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;
+}