[14];
-    b1[7] = b[7] + b[15];
-    fe448_mul_8(r2, a + 8, b + 8);
-    fe448_mul_8(r0, a, b);
-    fe448_mul_8(r1, a1, b1);
-    r[ 0] = r0[ 0] + r2[ 0] + r1[ 8] - r0[ 8];
-    r[ 1] = r0[ 1] + r2[ 1] + r1[ 9] - r0[ 9];
-    r[ 2] = r0[ 2] + r2[ 2] + r1[10] - r0[10];
-    r[ 3] = r0[ 3] + r2[ 3] + r1[11] - r0[11];
-    r[ 4] = r0[ 4] + r2[ 4] + r1[12] - r0[12];
-    r[ 5] = r0[ 5] + r2[ 5] + r1[13] - r0[13];
-    r[ 6] = r0[ 6] + r2[ 6] + r1[14] - r0[14];
-    r[ 7] = r0[ 7] + r2[ 7] + r1[15] - r0[15];
-    r[ 8] = r2[ 8]          + r1[ 0] - r0[ 0] + r1[ 8];
-    r[ 9] = r2[ 9]          + r1[ 1] - r0[ 1] + r1[ 9];
-    r[10] = r2[10]          + r1[ 2] - r0[ 2] + r1[10];
-    r[11] = r2[11]          + r1[ 3] - r0[ 3] + r1[11];
-    r[12] = r2[12]          + r1[ 4] - r0[ 4] + r1[12];
-    r[13] = r2[13]          + r1[ 5] - r0[ 5] + r1[13];
-    r[14] = r2[14]          + r1[ 6] - r0[ 6] + r1[14];
-    r[15] = r2[15]          + r1[ 7] - r0[ 7] + r1[15];
-}
-
-/* Square a field element. r = a * a
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to square.
- */
-static WC_INLINE void fe448_sqr_8(int32_t* r, const int32_t* a)
-{
-    int64_t t;
-    int64_t t0   =     (int64_t)a[ 0] * a[ 0];
-    int64_t t1   = 2 * (int64_t)a[ 0] * a[ 1];
-    int64_t t2   = 2 * (int64_t)a[ 0] * a[ 2];
-    int64_t t102 =     (int64_t)a[ 1] * a[ 1];
-    int64_t t3   = 2 * (int64_t)a[ 0] * a[ 3];
-    int64_t t103 = 2 * (int64_t)a[ 1] * a[ 2];
-    int64_t t4   = 2 * (int64_t)a[ 0] * a[ 4];
-    int64_t t104 = 2 * (int64_t)a[ 1] * a[ 3];
-    int64_t t204 =     (int64_t)a[ 2] * a[ 2];
-    int64_t t5   = 2 * (int64_t)a[ 0] * a[ 5];
-    int64_t t105 = 2 * (int64_t)a[ 1] * a[ 4];
-    int64_t t205 = 2 * (int64_t)a[ 2] * a[ 3];
-    int64_t t6   = 2 * (int64_t)a[ 0] * a[ 6];
-    int64_t t106 = 2 * (int64_t)a[ 1] * a[ 5];
-    int64_t t206 = 2 * (int64_t)a[ 2] * a[ 4];
-    int64_t t306 =     (int64_t)a[ 3] * a[ 3];
-    int64_t t7   = 2 * (int64_t)a[ 0] * a[ 7];
-    int64_t t107 = 2 * (int64_t)a[ 1] * a[ 6];
-    int64_t t207 = 2 * (int64_t)a[ 2] * a[ 5];
-    int64_t t307 = 2 * (int64_t)a[ 3] * a[ 4];
-    int64_t t8   = 2 * (int64_t)a[ 1] * a[ 7];
-    int64_t t108 = 2 * (int64_t)a[ 2] * a[ 6];
-    int64_t t208 = 2 * (int64_t)a[ 3] * a[ 5];
-    int64_t t308 =     (int64_t)a[ 4] * a[ 4];
-    int64_t t9   = 2 * (int64_t)a[ 2] * a[ 7];
-    int64_t t109 = 2 * (int64_t)a[ 3] * a[ 6];
-    int64_t t209 = 2 * (int64_t)a[ 4] * a[ 5];
-    int64_t t10  = 2 * (int64_t)a[ 3] * a[ 7];
-    int64_t t110 = 2 * (int64_t)a[ 4] * a[ 6];
-    int64_t t210 =     (int64_t)a[ 5] * a[ 5];
-    int64_t t11  = 2 * (int64_t)a[ 4] * a[ 7];
-    int64_t t111 = 2 * (int64_t)a[ 5] * a[ 6];
-    int64_t t12  = 2 * (int64_t)a[ 5] * a[ 7];
-    int64_t t112 =     (int64_t)a[ 6] * a[ 6];
-    int64_t t13  = 2 * (int64_t)a[ 6] * a[ 7];
-    int64_t t14  =     (int64_t)a[ 7] * a[ 7];
-    t2  += t102;
-    t3  += t103;
-    t4  += t104; t4  += t204;
-    t5  += t105; t5  += t205;
-    t6  += t106; t6  += t206; t6  += t306;
-    t7  += t107; t7  += t207; t7  += t307;
-    t8  += t108; t8  += t208; t8  += t308;
-    t9  += t109; t9  += t209;
-    t10 += t110; t10 += t210;
-    t11 += t111;
-    t12 += t112;
-    int64_t o = t14 >> 28;
-    int64_t t15 = o;
-    t14 -= o << 28;
-    o = t0  >> 28; t1  += o; t = (int64_t)o << 28; t0  -= t;
-    o = t1  >> 28; t2  += o; t = (int64_t)o << 28; t1  -= t;
-    o = t2  >> 28; t3  += o; t = (int64_t)o << 28; t2  -= t;
-    o = t3  >> 28; t4  += o; t = (int64_t)o << 28; t3  -= t;
-    o = t4  >> 28; t5  += o; t = (int64_t)o << 28; t4  -= t;
-    o = t5  >> 28; t6  += o; t = (int64_t)o << 28; t5  -= t;
-    o = t6  >> 28; t7  += o; t = (int64_t)o << 28; t6  -= t;
-    o = t7  >> 28; t8  += o; t = (int64_t)o << 28; t7  -= t;
-    o = t8  >> 28; t9  += o; t = (int64_t)o << 28; t8  -= t;
-    o = t9  >> 28; t10 += o; t = (int64_t)o << 28; t9  -= t;
-    o = t10 >> 28; t11 += o; t = (int64_t)o << 28; t10 -= t;
-    o = t11 >> 28; t12 += o; t = (int64_t)o << 28; t11 -= t;
-    o = t12 >> 28; t13 += o; t = (int64_t)o << 28; t12 -= t;
-    o = t13 >> 28; t14 += o; t = (int64_t)o << 28; t13 -= t;
-    o = t14 >> 28; t15 += o; t = (int64_t)o << 28; t14 -= t;
-    o = t15 >> 28; t0  += o;
-                   t8  += o; t = (int64_t)o << 28; t15 -= t;
-
-    /* Store */
-    r[0] = t0;
-    r[1] = t1;
-    r[2] = t2;
-    r[3] = t3;
-    r[4] = t4;
-    r[5] = t5;
-    r[6] = t6;
-    r[7] = t7;
-    r[8] = t8;
-    r[9] = t9;
-    r[10] = t10;
-    r[11] = t11;
-    r[12] = t12;
-    r[13] = t13;
-    r[14] = t14;
-    r[15] = t15;
-}
-
-/* Square a field element. r = (a * a) mod (2^448 - 2^224 - 1)
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to square.
- */
-void fe448_sqr(int32_t* r, const int32_t* a)
-{
-    int32_t r0[16];
-    int32_t r1[16];
-    int32_t* a1 = r1;
-    int32_t r2[16];
-    a1[0] = a[0] + a[8];
-    a1[1] = a[1] + a[9];
-    a1[2] = a[2] + a[10];
-    a1[3] = a[3] + a[11];
-    a1[4] = a[4] + a[12];
-    a1[5] = a[5] + a[13];
-    a1[6] = a[6] + a[14];
-    a1[7] = a[7] + a[15];
-    fe448_sqr_8(r2, a + 8);
-    fe448_sqr_8(r0, a);
-    fe448_sqr_8(r1, a1);
-    r[ 0] = r0[ 0] + r2[ 0] + r1[ 8] - r0[ 8];
-    r[ 1] = r0[ 1] + r2[ 1] + r1[ 9] - r0[ 9];
-    r[ 2] = r0[ 2] + r2[ 2] + r1[10] - r0[10];
-    r[ 3] = r0[ 3] + r2[ 3] + r1[11] - r0[11];
-    r[ 4] = r0[ 4] + r2[ 4] + r1[12] - r0[12];
-    r[ 5] = r0[ 5] + r2[ 5] + r1[13] - r0[13];
-    r[ 6] = r0[ 6] + r2[ 6] + r1[14] - r0[14];
-    r[ 7] = r0[ 7] + r2[ 7] + r1[15] - r0[15];
-    r[ 8] = r2[ 8]          + r1[ 0] - r0[ 0] + r1[ 8];
-    r[ 9] = r2[ 9]          + r1[ 1] - r0[ 1] + r1[ 9];
-    r[10] = r2[10]          + r1[ 2] - r0[ 2] + r1[10];
-    r[11] = r2[11]          + r1[ 3] - r0[ 3] + r1[11];
-    r[12] = r2[12]          + r1[ 4] - r0[ 4] + r1[12];
-    r[13] = r2[13]          + r1[ 5] - r0[ 5] + r1[13];
-    r[14] = r2[14]          + r1[ 6] - r0[ 6] + r1[14];
-    r[15] = r2[15]          + r1[ 7] - r0[ 7] + r1[15];
-}
-
-/* Invert the field element. (r * a) mod (2^448 - 2^224 - 1) = 1
- * Constant time implementation - using Fermat's little theorem:
- *   a^(p-1) mod p = 1 => a^(p-2) mod p = 1/a
- * For curve448: p - 2 = 2^448 - 2^224 - 3
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to invert.
- */
-void fe448_invert(int32_t* r, const int32_t* a)
-{
-    int32_t t1[16];
-    int32_t t2[16];
-    int32_t t3[16];
-    int32_t t4[16];
-    int i;
-
-    fe448_sqr(t1, a);
-    /* t1 = 2 */
-    fe448_mul(t1, t1, a);
-    /* t1 = 3 */
-    fe448_sqr(t2, t1); for (i = 1; i < 2; ++i) fe448_sqr(t2, t2);
-    /* t2 = c */
-    fe448_mul(t3, t2, a);
-    /* t3 = d */
-    fe448_mul(t1, t2, t1);
-    /* t1 = f */
-    fe448_sqr(t2, t1);
-    /* t2 = 1e */
-    fe448_mul(t4, t2, a);
-    /* t4 = 1f */
-    fe448_sqr(t2, t4); for (i = 1; i < 5; ++i) fe448_sqr(t2, t2);
-    /* t2 = 3e0 */
-    fe448_mul(t1, t2, t4);
-    /* t1 = 3ff */
-    fe448_sqr(t2, t1); for (i = 1; i < 10; ++i) fe448_sqr(t2, t2);
-    /* t2 = ffc00 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = fffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 5; ++i) fe448_sqr(t2, t2);
-    /* t2 = 1ffffe0 */
-    fe448_mul(t1, t2, t4);
-    /* t1 = 1ffffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 25; ++i) fe448_sqr(t2, t2);
-    /* t2 = 3fffffe000000 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = 3ffffffffffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 5; ++i) fe448_sqr(t2, t2);
-    /* t2 = 7fffffffffffe0 */
-    fe448_mul(t1, t2, t4);
-    /* t1 = 7fffffffffffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 55; ++i) fe448_sqr(t2, t2);
-    /* t2 = 3fffffffffffff80000000000000 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = 3fffffffffffffffffffffffffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 110; ++i) fe448_sqr(t2, t2);
-    /* t2 = fffffffffffffffffffffffffffc000000000000000000000000000 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = fffffffffffffffffffffffffffffffffffffffffffffffffffffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 4; ++i) fe448_sqr(t2, t2);
-    /* t2 = fffffffffffffffffffffffffffffffffffffffffffffffffffffff0 */
-    fe448_mul(t3, t3, t2);
-    /* t3 = fffffffffffffffffffffffffffffffffffffffffffffffffffffffd */
-    fe448_mul(t1, t3, a);
-    /* t1 = fffffffffffffffffffffffffffffffffffffffffffffffffffffffe */
-    fe448_sqr(t1, t1); for (i = 1; i < 224; ++i) fe448_sqr(t1, t1);
-    /* t1 = fffffffffffffffffffffffffffffffffffffffffffffffffffffffe00000000000000000000000000000000000000000000000000000000 */
-    fe448_mul(r, t3, t1);
-    /* r = fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffffffffffffffffffffffffffffffffffffffffffffffffffffd */
-}
-
-/* Scalar multiply the point by a number. r = n.a
- * Uses Montogmery ladder and only requires the x-ordinate.
- *
- * r  [in]  Field element to hold result.
- * n  [in]  Scalar as an array of bytes.
- * a  [in]  Point to multiply - x-ordinate only.
- */
-int curve448(byte* r, const byte* n, const byte* a)
-{
-    int32_t x1[16];
-    int32_t x2[16];
-    int32_t z2[16];
-    int32_t x3[16];
-    int32_t z3[16];
-    int32_t t0[16];
-    int32_t t1[16];
-    int i;
-    unsigned int swap;
-    unsigned int b;
-
-    fe448_from_bytes(x1, a);
-    fe448_1(x2);
-    fe448_0(z2);
-    fe448_copy(x3, x1);
-    fe448_1(z3);
-
-    swap = 0;
-    for (i = 447; i >= 0; --i) {
-        b = (n[i >> 3] >> (i & 7)) & 1;
-        swap ^= b;
-        fe448_cswap(x2, x3, swap);
-        fe448_cswap(z2, z3, swap);
-        swap = b;
-
-        /* Montgomery Ladder - double and add */
-        fe448_add(t0, x2, z2);
-        fe448_reduce(t0);
-        fe448_add(t1, x3, z3);
-        fe448_reduce(t1);
-        fe448_sub(x2, x2, z2);
-        fe448_sub(x3, x3, z3);
-        fe448_mul(t1, t1, x2);
-        fe448_mul(z3, x3, t0);
-        fe448_sqr(t0, t0);
-        fe448_sqr(x2, x2);
-        fe448_add(x3, z3, t1);
-        fe448_reduce(x3);
-        fe448_sqr(x3, x3);
-        fe448_sub(z3, z3, t1);
-        fe448_sqr(z3, z3);
-        fe448_mul(z3, z3, x1);
-        fe448_sub(t1, t0, x2);
-        fe448_mul(x2, t0, x2);
-        fe448_mul39081(z2, t1);
-        fe448_add(z2, t0, z2);
-        fe448_mul(z2, z2, t1);
-    }
-    /* Last two bits are 0 - no final swap check required. */
-
-    fe448_invert(z2, z2);
-    fe448_mul(x2, x2, z2);
-    fe448_to_bytes(r, x2);
-
-    return 0;
-}
-
-#ifdef HAVE_ED448
-/* Check whether field element is not 0.
- * Must convert to a normalized form before checking.
- *
- * a  [in]  Field element.
- * returns 0 when zero, and any other value otherwise.
- */
-int fe448_isnonzero(const int32_t* a)
-{
-    uint8_t b[56];
-    int i;
-    uint8_t c = 0;
-    fe448_to_bytes(b, a);
-    for (i = 0; i < 56; i++)
-        c |= b[i];
-    return c;
-}
-
-/* Check whether field element is negative.
- * Must convert to a normalized form before checking.
- *
- * a  [in]  Field element.
- * returns 1 when negative, and 0 otherwise.
- */
-int fe448_isnegative(const int32_t* a)
-{
-    uint8_t b[56];
-    fe448_to_bytes(b, a);
-    return b[0] & 1;
-}
-
-/* Negates the field element. r = -a
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element.
- */
-void fe448_neg(int32_t* r, const int32_t* a)
-{
-    r[0] = -a[0];
-    r[1] = -a[1];
-    r[2] = -a[2];
-    r[3] = -a[3];
-    r[4] = -a[4];
-    r[5] = -a[5];
-    r[6] = -a[6];
-    r[7] = -a[7];
-    r[8] = -a[8];
-    r[9] = -a[9];
-    r[10] = -a[10];
-    r[11] = -a[11];
-    r[12] = -a[12];
-    r[13] = -a[13];
-    r[14] = -a[14];
-    r[15] = -a[15];
-}
-
-/* Raise field element to (p-3) / 4: 2^446 - 2^222 - 1
- * Used for calcualting y-ordinate from x-ordinate for Ed448.
- *
- * r  [in]  Field element to hold result.
- * a  [in]  Field element to exponentiate.
- */
-void fe448_pow_2_446_222_1(int32_t* r, const int32_t* a)
-{
-    int32_t t1[16];
-    int32_t t2[16];
-    int32_t t3[16];
-    int32_t t4[16];
-    int32_t t5[16];
-    int i;
-
-    fe448_sqr(t3, a);
-    /* t3 = 2 */
-    fe448_mul(t1, t3, a);
-    /* t1 = 3 */
-    fe448_sqr(t5, t1);
-    /* t5 = 6 */
-    fe448_mul(t5, t5, a);
-    /* t5 = 7 */
-    fe448_sqr(t2, t1); for (i = 1; i < 2; ++i) fe448_sqr(t2, t2);
-    /* t2 = c */
-    fe448_mul(t3, t2, t3);
-    /* t3 = e */
-    fe448_mul(t1, t2, t1);
-    /* t1 = f */
-    fe448_sqr(t2, t1); for (i = 1; i < 3; ++i) fe448_sqr(t2, t2);
-    /* t2 = 78 */
-    fe448_mul(t5, t2, t5);
-    /* t5 = 7f */
-    fe448_sqr(t2, t1); for (i = 1; i < 4; ++i) fe448_sqr(t2, t2);
-    /* t2 = f0 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = ff */
-    fe448_mul(t3, t3, t2);
-    /* t3 = fe */
-    fe448_sqr(t2, t1); for (i = 1; i < 7; ++i) fe448_sqr(t2, t2);
-    /* t2 = 7f80 */
-    fe448_mul(t5, t2, t5);
-    /* t5 = 7fff */
-    fe448_sqr(t2, t1); for (i = 1; i < 8; ++i) fe448_sqr(t2, t2);
-    /* t2 = ff00 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = ffff */
-    fe448_mul(t3, t3, t2);
-    /* t3 = fffe */
-    fe448_sqr(t2, t5); for (i = 1; i < 15; ++i) fe448_sqr(t2, t2);
-    /* t2 = 3fff8000 */
-    fe448_mul(t5, t2, t5);
-    /* t5 = 3fffffff */
-    fe448_sqr(t2, t1); for (i = 1; i < 16; ++i) fe448_sqr(t2, t2);
-    /* t2 = ffff0000 */
-    fe448_mul(t1, t2, t1);
-    /* t1 = ffffffff */
-    fe448_mul(t3, t3, t2);
-    /* t3 = fffffffe */
-    fe448_sqr(t2, t1); for (i = 1; i < 32; ++i) fe448_sqr(t2, t2);
-    /* t2 = ffffffff00000000 */
-    fe448_mul(t2, t2, t1);
-    /* t2 = ffffffffffffffff */
-    fe448_sqr(t1, t2); for (i = 1; i < 64; ++i) fe448_sqr(t1, t1);
-    /* t1 = ffffffffffffffff0000000000000000 */
-    fe448_mul(t1, t1, t2);
-    /* t1 = ffffffffffffffffffffffffffffffff */
-    fe448_sqr(t1, t1); for (i = 1; i < 64; ++i) fe448_sqr(t1, t1);
-    /* t1 = ffffffffffffffffffffffffffffffff0000000000000000 */
-    fe448_mul(t4, t1, t2);
-    /* t4 = ffffffffffffffffffffffffffffffffffffffffffffffff */
-    fe448_sqr(t2, t4); for (i = 1; i < 32; ++i) fe448_sqr(t2, t2);
-    /* t2 = ffffffffffffffffffffffffffffffffffffffffffffffff00000000 */
-    fe448_mul(t3, t3, t2);
-    /* t3 = fffffffffffffffffffffffffffffffffffffffffffffffffffffffe */
-    fe448_sqr(t1, t3); for (i = 1; i < 192; ++i) fe448_sqr(t1, t1);
-    /* t1 = fffffffffffffffffffffffffffffffffffffffffffffffffffffffe000000000000000000000000000000000000000000000000 */
-    fe448_mul(t1, t1, t4);
-    /* t1 = fffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffff */
-    fe448_sqr(t1, t1); for (i = 1; i < 30; ++i) fe448_sqr(t1, t1);
-    /* t1 = 3fffffffffffffffffffffffffffffffffffffffffffffffffffffffbfffffffffffffffffffffffffffffffffffffffffffffffc0000000 */
-    fe448_mul(r, t5, t1);
-    /* r = 3fffffffffffffffffffffffffffffffffffffffffffffffffffffffbfffffffffffffffffffffffffffffffffffffffffffffffffffffff */
-}
-
-/* Constant time, conditional move of b into a.
- * a is not changed if the condition is 0.
- *
- * a  A field element.
- * b  A field element.
- * c  If 1 then copy and if 0 then don't copy.
- */
-void fe448_cmov(int32_t* a, const int32_t* b, int c)
-{
-    int32_t m = -(int32_t)c;
-    int32_t t0 = m & (a[0] ^ b[0]);
-    int32_t t1 = m & (a[1] ^ b[1]);
-    int32_t t2 = m & (a[2] ^ b[2]);
-    int32_t t3 = m & (a[3] ^ b[3]);
-    int32_t t4 = m & (a[4] ^ b[4]);
-    int32_t t5 = m & (a[5] ^ b[5]);
-    int32_t t6 = m & (a[6] ^ b[6]);
-    int32_t t7 = m & (a[7] ^ b[7]);
-    int32_t t8 = m & (a[8] ^ b[8]);
-    int32_t t9 = m & (a[9] ^ b[9]);
-    int32_t t10 = m & (a[10] ^ b[10]);
-    int32_t t11 = m & (a[11] ^ b[11]);
-    int32_t t12 = m & (a[12] ^ b[12]);
-    int32_t t13 = m & (a[13] ^ b[13]);
-    int32_t t14 = m & (a[14] ^ b[14]);
-    int32_t t15 = m & (a[15] ^ b[15]);
-
-    a[0] ^= t0;
-    a[1] ^= t1;
-    a[2] ^= t2;
-    a[3] ^= t3;
-    a[4] ^= t4;
-    a[5] ^= t5;
-    a[6] ^= t6;
-    a[7] ^= t7;
-    a[8] ^= t8;
-    a[9] ^= t9;
-    a[10] ^= t10;
-    a[11] ^= t11;
-    a[12] ^= t12;
-    a[13] ^= t13;
-    a[14] ^= t14;
-    a[15] ^= t15;
-}
-
-#endif /* HAVE_ED448 */
-#endif
-
-#endif /* HAVE_CURVE448 || HAVE_ED448 */