ecc.c 25.7 KB
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/*
 * 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>
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#include <crypto/rng.h>
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#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,
908
		     const u64 *private_key, unsigned int private_key_len)
909 910 911 912 913 914 915 916 917 918 919 920
{
	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;

921
	if (vli_is_zero(private_key, ndigits))
922 923 924
		return -EINVAL;

	/* Make sure the private key is in the range [1, n-1]. */
925
	if (vli_cmp(curve->n, private_key, ndigits) != 1)
926 927 928 929 930
		return -EINVAL;

	return 0;
}

931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966
/*
 * 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[ndigits];
	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)
		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())
967
		return -EFAULT;
968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985

	err = crypto_rng_get_bytes(crypto_default_rng, (u8 *)priv, nbytes);
	crypto_put_default_rng();
	if (err)
		return err;

	if (vli_is_zero(priv, ndigits))
		return -EINVAL;

	/* Make sure the private key is in the range [1, n-1]. */
	if (vli_cmp(curve->n, priv, ndigits) != 1)
		return -EINVAL;

	ecc_swap_digits(priv, privkey, ndigits);

	return 0;
}

986 987
int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
		     const u64 *private_key, u64 *public_key)
988 989 990 991 992 993 994 995 996 997 998
{
	int ret = 0;
	struct ecc_point *pk;
	u64 priv[ndigits];
	const struct ecc_curve *curve = ecc_get_curve(curve_id);

	if (!private_key || !curve) {
		ret = -EINVAL;
		goto out;
	}

999
	ecc_swap_digits(private_key, priv, ndigits);
1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012

	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;
	}

1013 1014
	ecc_swap_digits(pk->x, public_key, ndigits);
	ecc_swap_digits(pk->y, &public_key[ndigits], ndigits);
1015 1016 1017 1018 1019 1020 1021

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

1022
int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
1023 1024
			      const u64 *private_key, const u64 *public_key,
			      u64 *secret)
1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053
{
	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;
	}

1054 1055 1056
	ecc_swap_digits(public_key, pk->x, ndigits);
	ecc_swap_digits(&public_key[ndigits], pk->y, ndigits);
	ecc_swap_digits(private_key, priv, ndigits);
1057 1058 1059

	ecc_point_mult(product, pk, priv, rand_z, curve->p, ndigits);

1060
	ecc_swap_digits(product->x, secret, ndigits);
1061 1062 1063 1064 1065 1066 1067 1068 1069 1070

	if (ecc_point_is_zero(product))
		ret = -EFAULT;

	ecc_free_point(product);
err_alloc_product:
	ecc_free_point(pk);
out:
	return ret;
}