/*
(c) Matthew Dempsky
Public domain.
Derived from public domain code by D. J. Bernstein.
*/

// Modified slightly for ZeroTier but remains in the public domain as per
// its original license.

#include "C25519.hpp"

#include "SHA512.hpp"
#include "Utils.hpp"

#ifdef __WINDOWS__
#pragma warning(disable : 4146)
#endif

#ifdef __GNUC__
#pragma GCC diagnostic ignored "-Wunused-function"
#pragma GCC diagnostic ignored "-Wuninitialized"
#endif

using namespace ZeroTier;

namespace {

// --------------------------------------------------------------------------------------------------------------------

#define crypto_hash_sha512_BYTES 64
typedef uint8_t u8;
typedef int32_t s32;
typedef int64_t limb;

ZT_INLINE void fsum(limb *output, const limb *in)
{
    for (int i = 0; i < 10; i += 2) {
        output[0 + i] = output[0 + i] + in[0 + i];
        output[1 + i] = output[1 + i] + in[1 + i];
    }
}

ZT_INLINE void fdifference(limb *output, const limb *in)
{
    for (int i = 0; i < 10; ++i)
        output[i] = in[i] - output[i];
}

ZT_INLINE void fscalar_product(limb *output, const limb *in, const limb scalar)
{
    for (int i = 0; i < 10; ++i)
        output[i] = in[i] * scalar;
}

void fproduct(limb *output, const limb *in2, const limb *in)
{
    output[0] = ((limb)((s32)in2[0])) * ((s32)in[0]);
    output[1] = ((limb)((s32)in2[0])) * ((s32)in[1]) + ((limb)((s32)in2[1])) * ((s32)in[0]);
    output[2] = 2 * ((limb)((s32)in2[1])) * ((s32)in[1]) + ((limb)((s32)in2[0])) * ((s32)in[2])
                + ((limb)((s32)in2[2])) * ((s32)in[0]);
    output[3] = ((limb)((s32)in2[1])) * ((s32)in[2]) + ((limb)((s32)in2[2])) * ((s32)in[1])
                + ((limb)((s32)in2[0])) * ((s32)in[3]) + ((limb)((s32)in2[3])) * ((s32)in[0]);
    output[4] = ((limb)((s32)in2[2])) * ((s32)in[2])
                + 2 * (((limb)((s32)in2[1])) * ((s32)in[3]) + ((limb)((s32)in2[3])) * ((s32)in[1]))
                + ((limb)((s32)in2[0])) * ((s32)in[4]) + ((limb)((s32)in2[4])) * ((s32)in[0]);
    output[5] = ((limb)((s32)in2[2])) * ((s32)in[3]) + ((limb)((s32)in2[3])) * ((s32)in[2])
                + ((limb)((s32)in2[1])) * ((s32)in[4]) + ((limb)((s32)in2[4])) * ((s32)in[1])
                + ((limb)((s32)in2[0])) * ((s32)in[5]) + ((limb)((s32)in2[5])) * ((s32)in[0]);
    output[6] = 2
                    * (((limb)((s32)in2[3])) * ((s32)in[3]) + ((limb)((s32)in2[1])) * ((s32)in[5])
                       + ((limb)((s32)in2[5])) * ((s32)in[1]))
                + ((limb)((s32)in2[2])) * ((s32)in[4]) + ((limb)((s32)in2[4])) * ((s32)in[2])
                + ((limb)((s32)in2[0])) * ((s32)in[6]) + ((limb)((s32)in2[6])) * ((s32)in[0]);
    output[7] = ((limb)((s32)in2[3])) * ((s32)in[4]) + ((limb)((s32)in2[4])) * ((s32)in[3])
                + ((limb)((s32)in2[2])) * ((s32)in[5]) + ((limb)((s32)in2[5])) * ((s32)in[2])
                + ((limb)((s32)in2[1])) * ((s32)in[6]) + ((limb)((s32)in2[6])) * ((s32)in[1])
                + ((limb)((s32)in2[0])) * ((s32)in[7]) + ((limb)((s32)in2[7])) * ((s32)in[0]);
    output[8] = ((limb)((s32)in2[4])) * ((s32)in[4])
                + 2
                      * (((limb)((s32)in2[3])) * ((s32)in[5]) + ((limb)((s32)in2[5])) * ((s32)in[3])
                         + ((limb)((s32)in2[1])) * ((s32)in[7]) + ((limb)((s32)in2[7])) * ((s32)in[1]))
                + ((limb)((s32)in2[2])) * ((s32)in[6]) + ((limb)((s32)in2[6])) * ((s32)in[2])
                + ((limb)((s32)in2[0])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[0]);
    output[9] = ((limb)((s32)in2[4])) * ((s32)in[5]) + ((limb)((s32)in2[5])) * ((s32)in[4])
                + ((limb)((s32)in2[3])) * ((s32)in[6]) + ((limb)((s32)in2[6])) * ((s32)in[3])
                + ((limb)((s32)in2[2])) * ((s32)in[7]) + ((limb)((s32)in2[7])) * ((s32)in[2])
                + ((limb)((s32)in2[1])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[1])
                + ((limb)((s32)in2[0])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[0]);
    output[10] = 2
                     * (((limb)((s32)in2[5])) * ((s32)in[5]) + ((limb)((s32)in2[3])) * ((s32)in[7])
                        + ((limb)((s32)in2[7])) * ((s32)in[3]) + ((limb)((s32)in2[1])) * ((s32)in[9])
                        + ((limb)((s32)in2[9])) * ((s32)in[1]))
                 + ((limb)((s32)in2[4])) * ((s32)in[6]) + ((limb)((s32)in2[6])) * ((s32)in[4])
                 + ((limb)((s32)in2[2])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[2]);
    output[11] = ((limb)((s32)in2[5])) * ((s32)in[6]) + ((limb)((s32)in2[6])) * ((s32)in[5])
                 + ((limb)((s32)in2[4])) * ((s32)in[7]) + ((limb)((s32)in2[7])) * ((s32)in[4])
                 + ((limb)((s32)in2[3])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[3])
                 + ((limb)((s32)in2[2])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[2]);
    output[12] = ((limb)((s32)in2[6])) * ((s32)in[6])
                 + 2
                       * (((limb)((s32)in2[5])) * ((s32)in[7]) + ((limb)((s32)in2[7])) * ((s32)in[5])
                          + ((limb)((s32)in2[3])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[3]))
                 + ((limb)((s32)in2[4])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[4]);
    output[13] = ((limb)((s32)in2[6])) * ((s32)in[7]) + ((limb)((s32)in2[7])) * ((s32)in[6])
                 + ((limb)((s32)in2[5])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[5])
                 + ((limb)((s32)in2[4])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[4]);
    output[14] = 2
                     * (((limb)((s32)in2[7])) * ((s32)in[7]) + ((limb)((s32)in2[5])) * ((s32)in[9])
                        + ((limb)((s32)in2[9])) * ((s32)in[5]))
                 + ((limb)((s32)in2[6])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[6]);
    output[15] = ((limb)((s32)in2[7])) * ((s32)in[8]) + ((limb)((s32)in2[8])) * ((s32)in[7])
                 + ((limb)((s32)in2[6])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[6]);
    output[16] = ((limb)((s32)in2[8])) * ((s32)in[8])
                 + 2 * (((limb)((s32)in2[7])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[7]));
    output[17] = ((limb)((s32)in2[8])) * ((s32)in[9]) + ((limb)((s32)in2[9])) * ((s32)in[8]);
    output[18] = 2 * ((limb)((s32)in2[9])) * ((s32)in[9]);
}

ZT_INLINE void freduce_degree(limb *output)
{
    output[8] += output[18] << 4;
    output[8] += output[18] << 1;
    output[8] += output[18];
    output[7] += output[17] << 4;
    output[7] += output[17] << 1;
    output[7] += output[17];
    output[6] += output[16] << 4;
    output[6] += output[16] << 1;
    output[6] += output[16];
    output[5] += output[15] << 4;
    output[5] += output[15] << 1;
    output[5] += output[15];
    output[4] += output[14] << 4;
    output[4] += output[14] << 1;
    output[4] += output[14];
    output[3] += output[13] << 4;
    output[3] += output[13] << 1;
    output[3] += output[13];
    output[2] += output[12] << 4;
    output[2] += output[12] << 1;
    output[2] += output[12];
    output[1] += output[11] << 4;
    output[1] += output[11] << 1;
    output[1] += output[11];
    output[0] += output[10] << 4;
    output[0] += output[10] << 1;
    output[0] += output[10];
}

#if (-1 & 3) != 3
#error "This code only works on a two's complement system"
#endif

ZT_INLINE limb div_by_2_26(const limb v)
{
    const uint32_t highword = (uint32_t)(((uint64_t)v) >> 32);
    const int32_t sign      = ((int32_t)highword) >> 31;
    const int32_t roundoff  = ((uint32_t)sign) >> 6;
    return (v + roundoff) >> 26;
}

ZT_INLINE limb div_by_2_25(const limb v)
{
    const uint32_t highword = (uint32_t)(((uint64_t)v) >> 32);
    const int32_t sign      = ((int32_t)highword) >> 31;
    const int32_t roundoff  = ((uint32_t)sign) >> 7;
    return (v + roundoff) >> 25;
}

ZT_INLINE void freduce_coefficients(limb *output)
{
    output[10] = 0;
    for (int i = 0; i < 10; i += 2) {
        limb over = div_by_2_26(output[i]);
        output[i] -= over << 26;
        output[i + 1] += over;
        over = div_by_2_25(output[i + 1]);
        output[i + 1] -= over << 25;
        output[i + 2] += over;
    }
    output[0] += output[10] << 4;
    output[0] += output[10] << 1;
    output[0] += output[10];
    output[10] = 0;
    limb over  = div_by_2_26(output[0]);
    output[0] -= over << 26;
    output[1] += over;
}

ZT_INLINE void fmul(limb *output, const limb *in, const limb *in2)
{
    limb t[19];
    fproduct(t, in, in2);
    freduce_degree(t);
    freduce_coefficients(t);
    Utils::copy<sizeof(limb) * 10>(output, t);
}

void fsquare_inner(limb *output, const limb *in)
{
    output[0] = ((limb)((s32)in[0])) * ((s32)in[0]);
    output[1] = 2 * ((limb)((s32)in[0])) * ((s32)in[1]);
    output[2] = 2 * (((limb)((s32)in[1])) * ((s32)in[1]) + ((limb)((s32)in[0])) * ((s32)in[2]));
    output[3] = 2 * (((limb)((s32)in[1])) * ((s32)in[2]) + ((limb)((s32)in[0])) * ((s32)in[3]));
    output[4] = ((limb)((s32)in[2])) * ((s32)in[2]) + 4 * ((limb)((s32)in[1])) * ((s32)in[3])
                + 2 * ((limb)((s32)in[0])) * ((s32)in[4]);
    output[5] = 2
                * (((limb)((s32)in[2])) * ((s32)in[3]) + ((limb)((s32)in[1])) * ((s32)in[4])
                   + ((limb)((s32)in[0])) * ((s32)in[5]));
    output[6] = 2
                * (((limb)((s32)in[3])) * ((s32)in[3]) + ((limb)((s32)in[2])) * ((s32)in[4])
                   + ((limb)((s32)in[0])) * ((s32)in[6]) + 2 * ((limb)((s32)in[1])) * ((s32)in[5]));
    output[7] = 2
                * (((limb)((s32)in[3])) * ((s32)in[4]) + ((limb)((s32)in[2])) * ((s32)in[5])
                   + ((limb)((s32)in[1])) * ((s32)in[6]) + ((limb)((s32)in[0])) * ((s32)in[7]));
    output[8] = ((limb)((s32)in[4])) * ((s32)in[4])
                + 2
                      * (((limb)((s32)in[2])) * ((s32)in[6]) + ((limb)((s32)in[0])) * ((s32)in[8])
                         + 2 * (((limb)((s32)in[1])) * ((s32)in[7]) + ((limb)((s32)in[3])) * ((s32)in[5])));
    output[9] = 2
                * (((limb)((s32)in[4])) * ((s32)in[5]) + ((limb)((s32)in[3])) * ((s32)in[6])
                   + ((limb)((s32)in[2])) * ((s32)in[7]) + ((limb)((s32)in[1])) * ((s32)in[8])
                   + ((limb)((s32)in[0])) * ((s32)in[9]));
    output[10] = 2
                 * (((limb)((s32)in[5])) * ((s32)in[5]) + ((limb)((s32)in[4])) * ((s32)in[6])
                    + ((limb)((s32)in[2])) * ((s32)in[8])
                    + 2 * (((limb)((s32)in[3])) * ((s32)in[7]) + ((limb)((s32)in[1])) * ((s32)in[9])));
    output[11] = 2
                 * (((limb)((s32)in[5])) * ((s32)in[6]) + ((limb)((s32)in[4])) * ((s32)in[7])
                    + ((limb)((s32)in[3])) * ((s32)in[8]) + ((limb)((s32)in[2])) * ((s32)in[9]));
    output[12] = ((limb)((s32)in[6])) * ((s32)in[6])
                 + 2
                       * (((limb)((s32)in[4])) * ((s32)in[8])
                          + 2 * (((limb)((s32)in[5])) * ((s32)in[7]) + ((limb)((s32)in[3])) * ((s32)in[9])));
    output[13] = 2
                 * (((limb)((s32)in[6])) * ((s32)in[7]) + ((limb)((s32)in[5])) * ((s32)in[8])
                    + ((limb)((s32)in[4])) * ((s32)in[9]));
    output[14] = 2
                 * (((limb)((s32)in[7])) * ((s32)in[7]) + ((limb)((s32)in[6])) * ((s32)in[8])
                    + 2 * ((limb)((s32)in[5])) * ((s32)in[9]));
    output[15] = 2 * (((limb)((s32)in[7])) * ((s32)in[8]) + ((limb)((s32)in[6])) * ((s32)in[9]));
    output[16] = ((limb)((s32)in[8])) * ((s32)in[8]) + 4 * ((limb)((s32)in[7])) * ((s32)in[9]);
    output[17] = 2 * ((limb)((s32)in[8])) * ((s32)in[9]);
    output[18] = 2 * ((limb)((s32)in[9])) * ((s32)in[9]);
}

ZT_INLINE void fsquare(limb *output, const limb *in)
{
    limb t[19];
    fsquare_inner(t, in);
    freduce_degree(t);
    freduce_coefficients(t);
    Utils::copy<sizeof(limb) * 10>(output, t);
}

ZT_INLINE void fexpand(limb *output, const u8 *input)
{
#define F(n, start, shift, mask)                                                                                       \
    output[n] = ((((limb)input[start + 0]) | ((limb)input[start + 1]) << 8 | ((limb)input[start + 2]) << 16            \
                  | ((limb)input[start + 3]) << 24)                                                                    \
                 >> shift)                                                                                             \
                & mask
    F(0, 0, 0, 0x3ffffff);
    F(1, 3, 2, 0x1ffffff);
    F(2, 6, 3, 0x3ffffff);
    F(3, 9, 5, 0x1ffffff);
    F(4, 12, 6, 0x3ffffff);
    F(5, 16, 0, 0x1ffffff);
    F(6, 19, 1, 0x3ffffff);
    F(7, 22, 3, 0x1ffffff);
    F(8, 25, 4, 0x3ffffff);
    F(9, 28, 6, 0x1ffffff);
#undef F
}

#if (-32 >> 1) != -16
#error "This code only works when >> does sign-extension on negative numbers"
#endif

ZT_INLINE s32 s32_eq(s32 a, s32 b)
{
    a = ~(a ^ b);
    a &= a << 16;
    a &= a << 8;
    a &= a << 4;
    a &= a << 2;
    a &= a << 1;
    return a >> 31;
}

ZT_INLINE s32 s32_gte(s32 a, s32 b)
{
    a -= b;
    return ~(a >> 31);
}

void fcontract(u8 *output, limb *input_limbs)
{
    int i, j;
    s32 input[10], mask;

    for (i = 0; i < 10; i++) {
        input[i] = input_limbs[i];
    }
    for (j = 0; j < 2; ++j) {
        for (i = 0; i < 9; ++i) {
            if ((i & 1) == 1) {
                const s32 mm    = input[i] >> 31;
                const s32 carry = -((input[i] & mm) >> 25);
                input[i]        = input[i] + (carry << 25);
                input[i + 1]    = input[i + 1] - carry;
            }
            else {
                const s32 mm    = input[i] >> 31;
                const s32 carry = -((input[i] & mm) >> 26);
                input[i]        = input[i] + (carry << 26);
                input[i + 1]    = input[i + 1] - carry;
            }
        }
        {
            const s32 mm    = input[9] >> 31;
            const s32 carry = -((input[9] & mm) >> 25);
            input[9]        = input[9] + (carry << 25);
            input[0]        = input[0] - (carry * 19);
        }
    }
    {
        const s32 mm    = input[0] >> 31;
        const s32 carry = -((input[0] & mm) >> 26);
        input[0]        = input[0] + (carry << 26);
        input[1]        = input[1] - carry;
    }
    for (j = 0; j < 2; j++) {
        for (i = 0; i < 9; i++) {
            if ((i & 1) == 1) {
                const s32 carry = input[i] >> 25;
                input[i] &= 0x1ffffff;
                input[i + 1] += carry;
            }
            else {
                const s32 carry = input[i] >> 26;
                input[i] &= 0x3ffffff;
                input[i + 1] += carry;
            }
        }
        {
            const s32 carry = input[9] >> 25;
            input[9] &= 0x1ffffff;
            input[0] += 19 * carry;
        }
    }
    mask = s32_gte(input[0], 0x3ffffed);
    for (i = 1; i < 10; i++) {
        if ((i & 1) == 1) {
            mask &= s32_eq(input[i], 0x1ffffff);
        }
        else {
            mask &= s32_eq(input[i], 0x3ffffff);
        }
    }
    input[0] -= mask & 0x3ffffed;
    for (i = 1; i < 10; i++) {
        if ((i & 1) == 1) {
            input[i] -= mask & 0x1ffffff;
        }
        else {
            input[i] -= mask & 0x3ffffff;
        }
    }

    input[1] <<= 2;
    input[2] <<= 3;
    input[3] <<= 5;
    input[4] <<= 6;
    input[6] <<= 1;
    input[7] <<= 3;
    input[8] <<= 4;
    input[9] <<= 6;
#define F(i, s)                                                                                                        \
    output[s + 0] |= input[i] & 0xff;                                                                                  \
    output[s + 1] = (input[i] >> 8) & 0xff;                                                                            \
    output[s + 2] = (input[i] >> 16) & 0xff;                                                                           \
    output[s + 3] = (input[i] >> 24) & 0xff
    output[0]     = 0;
    output[16]    = 0;
    F(0, 0);
    F(1, 3);
    F(2, 6);
    F(3, 9);
    F(4, 12);
    F(5, 16);
    F(6, 19);
    F(7, 22);
    F(8, 25);
    F(9, 28);
#undef F
}

void fmonty(
    limb *x2, limb *z2,         /* output 2Q */
    limb *x3, limb *z3,         /* output Q + Q' */
    limb *x, limb *z,           /* input Q */
    limb *xprime, limb *zprime, /* input Q' */
    const limb *qmqp /* input Q - Q' */)
{
    limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19], zzprime[19], zzzprime[19], xxxprime[19];

    Utils::copy<10 * sizeof(limb)>(origx, x);
    fsum(x, z);
    fdifference(z, origx);

    Utils::copy<sizeof(limb) * 10>(origxprime, xprime);
    fsum(xprime, zprime);
    fdifference(zprime, origxprime);
    fproduct(xxprime, xprime, z);
    fproduct(zzprime, x, zprime);
    freduce_degree(xxprime);
    freduce_coefficients(xxprime);
    freduce_degree(zzprime);
    freduce_coefficients(zzprime);
    Utils::copy<sizeof(limb) * 10>(origxprime, xxprime);
    fsum(xxprime, zzprime);
    fdifference(zzprime, origxprime);
    fsquare(xxxprime, xxprime);
    fsquare(zzzprime, zzprime);
    fproduct(zzprime, zzzprime, qmqp);
    freduce_degree(zzprime);
    freduce_coefficients(zzprime);
    Utils::copy<sizeof(limb) * 10>(x3, xxxprime);
    Utils::copy<sizeof(limb) * 10>(z3, zzprime);

    fsquare(xx, x);
    fsquare(zz, z);
    fproduct(x2, xx, zz);
    freduce_degree(x2);
    freduce_coefficients(x2);
    fdifference(zz, xx);   // does zz = xx - zz
    Utils::zero<sizeof(limb) * 9>(zzz + 10);
    fscalar_product(zzz, zz, 121665);
    freduce_coefficients(zzz);
    fsum(zzz, xx);
    fproduct(z2, zz, zzz);
    freduce_degree(z2);
    freduce_coefficients(z2);
}

ZT_INLINE void swap_conditional(limb a[19], limb b[19], limb iswap)
{
    const s32 swap = (s32)-iswap;
    for (int i = 0; i < 10; ++i) {
        const s32 x = swap & (((s32)a[i]) ^ ((s32)b[i]));
        a[i]        = ((s32)a[i]) ^ x;
        b[i]        = ((s32)b[i]) ^ x;
    }
}

void cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q)
{
    limb a[19] = { 0 }, b[19] = { 1 }, c[19] = { 1 }, d[19] = { 0 };
    limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
    limb e[19] = { 0 }, f[19] = { 1 }, g[19] = { 0 }, h[19] = { 1 };
    limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;

    Utils::copy<sizeof(limb) * 10>(nqpqx, q);

    for (int i = 0; i < 32; ++i) {
        u8 byte = n[31 - i];
        for (int j = 0; j < 8; ++j) {
            const limb bit = byte >> 7;

            swap_conditional(nqx, nqpqx, bit);
            swap_conditional(nqz, nqpqz, bit);
            fmonty(nqx2, nqz2, nqpqx2, nqpqz2, nqx, nqz, nqpqx, nqpqz, q);
            swap_conditional(nqx2, nqpqx2, bit);
            swap_conditional(nqz2, nqpqz2, bit);

            t      = nqx;
            nqx    = nqx2;
            nqx2   = t;
            t      = nqz;
            nqz    = nqz2;
            nqz2   = t;
            t      = nqpqx;
            nqpqx  = nqpqx2;
            nqpqx2 = t;
            t      = nqpqz;
            nqpqz  = nqpqz2;
            nqpqz2 = t;

            byte <<= 1;
        }
    }

    Utils::copy<sizeof(limb) * 10>(resultx, nqx);
    Utils::copy<sizeof(limb) * 10>(resultz, nqz);
}

ZT_INLINE void crecip(limb *out, const limb *z)
{
    limb z2[10], z9[10], z11[10], z2_5_0[10], z2_10_0[10], z2_20_0[10], z2_50_0[10], z2_100_0[10], t0[10], t1[10];
    fsquare(z2, z);
    fsquare(t1, z2);
    fsquare(t0, t1);
    fmul(z9, t0, z);
    fmul(z11, z9, z2);
    fsquare(t0, z11);
    fmul(z2_5_0, t0, z9);
    fsquare(t0, z2_5_0);
    fsquare(t1, t0);
    fsquare(t0, t1);
    fsquare(t1, t0);
    fsquare(t0, t1);
    fmul(z2_10_0, t0, z2_5_0);
    fsquare(t0, z2_10_0);
    fsquare(t1, t0);
    for (int i = 2; i < 10; i += 2) {
        fsquare(t0, t1);
        fsquare(t1, t0);
    }
    fmul(z2_20_0, t1, z2_10_0);
    fsquare(t0, z2_20_0);
    fsquare(t1, t0);
    for (int i = 2; i < 20; i += 2) {
        fsquare(t0, t1);
        fsquare(t1, t0);
    }
    fmul(t0, t1, z2_20_0);
    fsquare(t1, t0);
    fsquare(t0, t1);
    for (int i = 2; i < 10; i += 2) {
        fsquare(t1, t0);
        fsquare(t0, t1);
    }
    fmul(z2_50_0, t0, z2_10_0);
    fsquare(t0, z2_50_0);
    fsquare(t1, t0);
    for (int i = 2; i < 50; i += 2) {
        fsquare(t0, t1);
        fsquare(t1, t0);
    }
    fmul(z2_100_0, t1, z2_50_0);
    fsquare(t1, z2_100_0);
    fsquare(t0, t1);
    for (int i = 2; i < 100; i += 2) {
        fsquare(t1, t0);
        fsquare(t0, t1);
    }
    fmul(t1, t0, z2_100_0);
    fsquare(t0, t1);
    fsquare(t1, t0);
    for (int i = 2; i < 50; i += 2) {
        fsquare(t0, t1);
        fsquare(t1, t0);
    }
    fmul(t0, t1, z2_50_0);
    fsquare(t1, t0);
    fsquare(t0, t1);
    fsquare(t1, t0);
    fsquare(t0, t1);
    fsquare(t1, t0);
    fmul(out, t1, z11);
}

void crypto_scalarmult(u8 *mypublic, const u8 *secret, const u8 *basepoint)
{
    limb bp[10], x[10], z[11], zmone[10];
    uint8_t e[32];
    int i;

    for (i = 0; i < 32; ++i)
        e[i] = secret[i];
    e[0] &= 248;
    e[31] &= 127;
    e[31] |= 64;

    fexpand(bp, basepoint);
    cmult(x, z, e, bp);
    crecip(zmone, z);
    fmul(z, x, zmone);
    fcontract(mypublic, z);
}

static const unsigned char s_base[32] = { 9 };
ZT_INLINE void crypto_scalarmult_base(unsigned char *q, const unsigned char *n) { crypto_scalarmult(q, n, s_base); }

// --------------------------------------------------------------------------------------------------------------------

// Ed25519 ref from: http://bench.cr.yp.to/supercop.html

typedef struct {
    uint32_t v[32];
} fe25519;

typedef struct {
    uint32_t v[32];
} sc25519;

typedef struct {
    fe25519 x, y, z, t;
} ge25519;

#define ge25519_p3 ge25519

typedef struct {
    fe25519 x, z, y, t;
} ge25519_p1p1;

typedef struct {
    fe25519 x, y, z;
} ge25519_p2;

typedef struct {
    fe25519 x, y;
} ge25519_aff;

void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y);

ZT_INLINE uint32_t equal(uint32_t a, uint32_t b)
{
    uint32_t x = a ^ b;
    x -= 1;
    x >>= 31;
    return x;
}

ZT_INLINE uint32_t ge(uint32_t a, uint32_t b)
{
    unsigned int x = a;
    x -= (unsigned int)b;
    x >>= 31;
    x ^= 1;
    return x;
}

ZT_INLINE uint32_t times19(uint32_t a) { return (a << 4) + (a << 1) + a; }
ZT_INLINE uint32_t times38(uint32_t a) { return (a << 5) + (a << 2) + (a << 1); }

void reduce_add_sub(fe25519 *r)
{
    for (int rep = 0; rep < 4; rep++) {
        uint32_t t = r->v[31] >> 7;
        r->v[31] &= 127;
        t = times19(t);
        r->v[0] += t;
        for (int i = 0; i < 31; i++) {
            t = r->v[i] >> 8;
            r->v[i + 1] += t;
            r->v[i] &= 255;
        }
    }
}

ZT_INLINE void reduce_mul(fe25519 *r)
{
    for (int rep = 0; rep < 2; rep++) {
        uint32_t t = r->v[31] >> 7;
        r->v[31] &= 127;
        t = times19(t);
        r->v[0] += t;
        for (int i = 0; i < 31; i++) {
            t = r->v[i] >> 8;
            r->v[i + 1] += t;
            r->v[i] &= 255;
        }
    }
}

void fe25519_freeze(fe25519 *r)
{
    uint32_t mm = equal(r->v[31], 127);
    for (int i = 30; i > 0; i--)
        mm &= equal(r->v[i], 255);
    mm &= ge(r->v[0], 237);
    mm = -mm;
    r->v[31] -= mm & 127;
    for (int i = 30; i > 0; i--)
        r->v[i] -= mm & 255;
    r->v[0] -= mm & 237;
}

ZT_INLINE void fe25519_unpack(fe25519 *r, const unsigned char x[32])
{
    for (int i = 0; i < 32; i++)
        r->v[i] = x[i];
    r->v[31] &= 127;
}

ZT_INLINE void fe25519_pack(unsigned char r[32], const fe25519 *x)
{
    fe25519 y = *x;
    fe25519_freeze(&y);
    for (int i = 0; i < 32; i++)
        r[i] = y.v[i];
}

ZT_INLINE int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y)
{
    fe25519 t1 = *x;
    fe25519 t2 = *y;
    fe25519_freeze(&t1);
    fe25519_freeze(&t2);
    for (int i = 0; i < 32; i++) {
        if (t1.v[i] != t2.v[i])
            return 0;
    }
    return 1;
}

ZT_INLINE void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b)
{
    uint32_t mask = b;
    mask          = -mask;
    for (int i = 0; i < 32; i++)
        r->v[i] ^= mask & (x->v[i] ^ r->v[i]);
}

ZT_INLINE unsigned char fe25519_getparity(const fe25519 *x)
{
    fe25519 t = *x;
    fe25519_freeze(&t);
    return t.v[0] & 1;
}

ZT_INLINE void fe25519_setone(fe25519 *r)
{
    r->v[0] = 1;
    for (int i = 1; i < 32; i++)
        r->v[i] = 0;
}

ZT_INLINE void fe25519_setzero(fe25519 *r)
{
    for (int i = 0; i < 32; i++)
        r->v[i] = 0;
}

void fe25519_neg(fe25519 *r, const fe25519 *x)
{
    fe25519 t;
    for (int i = 0; i < 32; i++)
        t.v[i] = x->v[i];
    fe25519_setzero(r);
    fe25519_sub(r, r, &t);
}

ZT_INLINE void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y)
{
    for (int i = 0; i < 32; i++)
        r->v[i] = x->v[i] + y->v[i];
    reduce_add_sub(r);
}

void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y)
{
    uint32_t t[32];
    t[0]  = x->v[0] + 0x1da;
    t[31] = x->v[31] + 0xfe;
    for (int i = 1; i < 31; i++)
        t[i] = x->v[i] + 0x1fe;
    for (int i = 0; i < 32; i++)
        r->v[i] = t[i] - y->v[i];
    reduce_add_sub(r);
}

void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y)
{
    uint32_t t[63];
    for (int i = 0; i < 63; i++)
        t[i] = 0;
    for (int i = 0; i < 32; i++) {
        for (int j = 0; j < 32; j++)
            t[i + j] += x->v[i] * y->v[j];
    }
    for (int i = 32; i < 63; i++)
        r->v[i - 32] = t[i - 32] + times38(t[i]);
    r->v[31] = t[31];
    reduce_mul(r);
}

ZT_INLINE void fe25519_square(fe25519 *r, const fe25519 *x) { fe25519_mul(r, x, x); }

ZT_INLINE void fe25519_invert(fe25519 *r, const fe25519 *x)
{
    fe25519 z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t0, t1;
    fe25519_square(&z2, x);
    fe25519_square(&t1, &z2);
    fe25519_square(&t0, &t1);
    fe25519_mul(&z9, &t0, x);
    fe25519_mul(&z11, &z9, &z2);
    fe25519_square(&t0, &z11);
    fe25519_mul(&z2_5_0, &t0, &z9);
    fe25519_square(&t0, &z2_5_0);
    fe25519_square(&t1, &t0);
    fe25519_square(&t0, &t1);
    fe25519_square(&t1, &t0);
    fe25519_square(&t0, &t1);
    fe25519_mul(&z2_10_0, &t0, &z2_5_0);
    fe25519_square(&t0, &z2_10_0);
    fe25519_square(&t1, &t0);
    for (int i = 2; i < 10; i += 2) {
        fe25519_square(&t0, &t1);
        fe25519_square(&t1, &t0);
    }
    fe25519_mul(&z2_20_0, &t1, &z2_10_0);
    fe25519_square(&t0, &z2_20_0);
    fe25519_square(&t1, &t0);
    for (int i = 2; i < 20; i += 2) {
        fe25519_square(&t0, &t1);
        fe25519_square(&t1, &t0);
    }
    fe25519_mul(&t0, &t1, &z2_20_0);
    fe25519_square(&t1, &t0);
    fe25519_square(&t0, &t1);
    for (int i = 2; i < 10; i += 2) {
        fe25519_square(&t1, &t0);
        fe25519_square(&t0, &t1);
    }
    fe25519_mul(&z2_50_0, &t0, &z2_10_0);
    fe25519_square(&t0, &z2_50_0);
    fe25519_square(&t1, &t0);
    for (int i = 2; i < 50; i += 2) {
        fe25519_square(&t0, &t1);
        fe25519_square(&t1, &t0);
    }
    fe25519_mul(&z2_100_0, &t1, &z2_50_0);
    fe25519_square(&t1, &z2_100_0);
    fe25519_square(&t0, &t1);
    for (int i = 2; i < 100; i += 2) {
        fe25519_square(&t1, &t0);
        fe25519_square(&t0, &t1);
    }
    fe25519_mul(&t1, &t0, &z2_100_0);
    fe25519_square(&t0, &t1);
    fe25519_square(&t1, &t0);
    for (int i = 2; i < 50; i += 2) {
        fe25519_square(&t0, &t1);
        fe25519_square(&t1, &t0);
    }
    fe25519_mul(&t0, &t1, &z2_50_0);
    fe25519_square(&t1, &t0);
    fe25519_square(&t0, &t1);
    fe25519_square(&t1, &t0);
    fe25519_square(&t0, &t1);
    fe25519_square(&t1, &t0);
    fe25519_mul(r, &t1, &z11);
}

ZT_INLINE void fe25519_pow2523(fe25519 *r, const fe25519 *x)
{
    fe25519 z2, z9, z11, z2_5_0, z2_10_0, z2_20_0, z2_50_0, z2_100_0, t;
    fe25519_square(&z2, x);
    fe25519_square(&t, &z2);
    fe25519_square(&t, &t);
    fe25519_mul(&z9, &t, x);
    fe25519_mul(&z11, &z9, &z2);
    fe25519_square(&t, &z11);
    fe25519_mul(&z2_5_0, &t, &z9);
    fe25519_square(&t, &z2_5_0);
    for (int i = 1; i < 5; i++)
        fe25519_square(&t, &t);
    fe25519_mul(&z2_10_0, &t, &z2_5_0);
    fe25519_square(&t, &z2_10_0);
    for (int i = 1; i < 10; i++)
        fe25519_square(&t, &t);
    fe25519_mul(&z2_20_0, &t, &z2_10_0);
    fe25519_square(&t, &z2_20_0);
    for (int i = 1; i < 20; i++)
        fe25519_square(&t, &t);
    fe25519_mul(&t, &t, &z2_20_0);
    fe25519_square(&t, &t);
    for (int i = 1; i < 10; i++)
        fe25519_square(&t, &t);
    fe25519_mul(&z2_50_0, &t, &z2_10_0);
    fe25519_square(&t, &z2_50_0);
    for (int i = 1; i < 50; i++)
        fe25519_square(&t, &t);
    fe25519_mul(&z2_100_0, &t, &z2_50_0);
    fe25519_square(&t, &z2_100_0);
    for (int i = 1; i < 100; i++)
        fe25519_square(&t, &t);
    fe25519_mul(&t, &t, &z2_100_0);
    fe25519_square(&t, &t);
    for (int i = 1; i < 50; i++)
        fe25519_square(&t, &t);
    fe25519_mul(&t, &t, &z2_50_0);
    fe25519_square(&t, &t);
    fe25519_square(&t, &t);
    fe25519_mul(r, &t, x);
}

const uint32_t m[32] = {
    0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2, 0xDE, 0xF9, 0xDE, 0x14,
    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10
};
const uint32_t mu[33] = { 0x1B, 0x13, 0x2C, 0x0A, 0xA3, 0xE5, 0x9C, 0xED, 0xA7, 0x29, 0x63,
                          0x08, 0x5D, 0x21, 0x06, 0x21, 0xEB, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
                          0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x0F };

ZT_INLINE uint32_t lt(uint32_t a, uint32_t b) /* 16-bit inputs */
{
    unsigned int x = a;
    x -= (unsigned int)b; /* 0..65535: no; 4294901761..4294967295: yes */
    x >>= 31;             /* 0: no; 1: yes */
    return x;
}

void reduce_add_sub(sc25519 *r)
{
    uint32_t pb = 0;
    uint32_t b;
    uint32_t mask;
    int i;
    unsigned char t[32];

    for (i = 0; i < 32; i++) {
        pb += m[i];
        b    = lt(r->v[i], pb);
        t[i] = r->v[i] - pb + (b << 8);
        pb   = b;
    }
    mask = b - 1;
    for (i = 0; i < 32; i++)
        r->v[i] ^= mask & (r->v[i] ^ t[i]);
}

void barrett_reduce(sc25519 *r, const uint32_t x[64])
{
    /* See HAC, Alg. 14.42 */
    int i, j;
    uint32_t q2[66];
    uint32_t *q3 = q2 + 33;
    uint32_t r1[33];
    uint32_t r2[33];
    uint32_t pb = 0;

    Utils::zero<sizeof(q2)>(q2);
    // for (i = 0;i < 66;++i) q2[i] = 0;
    Utils::zero<sizeof(r2)>(r2);
    // for (i = 0;i < 33;++i) r2[i] = 0;

    for (i = 0; i < 33; i++)
        for (j = 0; j < 33; j++)
            if (i + j >= 31)
                q2[i + j] += mu[i] * x[j + 31];
    q2[32] += (q2[31] >> 8);
    q2[33] += (q2[32] >> 8);

    for (i = 0; i < 33; i++)
        r1[i] = x[i];
    for (i = 0; i < 32; i++)
        for (j = 0; j < 33; j++)
            if (i + j < 33)
                r2[i + j] += m[i] * q3[j];

    for (i = 0; i < 32; i++) {
        r2[i + 1] += (r2[i] >> 8);
        r2[i] &= 0xff;
    }

    for (i = 0; i < 32; i++) {
        pb += r2[i];
        uint32_t b = lt(r1[i], pb);
        r->v[i]    = r1[i] - pb + (b << 8);
        pb         = b;
    }

    reduce_add_sub(r);
    reduce_add_sub(r);
}

ZT_INLINE void sc25519_from32bytes(sc25519 *r, const unsigned char x[32])
{
    int i;
    uint32_t t[64];
    for (i = 0; i < 32; i++)
        t[i] = x[i];
    for (i = 32; i < 64; ++i)
        t[i] = 0;
    barrett_reduce(r, t);
}

ZT_INLINE void sc25519_from64bytes(sc25519 *r, const unsigned char x[64])
{
    int i;
    uint32_t t[64];
    for (i = 0; i < 64; i++)
        t[i] = x[i];
    barrett_reduce(r, t);
}

ZT_INLINE void sc25519_to32bytes(unsigned char r[32], const sc25519 *x)
{
    int i;
    for (i = 0; i < 32; i++)
        r[i] = x->v[i];
}

ZT_INLINE void sc25519_add(sc25519 *r, const sc25519 *x, const sc25519 *y)
{
    int i;
    for (i = 0; i < 32; i++)
        r->v[i] = x->v[i] + y->v[i];
    for (i = 0; i < 31; i++) {
        r->v[i + 1] += (r->v[i] >> 8);
        r->v[i] &= 0xff;
    }
    reduce_add_sub(r);
}

ZT_INLINE void sc25519_mul(sc25519 *r, const sc25519 *x, const sc25519 *y)
{
    int i, j;
    uint32_t t[64];
    for (i = 0; i < 64; i++)
        t[i] = 0;

    for (i = 0; i < 32; i++)
        for (j = 0; j < 32; j++)
            t[i + j] += x->v[i] * y->v[j];

    for (i = 0; i < 63; i++) {
        t[i + 1] += (t[i] >> 8);
        t[i] &= 0xff;
    }

    barrett_reduce(r, t);
}

ZT_INLINE void sc25519_window3(signed char r[85], const sc25519 *s)
{
    char carry;
    int i;
    for (i = 0; i < 10; i++) {
        r[8 * i + 0] = s->v[3 * i + 0] & 7;
        r[8 * i + 1] = (s->v[3 * i + 0] >> 3) & 7;
        r[8 * i + 2] = (s->v[3 * i + 0] >> 6) & 7;
        r[8 * i + 2] ^= (s->v[3 * i + 1] << 2) & 7;
        r[8 * i + 3] = (s->v[3 * i + 1] >> 1) & 7;
        r[8 * i + 4] = (s->v[3 * i + 1] >> 4) & 7;
        r[8 * i + 5] = (s->v[3 * i + 1] >> 7) & 7;
        r[8 * i + 5] ^= (s->v[3 * i + 2] << 1) & 7;
        r[8 * i + 6] = (s->v[3 * i + 2] >> 2) & 7;
        r[8 * i + 7] = (s->v[3 * i + 2] >> 5) & 7;
    }
    r[8 * i + 0] = s->v[3 * i + 0] & 7;
    r[8 * i + 1] = (s->v[3 * i + 0] >> 3) & 7;
    r[8 * i + 2] = (s->v[3 * i + 0] >> 6) & 7;
    r[8 * i + 2] ^= (s->v[3 * i + 1] << 2) & 7;
    r[8 * i + 3] = (s->v[3 * i + 1] >> 1) & 7;
    r[8 * i + 4] = (s->v[3 * i + 1] >> 4) & 7;

    /* Making it signed */
    carry = 0;
    for (i = 0; i < 84; i++) {
        r[i] += carry;
        r[i + 1] += r[i] >> 3;
        r[i] &= 7;
        carry = r[i] >> 2;
        r[i] -= carry << 3;
    }
    r[84] += carry;
}

ZT_INLINE void sc25519_2interleave2(unsigned char r[127], const sc25519 *s1, const sc25519 *s2)
{
    int i;
    for (i = 0; i < 31; i++) {
        r[4 * i]     = (s1->v[i] & 3) ^ ((s2->v[i] & 3) << 2);
        r[4 * i + 1] = ((s1->v[i] >> 2) & 3) ^ (((s2->v[i] >> 2) & 3) << 2);
        r[4 * i + 2] = ((s1->v[i] >> 4) & 3) ^ (((s2->v[i] >> 4) & 3) << 2);
        r[4 * i + 3] = ((s1->v[i] >> 6) & 3) ^ (((s2->v[i] >> 6) & 3) << 2);
    }
    r[124] = (s1->v[31] & 3) ^ ((s2->v[31] & 3) << 2);
    r[125] = ((s1->v[31] >> 2) & 3) ^ (((s2->v[31] >> 2) & 3) << 2);
    r[126] = ((s1->v[31] >> 4) & 3) ^ (((s2->v[31] >> 4) & 3) << 2);
}

static const fe25519 ge25519_ecd    = { { 0xA3, 0x78, 0x59, 0x13, 0xCA, 0x4D, 0xEB, 0x75, 0xAB, 0xD8, 0x41,
                                       0x41, 0x4D, 0x0A, 0x70, 0x00, 0x98, 0xE8, 0x79, 0x77, 0x79, 0x40,
                                       0xC7, 0x8C, 0x73, 0xFE, 0x6F, 0x2B, 0xEE, 0x6C, 0x03, 0x52 } };
static const fe25519 ge25519_ec2d   = { { 0x59, 0xF1, 0xB2, 0x26, 0x94, 0x9B, 0xD6, 0xEB, 0x56, 0xB1, 0x83,
                                        0x82, 0x9A, 0x14, 0xE0, 0x00, 0x30, 0xD1, 0xF3, 0xEE, 0xF2, 0x80,
                                        0x8E, 0x19, 0xE7, 0xFC, 0xDF, 0x56, 0xDC, 0xD9, 0x06, 0x24 } };
static const fe25519 ge25519_sqrtm1 = { { 0xB0, 0xA0, 0x0E, 0x4A, 0x27, 0x1B, 0xEE, 0xC4, 0x78, 0xE4, 0x2F,
                                          0xAD, 0x06, 0x18, 0x43, 0x2F, 0xA7, 0xD7, 0xFB, 0x3D, 0x99, 0x00,
                                          0x4D, 0x2B, 0x0B, 0xDF, 0xC1, 0x4F, 0x80, 0x24, 0x83, 0x2B } };
static const ge25519 ge25519_base   = {
    { { 0x1A, 0xD5, 0x25, 0x8F, 0x60, 0x2D, 0x56, 0xC9, 0xB2, 0xA7, 0x25, 0x95, 0x60, 0xC7, 0x2C, 0x69,
        0x5C, 0xDC, 0xD6, 0xFD, 0x31, 0xE2, 0xA4, 0xC0, 0xFE, 0x53, 0x6E, 0xCD, 0xD3, 0x36, 0x69, 0x21 } },
    { { 0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
        0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66 } },
    { { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
        0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
    { { 0xA3, 0xDD, 0xB7, 0xA5, 0xB3, 0x8A, 0xDE, 0x6D, 0xF5, 0x52, 0x51, 0x77, 0x80, 0x9F, 0xF0, 0x20,
        0x7D, 0xE3, 0xAB, 0x64, 0x8E, 0x4E, 0xEA, 0x66, 0x65, 0x76, 0x8B, 0xD7, 0x0F, 0x5F, 0x87, 0x67 } }
};
static const ge25519_aff ge25519_base_multiples_affine[425] = {
    { { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
      { { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
    { { { 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95, 0x60, 0xc7, 0x2c, 0x69,
          0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0, 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21 } },
      { { 0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
          0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66 } } },
    { { { 0x0e, 0xce, 0x43, 0x28, 0x4e, 0xa1, 0xc5, 0x83, 0x5f, 0xa4, 0xd7, 0x15, 0x45, 0x8e, 0x0d, 0x08,
          0xac, 0xe7, 0x33, 0x18, 0x7d, 0x3b, 0x04, 0x3d, 0x6c, 0x04, 0x5a, 0x9f, 0x4c, 0x38, 0xab, 0x36 } },
      { { 0xc9, 0xa3, 0xf8, 0x6a, 0xae, 0x46, 0x5f, 0x0e, 0x56, 0x51, 0x38, 0x64, 0x51, 0x0f, 0x39, 0x97,
          0x56, 0x1f, 0xa2, 0xc9, 0xe8, 0x5e, 0xa2, 0x1d, 0xc2, 0x29, 0x23, 0x09, 0xf3, 0xcd, 0x60, 0x22 } } },
    { { { 0x5c, 0xe2, 0xf8, 0xd3, 0x5f, 0x48, 0x62, 0xac, 0x86, 0x48, 0x62, 0x81, 0x19, 0x98, 0x43, 0x63,
          0x3a, 0xc8, 0xda, 0x3e, 0x74, 0xae, 0xf4, 0x1f, 0x49, 0x8f, 0x92, 0x22, 0x4a, 0x9c, 0xae, 0x67 } },
      { { 0xd4, 0xb4, 0xf5, 0x78, 0x48, 0x68, 0xc3, 0x02, 0x04, 0x03, 0x24, 0x67, 0x17, 0xec, 0x16, 0x9f,
          0xf7, 0x9e, 0x26, 0x60, 0x8e, 0xa1, 0x26, 0xa1, 0xab, 0x69, 0xee, 0x77, 0xd1, 0xb1, 0x67, 0x12 } } },
    { { { 0x70, 0xf8, 0xc9, 0xc4, 0x57, 0xa6, 0x3a, 0x49, 0x47, 0x15, 0xce, 0x93, 0xc1, 0x9e, 0x73, 0x1a,
          0xf9, 0x20, 0x35, 0x7a, 0xb8, 0xd4, 0x25, 0x83, 0x46, 0xf1, 0xcf, 0x56, 0xdb, 0xa8, 0x3d, 0x20 } },
      { { 0x2f, 0x11, 0x32, 0xca, 0x61, 0xab, 0x38, 0xdf, 0xf0, 0x0f, 0x2f, 0xea, 0x32, 0x28, 0xf2, 0x4c,
          0x6c, 0x71, 0xd5, 0x80, 0x85, 0xb8, 0x0e, 0x47, 0xe1, 0x95, 0x15, 0xcb, 0x27, 0xe8, 0xd0, 0x47 } } },
    { { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
      { { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
    { { { 0xc8, 0x84, 0xa5, 0x08, 0xbc, 0xfd, 0x87, 0x3b, 0x99, 0x8b, 0x69, 0x80, 0x7b, 0xc6, 0x3a, 0xeb,
          0x93, 0xcf, 0x4e, 0xf8, 0x5c, 0x2d, 0x86, 0x42, 0xb6, 0x71, 0xd7, 0x97, 0x5f, 0xe1, 0x42, 0x67 } },
      { { 0xb4, 0xb9, 0x37, 0xfc, 0xa9, 0x5b, 0x2f, 0x1e, 0x93, 0xe4, 0x1e, 0x62, 0xfc, 0x3c, 0x78, 0x81,
          0x8f, 0xf3, 0x8a, 0x66, 0x09, 0x6f, 0xad, 0x6e, 0x79, 0x73, 0xe5, 0xc9, 0x00, 0x06, 0xd3, 0x21 } } },
    { { { 0xf8, 0xf9, 0x28, 0x6c, 0x6d, 0x59, 0xb2, 0x59, 0x74, 0x23, 0xbf, 0xe7, 0x33, 0x8d, 0x57, 0x09,
          0x91, 0x9c, 0x24, 0x08, 0x15, 0x2b, 0xe2, 0xb8, 0xee, 0x3a, 0xe5, 0x27, 0x06, 0x86, 0xa4, 0x23 } },
      { { 0xeb, 0x27, 0x67, 0xc1, 0x37, 0xab, 0x7a, 0xd8, 0x27, 0x9c, 0x07, 0x8e, 0xff, 0x11, 0x6a, 0xb0,
          0x78, 0x6e, 0xad, 0x3a, 0x2e, 0x0f, 0x98, 0x9f, 0x72, 0xc3, 0x7f, 0x82, 0xf2, 0x96, 0x96, 0x70 } } },
    { { { 0x81, 0x6b, 0x88, 0xe8, 0x1e, 0xc7, 0x77, 0x96, 0x0e, 0xa1, 0xa9, 0x52, 0xe0, 0xd8, 0x0e, 0x61,
          0x9e, 0x79, 0x2d, 0x95, 0x9c, 0x8d, 0x96, 0xe0, 0x06, 0x40, 0x5d, 0x87, 0x28, 0x5f, 0x98, 0x70 } },
      { { 0xf1, 0x79, 0x7b, 0xed, 0x4f, 0x44, 0xb2, 0xe7, 0x08, 0x0d, 0xc2, 0x08, 0x12, 0xd2, 0x9f, 0xdf,
          0xcd, 0x93, 0x20, 0x8a, 0xcf, 0x33, 0xca, 0x6d, 0x89, 0xb9, 0x77, 0xc8, 0x93, 0x1b, 0x4e, 0x60 } } },
    { { { 0x26, 0x4f, 0x7e, 0x97, 0xf6, 0x40, 0xdd, 0x4f, 0xfc, 0x52, 0x78, 0xf9, 0x90, 0x31, 0x03, 0xe6,
          0x7d, 0x56, 0x39, 0x0b, 0x1d, 0x56, 0x82, 0x85, 0xf9, 0x1a, 0x42, 0x17, 0x69, 0x6c, 0xcf, 0x39 } },
      { { 0x69, 0xd2, 0x06, 0x3a, 0x4f, 0x39, 0x2d, 0xf9, 0x38, 0x40, 0x8c, 0x4c, 0xe7, 0x05, 0x12, 0xb4,
          0x78, 0x8b, 0xf8, 0xc0, 0xec, 0x93, 0xde, 0x7a, 0x6b, 0xce, 0x2c, 0xe1, 0x0e, 0xa9, 0x34, 0x44 } } },
    { { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
      { { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
    { { { 0x0b, 0xa4, 0x3c, 0xb0, 0x0f, 0x7a, 0x51, 0xf1, 0x78, 0xd6, 0xd9, 0x6a, 0xfd, 0x46, 0xe8, 0xb8,
          0xa8, 0x79, 0x1d, 0x87, 0xf9, 0x90, 0xf2, 0x9c, 0x13, 0x29, 0xf8, 0x0b, 0x20, 0x64, 0xfa, 0x05 } },
      { { 0x26, 0x09, 0xda, 0x17, 0xaf, 0x95, 0xd6, 0xfb, 0x6a, 0x19, 0x0d, 0x6e, 0x5e, 0x12, 0xf1, 0x99,
          0x4c, 0xaa, 0xa8, 0x6f, 0x79, 0x86, 0xf4, 0x72, 0x28, 0x00, 0x26, 0xf9, 0xea, 0x9e, 0x19, 0x3d } } },
    { { { 0x87, 0xdd, 0xcf, 0xf0, 0x5b, 0x49, 0xa2, 0x5d, 0x40, 0x7a, 0x23, 0x26, 0xa4, 0x7a, 0x83, 0x8a,
          0xb7, 0x8b, 0xd2, 0x1a, 0xbf, 0xea, 0x02, 0x24, 0x08, 0x5f, 0x7b, 0xa9, 0xb1, 0xbe, 0x9d, 0x37 } },
      { { 0xfc, 0x86, 0x4b, 0x08, 0xee, 0xe7, 0xa0, 0xfd, 0x21, 0x45, 0x09, 0x34, 0xc1, 0x61, 0x32, 0x23,
          0xfc, 0x9b, 0x55, 0x48, 0x53, 0x99, 0xf7, 0x63, 0xd0, 0x99, 0xce, 0x01, 0xe0, 0x9f, 0xeb, 0x28 } } },
    { { { 0x47, 0xfc, 0xab, 0x5a, 0x17, 0xf0, 0x85, 0x56, 0x3a, 0x30, 0x86, 0x20, 0x28, 0x4b, 0x8e, 0x44,
          0x74, 0x3a, 0x6e, 0x02, 0xf1, 0x32, 0x8f, 0x9f, 0x3f, 0x08, 0x35, 0xe9, 0xca, 0x16, 0x5f, 0x6e } },
      { { 0x1c, 0x59, 0x1c, 0x65, 0x5d, 0x34, 0xa4, 0x09, 0xcd, 0x13, 0x9c, 0x70, 0x7d, 0xb1, 0x2a, 0xc5,
          0x88, 0xaf, 0x0b, 0x60, 0xc7, 0x9f, 0x34, 0x8d, 0xd6, 0xb7, 0x7f, 0xea, 0x78, 0x65, 0x8d, 0x77 } } },
    { { { 0x56, 0xa5, 0xc2, 0x0c, 0xdd, 0xbc, 0xb8, 0x20, 0x6d, 0x57, 0x61, 0xb5, 0xfb, 0x78, 0xb5, 0xd4,
          0x49, 0x54, 0x90, 0x26, 0xc1, 0xcb, 0xe9, 0xe6, 0xbf, 0xec, 0x1d, 0x4e, 0xed, 0x07, 0x7e, 0x5e } },
      { { 0xc7, 0xf6, 0x6c, 0x56, 0x31, 0x20, 0x14, 0x0e, 0xa8, 0xd9, 0x27, 0xc1, 0x9a, 0x3d, 0x1b, 0x7d,
          0x0e, 0x26, 0xd3, 0x81, 0xaa, 0xeb, 0xf5, 0x6b, 0x79, 0x02, 0xf1, 0x51, 0x5c, 0x75, 0x55, 0x0f } } },
    { { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
      { { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
    { { { 0x0a, 0x34, 0xcd, 0x82, 0x3c, 0x33, 0x09, 0x54, 0xd2, 0x61, 0x39, 0x30, 0x9b, 0xfd, 0xef, 0x21,
          0x26, 0xd4, 0x70, 0xfa, 0xee, 0xf9, 0x31, 0x33, 0x73, 0x84, 0xd0, 0xb3, 0x81, 0xbf, 0xec, 0x2e } },
      { { 0xe8, 0x93, 0x8b, 0x00, 0x64, 0xf7, 0x9c, 0xb8, 0x74, 0xe0, 0xe6, 0x49, 0x48, 0x4d, 0x4d, 0x48,
          0xb6, 0x19, 0xa1, 0x40, 0xb7, 0xd9, 0x32, 0x41, 0x7c, 0x82, 0x37, 0xa1, 0x2d, 0xdc, 0xd2, 0x54 } } },
    { { { 0x68, 0x2b, 0x4a, 0x5b, 0xd5, 0xc7, 0x51, 0x91, 0x1d, 0xe1, 0x2a, 0x4b, 0xc4, 0x47, 0xf1, 0xbc,
          0x7a, 0xb3, 0xcb, 0xc8, 0xb6, 0x7c, 0xac, 0x90, 0x05, 0xfd, 0xf3, 0xf9, 0x52, 0x3a, 0x11, 0x6b } },
      { { 0x3d, 0xc1, 0x27, 0xf3, 0x59, 0x43, 0x95, 0x90, 0xc5, 0x96, 0x79, 0xf5, 0xf4, 0x95, 0x65, 0x29,
          0x06, 0x9c, 0x51, 0x05, 0x18, 0xda, 0xb8, 0x2e, 0x79, 0x7e, 0x69, 0x59, 0x71, 0x01, 0xeb, 0x1a } } },
    { { { 0x15, 0x06, 0x49, 0xb6, 0x8a, 0x3c, 0xea, 0x2f, 0x34, 0x20, 0x14, 0xc3, 0xaa, 0xd6, 0xaf, 0x2c,
          0x3e, 0xbd, 0x65, 0x20, 0xe2, 0x4d, 0x4b, 0x3b, 0xeb, 0x9f, 0x4a, 0xc3, 0xad, 0xa4, 0x3b, 0x60 } },
      { { 0xbc, 0x58, 0xe6, 0xc0, 0x95, 0x2a, 0x2a, 0x81, 0x9a, 0x7a, 0xf3, 0xd2, 0x06, 0xbe, 0x48, 0xbc,
          0x0c, 0xc5, 0x46, 0xe0, 0x6a, 0xd4, 0xac, 0x0f, 0xd9, 0xcc, 0x82, 0x34, 0x2c, 0xaf, 0xdb, 0x1f } } },
    { { { 0xf7, 0x17, 0x13, 0xbd, 0xfb, 0xbc, 0xd2, 0xec, 0x45, 0xb3, 0x15, 0x31, 0xe9, 0xaf, 0x82, 0x84,
          0x3d, 0x28, 0xc6, 0xfc, 0x11, 0xf5, 0x41, 0xb5, 0x8b, 0xd3, 0x12, 0x76, 0x52, 0xe7, 0x1a, 0x3c } },
      { { 0x4e, 0x36, 0x11, 0x07, 0xa2, 0x15, 0x20, 0x51, 0xc4, 0x2a, 0xc3, 0x62, 0x8b, 0x5e, 0x7f, 0xa6,
          0x0f, 0xf9, 0x45, 0x85, 0x6c, 0x11, 0x86, 0xb7, 0x7e, 0xe5, 0xd7, 0xf9, 0xc3, 0x91, 0x1c, 0x05 } } },
    { { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
      { { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
    { { { 0xea, 0xd6, 0xde, 0x29, 0x3a, 0x00, 0xb9, 0x02, 0x59, 0xcb, 0x26, 0xc4, 0xba, 0x99, 0xb1, 0x97,
          0x2f, 0x8e, 0x00, 0x92, 0x26, 0x4f, 0x52, 0xeb, 0x47, 0x1b, 0x89, 0x8b, 0x24, 0xc0, 0x13, 0x7d } },
      { { 0xd5, 0x20, 0x5b, 0x80, 0xa6, 0x80, 0x20, 0x95, 0xc3, 0xe9, 0x9f, 0x8e, 0x87, 0x9e, 0x1e, 0x9e,
          0x7a, 0xc7, 0xcc, 0x75, 0x6c, 0xa5, 0xf1, 0x91, 0x1a, 0xa8, 0x01, 0x2c, 0xab, 0x76, 0xa9, 0x59 } } },
    { { { 0xde, 0xc9, 0xb1, 0x31, 0x10, 0x16, 0xaa, 0x35, 0x14, 0x6a, 0xd4, 0xb5, 0x34, 0x82, 0x71, 0xd2,
          0x4a, 0x5d, 0x9a, 0x1f, 0x53, 0x26, 0x3c, 0xe5, 0x8e, 0x8d, 0x33, 0x7f, 0xff, 0xa9, 0xd5, 0x17 } },
      { { 0x89, 0xaf, 0xf6, 0xa4, 0x64, 0xd5, 0x10, 0xe0, 0x1d, 0xad, 0xef, 0x44, 0xbd, 0xda, 0x83, 0xac,
          0x7a, 0xa8, 0xf0, 0x1c, 0x07, 0xf9, 0xc3, 0x43, 0x6c, 0x3f, 0xb7, 0xd3, 0x87, 0x22, 0x02, 0x73 } } },
    { { { 0x64, 0x1d, 0x49, 0x13, 0x2f, 0x71, 0xec, 0x69, 0x87, 0xd0, 0x42, 0xee, 0x13, 0xec, 0xe3, 0xed,
          0x56, 0x7b, 0xbf, 0xbd, 0x8c, 0x2f, 0x7d, 0x7b, 0x9d, 0x28, 0xec, 0x8e, 0x76, 0x2f, 0x6f, 0x08 } },
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          0xe6, 0xc6, 0x5a, 0x99, 0x9e, 0x1a, 0x9f, 0x04, 0x97, 0xe4, 0x4d, 0x0b, 0xbe, 0xba, 0x44, 0x40 } } },
    { { { 0xc1, 0x56, 0x96, 0x91, 0x5f, 0x1f, 0xbb, 0x54, 0x6f, 0x88, 0x89, 0x0a, 0xb2, 0xd6, 0x41, 0x42,
          0x6a, 0x82, 0xee, 0x14, 0xaa, 0x76, 0x30, 0x65, 0x0f, 0x67, 0x39, 0xa6, 0x51, 0x7c, 0x49, 0x24 } },
      { { 0x35, 0xa3, 0x78, 0xd1, 0x11, 0x0f, 0x75, 0xd3, 0x70, 0x46, 0xdb, 0x20, 0x51, 0xcb, 0x92, 0x80,
          0x54, 0x10, 0x74, 0x36, 0x86, 0xa9, 0xd7, 0xa3, 0x08, 0x78, 0xf1, 0x01, 0x29, 0xf8, 0x80, 0x3b } } },
    { { { 0xdb, 0xa7, 0x9d, 0x9d, 0xbf, 0xa0, 0xcc, 0xed, 0x53, 0xa2, 0xa2, 0x19, 0x39, 0x48, 0x83, 0x19,
          0x37, 0x58, 0xd1, 0x04, 0x28, 0x40, 0xf7, 0x8a, 0xc2, 0x08, 0xb7, 0xa5, 0x42, 0xcf, 0x53, 0x4c } },
      { { 0xa7, 0xbb, 0xf6, 0x8e, 0xad, 0xdd, 0xf7, 0x90, 0xdd, 0x5f, 0x93, 0x89, 0xae, 0x04, 0x37, 0xe6,
          0x9a, 0xb7, 0xe8, 0xc0, 0xdf, 0x16, 0x2a, 0xbf, 0xc4, 0x3a, 0x3c, 0x41, 0xd5, 0x89, 0x72, 0x5a } } },
    { { { 0x1f, 0x96, 0xff, 0x34, 0x2c, 0x13, 0x21, 0xcb, 0x0a, 0x89, 0x85, 0xbe, 0xb3, 0x70, 0x9e, 0x1e,
          0xde, 0x97, 0xaf, 0x96, 0x30, 0xf7, 0x48, 0x89, 0x40, 0x8d, 0x07, 0xf1, 0x25, 0xf0, 0x30, 0x58 } },
      { { 0x1e, 0xd4, 0x93, 0x57, 0xe2, 0x17, 0xe7, 0x9d, 0xab, 0x3c, 0x55, 0x03, 0x82, 0x2f, 0x2b, 0xdb,
          0x56, 0x1e, 0x30, 0x2e, 0x24, 0x47, 0x6e, 0xe6, 0xff, 0x33, 0x24, 0x2c, 0x75, 0x51, 0xd4, 0x67 } } },
    { { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
      { { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
    { { { 0x2b, 0x06, 0xd9, 0xa1, 0x5d, 0xe1, 0xf4, 0xd1, 0x1e, 0x3c, 0x9a, 0xc6, 0x29, 0x2b, 0x13, 0x13,
          0x78, 0xc0, 0xd8, 0x16, 0x17, 0x2d, 0x9e, 0xa9, 0xc9, 0x79, 0x57, 0xab, 0x24, 0x91, 0x92, 0x19 } },
      { { 0x69, 0xfb, 0xa1, 0x9c, 0xa6, 0x75, 0x49, 0x7d, 0x60, 0x73, 0x40, 0x42, 0xc4, 0x13, 0x0a, 0x95,
          0x79, 0x1e, 0x04, 0x83, 0x94, 0x99, 0x9b, 0x1e, 0x0c, 0xe8, 0x1f, 0x54, 0xef, 0xcb, 0xc0, 0x52 } } },
    { { { 0x14, 0x89, 0x73, 0xa1, 0x37, 0x87, 0x6a, 0x7a, 0xcf, 0x1d, 0xd9, 0x2e, 0x1a, 0x67, 0xed, 0x74,
          0xc0, 0xf0, 0x9c, 0x33, 0xdd, 0xdf, 0x08, 0xbf, 0x7b, 0xd1, 0x66, 0xda, 0xe6, 0xc9, 0x49, 0x08 } },
      { { 0xe9, 0xdd, 0x5e, 0x55, 0xb0, 0x0a, 0xde, 0x21, 0x4c, 0x5a, 0x2e, 0xd4, 0x80, 0x3a, 0x57, 0x92,
          0x7a, 0xf1, 0xc4, 0x2c, 0x40, 0xaf, 0x2f, 0xc9, 0x92, 0x03, 0xe5, 0x5a, 0xbc, 0xdc, 0xf4, 0x09 } } },
    { { { 0xf3, 0xe1, 0x2b, 0x7c, 0x05, 0x86, 0x80, 0x93, 0x4a, 0xad, 0xb4, 0x8f, 0x7e, 0x99, 0x0c, 0xfd,
          0xcd, 0xef, 0xd1, 0xff, 0x2c, 0x69, 0x34, 0x13, 0x41, 0x64, 0xcf, 0x3b, 0xd0, 0x90, 0x09, 0x1e } },
      { { 0x9d, 0x45, 0xd6, 0x80, 0xe6, 0x45, 0xaa, 0xf4, 0x15, 0xaa, 0x5c, 0x34, 0x87, 0x99, 0xa2, 0x8c,
          0x26, 0x84, 0x62, 0x7d, 0xb6, 0x29, 0xc0, 0x52, 0xea, 0xf5, 0x81, 0x18, 0x0f, 0x35, 0xa9, 0x0e } } },
    { { { 0xe7, 0x20, 0x72, 0x7c, 0x6d, 0x94, 0x5f, 0x52, 0x44, 0x54, 0xe3, 0xf1, 0xb2, 0xb0, 0x36, 0x46,
          0x0f, 0xae, 0x92, 0xe8, 0x70, 0x9d, 0x6e, 0x79, 0xb1, 0xad, 0x37, 0xa9, 0x5f, 0xc0, 0xde, 0x03 } },
      { { 0x15, 0x55, 0x37, 0xc6, 0x1c, 0x27, 0x1c, 0x6d, 0x14, 0x4f, 0xca, 0xa4, 0xc4, 0x88, 0x25, 0x46,
          0x39, 0xfc, 0x5a, 0xe5, 0xfe, 0x29, 0x11, 0x69, 0xf5, 0x72, 0x84, 0x4d, 0x78, 0x9f, 0x94, 0x15 } } },
    { { { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } },
      { { 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
          0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 } } },
    { { { 0xec, 0xd3, 0xff, 0x57, 0x0b, 0xb0, 0xb2, 0xdc, 0xf8, 0x4f, 0xe2, 0x12, 0xd5, 0x36, 0xbe, 0x6b,
          0x09, 0x43, 0x6d, 0xa3, 0x4d, 0x90, 0x2d, 0xb8, 0x74, 0xe8, 0x71, 0x45, 0x19, 0x8b, 0x0c, 0x6a } },
      { { 0xb8, 0x42, 0x1c, 0x03, 0xad, 0x2c, 0x03, 0x8e, 0xac, 0xd7, 0x98, 0x29, 0x13, 0xc6, 0x02, 0x29,
          0xb5, 0xd4, 0xe7, 0xcf, 0xcc, 0x8b, 0x83, 0xec, 0x35, 0xc7, 0x9c, 0x74, 0xb7, 0xad, 0x85, 0x5f } } },
    { { { 0x78, 0x84, 0xe1, 0x56, 0x45, 0x69, 0x68, 0x5a, 0x4f, 0xb8, 0xb1, 0x29, 0xff, 0x33, 0x03, 0x31,
          0xb7, 0xcb, 0x96, 0x25, 0xe6, 0xe6, 0x41, 0x98, 0x1a, 0xbb, 0x03, 0x56, 0xf2, 0xb2, 0x91, 0x34 } },
      { { 0x2c, 0x6c, 0xf7, 0x66, 0xa4, 0x62, 0x6b, 0x39, 0xb3, 0xba, 0x65, 0xd3, 0x1c, 0xf8, 0x11, 0xaa,
          0xbe, 0xdc, 0x80, 0x59, 0x87, 0xf5, 0x7b, 0xe5, 0xe3, 0xb3, 0x3e, 0x39, 0xda, 0xbe, 0x88, 0x09 } } },
    { { { 0x8b, 0xf1, 0xa0, 0xf5, 0xdc, 0x29, 0xb4, 0xe2, 0x07, 0xc6, 0x7a, 0x00, 0xd0, 0x89, 0x17, 0x51,
          0xd4, 0xbb, 0xd4, 0x22, 0xea, 0x7e, 0x7d, 0x7c, 0x24, 0xea, 0xf2, 0xe8, 0x22, 0x12, 0x95, 0x06 } },
      { { 0xda, 0x7c, 0xa4, 0x0c, 0xf4, 0xba, 0x6e, 0xe1, 0x89, 0xb5, 0x59, 0xca, 0xf1, 0xc0, 0x29, 0x36,
          0x09, 0x44, 0xe2, 0x7f, 0xd1, 0x63, 0x15, 0x99, 0xea, 0x25, 0xcf, 0x0c, 0x9d, 0xc0, 0x44, 0x6f } } },
    { { { 0x1d, 0x86, 0x4e, 0xcf, 0xf7, 0x37, 0x10, 0x25, 0x8f, 0x12, 0xfb, 0x19, 0xfb, 0xe0, 0xed, 0x10,
          0xc8, 0xe2, 0xf5, 0x75, 0xb1, 0x33, 0xc0, 0x96, 0x0d, 0xfb, 0x15, 0x6c, 0x0d, 0x07, 0x5f, 0x05 } },
      { { 0x69, 0x3e, 0x47, 0x97, 0x2c, 0xaf, 0x52, 0x7c, 0x78, 0x83, 0xad, 0x1b, 0x39, 0x82, 0x2f, 0x02,
          0x6f, 0x47, 0xdb, 0x2a, 0xb0, 0xe1, 0x91, 0x99, 0x55, 0xb8, 0x99, 0x3a, 0xa0, 0x44, 0x11, 0x51 } } }
};

ZT_INLINE void p1p1_to_p2(ge25519_p2 *r, const ge25519_p1p1 *p)
{
    fe25519_mul(&r->x, &p->x, &p->t);
    fe25519_mul(&r->y, &p->y, &p->z);
    fe25519_mul(&r->z, &p->z, &p->t);
}

ZT_INLINE void p1p1_to_p2_2(ge25519_p3 *r, const ge25519_p1p1 *p)
{
    fe25519_mul(&r->x, &p->x, &p->t);
    fe25519_mul(&r->y, &p->y, &p->z);
    fe25519_mul(&r->z, &p->z, &p->t);
}

ZT_INLINE void p1p1_to_p3(ge25519_p3 *r, const ge25519_p1p1 *p)
{
    p1p1_to_p2_2(r, p);
    fe25519_mul(&r->t, &p->x, &p->y);
}

ZT_INLINE void ge25519_mixadd2(ge25519_p3 *r, const ge25519_aff *q)
{
    fe25519 a, b, t1, t2, c, d, e, f, g, h, qt;
    fe25519_mul(&qt, &q->x, &q->y);
    fe25519_sub(&a, &r->y, &r->x);
    fe25519_add(&b, &r->y, &r->x);
    fe25519_sub(&t1, &q->y, &q->x);
    fe25519_add(&t2, &q->y, &q->x);
    fe25519_mul(&a, &a, &t1);
    fe25519_mul(&b, &b, &t2);
    fe25519_sub(&e, &b, &a);
    fe25519_add(&h, &b, &a);
    fe25519_mul(&c, &r->t, &qt);
    fe25519_mul(&c, &c, &ge25519_ec2d);
    fe25519_add(&d, &r->z, &r->z);
    fe25519_sub(&f, &d, &c);
    fe25519_add(&g, &d, &c);
    fe25519_mul(&r->x, &e, &f);
    fe25519_mul(&r->y, &h, &g);
    fe25519_mul(&r->z, &g, &f);
    fe25519_mul(&r->t, &e, &h);
}

ZT_INLINE void add_p1p1(ge25519_p1p1 *r, const ge25519_p3 *p, const ge25519_p3 *q)
{
    fe25519 a, b, c, d, t;
    fe25519_sub(&a, &p->y, &p->x);
    fe25519_sub(&t, &q->y, &q->x);
    fe25519_mul(&a, &a, &t);
    fe25519_add(&b, &p->x, &p->y);
    fe25519_add(&t, &q->x, &q->y);
    fe25519_mul(&b, &b, &t);
    fe25519_mul(&c, &p->t, &q->t);
    fe25519_mul(&c, &c, &ge25519_ec2d);
    fe25519_mul(&d, &p->z, &q->z);
    fe25519_add(&d, &d, &d);
    fe25519_sub(&r->x, &b, &a);
    fe25519_sub(&r->t, &d, &c);
    fe25519_add(&r->z, &d, &c);
    fe25519_add(&r->y, &b, &a);
}

ZT_INLINE void dbl_p1p1(ge25519_p1p1 *r, const ge25519_p2 *p)
{
    fe25519 a, b, c, d;
    fe25519_square(&a, &p->x);
    fe25519_square(&b, &p->y);
    fe25519_square(&c, &p->z);
    fe25519_add(&c, &c, &c);
    fe25519_neg(&d, &a);
    fe25519_add(&r->x, &p->x, &p->y);
    fe25519_square(&r->x, &r->x);
    fe25519_sub(&r->x, &r->x, &a);
    fe25519_sub(&r->x, &r->x, &b);
    fe25519_add(&r->z, &d, &b);
    fe25519_sub(&r->t, &r->z, &c);
    fe25519_sub(&r->y, &d, &b);
}

ZT_INLINE void cmov_aff(ge25519_aff *r, const ge25519_aff *p, unsigned char b)
{
    fe25519_cmov(&r->x, &p->x, b);
    fe25519_cmov(&r->y, &p->y, b);
}

ZT_INLINE unsigned char equal(signed char b, signed char c)
{
    unsigned char ub = b, uc = c, x = ub ^ uc;
    uint32_t y = x;
    y -= 1;
    y >>= 31;
    return (unsigned char)y;
}

ZT_INLINE unsigned char negative(signed char b)
{
    unsigned long long x = b;
    x >>= 63;
    return (unsigned char)x;
}

ZT_INLINE void choose_t(ge25519_aff *t, unsigned long long pos, signed char b)
{
    fe25519 v;
    *t = ge25519_base_multiples_affine[5 * pos + 0];
    cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 1], equal(b, 1) | equal(b, -1));
    cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 2], equal(b, 2) | equal(b, -2));
    cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 3], equal(b, 3) | equal(b, -3));
    cmov_aff(t, &ge25519_base_multiples_affine[5 * pos + 4], equal(b, -4));
    fe25519_neg(&v, &t->x);
    fe25519_cmov(&t->x, &v, negative(b));
}

ZT_INLINE void setneutral(ge25519 *r)
{
    fe25519_setzero(&r->x);
    fe25519_setone(&r->y);
    fe25519_setone(&r->z);
    fe25519_setzero(&r->t);
}

ZT_INLINE int ge25519_unpackneg_vartime(ge25519_p3 *r, const unsigned char p[32])
{
    unsigned char par;
    fe25519 t, chk, num, den, den2, den4, den6;
    fe25519_setone(&r->z);
    par = p[31] >> 7;
    fe25519_unpack(&r->y, p);
    fe25519_square(&num, &r->y);
    fe25519_mul(&den, &num, &ge25519_ecd);
    fe25519_sub(&num, &num, &r->z);
    fe25519_add(&den, &r->z, &den);
    fe25519_square(&den2, &den);
    fe25519_square(&den4, &den2);
    fe25519_mul(&den6, &den4, &den2);
    fe25519_mul(&t, &den6, &num);
    fe25519_mul(&t, &t, &den);
    fe25519_pow2523(&t, &t);
    fe25519_mul(&t, &t, &num);
    fe25519_mul(&t, &t, &den);
    fe25519_mul(&t, &t, &den);
    fe25519_mul(&r->x, &t, &den);
    fe25519_square(&chk, &r->x);
    fe25519_mul(&chk, &chk, &den);
    if (!fe25519_iseq_vartime(&chk, &num))
        fe25519_mul(&r->x, &r->x, &ge25519_sqrtm1);
    fe25519_square(&chk, &r->x);
    fe25519_mul(&chk, &chk, &den);
    if (!fe25519_iseq_vartime(&chk, &num))
        return -1;
    if (fe25519_getparity(&r->x) != (1 - par))
        fe25519_neg(&r->x, &r->x);
    fe25519_mul(&r->t, &r->x, &r->y);
    return 0;
}

void ge25519_pack(unsigned char r[32], const ge25519_p3 *p)
{
    fe25519 tx, ty, zi;
    fe25519_invert(&zi, &p->z);
    fe25519_mul(&tx, &p->x, &zi);
    fe25519_mul(&ty, &p->y, &zi);
    fe25519_pack(r, &ty);
    r[31] ^= fe25519_getparity(&tx) << 7;
}

ZT_INLINE void ge25519_double_scalarmult_vartime(
    ge25519_p3 *r, const ge25519_p3 *p1, const sc25519 *s1, const ge25519_p3 *p2, const sc25519 *s2)
{
    ge25519_p1p1 tp1p1;
    ge25519_p3 pre[16];
    char *pre5 = (char *)(&(pre[5]));
    unsigned char b[127];
    setneutral(pre); /* 00 00 */
    pre[1] = *p1;    /* 00 01 */
    dbl_p1p1(&tp1p1, (ge25519_p2 *)p1);
    p1p1_to_p3(&pre[2], &tp1p1); /* 00 10 */
    add_p1p1(&tp1p1, &pre[1], &pre[2]);
    p1p1_to_p3(&pre[3], &tp1p1); /* 00 11 */
    pre[4] = *p2;                /* 01 00 */
    add_p1p1(&tp1p1, &pre[1], &pre[4]);
    p1p1_to_p3(&pre[5], &tp1p1); /* 01 01 */
    add_p1p1(&tp1p1, &pre[2], &pre[4]);
    p1p1_to_p3(&pre[6], &tp1p1); /* 01 10 */
    add_p1p1(&tp1p1, &pre[3], &pre[4]);
    p1p1_to_p3(&pre[7], &tp1p1); /* 01 11 */
    dbl_p1p1(&tp1p1, (ge25519_p2 *)p2);
    p1p1_to_p3(&pre[8], &tp1p1); /* 10 00 */
    add_p1p1(&tp1p1, &pre[1], &pre[8]);
    p1p1_to_p3(&pre[9], &tp1p1); /* 10 01 */
    dbl_p1p1(&tp1p1, (ge25519_p2 *)pre5);
    p1p1_to_p3(&pre[10], &tp1p1); /* 10 10 */
    add_p1p1(&tp1p1, &pre[3], &pre[8]);
    p1p1_to_p3(&pre[11], &tp1p1); /* 10 11 */
    add_p1p1(&tp1p1, &pre[4], &pre[8]);
    p1p1_to_p3(&pre[12], &tp1p1); /* 11 00 */
    add_p1p1(&tp1p1, &pre[1], &pre[12]);
    p1p1_to_p3(&pre[13], &tp1p1); /* 11 01 */
    add_p1p1(&tp1p1, &pre[2], &pre[12]);
    p1p1_to_p3(&pre[14], &tp1p1); /* 11 10 */
    add_p1p1(&tp1p1, &pre[3], &pre[12]);
    p1p1_to_p3(&pre[15], &tp1p1); /* 11 11 */
    sc25519_2interleave2(b, s1, s2);
    *r = pre[b[126]];
    for (int i = 125; i >= 0; i--) {
        dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
        p1p1_to_p2((ge25519_p2 *)r, &tp1p1);
        dbl_p1p1(&tp1p1, (ge25519_p2 *)r);
        if (b[i] != 0) {
            p1p1_to_p3(r, &tp1p1);
            add_p1p1(&tp1p1, r, &pre[b[i]]);
        }
        if (i != 0)
            p1p1_to_p2((ge25519_p2 *)r, &tp1p1);
        else
            p1p1_to_p3(r, &tp1p1);
    }
}

void ge25519_scalarmult_base(ge25519_p3 *r, const sc25519 *s)
{
    signed char b[85];
    ge25519_aff t;
    sc25519_window3(b, s);
    choose_t((ge25519_aff *)r, 0, b[0]);
    fe25519_setone(&r->z);
    fe25519_mul(&r->t, &r->x, &r->y);
    for (int i = 1; i < 85; i++) {
        choose_t(&t, (unsigned long long)i, b[i]);
        ge25519_mixadd2(r, &t);
    }
}

ZT_INLINE void get_hram(
    unsigned char *hram, const unsigned char *sm, const unsigned char *pk, unsigned char *playground,
    unsigned long long smlen)
{
    for (int i = 0; i < 32; ++i)
        playground[i] = sm[i];
    for (int i = 32; i < 64; ++i)
        playground[i] = pk[i - 32];
    for (int i = 64; i < smlen; ++i)
        playground[i] = sm[i];
    ZeroTier::SHA512(hram, playground, (unsigned int)smlen);
}

// --------------------------------------------------------------------------------------------------------------------

}   // anonymous namespace

namespace ZeroTier {

void C25519::generateCombined(uint8_t *pub, uint8_t *priv)
{
    Utils::getSecureRandom(priv, ZT_C25519_COMBINED_PRIVATE_KEY_SIZE);
    s_calcPubDH(pub, priv);
    s_calcPubED(pub, priv);
}

void C25519::generateC25519(uint8_t pub[ZT_C25519_ECDH_PUBLIC_KEY_SIZE], uint8_t priv[ZT_C25519_ECDH_PRIVATE_KEY_SIZE])
{
    Utils::getSecureRandom(priv, ZT_C25519_ECDH_PRIVATE_KEY_SIZE);
    s_calcPubDH(pub, priv);
}

void C25519::agree(
    const uint8_t mine[ZT_C25519_ECDH_PRIVATE_KEY_SIZE], const uint8_t their[ZT_C25519_ECDH_PUBLIC_KEY_SIZE],
    uint8_t rawkey[ZT_C25519_ECDH_SHARED_SECRET_SIZE])
{
    crypto_scalarmult(rawkey, mine, their);
}

void C25519::sign(
    const uint8_t myPrivate[ZT_C25519_COMBINED_PRIVATE_KEY_SIZE],
    const uint8_t myPublic[ZT_C25519_COMBINED_PUBLIC_KEY_SIZE], const void *msg, unsigned int len, void *signature)
{
    unsigned char digest[64];   // we sign the first 32 bytes of SHA-512(msg)
    SHA512(digest, msg, len);

    sc25519 sck, scs, scsk;
    ge25519 ger;
    unsigned char r[32];
    unsigned char s[32];
    unsigned char extsk[64];
    unsigned char hmg[crypto_hash_sha512_BYTES];
    unsigned char hram[crypto_hash_sha512_BYTES];
    unsigned char *sig = (unsigned char *)signature;

    SHA512(extsk, myPrivate + 32, 32);
    extsk[0] &= 248;
    extsk[31] &= 127;
    extsk[31] |= 64;

    for (unsigned int i = 0; i < 32; i++)
        sig[32 + i] = extsk[32 + i];
    for (unsigned int i = 0; i < 32; i++)
        sig[64 + i] = digest[i];

    SHA512(hmg, sig + 32, 64);

    /* Computation of R */
    sc25519_from64bytes(&sck, hmg);
    ge25519_scalarmult_base(&ger, &sck);
    ge25519_pack(r, &ger);

    /* Computation of s */
    for (unsigned int i = 0; i < 32; i++)
        sig[i] = r[i];

    get_hram(hram, sig, myPublic + 32, sig, 96);

    sc25519_from64bytes(&scs, hram);
    sc25519_from32bytes(&scsk, extsk);
    sc25519_mul(&scs, &scs, &scsk);

    sc25519_add(&scs, &scs, &sck);

    sc25519_to32bytes(s, &scs); /* cat s */
    for (unsigned int i = 0; i < 32; i++)
        sig[32 + i] = s[i];
}

bool C25519::verify(
    const uint8_t their[ZT_C25519_COMBINED_PUBLIC_KEY_SIZE], const void *msg, unsigned int len, const void *signature,
    const unsigned int siglen)
{
    if (siglen < 64)
        return false;

    const unsigned char *sig = (const unsigned char *)signature;
    unsigned char digest[64];   // we sign the first 32 bytes of SHA-512(msg)
    unsigned char sigtmp[96];
    SHA512(digest, msg, len);

    if ((siglen == 96) && (!Utils::secureEq(sig + 64, digest, 32))) {
        return false;
    }
    else if (siglen == 64) {
        Utils::copy<64>(sigtmp, sig);
        Utils::copy<32>(sigtmp + 64, digest);
        sig = sigtmp;
    }

    unsigned char t2[32];
    ge25519 get1, get2;
    sc25519 schram, scs;
    unsigned char hram[crypto_hash_sha512_BYTES];
    unsigned char m[96];

    if (ge25519_unpackneg_vartime(&get1, their + 32))
        return false;

    get_hram(hram, sig, their + 32, m, 96);

    sc25519_from64bytes(&schram, hram);

    sc25519_from32bytes(&scs, sig + 32);

    ge25519_double_scalarmult_vartime(&get2, &get1, &schram, &ge25519_base, &scs);
    ge25519_pack(t2, &get2);

    return Utils::secureEq(sig, t2, 32);
}

void C25519::s_calcPubDH(uint8_t *pub, const uint8_t *priv)
{
    // First 32 bytes of pub and priv are the keys for ECDH key
    // agreement. This generates the public portion from the private.
    crypto_scalarmult_base(pub, priv);
}

void C25519::s_calcPubED(uint8_t *pub, const uint8_t *priv)
{
    struct {
        uint8_t extsk[64];
        sc25519 scsk;
        ge25519 gepk;
    } s;

    // Second 32 bytes of pub and priv are the keys for ed25519
    // signing and verification.
    SHA512(s.extsk, priv + 32, 32);
    s.extsk[0] &= 248U;
    s.extsk[31] &= 127U;
    s.extsk[31] |= 64U;
    sc25519_from32bytes(&s.scsk, s.extsk);
    ge25519_scalarmult_base(&s.gepk, &s.scsk);
    ge25519_pack(pub + 32, &s.gepk);

    // In NaCl, the public key is crammed into the next 32 bytes
    // of the private key for signing since both keys are required
    // to sign. In this version we just get it from kp.pub, so we
    // leave that out of private.

    Utils::burn(&s, sizeof(s));
}

}   // namespace ZeroTier