/*
 * Copyright (c) 2013, Kenneth MacKay
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:
 *  * Redistributions of source code must retain the above copyright
 *   notice, this list of conditions and the following disclaimer.
 *  * Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 * HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#include <linux/random.h>

#include "ecc.h"

/* 256-bit curve */
#define ECC_BYTES 32

#define MAX_TRIES 16

/* Number of u64's needed */
#define NUM_ECC_DIGITS (ECC_BYTES / 8)

struct ecc_point {
        u64 x[NUM_ECC_DIGITS];
        u64 y[NUM_ECC_DIGITS];
};

typedef struct {
        u64 m_low;
        u64 m_high;
} uint128_t;

#define CURVE_P_32 {    0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull, \
                        0x0000000000000000ull, 0xFFFFFFFF00000001ull }

#define CURVE_G_32 { \
                {       0xF4A13945D898C296ull, 0x77037D812DEB33A0ull,   \
                        0xF8BCE6E563A440F2ull, 0x6B17D1F2E12C4247ull }, \
                {       0xCBB6406837BF51F5ull, 0x2BCE33576B315ECEull,   \
                        0x8EE7EB4A7C0F9E16ull, 0x4FE342E2FE1A7F9Bull }  \
}

#define CURVE_N_32 {    0xF3B9CAC2FC632551ull, 0xBCE6FAADA7179E84ull,   \
                        0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFF00000000ull }

static u64 curve_p[NUM_ECC_DIGITS] = CURVE_P_32;
static struct ecc_point curve_g = CURVE_G_32;
static u64 curve_n[NUM_ECC_DIGITS] = CURVE_N_32;

static void vli_clear(u64 *vli)
{
        int i;

        for (i = 0; i < NUM_ECC_DIGITS; i++)
                vli[i] = 0;
}

/* Returns true if vli == 0, false otherwise. */
static bool vli_is_zero(const u64 *vli)
{
        int i;

        for (i = 0; i < NUM_ECC_DIGITS; i++) {
                if (vli[i])
                        return false;
        }

        return true;
}

/* Returns nonzero if bit bit of vli is set. */
static u64 vli_test_bit(const u64 *vli, unsigned int bit)
{
        return (vli[bit / 64] & ((u64) 1 << (bit % 64)));
}

/* Counts the number of 64-bit "digits" in vli. */
static unsigned int vli_num_digits(const u64 *vli)
{
        int i;

        /* Search from the end until we find a non-zero digit.
         * We do it in reverse because we expect that most digits will
         * be nonzero.
         */
        for (i = NUM_ECC_DIGITS - 1; i >= 0 && vli[i] == 0; i--);

        return (i + 1);
}

/* Counts the number of bits required for vli. */
static unsigned int vli_num_bits(const u64 *vli)
{
        unsigned int i, num_digits;
        u64 digit;

        num_digits = vli_num_digits(vli);
        if (num_digits == 0)
                return 0;

        digit = vli[num_digits - 1];
        for (i = 0; digit; i++)
                digit >>= 1;

        return ((num_digits - 1) * 64 + i);
}

/* Sets dest = src. */
static void vli_set(u64 *dest, const u64 *src)
{
        int i;

        for (i = 0; i < NUM_ECC_DIGITS; i++)
                dest[i] = src[i];
}

/* Returns sign of left - right. */
static int vli_cmp(const u64 *left, const u64 *right)
{
    int i;

    for (i = NUM_ECC_DIGITS - 1; i >= 0; i--) {
            if (left[i] > right[i])
                    return 1;
            else if (left[i] < right[i])
                    return -1;
    }

    return 0;
}

/* Computes result = in << c, returning carry. Can modify in place
 * (if result == in). 0 < shift < 64.
 */
static u64 vli_lshift(u64 *result, const u64 *in,
                           unsigned int shift)
{
        u64 carry = 0;
        int i;

        for (i = 0; i < NUM_ECC_DIGITS; i++) {
                u64 temp = in[i];

                result[i] = (temp << shift) | carry;
                carry = temp >> (64 - shift);
        }

        return carry;
}

/* Computes vli = vli >> 1. */
static void vli_rshift1(u64 *vli)
{
        u64 *end = vli;
        u64 carry = 0;

        vli += NUM_ECC_DIGITS;

        while (vli-- > end) {
                u64 temp = *vli;
                *vli = (temp >> 1) | carry;
                carry = temp << 63;
        }
}

/* Computes result = left + right, returning carry. Can modify in place. */
static u64 vli_add(u64 *result, const u64 *left,
                        const u64 *right)
{
        u64 carry = 0;
        int i;

        for (i = 0; i < NUM_ECC_DIGITS; i++) {
                u64 sum;

                sum = left[i] + right[i] + carry;
                if (sum != left[i])
                        carry = (sum < left[i]);

                result[i] = sum;
        }

        return carry;
}

/* Computes result = left - right, returning borrow. Can modify in place. */
static u64 vli_sub(u64 *result, const u64 *left, const u64 *right)
{
        u64 borrow = 0;
        int i;

        for (i = 0; i < NUM_ECC_DIGITS; i++) {
                u64 diff;

                diff = left[i] - right[i] - borrow;
                if (diff != left[i])
                        borrow = (diff > left[i]);

                result[i] = diff;
        }

        return borrow;
}

static uint128_t mul_64_64(u64 left, u64 right)
{
        u64 a0 = left & 0xffffffffull;
        u64 a1 = left >> 32;
        u64 b0 = right & 0xffffffffull;
        u64 b1 = right >> 32;
        u64 m0 = a0 * b0;
        u64 m1 = a0 * b1;
        u64 m2 = a1 * b0;
        u64 m3 = a1 * b1;
        uint128_t result;

        m2 += (m0 >> 32);
        m2 += m1;

        /* Overflow */
        if (m2 < m1)
                m3 += 0x100000000ull;

        result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
        result.m_high = m3 + (m2 >> 32);

        return result;
}

static uint128_t add_128_128(uint128_t a, uint128_t b)
{
        uint128_t result;

        result.m_low = a.m_low + b.m_low;
        result.m_high = a.m_high + b.m_high + (result.m_low < a.m_low);

        return result;
}

static void vli_mult(u64 *result, const u64 *left, const u64 *right)
{
        uint128_t r01 = { 0, 0 };
        u64 r2 = 0;
        unsigned int i, k;

        /* Compute each digit of result in sequence, maintaining the
         * carries.
         */
        for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; k++) {
                unsigned int min;

                if (k < NUM_ECC_DIGITS)
                        min = 0;
                else
                        min = (k + 1) - NUM_ECC_DIGITS;

                for (i = min; i <= k && i < NUM_ECC_DIGITS; i++) {
                        uint128_t product;

                        product = mul_64_64(left[i], right[k - i]);

                        r01 = add_128_128(r01, product);
                        r2 += (r01.m_high < product.m_high);
                }

                result[k] = r01.m_low;
                r01.m_low = r01.m_high;
                r01.m_high = r2;
                r2 = 0;
        }

        result[NUM_ECC_DIGITS * 2 - 1] = r01.m_low;
}

static void vli_square(u64 *result, const u64 *left)
{
        uint128_t r01 = { 0, 0 };
        u64 r2 = 0;
        int i, k;

        for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; k++) {
                unsigned int min;

                if (k < NUM_ECC_DIGITS)
                        min = 0;
                else
                        min = (k + 1) - NUM_ECC_DIGITS;

                for (i = min; i <= k && i <= k - i; i++) {
                        uint128_t product;

                        product = mul_64_64(left[i], left[k - i]);

                        if (i < k - i) {
                                r2 += product.m_high >> 63;
                                product.m_high = (product.m_high << 1) |
                                                 (product.m_low >> 63);
                                product.m_low <<= 1;
                        }

                        r01 = add_128_128(r01, product);
                        r2 += (r01.m_high < product.m_high);
                }

                result[k] = r01.m_low;
                r01.m_low = r01.m_high;
                r01.m_high = r2;
                r2 = 0;
        }

        result[NUM_ECC_DIGITS * 2 - 1] = r01.m_low;
}

/* Computes result = (left + right) % mod.
 * Assumes that left < mod and right < mod, result != mod.
 */
static void vli_mod_add(u64 *result, const u64 *left, const u64 *right,
                        const u64 *mod)
{
        u64 carry;

        carry = vli_add(result, left, right);

        /* result > mod (result = mod + remainder), so subtract mod to
         * get remainder.
         */
        if (carry || vli_cmp(result, mod) >= 0)
                vli_sub(result, result, mod);
}

/* Computes result = (left - right) % mod.
 * Assumes that left < mod and right < mod, result != mod.
 */
static void vli_mod_sub(u64 *result, const u64 *left, const u64 *right,
                        const u64 *mod)
{
        u64 borrow = vli_sub(result, left, right);

        /* In this case, p_result == -diff == (max int) - diff.
         * Since -x % d == d - x, we can get the correct result from
         * result + mod (with overflow).
         */
        if (borrow)
                vli_add(result, result, mod);
}

/* Computes result = product % curve_p
   from http://www.nsa.gov/ia/_files/nist-routines.pdf */
static void vli_mmod_fast(u64 *result, const u64 *product)
{
        u64 tmp[NUM_ECC_DIGITS];
        int carry;

        /* t */
        vli_set(result, product);

        /* s1 */
        tmp[0] = 0;
        tmp[1] = product[5] & 0xffffffff00000000ull;
        tmp[2] = product[6];
        tmp[3] = product[7];
        carry = vli_lshift(tmp, tmp, 1);
        carry += vli_add(result, result, tmp);

        /* s2 */
        tmp[1] = product[6] << 32;
        tmp[2] = (product[6] >> 32) | (product[7] << 32);
        tmp[3] = product[7] >> 32;
        carry += vli_lshift(tmp, tmp, 1);
        carry += vli_add(result, result, tmp);

        /* s3 */
        tmp[0] = product[4];
        tmp[1] = product[5] & 0xffffffff;
        tmp[2] = 0;
        tmp[3] = product[7];
        carry += vli_add(result, result, tmp);

        /* s4 */
        tmp[0] = (product[4] >> 32) | (product[5] << 32);
        tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
        tmp[2] = product[7];
        tmp[3] = (product[6] >> 32) | (product[4] << 32);
        carry += vli_add(result, result, tmp);

        /* d1 */
        tmp[0] = (product[5] >> 32) | (product[6] << 32);
        tmp[1] = (product[6] >> 32);
        tmp[2] = 0;
        tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
        carry -= vli_sub(result, result, tmp);

        /* d2 */
        tmp[0] = product[6];
        tmp[1] = product[7];
        tmp[2] = 0;
        tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
        carry -= vli_sub(result, result, tmp);

        /* d3 */
        tmp[0] = (product[6] >> 32) | (product[7] << 32);
        tmp[1] = (product[7] >> 32) | (product[4] << 32);
        tmp[2] = (product[4] >> 32) | (product[5] << 32);
        tmp[3] = (product[6] << 32);
        carry -= vli_sub(result, result, tmp);

        /* d4 */
        tmp[0] = product[7];
        tmp[1] = product[4] & 0xffffffff00000000ull;
        tmp[2] = product[5];
        tmp[3] = product[6] & 0xffffffff00000000ull;
        carry -= vli_sub(result, result, tmp);

        if (carry < 0) {
                do {
                        carry += vli_add(result, result, curve_p);
                } while (carry < 0);
        } else {
                while (carry || vli_cmp(curve_p, result) != 1)
                        carry -= vli_sub(result, result, curve_p);
        }
}

/* Computes result = (left * right) % curve_p. */
static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right)
{
        u64 product[2 * NUM_ECC_DIGITS];

        vli_mult(product, left, right);
        vli_mmod_fast(result, product);
}

/* Computes result = left^2 % curve_p. */
static void vli_mod_square_fast(u64 *result, const u64 *left)
{
        u64 product[2 * NUM_ECC_DIGITS];

        vli_square(product, left);
        vli_mmod_fast(result, product);
}

#define EVEN(vli) (!(vli[0] & 1))
/* Computes result = (1 / p_input) % mod. All VLIs are the same size.
 * See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
 * https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf
 */
static void vli_mod_inv(u64 *result, const u64 *input, const u64 *mod)
{
        u64 a[NUM_ECC_DIGITS], b[NUM_ECC_DIGITS];
        u64 u[NUM_ECC_DIGITS], v[NUM_ECC_DIGITS];
        u64 carry;
        int cmp_result;

        if (vli_is_zero(input)) {
                vli_clear(result);
                return;
        }

        vli_set(a, input);
        vli_set(b, mod);
        vli_clear(u);
        u[0] = 1;
        vli_clear(v);

        while ((cmp_result = vli_cmp(a, b)) != 0) {
                carry = 0;

                if (EVEN(a)) {
                        vli_rshift1(a);

                        if (!EVEN(u))
                                carry = vli_add(u, u, mod);

                        vli_rshift1(u);
                        if (carry)
                                u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
                } else if (EVEN(b)) {
                        vli_rshift1(b);

                        if (!EVEN(v))
                                carry = vli_add(v, v, mod);

                        vli_rshift1(v);
                        if (carry)
                                v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
                } else if (cmp_result > 0) {
                        vli_sub(a, a, b);
                        vli_rshift1(a);

                        if (vli_cmp(u, v) < 0)
                                vli_add(u, u, mod);

                        vli_sub(u, u, v);
                        if (!EVEN(u))
                                carry = vli_add(u, u, mod);

                        vli_rshift1(u);
                        if (carry)
                                u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
                } else {
                        vli_sub(b, b, a);
                        vli_rshift1(b);

                        if (vli_cmp(v, u) < 0)
                                vli_add(v, v, mod);

                        vli_sub(v, v, u);
                        if (!EVEN(v))
                                carry = vli_add(v, v, mod);

                        vli_rshift1(v);
                        if (carry)
                                v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull;
                }
        }

        vli_set(result, u);
}

/* ------ Point operations ------ */

/* Returns true if p_point is the point at infinity, false otherwise. */
static bool ecc_point_is_zero(const struct ecc_point *point)
{
        return (vli_is_zero(point->x) && vli_is_zero(point->y));
}

/* Point multiplication algorithm using Montgomery's ladder with co-Z
 * coordinates. From http://eprint.iacr.org/2011/338.pdf
 */

/* Double in place */
static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1)
{
        /* t1 = x, t2 = y, t3 = z */
        u64 t4[NUM_ECC_DIGITS];
        u64 t5[NUM_ECC_DIGITS];

        if (vli_is_zero(z1))
                return;

        vli_mod_square_fast(t4, y1);   /* t4 = y1^2 */
        vli_mod_mult_fast(t5, x1, t4); /* t5 = x1*y1^2 = A */
        vli_mod_square_fast(t4, t4);   /* t4 = y1^4 */
        vli_mod_mult_fast(y1, y1, z1); /* t2 = y1*z1 = z3 */
        vli_mod_square_fast(z1, z1);   /* t3 = z1^2 */

        vli_mod_add(x1, x1, z1, curve_p); /* t1 = x1 + z1^2 */
        vli_mod_add(z1, z1, z1, curve_p); /* t3 = 2*z1^2 */
        vli_mod_sub(z1, x1, z1, curve_p); /* t3 = x1 - z1^2 */
        vli_mod_mult_fast(x1, x1, z1);    /* t1 = x1^2 - z1^4 */

        vli_mod_add(z1, x1, x1, curve_p); /* t3 = 2*(x1^2 - z1^4) */
        vli_mod_add(x1, x1, z1, curve_p); /* t1 = 3*(x1^2 - z1^4) */
        if (vli_test_bit(x1, 0)) {
                u64 carry = vli_add(x1, x1, curve_p);
                vli_rshift1(x1);
                x1[NUM_ECC_DIGITS - 1] |= carry << 63;
        } else {
                vli_rshift1(x1);
        }
        /* t1 = 3/2*(x1^2 - z1^4) = B */

        vli_mod_square_fast(z1, x1);      /* t3 = B^2 */
        vli_mod_sub(z1, z1, t5, curve_p); /* t3 = B^2 - A */
        vli_mod_sub(z1, z1, t5, curve_p); /* t3 = B^2 - 2A = x3 */
        vli_mod_sub(t5, t5, z1, curve_p); /* t5 = A - x3 */
        vli_mod_mult_fast(x1, x1, t5);    /* t1 = B * (A - x3) */
        vli_mod_sub(t4, x1, t4, curve_p); /* t4 = B * (A - x3) - y1^4 = y3 */

        vli_set(x1, z1);
        vli_set(z1, y1);
        vli_set(y1, t4);
}

/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
static void apply_z(u64 *x1, u64 *y1, u64 *z)
{
        u64 t1[NUM_ECC_DIGITS];

        vli_mod_square_fast(t1, z);    /* z^2 */
        vli_mod_mult_fast(x1, x1, t1); /* x1 * z^2 */
        vli_mod_mult_fast(t1, t1, z);  /* z^3 */
        vli_mod_mult_fast(y1, y1, t1); /* y1 * z^3 */
}

/* P = (x1, y1) => 2P, (x2, y2) => P' */
static void xycz_initial_double(u64 *x1, u64 *y1, u64 *x2, u64 *y2,
                                u64 *p_initial_z)
{
        u64 z[NUM_ECC_DIGITS];

        vli_set(x2, x1);
        vli_set(y2, y1);

        vli_clear(z);
        z[0] = 1;

        if (p_initial_z)
                vli_set(z, p_initial_z);

        apply_z(x1, y1, z);

        ecc_point_double_jacobian(x1, y1, z);

        apply_z(x2, y2, z);
}

/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
 * Output P' = (x1', y1', Z3), P + Q = (x3, y3, Z3)
 * or P => P', Q => P + Q
 */
static void xycz_add(u64 *x1, u64 *y1, u64 *x2, u64 *y2)
{
        /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
        u64 t5[NUM_ECC_DIGITS];

        vli_mod_sub(t5, x2, x1, curve_p); /* t5 = x2 - x1 */
        vli_mod_square_fast(t5, t5);      /* t5 = (x2 - x1)^2 = A */
        vli_mod_mult_fast(x1, x1, t5);    /* t1 = x1*A = B */
        vli_mod_mult_fast(x2, x2, t5);    /* t3 = x2*A = C */
        vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y2 - y1 */
        vli_mod_square_fast(t5, y2);      /* t5 = (y2 - y1)^2 = D */

        vli_mod_sub(t5, t5, x1, curve_p); /* t5 = D - B */
        vli_mod_sub(t5, t5, x2, curve_p); /* t5 = D - B - C = x3 */
        vli_mod_sub(x2, x2, x1, curve_p); /* t3 = C - B */
        vli_mod_mult_fast(y1, y1, x2);    /* t2 = y1*(C - B) */
        vli_mod_sub(x2, x1, t5, curve_p); /* t3 = B - x3 */
        vli_mod_mult_fast(y2, y2, x2);    /* t4 = (y2 - y1)*(B - x3) */
        vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y3 */

        vli_set(x2, t5);
}

/* Input P = (x1, y1, Z), Q = (x2, y2, Z)
 * Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3)
 * or P => P - Q, Q => P + Q
 */
static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2)
{
        /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
        u64 t5[NUM_ECC_DIGITS];
        u64 t6[NUM_ECC_DIGITS];
        u64 t7[NUM_ECC_DIGITS];

        vli_mod_sub(t5, x2, x1, curve_p); /* t5 = x2 - x1 */
        vli_mod_square_fast(t5, t5);      /* t5 = (x2 - x1)^2 = A */
        vli_mod_mult_fast(x1, x1, t5);    /* t1 = x1*A = B */
        vli_mod_mult_fast(x2, x2, t5);    /* t3 = x2*A = C */
        vli_mod_add(t5, y2, y1, curve_p); /* t4 = y2 + y1 */
        vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y2 - y1 */

        vli_mod_sub(t6, x2, x1, curve_p); /* t6 = C - B */
        vli_mod_mult_fast(y1, y1, t6);    /* t2 = y1 * (C - B) */
        vli_mod_add(t6, x1, x2, curve_p); /* t6 = B + C */
        vli_mod_square_fast(x2, y2);      /* t3 = (y2 - y1)^2 */
        vli_mod_sub(x2, x2, t6, curve_p); /* t3 = x3 */

        vli_mod_sub(t7, x1, x2, curve_p); /* t7 = B - x3 */
        vli_mod_mult_fast(y2, y2, t7);    /* t4 = (y2 - y1)*(B - x3) */
        vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y3 */

        vli_mod_square_fast(t7, t5);      /* t7 = (y2 + y1)^2 = F */
        vli_mod_sub(t7, t7, t6, curve_p); /* t7 = x3' */
        vli_mod_sub(t6, t7, x1, curve_p); /* t6 = x3' - B */
        vli_mod_mult_fast(t6, t6, t5);    /* t6 = (y2 + y1)*(x3' - B) */
        vli_mod_sub(y1, t6, y1, curve_p); /* t2 = y3' */

        vli_set(x1, t7);
}

static void ecc_point_mult(struct ecc_point *result,
                           const struct ecc_point *point, u64 *scalar,
                           u64 *initial_z, int num_bits)
{
        /* R0 and R1 */
        u64 rx[2][NUM_ECC_DIGITS];
        u64 ry[2][NUM_ECC_DIGITS];
        u64 z[NUM_ECC_DIGITS];
        int i, nb;

        vli_set(rx[1], point->x);
        vli_set(ry[1], point->y);

        xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z);

        for (i = num_bits - 2; i > 0; i--) {
                nb = !vli_test_bit(scalar, i);
                xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb]);
                xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb]);
        }

        nb = !vli_test_bit(scalar, 0);
        xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb]);

        /* Find final 1/Z value. */
        vli_mod_sub(z, rx[1], rx[0], curve_p); /* X1 - X0 */
        vli_mod_mult_fast(z, z, ry[1 - nb]); /* Yb * (X1 - X0) */
        vli_mod_mult_fast(z, z, point->x);   /* xP * Yb * (X1 - X0) */
        vli_mod_inv(z, z, curve_p);          /* 1 / (xP * Yb * (X1 - X0)) */
        vli_mod_mult_fast(z, z, point->y);   /* yP / (xP * Yb * (X1 - X0)) */
        vli_mod_mult_fast(z, z, rx[1 - nb]); /* Xb * yP / (xP * Yb * (X1 - X0)) */
        /* End 1/Z calculation */

        xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb]);

        apply_z(rx[0], ry[0], z);

        vli_set(result->x, rx[0]);
        vli_set(result->y, ry[0]);
}

static void ecc_bytes2native(const u8 bytes[ECC_BYTES],
                             u64 native[NUM_ECC_DIGITS])
{
        int i;

        for (i = 0; i < NUM_ECC_DIGITS; i++) {
                const u8 *digit = bytes + 8 * (NUM_ECC_DIGITS - 1 - i);

                native[NUM_ECC_DIGITS - 1 - i] =
                                ((u64) digit[0] << 0) |
                                ((u64) digit[1] << 8) |
                                ((u64) digit[2] << 16) |
                                ((u64) digit[3] << 24) |
                                ((u64) digit[4] << 32) |
                                ((u64) digit[5] << 40) |
                                ((u64) digit[6] << 48) |
                                ((u64) digit[7] << 56);
        }
}

static void ecc_native2bytes(const u64 native[NUM_ECC_DIGITS],
                             u8 bytes[ECC_BYTES])
{
        int i;

        for (i = 0; i < NUM_ECC_DIGITS; i++) {
                u8 *digit = bytes + 8 * (NUM_ECC_DIGITS - 1 - i);

                digit[0] = native[NUM_ECC_DIGITS - 1 - i] >> 0;
                digit[1] = native[NUM_ECC_DIGITS - 1 - i] >> 8;
                digit[2] = native[NUM_ECC_DIGITS - 1 - i] >> 16;
                digit[3] = native[NUM_ECC_DIGITS - 1 - i] >> 24;
                digit[4] = native[NUM_ECC_DIGITS - 1 - i] >> 32;
                digit[5] = native[NUM_ECC_DIGITS - 1 - i] >> 40;
                digit[6] = native[NUM_ECC_DIGITS - 1 - i] >> 48;
                digit[7] = native[NUM_ECC_DIGITS - 1 - i] >> 56;
        }
}

bool ecc_make_key(u8 public_key[64], u8 private_key[32])
{
        struct ecc_point pk;
        u64 priv[NUM_ECC_DIGITS];
        unsigned int tries = 0;

        do {
                if (tries++ >= MAX_TRIES)
                        return false;

                get_random_bytes(priv, ECC_BYTES);

                if (vli_is_zero(priv))
                        continue;

                /* Make sure the private key is in the range [1, n-1]. */
                if (vli_cmp(curve_n, priv) != 1)
                        continue;

                ecc_point_mult(&pk, &curve_g, priv, NULL, vli_num_bits(priv));
        } while (ecc_point_is_zero(&pk));

        ecc_native2bytes(priv, private_key);
        ecc_native2bytes(pk.x, public_key);
        ecc_native2bytes(pk.y, &public_key[32]);

        return true;
}

bool ecdh_shared_secret(const u8 public_key[64], const u8 private_key[32],
                        u8 secret[32])
{
        u64 priv[NUM_ECC_DIGITS];
        u64 rand[NUM_ECC_DIGITS];
        struct ecc_point product, pk;

        get_random_bytes(rand, ECC_BYTES);

        ecc_bytes2native(public_key, pk.x);
        ecc_bytes2native(&public_key[32], pk.y);
        ecc_bytes2native(private_key, priv);

        ecc_point_mult(&product, &pk, priv, rand, vli_num_bits(priv));

        ecc_native2bytes(product.x, secret);

        return !ecc_point_is_zero(&product);
}