/*
   * 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 <linux/slab.h>
  #include <linux/swab.h>
  #include <linux/fips.h>
  #include <crypto/ecdh.h>

  #include <crypto/rng.h>

  
  #include "ecc.h"
  #include "ecc_curve_defs.h"
  
  typedef struct {
  	u64 m_low;
  	u64 m_high;
  } uint128_t;
  
  static inline const struct ecc_curve *ecc_get_curve(unsigned int curve_id)
  {
  	switch (curve_id) {
  	/* In FIPS mode only allow P256 and higher */
  	case ECC_CURVE_NIST_P192:
  		return fips_enabled ? NULL : &nist_p192;
  	case ECC_CURVE_NIST_P256:
  		return &nist_p256;
  	default:
  		return NULL;
  	}
  }
  
  static u64 *ecc_alloc_digits_space(unsigned int ndigits)
  {
  	size_t len = ndigits * sizeof(u64);
  
  	if (!len)
  		return NULL;
  
  	return kmalloc(len, GFP_KERNEL);
  }
  
  static void ecc_free_digits_space(u64 *space)
  {
  	kzfree(space);
  }
  
  static struct ecc_point *ecc_alloc_point(unsigned int ndigits)
  {
  	struct ecc_point *p = kmalloc(sizeof(*p), GFP_KERNEL);
  
  	if (!p)
  		return NULL;
  
  	p->x = ecc_alloc_digits_space(ndigits);
  	if (!p->x)
  		goto err_alloc_x;
  
  	p->y = ecc_alloc_digits_space(ndigits);
  	if (!p->y)
  		goto err_alloc_y;
  
  	p->ndigits = ndigits;
  
  	return p;
  
  err_alloc_y:
  	ecc_free_digits_space(p->x);
  err_alloc_x:
  	kfree(p);
  	return NULL;
  }
  
  static void ecc_free_point(struct ecc_point *p)
  {
  	if (!p)
  		return;
  
  	kzfree(p->x);
  	kzfree(p->y);
  	kzfree(p);
  }
  
  static void vli_clear(u64 *vli, unsigned int ndigits)
  {
  	int i;
  
  	for (i = 0; i < ndigits; i++)
  		vli[i] = 0;
  }
  
  /* Returns true if vli == 0, false otherwise. */
  static bool vli_is_zero(const u64 *vli, unsigned int ndigits)
  {
  	int i;
  
  	for (i = 0; i < ndigits; 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, unsigned int ndigits)
  {
  	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 = ndigits - 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 ndigits)
  {
  	unsigned int i, num_digits;
  	u64 digit;
  
  	num_digits = vli_num_digits(vli, ndigits);
  	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, unsigned int ndigits)
  {
  	int i;
  
  	for (i = 0; i < ndigits; i++)
  		dest[i] = src[i];
  }
  
  /* Returns sign of left - right. */
  static int vli_cmp(const u64 *left, const u64 *right, unsigned int ndigits)
  {
  	int i;
  
  	for (i = ndigits - 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,
  		      unsigned int ndigits)
  {
  	u64 carry = 0;
  	int i;
  
  	for (i = 0; i < ndigits; 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, unsigned int ndigits)
  {
  	u64 *end = vli;
  	u64 carry = 0;
  
  	vli += ndigits;
  
  	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,
  		   unsigned int ndigits)
  {
  	u64 carry = 0;
  	int i;
  
  	for (i = 0; i < ndigits; 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,
  		   unsigned int ndigits)
  {
  	u64 borrow = 0;
  	int i;
  
  	for (i = 0; i < ndigits; 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,
  		     unsigned int ndigits)
  {
  	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 < ndigits * 2 - 1; k++) {
  		unsigned int min;
  
  		if (k < ndigits)
  			min = 0;
  		else
  			min = (k + 1) - ndigits;
  
  		for (i = min; i <= k && i < ndigits; 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[ndigits * 2 - 1] = r01.m_low;
  }
  
  static void vli_square(u64 *result, const u64 *left, unsigned int ndigits)
  {
  	uint128_t r01 = { 0, 0 };
  	u64 r2 = 0;
  	int i, k;
  
  	for (k = 0; k < ndigits * 2 - 1; k++) {
  		unsigned int min;
  
  		if (k < ndigits)
  			min = 0;
  		else
  			min = (k + 1) - ndigits;
  
  		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[ndigits * 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, unsigned int ndigits)
  {
  	u64 carry;
  
  	carry = vli_add(result, left, right, ndigits);
  
  	/* result > mod (result = mod + remainder), so subtract mod to
  	 * get remainder.
  	 */
  	if (carry || vli_cmp(result, mod, ndigits) >= 0)
  		vli_sub(result, result, mod, ndigits);
  }
  
  /* 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, unsigned int ndigits)
  {
  	u64 borrow = vli_sub(result, left, right, ndigits);
  
  	/* 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, ndigits);
  }
  
  /* Computes p_result = p_product % curve_p.
   * See algorithm 5 and 6 from
   * http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf
   */
  static void vli_mmod_fast_192(u64 *result, const u64 *product,
  			      const u64 *curve_prime, u64 *tmp)
  {
  	const unsigned int ndigits = 3;
  	int carry;
  
  	vli_set(result, product, ndigits);
  
  	vli_set(tmp, &product[3], ndigits);
  	carry = vli_add(result, result, tmp, ndigits);
  
  	tmp[0] = 0;
  	tmp[1] = product[3];
  	tmp[2] = product[4];
  	carry += vli_add(result, result, tmp, ndigits);
  
  	tmp[0] = tmp[1] = product[5];
  	tmp[2] = 0;
  	carry += vli_add(result, result, tmp, ndigits);
  
  	while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
  		carry -= vli_sub(result, result, curve_prime, ndigits);
  }
  
  /* Computes result = product % curve_prime
   * from http://www.nsa.gov/ia/_files/nist-routines.pdf
   */
  static void vli_mmod_fast_256(u64 *result, const u64 *product,
  			      const u64 *curve_prime, u64 *tmp)
  {
  	int carry;
  	const unsigned int ndigits = 4;
  
  	/* t */
  	vli_set(result, product, ndigits);
  
  	/* s1 */
  	tmp[0] = 0;
  	tmp[1] = product[5] & 0xffffffff00000000ull;
  	tmp[2] = product[6];
  	tmp[3] = product[7];
  	carry = vli_lshift(tmp, tmp, 1, ndigits);
  	carry += vli_add(result, result, tmp, ndigits);
  
  	/* 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, ndigits);
  	carry += vli_add(result, result, tmp, ndigits);
  
  	/* s3 */
  	tmp[0] = product[4];
  	tmp[1] = product[5] & 0xffffffff;
  	tmp[2] = 0;
  	tmp[3] = product[7];
  	carry += vli_add(result, result, tmp, ndigits);
  
  	/* 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, ndigits);
  
  	/* 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, ndigits);
  
  	/* 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, ndigits);
  
  	/* 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, ndigits);
  
  	/* 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, ndigits);
  
  	if (carry < 0) {
  		do {
  			carry += vli_add(result, result, curve_prime, ndigits);
  		} while (carry < 0);
  	} else {
  		while (carry || vli_cmp(curve_prime, result, ndigits) != 1)
  			carry -= vli_sub(result, result, curve_prime, ndigits);
  	}
  }
  
  /* Computes result = product % curve_prime
   *  from http://www.nsa.gov/ia/_files/nist-routines.pdf
  */
  static bool vli_mmod_fast(u64 *result, u64 *product,
  			  const u64 *curve_prime, unsigned int ndigits)
  {

  	u64 tmp[2 * ECC_MAX_DIGITS];

  
  	switch (ndigits) {
  	case 3:
  		vli_mmod_fast_192(result, product, curve_prime, tmp);
  		break;
  	case 4:
  		vli_mmod_fast_256(result, product, curve_prime, tmp);
  		break;
  	default:
  		pr_err("unsupports digits size!
  ");
  		return false;
  	}
  
  	return true;
  }
  
  /* Computes result = (left * right) % curve_prime. */
  static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
  			      const u64 *curve_prime, unsigned int ndigits)
  {

  	u64 product[2 * ECC_MAX_DIGITS];

  
  	vli_mult(product, left, right, ndigits);
  	vli_mmod_fast(result, product, curve_prime, ndigits);
  }
  
  /* Computes result = left^2 % curve_prime. */
  static void vli_mod_square_fast(u64 *result, const u64 *left,
  				const u64 *curve_prime, unsigned int ndigits)
  {

  	u64 product[2 * ECC_MAX_DIGITS];

  
  	vli_square(product, left, ndigits);
  	vli_mmod_fast(result, product, curve_prime, ndigits);
  }
  
  #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,
  			unsigned int ndigits)
  {

  	u64 a[ECC_MAX_DIGITS], b[ECC_MAX_DIGITS];
  	u64 u[ECC_MAX_DIGITS], v[ECC_MAX_DIGITS];

  	u64 carry;
  	int cmp_result;
  
  	if (vli_is_zero(input, ndigits)) {
  		vli_clear(result, ndigits);
  		return;
  	}
  
  	vli_set(a, input, ndigits);
  	vli_set(b, mod, ndigits);
  	vli_clear(u, ndigits);
  	u[0] = 1;
  	vli_clear(v, ndigits);
  
  	while ((cmp_result = vli_cmp(a, b, ndigits)) != 0) {
  		carry = 0;
  
  		if (EVEN(a)) {
  			vli_rshift1(a, ndigits);
  
  			if (!EVEN(u))
  				carry = vli_add(u, u, mod, ndigits);
  
  			vli_rshift1(u, ndigits);
  			if (carry)
  				u[ndigits - 1] |= 0x8000000000000000ull;
  		} else if (EVEN(b)) {
  			vli_rshift1(b, ndigits);
  
  			if (!EVEN(v))
  				carry = vli_add(v, v, mod, ndigits);
  
  			vli_rshift1(v, ndigits);
  			if (carry)
  				v[ndigits - 1] |= 0x8000000000000000ull;
  		} else if (cmp_result > 0) {
  			vli_sub(a, a, b, ndigits);
  			vli_rshift1(a, ndigits);
  
  			if (vli_cmp(u, v, ndigits) < 0)
  				vli_add(u, u, mod, ndigits);
  
  			vli_sub(u, u, v, ndigits);
  			if (!EVEN(u))
  				carry = vli_add(u, u, mod, ndigits);
  
  			vli_rshift1(u, ndigits);
  			if (carry)
  				u[ndigits - 1] |= 0x8000000000000000ull;
  		} else {
  			vli_sub(b, b, a, ndigits);
  			vli_rshift1(b, ndigits);
  
  			if (vli_cmp(v, u, ndigits) < 0)
  				vli_add(v, v, mod, ndigits);
  
  			vli_sub(v, v, u, ndigits);
  			if (!EVEN(v))
  				carry = vli_add(v, v, mod, ndigits);
  
  			vli_rshift1(v, ndigits);
  			if (carry)
  				v[ndigits - 1] |= 0x8000000000000000ull;
  		}
  	}
  
  	vli_set(result, u, ndigits);
  }
  
  /* ------ 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, point->ndigits) &&
  		vli_is_zero(point->y, point->ndigits));
  }
  
  /* 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,
  				      u64 *curve_prime, unsigned int ndigits)
  {
  	/* t1 = x, t2 = y, t3 = z */

  	u64 t4[ECC_MAX_DIGITS];
  	u64 t5[ECC_MAX_DIGITS];

  
  	if (vli_is_zero(z1, ndigits))
  		return;
  
  	/* t4 = y1^2 */
  	vli_mod_square_fast(t4, y1, curve_prime, ndigits);
  	/* t5 = x1*y1^2 = A */
  	vli_mod_mult_fast(t5, x1, t4, curve_prime, ndigits);
  	/* t4 = y1^4 */
  	vli_mod_square_fast(t4, t4, curve_prime, ndigits);
  	/* t2 = y1*z1 = z3 */
  	vli_mod_mult_fast(y1, y1, z1, curve_prime, ndigits);
  	/* t3 = z1^2 */
  	vli_mod_square_fast(z1, z1, curve_prime, ndigits);
  
  	/* t1 = x1 + z1^2 */
  	vli_mod_add(x1, x1, z1, curve_prime, ndigits);
  	/* t3 = 2*z1^2 */
  	vli_mod_add(z1, z1, z1, curve_prime, ndigits);
  	/* t3 = x1 - z1^2 */
  	vli_mod_sub(z1, x1, z1, curve_prime, ndigits);
  	/* t1 = x1^2 - z1^4 */
  	vli_mod_mult_fast(x1, x1, z1, curve_prime, ndigits);
  
  	/* t3 = 2*(x1^2 - z1^4) */
  	vli_mod_add(z1, x1, x1, curve_prime, ndigits);
  	/* t1 = 3*(x1^2 - z1^4) */
  	vli_mod_add(x1, x1, z1, curve_prime, ndigits);
  	if (vli_test_bit(x1, 0)) {
  		u64 carry = vli_add(x1, x1, curve_prime, ndigits);
  
  		vli_rshift1(x1, ndigits);
  		x1[ndigits - 1] |= carry << 63;
  	} else {
  		vli_rshift1(x1, ndigits);
  	}
  	/* t1 = 3/2*(x1^2 - z1^4) = B */
  
  	/* t3 = B^2 */
  	vli_mod_square_fast(z1, x1, curve_prime, ndigits);
  	/* t3 = B^2 - A */
  	vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
  	/* t3 = B^2 - 2A = x3 */
  	vli_mod_sub(z1, z1, t5, curve_prime, ndigits);
  	/* t5 = A - x3 */
  	vli_mod_sub(t5, t5, z1, curve_prime, ndigits);
  	/* t1 = B * (A - x3) */
  	vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
  	/* t4 = B * (A - x3) - y1^4 = y3 */
  	vli_mod_sub(t4, x1, t4, curve_prime, ndigits);
  
  	vli_set(x1, z1, ndigits);
  	vli_set(z1, y1, ndigits);
  	vli_set(y1, t4, ndigits);
  }
  
  /* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
  static void apply_z(u64 *x1, u64 *y1, u64 *z, u64 *curve_prime,
  		    unsigned int ndigits)
  {

  	u64 t1[ECC_MAX_DIGITS];

  
  	vli_mod_square_fast(t1, z, curve_prime, ndigits);    /* z^2 */
  	vli_mod_mult_fast(x1, x1, t1, curve_prime, ndigits); /* x1 * z^2 */
  	vli_mod_mult_fast(t1, t1, z, curve_prime, ndigits);  /* z^3 */
  	vli_mod_mult_fast(y1, y1, t1, curve_prime, ndigits); /* 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 *curve_prime,
  				unsigned int ndigits)
  {

  	u64 z[ECC_MAX_DIGITS];

  
  	vli_set(x2, x1, ndigits);
  	vli_set(y2, y1, ndigits);
  
  	vli_clear(z, ndigits);
  	z[0] = 1;
  
  	if (p_initial_z)
  		vli_set(z, p_initial_z, ndigits);
  
  	apply_z(x1, y1, z, curve_prime, ndigits);
  
  	ecc_point_double_jacobian(x1, y1, z, curve_prime, ndigits);
  
  	apply_z(x2, y2, z, curve_prime, ndigits);
  }
  
  /* 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, u64 *curve_prime,
  		     unsigned int ndigits)
  {
  	/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */

  	u64 t5[ECC_MAX_DIGITS];

  
  	/* t5 = x2 - x1 */
  	vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
  	/* t5 = (x2 - x1)^2 = A */
  	vli_mod_square_fast(t5, t5, curve_prime, ndigits);
  	/* t1 = x1*A = B */
  	vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
  	/* t3 = x2*A = C */
  	vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
  	/* t4 = y2 - y1 */
  	vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
  	/* t5 = (y2 - y1)^2 = D */
  	vli_mod_square_fast(t5, y2, curve_prime, ndigits);
  
  	/* t5 = D - B */
  	vli_mod_sub(t5, t5, x1, curve_prime, ndigits);
  	/* t5 = D - B - C = x3 */
  	vli_mod_sub(t5, t5, x2, curve_prime, ndigits);
  	/* t3 = C - B */
  	vli_mod_sub(x2, x2, x1, curve_prime, ndigits);
  	/* t2 = y1*(C - B) */
  	vli_mod_mult_fast(y1, y1, x2, curve_prime, ndigits);
  	/* t3 = B - x3 */
  	vli_mod_sub(x2, x1, t5, curve_prime, ndigits);
  	/* t4 = (y2 - y1)*(B - x3) */
  	vli_mod_mult_fast(y2, y2, x2, curve_prime, ndigits);
  	/* t4 = y3 */
  	vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
  
  	vli_set(x2, t5, ndigits);
  }
  
  /* 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, u64 *curve_prime,
  		       unsigned int ndigits)
  {
  	/* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */

  	u64 t5[ECC_MAX_DIGITS];
  	u64 t6[ECC_MAX_DIGITS];
  	u64 t7[ECC_MAX_DIGITS];

  
  	/* t5 = x2 - x1 */
  	vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
  	/* t5 = (x2 - x1)^2 = A */
  	vli_mod_square_fast(t5, t5, curve_prime, ndigits);
  	/* t1 = x1*A = B */
  	vli_mod_mult_fast(x1, x1, t5, curve_prime, ndigits);
  	/* t3 = x2*A = C */
  	vli_mod_mult_fast(x2, x2, t5, curve_prime, ndigits);
  	/* t4 = y2 + y1 */
  	vli_mod_add(t5, y2, y1, curve_prime, ndigits);
  	/* t4 = y2 - y1 */
  	vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
  
  	/* t6 = C - B */
  	vli_mod_sub(t6, x2, x1, curve_prime, ndigits);
  	/* t2 = y1 * (C - B) */
  	vli_mod_mult_fast(y1, y1, t6, curve_prime, ndigits);
  	/* t6 = B + C */
  	vli_mod_add(t6, x1, x2, curve_prime, ndigits);
  	/* t3 = (y2 - y1)^2 */
  	vli_mod_square_fast(x2, y2, curve_prime, ndigits);
  	/* t3 = x3 */
  	vli_mod_sub(x2, x2, t6, curve_prime, ndigits);
  
  	/* t7 = B - x3 */
  	vli_mod_sub(t7, x1, x2, curve_prime, ndigits);
  	/* t4 = (y2 - y1)*(B - x3) */
  	vli_mod_mult_fast(y2, y2, t7, curve_prime, ndigits);
  	/* t4 = y3 */
  	vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
  
  	/* t7 = (y2 + y1)^2 = F */
  	vli_mod_square_fast(t7, t5, curve_prime, ndigits);
  	/* t7 = x3' */
  	vli_mod_sub(t7, t7, t6, curve_prime, ndigits);
  	/* t6 = x3' - B */
  	vli_mod_sub(t6, t7, x1, curve_prime, ndigits);
  	/* t6 = (y2 + y1)*(x3' - B) */
  	vli_mod_mult_fast(t6, t6, t5, curve_prime, ndigits);
  	/* t2 = y3' */
  	vli_mod_sub(y1, t6, y1, curve_prime, ndigits);
  
  	vli_set(x1, t7, ndigits);
  }
  
  static void ecc_point_mult(struct ecc_point *result,
  			   const struct ecc_point *point, const u64 *scalar,

  			   u64 *initial_z, const struct ecc_curve *curve,

  			   unsigned int ndigits)
  {
  	/* R0 and R1 */

  	u64 rx[2][ECC_MAX_DIGITS];
  	u64 ry[2][ECC_MAX_DIGITS];
  	u64 z[ECC_MAX_DIGITS];

  	u64 sk[2][ECC_MAX_DIGITS];
  	u64 *curve_prime = curve->p;

  	int i, nb;

  	int num_bits;
  	int carry;
  
  	carry = vli_add(sk[0], scalar, curve->n, ndigits);
  	vli_add(sk[1], sk[0], curve->n, ndigits);
  	scalar = sk[!carry];
  	num_bits = sizeof(u64) * ndigits * 8 + 1;

  
  	vli_set(rx[1], point->x, ndigits);
  	vli_set(ry[1], point->y, ndigits);
  
  	xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z, curve_prime,
  			    ndigits);
  
  	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], curve_prime,
  			   ndigits);
  		xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime,
  			 ndigits);
  	}
  
  	nb = !vli_test_bit(scalar, 0);
  	xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve_prime,
  		   ndigits);
  
  	/* Find final 1/Z value. */
  	/* X1 - X0 */
  	vli_mod_sub(z, rx[1], rx[0], curve_prime, ndigits);
  	/* Yb * (X1 - X0) */
  	vli_mod_mult_fast(z, z, ry[1 - nb], curve_prime, ndigits);
  	/* xP * Yb * (X1 - X0) */
  	vli_mod_mult_fast(z, z, point->x, curve_prime, ndigits);
  
  	/* 1 / (xP * Yb * (X1 - X0)) */
  	vli_mod_inv(z, z, curve_prime, point->ndigits);
  
  	/* yP / (xP * Yb * (X1 - X0)) */
  	vli_mod_mult_fast(z, z, point->y, curve_prime, ndigits);
  	/* Xb * yP / (xP * Yb * (X1 - X0)) */
  	vli_mod_mult_fast(z, z, rx[1 - nb], curve_prime, ndigits);
  	/* End 1/Z calculation */
  
  	xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve_prime, ndigits);
  
  	apply_z(rx[0], ry[0], z, curve_prime, ndigits);
  
  	vli_set(result->x, rx[0], ndigits);
  	vli_set(result->y, ry[0], ndigits);
  }
  
  static inline void ecc_swap_digits(const u64 *in, u64 *out,
  				   unsigned int ndigits)
  {
  	int i;
  
  	for (i = 0; i < ndigits; i++)
  		out[i] = __swab64(in[ndigits - 1 - i]);
  }
  
  int ecc_is_key_valid(unsigned int curve_id, unsigned int ndigits,

  		     const u64 *private_key, unsigned int private_key_len)

  {
  	int nbytes;
  	const struct ecc_curve *curve = ecc_get_curve(curve_id);
  
  	if (!private_key)
  		return -EINVAL;
  
  	nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
  
  	if (private_key_len != nbytes)
  		return -EINVAL;

  	if (vli_is_zero(private_key, ndigits))

  		return -EINVAL;
  
  	/* Make sure the private key is in the range [1, n-1]. */

  	if (vli_cmp(curve->n, private_key, ndigits) != 1)

  		return -EINVAL;
  
  	return 0;
  }

  /*
   * ECC private keys are generated using the method of extra random bits,
   * equivalent to that described in FIPS 186-4, Appendix B.4.1.
   *
   * d = (c mod(n–1)) + 1    where c is a string of random bits, 64 bits longer
   *                         than requested
   * 0 <= c mod(n-1) <= n-2  and implies that
   * 1 <= d <= n-1
   *
   * This method generates a private key uniformly distributed in the range
   * [1, n-1].
   */
  int ecc_gen_privkey(unsigned int curve_id, unsigned int ndigits, u64 *privkey)
  {
  	const struct ecc_curve *curve = ecc_get_curve(curve_id);

  	u64 priv[ECC_MAX_DIGITS];

  	unsigned int nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
  	unsigned int nbits = vli_num_bits(curve->n, ndigits);
  	int err;
  
  	/* Check that N is included in Table 1 of FIPS 186-4, section 6.1.1 */

  	if (nbits < 160 || ndigits > ARRAY_SIZE(priv))

  		return -EINVAL;
  
  	/*
  	 * FIPS 186-4 recommends that the private key should be obtained from a
  	 * RBG with a security strength equal to or greater than the security
  	 * strength associated with N.
  	 *
  	 * The maximum security strength identified by NIST SP800-57pt1r4 for
  	 * ECC is 256 (N >= 512).
  	 *
  	 * This condition is met by the default RNG because it selects a favored
  	 * DRBG with a security strength of 256.
  	 */
  	if (crypto_get_default_rng())

  		return -EFAULT;

  
  	err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes);
  	crypto_put_default_rng();
  	if (err)
  		return err;
  
  	if (vli_is_zero(priv, ndigits))
  		return -EINVAL;
  
  	/* Make sure the private key is in the range [1, n-1]. */
  	if (vli_cmp(curve->n, priv, ndigits) != 1)
  		return -EINVAL;
  
  	ecc_swap_digits(priv, privkey, ndigits);
  
  	return 0;
  }

  int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
  		     const u64 *private_key, u64 *public_key)

  {
  	int ret = 0;
  	struct ecc_point *pk;

  	u64 priv[ECC_MAX_DIGITS];

  	const struct ecc_curve *curve = ecc_get_curve(curve_id);

  	if (!private_key || !curve || ndigits > ARRAY_SIZE(priv)) {

  		ret = -EINVAL;
  		goto out;
  	}

  	ecc_swap_digits(private_key, priv, ndigits);

  
  	pk = ecc_alloc_point(ndigits);
  	if (!pk) {
  		ret = -ENOMEM;
  		goto out;
  	}

  	ecc_point_mult(pk, &curve->g, priv, NULL, curve, ndigits);

  	if (ecc_point_is_zero(pk)) {
  		ret = -EAGAIN;
  		goto err_free_point;
  	}

  	ecc_swap_digits(pk->x, public_key, ndigits);
  	ecc_swap_digits(pk->y, &public_key[ndigits], ndigits);

  
  err_free_point:
  	ecc_free_point(pk);
  out:
  	return ret;
  }

  /* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
  static int ecc_is_pubkey_valid_partial(const struct ecc_curve *curve,
  				       struct ecc_point *pk)
  {
  	u64 yy[ECC_MAX_DIGITS], xxx[ECC_MAX_DIGITS], w[ECC_MAX_DIGITS];
  
  	/* Check 1: Verify key is not the zero point. */
  	if (ecc_point_is_zero(pk))
  		return -EINVAL;
  
  	/* Check 2: Verify key is in the range [1, p-1]. */
  	if (vli_cmp(curve->p, pk->x, pk->ndigits) != 1)
  		return -EINVAL;
  	if (vli_cmp(curve->p, pk->y, pk->ndigits) != 1)
  		return -EINVAL;
  
  	/* Check 3: Verify that y^2 == (x^3 + a·x + b) mod p */
  	vli_mod_square_fast(yy, pk->y, curve->p, pk->ndigits); /* y^2 */
  	vli_mod_square_fast(xxx, pk->x, curve->p, pk->ndigits); /* x^2 */
  	vli_mod_mult_fast(xxx, xxx, pk->x, curve->p, pk->ndigits); /* x^3 */
  	vli_mod_mult_fast(w, curve->a, pk->x, curve->p, pk->ndigits); /* a·x */
  	vli_mod_add(w, w, curve->b, curve->p, pk->ndigits); /* a·x + b */
  	vli_mod_add(w, w, xxx, curve->p, pk->ndigits); /* x^3 + a·x + b */
  	if (vli_cmp(yy, w, pk->ndigits) != 0) /* Equation */
  		return -EINVAL;
  
  	return 0;
  
  }

  int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,

  			      const u64 *private_key, const u64 *public_key,
  			      u64 *secret)

  {
  	int ret = 0;
  	struct ecc_point *product, *pk;

  	u64 priv[ECC_MAX_DIGITS];
  	u64 rand_z[ECC_MAX_DIGITS];
  	unsigned int nbytes;

  	const struct ecc_curve *curve = ecc_get_curve(curve_id);

  	if (!private_key || !public_key || !curve ||
  	    ndigits > ARRAY_SIZE(priv) || ndigits > ARRAY_SIZE(rand_z)) {

  		ret = -EINVAL;
  		goto out;
  	}

  	nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;

  	get_random_bytes(rand_z, nbytes);

  
  	pk = ecc_alloc_point(ndigits);
  	if (!pk) {
  		ret = -ENOMEM;

  		goto out;

  	}

  	ecc_swap_digits(public_key, pk->x, ndigits);
  	ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
  	ret = ecc_is_pubkey_valid_partial(curve, pk);
  	if (ret)
  		goto err_alloc_product;
  
  	ecc_swap_digits(private_key, priv, ndigits);

  	product = ecc_alloc_point(ndigits);
  	if (!product) {
  		ret = -ENOMEM;
  		goto err_alloc_product;
  	}

  	ecc_point_mult(product, pk, priv, rand_z, curve, ndigits);

  	ecc_swap_digits(product->x, secret, ndigits);

  
  	if (ecc_point_is_zero(product))
  		ret = -EFAULT;
  
  	ecc_free_point(product);
  err_alloc_product:
  	ecc_free_point(pk);
  out:
  	return ret;
  }