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	Version: linux-6.0.1 spark-3.0.0 hadoop-3.2.0-src hadoop-3.3.0-src spark-2.4.7 linux-4.15.13 hadoop-2.7.4-src Revert   Change

 /*
  * Copyright (c) 2013, 2014 Kenneth MacKay. All rights reserved.
  * Copyright (c) 2019 Vitaly Chikunov <vt@altlinux.org>
  *
  * 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 <crypto/ecc_curve.h>
 #include <linux/module.h>
 #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 <crypto/internal/ecc.h>
 #include <asm/unaligned.h>
 #include <linux/ratelimit.h>
 
 #include "ecc_curve_defs.h"
 
 typedef struct {
     u64 m_low;
     u64 m_high;
 } uint128_t;
 
 /* Returns curv25519 curve param */
 const struct ecc_curve *ecc_get_curve25519(void)
 {
     return &ecc_25519;
 }
 EXPORT_SYMBOL(ecc_get_curve25519);
 
 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;
     case ECC_CURVE_NIST_P384:
         return &nist_p384;
     default:
         return NULL;
     }
 }
 EXPORT_SYMBOL(ecc_get_curve);
 
 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)
 {
     kfree_sensitive(space);
 }
 
 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;
 }
 EXPORT_SYMBOL(ecc_alloc_point);
 
 void ecc_free_point(struct ecc_point *p)
 {
     if (!p)
         return;
 
     kfree_sensitive(p->x);
     kfree_sensitive(p->y);
     kfree_sensitive(p);
 }
 EXPORT_SYMBOL(ecc_free_point);
 
 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. */
 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;
 }
 EXPORT_SYMBOL(vli_is_zero);
 
 /* Returns nonzero if bit of vli is set. */
 static u64 vli_test_bit(const u64 *vli, unsigned int bit)
 {
     return (vli[bit / 64] & ((u64)1 << (bit % 64)));
 }
 
 static bool vli_is_negative(const u64 *vli, unsigned int ndigits)
 {
     return vli_test_bit(vli, ndigits * 64 - 1);
 }
 
 /* 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. */
 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);
 }
 EXPORT_SYMBOL(vli_num_bits);
 
 /* Set dest from unaligned bit string src. */
 void vli_from_be64(u64 *dest, const void *src, unsigned int ndigits)
 {
     int i;
     const u64 *from = src;
 
     for (i = 0; i < ndigits; i++)
         dest[i] = get_unaligned_be64(&from[ndigits - 1 - i]);
 }
 EXPORT_SYMBOL(vli_from_be64);
 
 void vli_from_le64(u64 *dest, const void *src, unsigned int ndigits)
 {
     int i;
     const u64 *from = src;
 
     for (i = 0; i < ndigits; i++)
         dest[i] = get_unaligned_le64(&from[i]);
 }
 EXPORT_SYMBOL(vli_from_le64);
 
 /* 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. */
 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;
 }
 EXPORT_SYMBOL(vli_cmp);
 
 /* 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 carry. Can modify in place. */
 static u64 vli_uadd(u64 *result, const u64 *left, u64 right,
             unsigned int ndigits)
 {
     u64 carry = right;
     int i;
 
     for (i = 0; i < ndigits; i++) {
         u64 sum;
 
         sum = left[i] + carry;
         if (sum != left[i])
             carry = (sum < left[i]);
         else
             carry = !!carry;
 
         result[i] = sum;
     }
 
     return carry;
 }
 
 /* Computes result = left - right, returning borrow. Can modify in place. */
 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;
 }
 EXPORT_SYMBOL(vli_sub);
 
 /* Computes result = left - right, returning borrow. Can modify in place. */
 static u64 vli_usub(u64 *result, const u64 *left, u64 right,
          unsigned int ndigits)
 {
     u64 borrow = right;
     int i;
 
     for (i = 0; i < ndigits; i++) {
         u64 diff;
 
         diff = left[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)
 {
     uint128_t result;
 #if defined(CONFIG_ARCH_SUPPORTS_INT128)
     unsigned __int128 m = (unsigned __int128)left * right;
 
     result.m_low  = m;
     result.m_high = m >> 64;
 #else
     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;
 
     m2 += (m0 >> 32);
     m2 += m1;
 
     /* Overflow */
     if (m2 < m1)
         m3 += 0x100000000ull;
 
     result.m_low = (m0 & 0xffffffffull) | (m2 << 32);
     result.m_high = m3 + (m2 >> 32);
 #endif
     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;
 }
 
 /* Compute product = left * right, for a small right value. */
 static void vli_umult(u64 *result, const u64 *left, u32 right,
               unsigned int ndigits)
 {
     uint128_t r01 = { 0 };
     unsigned int k;
 
     for (k = 0; k < ndigits; k++) {
         uint128_t product;
 
         product = mul_64_64(left[k], right);
         r01 = add_128_128(r01, product);
         /* no carry */
         result[k] = r01.m_low;
         r01.m_low = r01.m_high;
         r01.m_high = 0;
     }
     result[k] = r01.m_low;
     for (++k; k < ndigits * 2; k++)
         result[k] = 0;
 }
 
 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 result = product % mod
  * for special form moduli: p = 2^k-c, for small c (note the minus sign)
  *
  * References:
  * R. Crandall, C. Pomerance. Prime Numbers: A Computational Perspective.
  * 9 Fast Algorithms for Large-Integer Arithmetic. 9.2.3 Moduli of special form
  * Algorithm 9.2.13 (Fast mod operation for special-form moduli).
  */
 static void vli_mmod_special(u64 *result, const u64 *product,
                   const u64 *mod, unsigned int ndigits)
 {
     u64 c = -mod[0];
     u64 t[ECC_MAX_DIGITS * 2];
     u64 r[ECC_MAX_DIGITS * 2];
 
     vli_set(r, product, ndigits * 2);
     while (!vli_is_zero(r + ndigits, ndigits)) {
         vli_umult(t, r + ndigits, c, ndigits);
         vli_clear(r + ndigits, ndigits);
         vli_add(r, r, t, ndigits * 2);
     }
     vli_set(t, mod, ndigits);
     vli_clear(t + ndigits, ndigits);
     while (vli_cmp(r, t, ndigits * 2) >= 0)
         vli_sub(r, r, t, ndigits * 2);
     vli_set(result, r, ndigits);
 }
 
 /*
  * Computes result = product % mod
  * for special form moduli: p = 2^{k-1}+c, for small c (note the plus sign)
  * where k-1 does not fit into qword boundary by -1 bit (such as 255).
 
  * References (loosely based on):
  * A. Menezes, P. van Oorschot, S. Vanstone. Handbook of Applied Cryptography.
  * 14.3.4 Reduction methods for moduli of special form. Algorithm 14.47.
  * URL: http://cacr.uwaterloo.ca/hac/about/chap14.pdf
  *
  * H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen, F. Vercauteren.
  * Handbook of Elliptic and Hyperelliptic Curve Cryptography.
  * Algorithm 10.25 Fast reduction for special form moduli
  */
 static void vli_mmod_special2(u64 *result, const u64 *product,
                    const u64 *mod, unsigned int ndigits)
 {
     u64 c2 = mod[0] * 2;
     u64 q[ECC_MAX_DIGITS];
     u64 r[ECC_MAX_DIGITS * 2];
     u64 m[ECC_MAX_DIGITS * 2]; /* expanded mod */
     int carry; /* last bit that doesn't fit into q */
     int i;
 
     vli_set(m, mod, ndigits);
     vli_clear(m + ndigits, ndigits);
 
     vli_set(r, product, ndigits);
     /* q and carry are top bits */
     vli_set(q, product + ndigits, ndigits);
     vli_clear(r + ndigits, ndigits);
     carry = vli_is_negative(r, ndigits);
     if (carry)
         r[ndigits - 1] &= (1ull << 63) - 1;
     for (i = 1; carry || !vli_is_zero(q, ndigits); i++) {
         u64 qc[ECC_MAX_DIGITS * 2];
 
         vli_umult(qc, q, c2, ndigits);
         if (carry)
             vli_uadd(qc, qc, mod[0], ndigits * 2);
         vli_set(q, qc + ndigits, ndigits);
         vli_clear(qc + ndigits, ndigits);
         carry = vli_is_negative(qc, ndigits);
         if (carry)
             qc[ndigits - 1] &= (1ull << 63) - 1;
         if (i & 1)
             vli_sub(r, r, qc, ndigits * 2);
         else
             vli_add(r, r, qc, ndigits * 2);
     }
     while (vli_is_negative(r, ndigits * 2))
         vli_add(r, r, m, ndigits * 2);
     while (vli_cmp(r, m, ndigits * 2) >= 0)
         vli_sub(r, r, m, ndigits * 2);
 
     vli_set(result, r, ndigits);
 }
 
 /*
  * Computes result = product % mod, where product is 2N words long.
  * Reference: Ken MacKay's micro-ecc.
  * Currently only designed to work for curve_p or curve_n.
  */
 static void vli_mmod_slow(u64 *result, u64 *product, const u64 *mod,
               unsigned int ndigits)
 {
     u64 mod_m[2 * ECC_MAX_DIGITS];
     u64 tmp[2 * ECC_MAX_DIGITS];
     u64 *v[2] = { tmp, product };
     u64 carry = 0;
     unsigned int i;
     /* Shift mod so its highest set bit is at the maximum position. */
     int shift = (ndigits * 2 * 64) - vli_num_bits(mod, ndigits);
     int word_shift = shift / 64;
     int bit_shift = shift % 64;
 
     vli_clear(mod_m, word_shift);
     if (bit_shift > 0) {
         for (i = 0; i < ndigits; ++i) {
             mod_m[word_shift + i] = (mod[i] << bit_shift) | carry;
             carry = mod[i] >> (64 - bit_shift);
         }
     } else
         vli_set(mod_m + word_shift, mod, ndigits);
 
     for (i = 1; shift >= 0; --shift) {
         u64 borrow = 0;
         unsigned int j;
 
         for (j = 0; j < ndigits * 2; ++j) {
             u64 diff = v[i][j] - mod_m[j] - borrow;
 
             if (diff != v[i][j])
                 borrow = (diff > v[i][j]);
             v[1 - i][j] = diff;
         }
         i = !(i ^ borrow); /* Swap the index if there was no borrow */
         vli_rshift1(mod_m, ndigits);
         mod_m[ndigits - 1] |= mod_m[ndigits] << (64 - 1);
         vli_rshift1(mod_m + ndigits, ndigits);
     }
     vli_set(result, v[i], ndigits);
 }
 
 /* Computes result = product % mod using Barrett's reduction with precomputed
  * value mu appended to the mod after ndigits, mu = (2^{2w} / mod) and have
  * length ndigits + 1, where mu * (2^w - 1) should not overflow ndigits
  * boundary.
  *
  * Reference:
  * R. Brent, P. Zimmermann. Modern Computer Arithmetic. 2010.
  * 2.4.1 Barrett's algorithm. Algorithm 2.5.
  */
 static void vli_mmod_barrett(u64 *result, u64 *product, const u64 *mod,
                  unsigned int ndigits)
 {
     u64 q[ECC_MAX_DIGITS * 2];
     u64 r[ECC_MAX_DIGITS * 2];
     const u64 *mu = mod + ndigits;
 
     vli_mult(q, product + ndigits, mu, ndigits);
     if (mu[ndigits])
         vli_add(q + ndigits, q + ndigits, product + ndigits, ndigits);
     vli_mult(r, mod, q + ndigits, ndigits);
     vli_sub(r, product, r, ndigits * 2);
     while (!vli_is_zero(r + ndigits, ndigits) ||
            vli_cmp(r, mod, ndigits) != -1) {
         u64 carry;
 
         carry = vli_sub(r, r, mod, ndigits);
         vli_usub(r + ndigits, r + ndigits, carry, ndigits);
     }
     vli_set(result, r, 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);
     }
 }
 
 #define SL32OR32(x32, y32) (((u64)x32 << 32) | y32)
 #define AND64H(x64)  (x64 & 0xffFFffFF00000000ull)
 #define AND64L(x64)  (x64 & 0x00000000ffFFffFFull)
 
 /* Computes result = product % curve_prime
  * from "Mathematical routines for the NIST prime elliptic curves"
  */
 static void vli_mmod_fast_384(u64 *result, const u64 *product,
                 const u64 *curve_prime, u64 *tmp)
 {
     int carry;
     const unsigned int ndigits = 6;
 
     /* t */
     vli_set(result, product, ndigits);
 
     /* s1 */
     tmp[0] = 0;     // 0 || 0
     tmp[1] = 0;     // 0 || 0
     tmp[2] = SL32OR32(product[11], (product[10]>>32));  //a22||a21
     tmp[3] = product[11]>>32;   // 0 ||a23
     tmp[4] = 0;     // 0 || 0
     tmp[5] = 0;     // 0 || 0
     carry = vli_lshift(tmp, tmp, 1, ndigits);
     carry += vli_add(result, result, tmp, ndigits);
 
     /* s2 */
     tmp[0] = product[6];    //a13||a12
     tmp[1] = product[7];    //a15||a14
     tmp[2] = product[8];    //a17||a16
     tmp[3] = product[9];    //a19||a18
     tmp[4] = product[10];   //a21||a20
     tmp[5] = product[11];   //a23||a22
     carry += vli_add(result, result, tmp, ndigits);
 
     /* s3 */
     tmp[0] = SL32OR32(product[11], (product[10]>>32));  //a22||a21
     tmp[1] = SL32OR32(product[6], (product[11]>>32));   //a12||a23
     tmp[2] = SL32OR32(product[7], (product[6])>>32);    //a14||a13
     tmp[3] = SL32OR32(product[8], (product[7]>>32));    //a16||a15
     tmp[4] = SL32OR32(product[9], (product[8]>>32));    //a18||a17
     tmp[5] = SL32OR32(product[10], (product[9]>>32));   //a20||a19
     carry += vli_add(result, result, tmp, ndigits);
 
     /* s4 */
     tmp[0] = AND64H(product[11]);   //a23|| 0
     tmp[1] = (product[10]<<32); //a20|| 0
     tmp[2] = product[6];    //a13||a12
     tmp[3] = product[7];    //a15||a14
     tmp[4] = product[8];    //a17||a16
     tmp[5] = product[9];    //a19||a18
     carry += vli_add(result, result, tmp, ndigits);
 
     /* s5 */
     tmp[0] = 0;     //  0|| 0
     tmp[1] = 0;     //  0|| 0
     tmp[2] = product[10];   //a21||a20
     tmp[3] = product[11];   //a23||a22
     tmp[4] = 0;     //  0|| 0
     tmp[5] = 0;     //  0|| 0
     carry += vli_add(result, result, tmp, ndigits);
 
     /* s6 */
     tmp[0] = AND64L(product[10]);   // 0 ||a20
     tmp[1] = AND64H(product[10]);   //a21|| 0
     tmp[2] = product[11];   //a23||a22
     tmp[3] = 0;     // 0 || 0
     tmp[4] = 0;     // 0 || 0
     tmp[5] = 0;     // 0 || 0
     carry += vli_add(result, result, tmp, ndigits);
 
     /* d1 */
     tmp[0] = SL32OR32(product[6], (product[11]>>32));   //a12||a23
     tmp[1] = SL32OR32(product[7], (product[6]>>32));    //a14||a13
     tmp[2] = SL32OR32(product[8], (product[7]>>32));    //a16||a15
     tmp[3] = SL32OR32(product[9], (product[8]>>32));    //a18||a17
     tmp[4] = SL32OR32(product[10], (product[9]>>32));   //a20||a19
     tmp[5] = SL32OR32(product[11], (product[10]>>32));  //a22||a21
     carry -= vli_sub(result, result, tmp, ndigits);
 
     /* d2 */
     tmp[0] = (product[10]<<32); //a20|| 0
     tmp[1] = SL32OR32(product[11], (product[10]>>32));  //a22||a21
     tmp[2] = (product[11]>>32); // 0 ||a23
     tmp[3] = 0;     // 0 || 0
     tmp[4] = 0;     // 0 || 0
     tmp[5] = 0;     // 0 || 0
     carry -= vli_sub(result, result, tmp, ndigits);
 
     /* d3 */
     tmp[0] = 0;     // 0 || 0
     tmp[1] = AND64H(product[11]);   //a23|| 0
     tmp[2] = product[11]>>32;   // 0 ||a23
     tmp[3] = 0;     // 0 || 0
     tmp[4] = 0;     // 0 || 0
     tmp[5] = 0;     // 0 || 0
     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);
     }
 
 }
 
 #undef SL32OR32
 #undef AND64H
 #undef AND64L
 
 /* Computes result = product % curve_prime for different curve_primes.
  *
  * Note that curve_primes are distinguished just by heuristic check and
  * not by complete conformance check.
  */
 static bool vli_mmod_fast(u64 *result, u64 *product,
               const struct ecc_curve *curve)
 {
     u64 tmp[2 * ECC_MAX_DIGITS];
     const u64 *curve_prime = curve->p;
     const unsigned int ndigits = curve->g.ndigits;
 
     /* All NIST curves have name prefix 'nist_' */
     if (strncmp(curve->name, "nist_", 5) != 0) {
         /* Try to handle Pseudo-Marsenne primes. */
         if (curve_prime[ndigits - 1] == -1ull) {
             vli_mmod_special(result, product, curve_prime,
                      ndigits);
             return true;
         } else if (curve_prime[ndigits - 1] == 1ull << 63 &&
                curve_prime[ndigits - 2] == 0) {
             vli_mmod_special2(result, product, curve_prime,
                       ndigits);
             return true;
         }
         vli_mmod_barrett(result, product, curve_prime, ndigits);
         return true;
     }
 
     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;
     case 6:
         vli_mmod_fast_384(result, product, curve_prime, tmp);
         break;
     default:
         pr_err_ratelimited("ecc: unsupported digits size!\n");
         return false;
     }
 
     return true;
 }
 
 /* Computes result = (left * right) % mod.
  * Assumes that mod is big enough curve order.
  */
 void vli_mod_mult_slow(u64 *result, const u64 *left, const u64 *right,
                const u64 *mod, unsigned int ndigits)
 {
     u64 product[ECC_MAX_DIGITS * 2];
 
     vli_mult(product, left, right, ndigits);
     vli_mmod_slow(result, product, mod, ndigits);
 }
 EXPORT_SYMBOL(vli_mod_mult_slow);
 
 /* Computes result = (left * right) % curve_prime. */
 static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right,
                   const struct ecc_curve *curve)
 {
     u64 product[2 * ECC_MAX_DIGITS];
 
     vli_mult(product, left, right, curve->g.ndigits);
     vli_mmod_fast(result, product, curve);
 }
 
 /* Computes result = left^2 % curve_prime. */
 static void vli_mod_square_fast(u64 *result, const u64 *left,
                 const struct ecc_curve *curve)
 {
     u64 product[2 * ECC_MAX_DIGITS];
 
     vli_square(product, left, curve->g.ndigits);
     vli_mmod_fast(result, product, curve);
 }
 
 #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
  */
 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);
 }
 EXPORT_SYMBOL(vli_mod_inv);
 
 /* ------ Point operations ------ */
 
 /* Returns true if p_point is the point at infinity, false otherwise. */
 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));
 }
 EXPORT_SYMBOL(ecc_point_is_zero);
 
 /* Point multiplication algorithm using Montgomery's ladder with co-Z
  * coordinates. From https://eprint.iacr.org/2011/338.pdf
  */
 
 /* Double in place */
 static void ecc_point_double_jacobian(u64 *x1, u64 *y1, u64 *z1,
                     const struct ecc_curve *curve)
 {
     /* t1 = x, t2 = y, t3 = z */
     u64 t4[ECC_MAX_DIGITS];
     u64 t5[ECC_MAX_DIGITS];
     const u64 *curve_prime = curve->p;
     const unsigned int ndigits = curve->g.ndigits;
 
     if (vli_is_zero(z1, ndigits))
         return;
 
     /* t4 = y1^2 */
     vli_mod_square_fast(t4, y1, curve);
     /* t5 = x1*y1^2 = A */
     vli_mod_mult_fast(t5, x1, t4, curve);
     /* t4 = y1^4 */
     vli_mod_square_fast(t4, t4, curve);
     /* t2 = y1*z1 = z3 */
     vli_mod_mult_fast(y1, y1, z1, curve);
     /* t3 = z1^2 */
     vli_mod_square_fast(z1, z1, curve);
 
     /* 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);
 
     /* 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);
     /* 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);
     /* 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, const struct ecc_curve *curve)
 {
     u64 t1[ECC_MAX_DIGITS];
 
     vli_mod_square_fast(t1, z, curve);      /* z^2 */
     vli_mod_mult_fast(x1, x1, t1, curve);   /* x1 * z^2 */
     vli_mod_mult_fast(t1, t1, z, curve);    /* z^3 */
     vli_mod_mult_fast(y1, y1, t1, curve);   /* 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, const struct ecc_curve *curve)
 {
     u64 z[ECC_MAX_DIGITS];
     const unsigned int ndigits = curve->g.ndigits;
 
     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);
 
     ecc_point_double_jacobian(x1, y1, z, curve);
 
     apply_z(x2, y2, z, curve);
 }
 
 /* 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,
             const struct ecc_curve *curve)
 {
     /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
     u64 t5[ECC_MAX_DIGITS];
     const u64 *curve_prime = curve->p;
     const unsigned int ndigits = curve->g.ndigits;
 
     /* t5 = x2 - x1 */
     vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
     /* t5 = (x2 - x1)^2 = A */
     vli_mod_square_fast(t5, t5, curve);
     /* t1 = x1*A = B */
     vli_mod_mult_fast(x1, x1, t5, curve);
     /* t3 = x2*A = C */
     vli_mod_mult_fast(x2, x2, t5, curve);
     /* t4 = y2 - y1 */
     vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
     /* t5 = (y2 - y1)^2 = D */
     vli_mod_square_fast(t5, y2, curve);
 
     /* 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);
     /* 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);
     /* 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,
             const struct ecc_curve *curve)
 {
     /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
     u64 t5[ECC_MAX_DIGITS];
     u64 t6[ECC_MAX_DIGITS];
     u64 t7[ECC_MAX_DIGITS];
     const u64 *curve_prime = curve->p;
     const unsigned int ndigits = curve->g.ndigits;
 
     /* t5 = x2 - x1 */
     vli_mod_sub(t5, x2, x1, curve_prime, ndigits);
     /* t5 = (x2 - x1)^2 = A */
     vli_mod_square_fast(t5, t5, curve);
     /* t1 = x1*A = B */
     vli_mod_mult_fast(x1, x1, t5, curve);
     /* t3 = x2*A = C */
     vli_mod_mult_fast(x2, x2, t5, curve);
     /* 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);
     /* t6 = B + C */
     vli_mod_add(t6, x1, x2, curve_prime, ndigits);
     /* t3 = (y2 - y1)^2 */
     vli_mod_square_fast(x2, y2, curve);
     /* 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);
     /* t4 = y3 */
     vli_mod_sub(y2, y2, y1, curve_prime, ndigits);
 
     /* t7 = (y2 + y1)^2 = F */
     vli_mod_square_fast(t7, t5, curve);
     /* 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);
     /* 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);
 
     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);
         xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
     }
 
     nb = !vli_test_bit(scalar, 0);
     xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb], curve);
 
     /* 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);
     /* xP * Yb * (X1 - X0) */
     vli_mod_mult_fast(z, z, point->x, curve);
 
     /* 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);
     /* Xb * yP / (xP * Yb * (X1 - X0)) */
     vli_mod_mult_fast(z, z, rx[1 - nb], curve);
     /* End 1/Z calculation */
 
     xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb], curve);
 
     apply_z(rx[0], ry[0], z, curve);
 
     vli_set(result->x, rx[0], ndigits);
     vli_set(result->y, ry[0], ndigits);
 }
 
 /* Computes R = P + Q mod p */
 static void ecc_point_add(const struct ecc_point *result,
            const struct ecc_point *p, const struct ecc_point *q,
            const struct ecc_curve *curve)
 {
     u64 z[ECC_MAX_DIGITS];
     u64 px[ECC_MAX_DIGITS];
     u64 py[ECC_MAX_DIGITS];
     unsigned int ndigits = curve->g.ndigits;
 
     vli_set(result->x, q->x, ndigits);
     vli_set(result->y, q->y, ndigits);
     vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
     vli_set(px, p->x, ndigits);
     vli_set(py, p->y, ndigits);
     xycz_add(px, py, result->x, result->y, curve);
     vli_mod_inv(z, z, curve->p, ndigits);
     apply_z(result->x, result->y, z, curve);
 }
 
 /* Computes R = u1P + u2Q mod p using Shamir's trick.
  * Based on: Kenneth MacKay's micro-ecc (2014).
  */
 void ecc_point_mult_shamir(const struct ecc_point *result,
                const u64 *u1, const struct ecc_point *p,
                const u64 *u2, const struct ecc_point *q,
                const struct ecc_curve *curve)
 {
     u64 z[ECC_MAX_DIGITS];
     u64 sump[2][ECC_MAX_DIGITS];
     u64 *rx = result->x;
     u64 *ry = result->y;
     unsigned int ndigits = curve->g.ndigits;
     unsigned int num_bits;
     struct ecc_point sum = ECC_POINT_INIT(sump[0], sump[1], ndigits);
     const struct ecc_point *points[4];
     const struct ecc_point *point;
     unsigned int idx;
     int i;
 
     ecc_point_add(&sum, p, q, curve);
     points[0] = NULL;
     points[1] = p;
     points[2] = q;
     points[3] = &sum;
 
     num_bits = max(vli_num_bits(u1, ndigits), vli_num_bits(u2, ndigits));
     i = num_bits - 1;
     idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
     point = points[idx];
 
     vli_set(rx, point->x, ndigits);
     vli_set(ry, point->y, ndigits);
     vli_clear(z + 1, ndigits - 1);
     z[0] = 1;
 
     for (--i; i >= 0; i--) {
         ecc_point_double_jacobian(rx, ry, z, curve);
         idx = (!!vli_test_bit(u1, i)) | ((!!vli_test_bit(u2, i)) << 1);
         point = points[idx];
         if (point) {
             u64 tx[ECC_MAX_DIGITS];
             u64 ty[ECC_MAX_DIGITS];
             u64 tz[ECC_MAX_DIGITS];
 
             vli_set(tx, point->x, ndigits);
             vli_set(ty, point->y, ndigits);
             apply_z(tx, ty, z, curve);
             vli_mod_sub(tz, rx, tx, curve->p, ndigits);
             xycz_add(tx, ty, rx, ry, curve);
             vli_mod_mult_fast(z, z, tz, curve);
         }
     }
     vli_mod_inv(z, z, curve->p, ndigits);
     apply_z(rx, ry, z, curve);
 }
 EXPORT_SYMBOL(ecc_point_mult_shamir);
 
 static int __ecc_is_key_valid(const struct ecc_curve *curve,
                   const u64 *private_key, unsigned int ndigits)
 {
     u64 one[ECC_MAX_DIGITS] = { 1, };
     u64 res[ECC_MAX_DIGITS];
 
     if (!private_key)
         return -EINVAL;
 
     if (curve->g.ndigits != ndigits)
         return -EINVAL;
 
     /* Make sure the private key is in the range [2, n-3]. */
     if (vli_cmp(one, private_key, ndigits) != -1)
         return -EINVAL;
     vli_sub(res, curve->n, one, ndigits);
     vli_sub(res, res, one, ndigits);
     if (vli_cmp(res, private_key, ndigits) != 1)
         return -EINVAL;
 
     return 0;
 }
 
 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);
 
     nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
 
     if (private_key_len != nbytes)
         return -EINVAL;
 
     return __ecc_is_key_valid(curve, private_key, ndigits);
 }
 EXPORT_SYMBOL(ecc_is_key_valid);
 
 /*
  * 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;
 
     /* Make sure the private key is in the valid range. */
     if (__ecc_is_key_valid(curve, priv, ndigits))
         return -EINVAL;
 
     ecc_swap_digits(priv, privkey, ndigits);
 
     return 0;
 }
 EXPORT_SYMBOL(ecc_gen_privkey);
 
 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);
 
     /* SP800-56A rev 3 5.6.2.1.3 key check */
     if (ecc_is_pubkey_valid_full(curve, 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;
 }
 EXPORT_SYMBOL(ecc_make_pub_key);
 
 /* SP800-56A section 5.6.2.3.4 partial verification: ephemeral keys only */
 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];
 
     if (WARN_ON(pk->ndigits != curve->g.ndigits))
         return -EINVAL;
 
     /* 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); /* y^2 */
     vli_mod_square_fast(xxx, pk->x, curve); /* x^2 */
     vli_mod_mult_fast(xxx, xxx, pk->x, curve); /* x^3 */
     vli_mod_mult_fast(w, curve->a, pk->x, curve); /* 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;
 }
 EXPORT_SYMBOL(ecc_is_pubkey_valid_partial);
 
 /* SP800-56A section 5.6.2.3.3 full verification */
 int ecc_is_pubkey_valid_full(const struct ecc_curve *curve,
                  struct ecc_point *pk)
 {
     struct ecc_point *nQ;
 
     /* Checks 1 through 3 */
     int ret = ecc_is_pubkey_valid_partial(curve, pk);
 
     if (ret)
         return ret;
 
     /* Check 4: Verify that nQ is the zero point. */
     nQ = ecc_alloc_point(pk->ndigits);
     if (!nQ)
         return -ENOMEM;
 
     ecc_point_mult(nQ, pk, curve->n, NULL, curve, pk->ndigits);
     if (!ecc_point_is_zero(nQ))
         ret = -EINVAL;
 
     ecc_free_point(nQ);
 
     return ret;
 }
 EXPORT_SYMBOL(ecc_is_pubkey_valid_full);
 
 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);
 
     if (ecc_point_is_zero(product)) {
         ret = -EFAULT;
         goto err_validity;
     }
 
     ecc_swap_digits(product->x, secret, ndigits);
 
 err_validity:
     memzero_explicit(priv, sizeof(priv));
     memzero_explicit(rand_z, sizeof(rand_z));
     ecc_free_point(product);
 err_alloc_product:
     ecc_free_point(pk);
 out:
     return ret;
 }
 EXPORT_SYMBOL(crypto_ecdh_shared_secret);
 
 MODULE_LICENSE("Dual BSD/GPL");

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