From: Johan Hedberg <johan.hedberg@xxxxxxxxx> This patch adds a simple ECC library that will act as a fundamental building block for LE Secure Connections. The library has a simple API consisting of two functions: one for generating a public/private key pair and another one for generating a Diffie-Hellman key from a local private key and a remote public key. The code has been taken from https://github.com/kmackay/easy-ecc and modified to conform with the kernel coding style. Signed-off-by: Johan Hedberg <johan.hedberg@xxxxxxxxx> --- net/bluetooth/Makefile | 2 +- net/bluetooth/ecc.c | 816 +++++++++++++++++++++++++++++++++++++++++++++++++ net/bluetooth/ecc.h | 54 ++++ 3 files changed, 871 insertions(+), 1 deletion(-) create mode 100644 net/bluetooth/ecc.c create mode 100644 net/bluetooth/ecc.h diff --git a/net/bluetooth/Makefile b/net/bluetooth/Makefile index 886e9aa3ecf1..a5432a6a0ae6 100644 --- a/net/bluetooth/Makefile +++ b/net/bluetooth/Makefile @@ -13,6 +13,6 @@ bluetooth_6lowpan-y := 6lowpan.o bluetooth-y := af_bluetooth.o hci_core.o hci_conn.o hci_event.o mgmt.o \ hci_sock.o hci_sysfs.o l2cap_core.o l2cap_sock.o smp.o sco.o lib.o \ - a2mp.o amp.o + a2mp.o amp.o ecc.o subdir-ccflags-y += -D__CHECK_ENDIAN__ diff --git a/net/bluetooth/ecc.c b/net/bluetooth/ecc.c new file mode 100644 index 000000000000..e1709f8467ac --- /dev/null +++ b/net/bluetooth/ecc.c @@ -0,0 +1,816 @@ +/* + * 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 "ecc.h" + +/* 256-bit curve */ +#define ECC_BYTES 32 + +#define MAX_TRIES 16 + +/* Number of u64's needed */ +#define NUM_ECC_DIGITS (ECC_BYTES / 8) + +struct ecc_point { + u64 x[NUM_ECC_DIGITS]; + u64 y[NUM_ECC_DIGITS]; +}; + +typedef struct { + u64 m_low; + u64 m_high; +} uint128_t; + +#define CURVE_P_32 { 0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull, \ + 0x0000000000000000ull, 0xFFFFFFFF00000001ull } + +#define CURVE_G_32 { \ + { 0xF4A13945D898C296ull, 0x77037D812DEB33A0ull, \ + 0xF8BCE6E563A440F2ull, 0x6B17D1F2E12C4247ull }, \ + { 0xCBB6406837BF51F5ull, 0x2BCE33576B315ECEull, \ + 0x8EE7EB4A7C0F9E16ull, 0x4FE342E2FE1A7F9Bull } \ +} + +#define CURVE_N_32 { 0xF3B9CAC2FC632551ull, 0xBCE6FAADA7179E84ull, \ + 0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFF00000000ull } + +static u64 curve_p[NUM_ECC_DIGITS] = CURVE_P_32; +static struct ecc_point curve_g = CURVE_G_32; +static u64 curve_n[NUM_ECC_DIGITS] = CURVE_N_32; + +static void vli_clear(u64 *vli) +{ + int i; + + for (i = 0; i < NUM_ECC_DIGITS; i++) + vli[i] = 0; +} + +/* Returns true if vli == 0, false otherwise. */ +static bool vli_is_zero(const u64 *vli) +{ + int i; + + for (i = 0; i < NUM_ECC_DIGITS; 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) +{ + 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 = NUM_ECC_DIGITS - 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 i, num_digits; + u64 digit; + + num_digits = vli_num_digits(vli); + 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) +{ + int i; + + for (i = 0; i < NUM_ECC_DIGITS; i++) + dest[i] = src[i]; +} + +/* Returns sign of left - right. */ +static int vli_cmp(const u64 *left, const u64 *right) +{ + int i; + + for (i = NUM_ECC_DIGITS - 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) +{ + u64 carry = 0; + int i; + + for (i = 0; i < NUM_ECC_DIGITS; 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) +{ + u64 *end = vli; + u64 carry = 0; + + vli += NUM_ECC_DIGITS; + + 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) +{ + u64 carry = 0; + int i; + + for (i = 0; i < NUM_ECC_DIGITS; 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) +{ + u64 borrow = 0; + int i; + + for (i = 0; i < NUM_ECC_DIGITS; 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) +{ + 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 < NUM_ECC_DIGITS * 2 - 1; k++) { + unsigned int min; + + if (k < NUM_ECC_DIGITS) + min = 0; + else + min = (k + 1) - NUM_ECC_DIGITS; + + for (i = min; i <= k && i < NUM_ECC_DIGITS; 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[NUM_ECC_DIGITS * 2 - 1] = r01.m_low; +} + +static void vli_square(u64 *result, const u64 *left) +{ + uint128_t r01 = { 0, 0 }; + u64 r2 = 0; + int i, k; + + for (k = 0; k < NUM_ECC_DIGITS * 2 - 1; k++) { + unsigned int min; + + if (k < NUM_ECC_DIGITS) + min = 0; + else + min = (k + 1) - NUM_ECC_DIGITS; + + 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[NUM_ECC_DIGITS * 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) +{ + u64 carry; + + carry = vli_add(result, left, right); + + /* result > mod (result = mod + remainder), so subtract mod to + * get remainder. + */ + if (carry || vli_cmp(result, mod) >= 0) + vli_sub(result, result, mod); +} + +/* 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) +{ + u64 borrow = vli_sub(result, left, right); + + /* 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); +} + +/* Computes result = product % curve_p + from http://www.nsa.gov/ia/_files/nist-routines.pdf */ +static void vli_mmod_fast(u64 *result, const u64 *product) +{ + u64 tmp[NUM_ECC_DIGITS]; + int carry; + + /* t */ + vli_set(result, product); + + /* s1 */ + tmp[0] = 0; + tmp[1] = product[5] & 0xffffffff00000000ull; + tmp[2] = product[6]; + tmp[3] = product[7]; + carry = vli_lshift(tmp, tmp, 1); + carry += vli_add(result, result, tmp); + + /* 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); + carry += vli_add(result, result, tmp); + + /* s3 */ + tmp[0] = product[4]; + tmp[1] = product[5] & 0xffffffff; + tmp[2] = 0; + tmp[3] = product[7]; + carry += vli_add(result, result, tmp); + + /* 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); + + /* 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); + + /* 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); + + /* 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); + + /* 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); + + if (carry < 0) { + do { + carry += vli_add(result, result, curve_p); + } while (carry < 0); + } else { + while (carry || vli_cmp(curve_p, result) != 1) + carry -= vli_sub(result, result, curve_p); + } +} + +/* Computes result = (left * right) % curve_p. */ +static void vli_mod_mult_fast(u64 *result, const u64 *left, const u64 *right) +{ + u64 product[2 * NUM_ECC_DIGITS]; + + vli_mult(product, left, right); + vli_mmod_fast(result, product); +} + +/* Computes result = left^2 % curve_p. */ +static void vli_mod_square_fast(u64 *result, const u64 *left) +{ + u64 product[2 * NUM_ECC_DIGITS]; + + vli_square(product, left); + vli_mmod_fast(result, product); +} + +#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) +{ + u64 a[NUM_ECC_DIGITS], b[NUM_ECC_DIGITS]; + u64 u[NUM_ECC_DIGITS], v[NUM_ECC_DIGITS]; + u64 carry; + int cmp_result; + + if (vli_is_zero(input)) { + vli_clear(result); + return; + } + + vli_set(a, input); + vli_set(b, mod); + vli_clear(u); + u[0] = 1; + vli_clear(v); + + while ((cmp_result = vli_cmp(a, b)) != 0) { + carry = 0; + + if (EVEN(a)) { + vli_rshift1(a); + + if (!EVEN(u)) + carry = vli_add(u, u, mod); + + vli_rshift1(u); + if (carry) + u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull; + } else if (EVEN(b)) { + vli_rshift1(b); + + if (!EVEN(v)) + carry = vli_add(v, v, mod); + + vli_rshift1(v); + if (carry) + v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull; + } else if (cmp_result > 0) { + vli_sub(a, a, b); + vli_rshift1(a); + + if (vli_cmp(u, v) < 0) + vli_add(u, u, mod); + + vli_sub(u, u, v); + if (!EVEN(u)) + carry = vli_add(u, u, mod); + + vli_rshift1(u); + if (carry) + u[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull; + } else { + vli_sub(b, b, a); + vli_rshift1(b); + + if (vli_cmp(v, u) < 0) + vli_add(v, v, mod); + + vli_sub(v, v, u); + if (!EVEN(v)) + carry = vli_add(v, v, mod); + + vli_rshift1(v); + if (carry) + v[NUM_ECC_DIGITS - 1] |= 0x8000000000000000ull; + } + } + + vli_set(result, u); +} + +/* ------ 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) && vli_is_zero(point->y)); +} + +/* 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) +{ + /* t1 = x, t2 = y, t3 = z */ + u64 t4[NUM_ECC_DIGITS]; + u64 t5[NUM_ECC_DIGITS]; + + if (vli_is_zero(z1)) + return; + + vli_mod_square_fast(t4, y1); /* t4 = y1^2 */ + vli_mod_mult_fast(t5, x1, t4); /* t5 = x1*y1^2 = A */ + vli_mod_square_fast(t4, t4); /* t4 = y1^4 */ + vli_mod_mult_fast(y1, y1, z1); /* t2 = y1*z1 = z3 */ + vli_mod_square_fast(z1, z1); /* t3 = z1^2 */ + + vli_mod_add(x1, x1, z1, curve_p); /* t1 = x1 + z1^2 */ + vli_mod_add(z1, z1, z1, curve_p); /* t3 = 2*z1^2 */ + vli_mod_sub(z1, x1, z1, curve_p); /* t3 = x1 - z1^2 */ + vli_mod_mult_fast(x1, x1, z1); /* t1 = x1^2 - z1^4 */ + + vli_mod_add(z1, x1, x1, curve_p); /* t3 = 2*(x1^2 - z1^4) */ + vli_mod_add(x1, x1, z1, curve_p); /* t1 = 3*(x1^2 - z1^4) */ + if (vli_test_bit(x1, 0)) { + u64 carry = vli_add(x1, x1, curve_p); + vli_rshift1(x1); + x1[NUM_ECC_DIGITS - 1] |= carry << 63; + } else { + vli_rshift1(x1); + } + /* t1 = 3/2*(x1^2 - z1^4) = B */ + + vli_mod_square_fast(z1, x1); /* t3 = B^2 */ + vli_mod_sub(z1, z1, t5, curve_p); /* t3 = B^2 - A */ + vli_mod_sub(z1, z1, t5, curve_p); /* t3 = B^2 - 2A = x3 */ + vli_mod_sub(t5, t5, z1, curve_p); /* t5 = A - x3 */ + vli_mod_mult_fast(x1, x1, t5); /* t1 = B * (A - x3) */ + vli_mod_sub(t4, x1, t4, curve_p); /* t4 = B * (A - x3) - y1^4 = y3 */ + + vli_set(x1, z1); + vli_set(z1, y1); + vli_set(y1, t4); +} + +/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ +static void apply_z(u64 *x1, u64 *y1, u64 *z) +{ + u64 t1[NUM_ECC_DIGITS]; + + vli_mod_square_fast(t1, z); /* z^2 */ + vli_mod_mult_fast(x1, x1, t1); /* x1 * z^2 */ + vli_mod_mult_fast(t1, t1, z); /* z^3 */ + vli_mod_mult_fast(y1, y1, t1); /* 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 z[NUM_ECC_DIGITS]; + + vli_set(x2, x1); + vli_set(y2, y1); + + vli_clear(z); + z[0] = 1; + + if (p_initial_z) + vli_set(z, p_initial_z); + + apply_z(x1, y1, z); + + ecc_point_double_jacobian(x1, y1, z); + + apply_z(x2, y2, z); +} + +/* 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) +{ + /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ + u64 t5[NUM_ECC_DIGITS]; + + vli_mod_sub(t5, x2, x1, curve_p); /* t5 = x2 - x1 */ + vli_mod_square_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */ + vli_mod_mult_fast(x1, x1, t5); /* t1 = x1*A = B */ + vli_mod_mult_fast(x2, x2, t5); /* t3 = x2*A = C */ + vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y2 - y1 */ + vli_mod_square_fast(t5, y2); /* t5 = (y2 - y1)^2 = D */ + + vli_mod_sub(t5, t5, x1, curve_p); /* t5 = D - B */ + vli_mod_sub(t5, t5, x2, curve_p); /* t5 = D - B - C = x3 */ + vli_mod_sub(x2, x2, x1, curve_p); /* t3 = C - B */ + vli_mod_mult_fast(y1, y1, x2); /* t2 = y1*(C - B) */ + vli_mod_sub(x2, x1, t5, curve_p); /* t3 = B - x3 */ + vli_mod_mult_fast(y2, y2, x2); /* t4 = (y2 - y1)*(B - x3) */ + vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y3 */ + + vli_set(x2, t5); +} + +/* 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) +{ + /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ + u64 t5[NUM_ECC_DIGITS]; + u64 t6[NUM_ECC_DIGITS]; + u64 t7[NUM_ECC_DIGITS]; + + vli_mod_sub(t5, x2, x1, curve_p); /* t5 = x2 - x1 */ + vli_mod_square_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */ + vli_mod_mult_fast(x1, x1, t5); /* t1 = x1*A = B */ + vli_mod_mult_fast(x2, x2, t5); /* t3 = x2*A = C */ + vli_mod_add(t5, y2, y1, curve_p); /* t4 = y2 + y1 */ + vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y2 - y1 */ + + vli_mod_sub(t6, x2, x1, curve_p); /* t6 = C - B */ + vli_mod_mult_fast(y1, y1, t6); /* t2 = y1 * (C - B) */ + vli_mod_add(t6, x1, x2, curve_p); /* t6 = B + C */ + vli_mod_square_fast(x2, y2); /* t3 = (y2 - y1)^2 */ + vli_mod_sub(x2, x2, t6, curve_p); /* t3 = x3 */ + + vli_mod_sub(t7, x1, x2, curve_p); /* t7 = B - x3 */ + vli_mod_mult_fast(y2, y2, t7); /* t4 = (y2 - y1)*(B - x3) */ + vli_mod_sub(y2, y2, y1, curve_p); /* t4 = y3 */ + + vli_mod_square_fast(t7, t5); /* t7 = (y2 + y1)^2 = F */ + vli_mod_sub(t7, t7, t6, curve_p); /* t7 = x3' */ + vli_mod_sub(t6, t7, x1, curve_p); /* t6 = x3' - B */ + vli_mod_mult_fast(t6, t6, t5); /* t6 = (y2 + y1)*(x3' - B) */ + vli_mod_sub(y1, t6, y1, curve_p); /* t2 = y3' */ + + vli_set(x1, t7); +} + +static void ecc_point_mult(struct ecc_point *result, + const struct ecc_point *point, u64 *scalar, + u64 *initial_z, int num_bits) +{ + /* R0 and R1 */ + u64 rx[2][NUM_ECC_DIGITS]; + u64 ry[2][NUM_ECC_DIGITS]; + u64 z[NUM_ECC_DIGITS]; + int i, nb; + + vli_set(rx[1], point->x); + vli_set(ry[1], point->y); + + xycz_initial_double(rx[1], ry[1], rx[0], ry[0], initial_z); + + 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]); + xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb]); + } + + nb = !vli_test_bit(scalar, 0); + xycz_add_c(rx[1 - nb], ry[1 - nb], rx[nb], ry[nb]); + + /* Find final 1/Z value. */ + vli_mod_sub(z, rx[1], rx[0], curve_p); /* X1 - X0 */ + vli_mod_mult_fast(z, z, ry[1 - nb]); /* Yb * (X1 - X0) */ + vli_mod_mult_fast(z, z, point->x); /* xP * Yb * (X1 - X0) */ + vli_mod_inv(z, z, curve_p); /* 1 / (xP * Yb * (X1 - X0)) */ + vli_mod_mult_fast(z, z, point->y); /* yP / (xP * Yb * (X1 - X0)) */ + vli_mod_mult_fast(z, z, rx[1 - nb]); /* Xb * yP / (xP * Yb * (X1 - X0)) */ + /* End 1/Z calculation */ + + xycz_add(rx[nb], ry[nb], rx[1 - nb], ry[1 - nb]); + + apply_z(rx[0], ry[0], z); + + vli_set(result->x, rx[0]); + vli_set(result->y, ry[0]); +} + +static void ecc_bytes2native(const u8 bytes[ECC_BYTES], + u64 native[NUM_ECC_DIGITS]) +{ + int i; + + for (i = 0; i < NUM_ECC_DIGITS; i++) { + const u8 *digit = bytes + 8 * (NUM_ECC_DIGITS - 1 - i); + + native[NUM_ECC_DIGITS - 1 - i] = + ((u64) digit[0] << 0) | + ((u64) digit[1] << 8) | + ((u64) digit[2] << 16) | + ((u64) digit[3] << 24) | + ((u64) digit[4] << 32) | + ((u64) digit[5] << 40) | + ((u64) digit[6] << 48) | + ((u64) digit[7] << 56); + } +} + +static void ecc_native2bytes(const u64 native[NUM_ECC_DIGITS], + u8 bytes[ECC_BYTES]) +{ + int i; + + for (i = 0; i < NUM_ECC_DIGITS; i++) { + u8 *digit = bytes + 8 * (NUM_ECC_DIGITS - 1 - i); + + digit[0] = native[NUM_ECC_DIGITS - 1 - i] >> 0; + digit[1] = native[NUM_ECC_DIGITS - 1 - i] >> 8; + digit[2] = native[NUM_ECC_DIGITS - 1 - i] >> 16; + digit[3] = native[NUM_ECC_DIGITS - 1 - i] >> 24; + digit[4] = native[NUM_ECC_DIGITS - 1 - i] >> 32; + digit[5] = native[NUM_ECC_DIGITS - 1 - i] >> 40; + digit[6] = native[NUM_ECC_DIGITS - 1 - i] >> 48; + digit[7] = native[NUM_ECC_DIGITS - 1 - i] >> 56; + } +} + +bool ecc_make_key(u8 public_key[64], u8 private_key[32]) +{ + struct ecc_point pk; + u64 priv[NUM_ECC_DIGITS]; + unsigned int tries = 0; + + do { + if (tries++ >= MAX_TRIES) + return false; + + get_random_bytes(priv, ECC_BYTES); + + if (vli_is_zero(priv)) + continue; + + /* Make sure the private key is in the range [1, n-1]. */ + if (vli_cmp(curve_n, priv) != 1) + continue; + + ecc_point_mult(&pk, &curve_g, priv, NULL, vli_num_bits(priv)); + } while (ecc_point_is_zero(&pk)); + + ecc_native2bytes(priv, private_key); + ecc_native2bytes(pk.x, public_key); + ecc_native2bytes(pk.y, &public_key[32]); + + return true; +} + +bool ecdh_shared_secret(const u8 public_key[64], const u8 private_key[32], + u8 secret[32]) +{ + u64 priv[NUM_ECC_DIGITS]; + u64 rand[NUM_ECC_DIGITS]; + struct ecc_point product, pk; + + get_random_bytes(rand, ECC_BYTES); + + ecc_bytes2native(public_key, pk.x); + ecc_bytes2native(&public_key[32], pk.y); + ecc_bytes2native(private_key, priv); + + ecc_point_mult(&product, &pk, priv, rand, vli_num_bits(priv)); + + ecc_native2bytes(product.x, secret); + + return !ecc_point_is_zero(&product); +} diff --git a/net/bluetooth/ecc.h b/net/bluetooth/ecc.h new file mode 100644 index 000000000000..8d6a2f4d1905 --- /dev/null +++ b/net/bluetooth/ecc.h @@ -0,0 +1,54 @@ +/* + * 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. + */ + +/* Create a public/private key pair. + * Outputs: + * public_key - Will be filled in with the public key. + * private_key - Will be filled in with the private key. + * + * Returns true if the key pair was generated successfully, false + * if an error occurred. The keys are with the LSB first. + */ +bool ecc_make_key(u8 public_key[64], u8 private_key[32]); + +/* Compute a shared secret given your secret key and someone else's + * public key. + * Note: It is recommended that you hash the result of ecdh_shared_secret + * before using it for symmetric encryption or HMAC. + * + * Inputs: + * public_key - The public key of the remote party + * private_key - Your private key. + * + * Outputs: + * secret - Will be filled in with the shared secret value. + * + * Returns true if the shared secret was generated successfully, false + * if an error occurred. Both input and output parameters are with the + * LSB first. + */ +bool ecdh_shared_secret(const u8 public_key[64], const u8 private_key[32], + u8 secret[32]); -- 2.1.0 -- To unsubscribe from this list: send the line "unsubscribe linux-bluetooth" in the body of a message to majordomo@xxxxxxxxxxxxxxx More majordomo info at http://vger.kernel.org/majordomo-info.html
