crypto: ecdh - Add ECDH software support

* Implement ECDH under kpp API
 * Provide ECC software support for curve P-192 and
   P-256.
 * Add kpp test for ECDH with data generated by OpenSSL

Signed-off-by: Salvatore Benedetto <salvatore.benedetto@intel.com>
Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>

1 files changed, 1018 insertions, 0 deletions

diff --git a/crypto/ecc.c b/crypto/ecc.c
new file mode 100644
index 000000000000..9aedec6bbe72
--- /dev/null
+++ b/crypto/ecc.c
@@ -0,0 +1,1018 @@
+/*
+ * 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 "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 * ndigits];
+
+        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!\n");
+                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 * ndigits];
+
+        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 * ndigits];
+
+        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[ndigits], b[ndigits];
+        u64 u[ndigits], v[ndigits];
+        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[ndigits];
+        u64 t5[ndigits];
+
+        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[ndigits];
+
+        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[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_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[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_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[ndigits];
+        u64 t6[ndigits];
+        u64 t7[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_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, u64 *curve_prime,
+                           unsigned int ndigits)
+{
+        /* R0 and R1 */
+        u64 rx[2][ndigits];
+        u64 ry[2][ndigits];
+        u64 z[ndigits];
+        int i, nb;
+        int num_bits = vli_num_bits(scalar, ndigits);
+
+        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 u8 *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((const u64 *)&private_key[0], ndigits))
+                return -EINVAL;
+
+        /* Make sure the private key is in the range [1, n-1]. */
+        if (vli_cmp(curve->n, (const u64 *)&private_key[0], ndigits) != 1)
+                return -EINVAL;
+
+        return 0;
+}
+
+int ecdh_make_pub_key(unsigned int curve_id, unsigned int ndigits,
+                      const u8 *private_key, unsigned int private_key_len,
+                      u8 *public_key, unsigned int public_key_len)
+{
+        int ret = 0;
+        struct ecc_point *pk;
+        u64 priv[ndigits];
+        unsigned int nbytes;
+        const struct ecc_curve *curve = ecc_get_curve(curve_id);
+
+        if (!private_key || !curve) {
+                ret = -EINVAL;
+                goto out;
+        }
+
+        ecc_swap_digits((const u64 *)private_key, priv, ndigits);
+
+        pk = ecc_alloc_point(ndigits);
+        if (!pk) {
+                ret = -ENOMEM;
+                goto out;
+        }
+
+        ecc_point_mult(pk, &curve->g, priv, NULL, curve->p, ndigits);
+        if (ecc_point_is_zero(pk)) {
+                ret = -EAGAIN;
+                goto err_free_point;
+        }
+
+        nbytes = ndigits << ECC_DIGITS_TO_BYTES_SHIFT;
+        ecc_swap_digits(pk->x, (u64 *)public_key, ndigits);
+        ecc_swap_digits(pk->y, (u64 *)&public_key[nbytes], ndigits);
+
+err_free_point:
+        ecc_free_point(pk);
+out:
+        return ret;
+}
+
+int ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
+                       const u8 *private_key, unsigned int private_key_len,
+                       const u8 *public_key, unsigned int public_key_len,
+                       u8 *secret, unsigned int secret_len)
+{
+        int ret = 0;
+        struct ecc_point *product, *pk;
+        u64 priv[ndigits];
+        u64 rand_z[ndigits];
+        unsigned int nbytes;
+        const struct ecc_curve *curve = ecc_get_curve(curve_id);
+
+        if (!private_key || !public_key || !curve) {
+                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;
+        }
+
+        product = ecc_alloc_point(ndigits);
+        if (!product) {
+                ret = -ENOMEM;
+                goto err_alloc_product;
+        }
+
+        ecc_swap_digits((const u64 *)public_key, pk->x, ndigits);
+        ecc_swap_digits((const u64 *)&public_key[nbytes], pk->y, ndigits);
+        ecc_swap_digits((const u64 *)private_key, priv, ndigits);
+
+        ecc_point_mult(product, pk, priv, rand_z, curve->p, ndigits);
+
+        ecc_swap_digits(product->x, (u64 *)secret, ndigits);
+
+        if (ecc_point_is_zero(product))
+                ret = -EFAULT;
+
+        ecc_free_point(product);
+err_alloc_product:
+        ecc_free_point(pk);
+out:
+        return ret;
+}