/* Copyright (C) 2022-2024 Andreas Shimokawa
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This file is part of Gadgetbridge.
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Gadgetbridge is free software: you can redistribute it and/or modify
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it under the terms of the GNU Affero General Public License as published
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by the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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Gadgetbridge is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Affero General Public License for more details.
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You should have received a copy of the GNU Affero General Public License
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along with this program. If not, see <https://www.gnu.org/licenses/>. */
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/*
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This class is a really dumb pure java port of tiny-EDCH from here
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https://github.com/kokke/tiny-ECDH-c/
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What I did:
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- remove all curves except B163 to make porting easier
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- port to java with brain switched off
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- fix the "java has no unsigned" bugs
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- add some helpers to convert int[] to byte[] and back because java has no casts
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The result is ugly, no one would write such crappy code from scratch, but I tried to
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keep it as close to the C code as possible to prevent bugs. Since I did not know what
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I was doing.
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*/
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package nodomain.freeyourgadget.gadgetbridge.util;
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public class ECDH_B163 {
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static final int CURVE_DEGREE = 163;
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static final int ECC_PRV_KEY_SIZE = 24;
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static final int ECC_PUB_KEY_SIZE = 2 * ECC_PRV_KEY_SIZE;
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/* margin for overhead needed in intermediate calculations */
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static final int BITVEC_MARGIN = 3;
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static final int BITVEC_NBITS = (CURVE_DEGREE + BITVEC_MARGIN);
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static final int BITVEC_NWORDS = ((BITVEC_NBITS + 31) / 32);
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static final int BITVEC_NBYTES = (4 * BITVEC_NWORDS);
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/******************************************************************************/
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/* Here the curve parameters are defined. */
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/* NIST B-163 */
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static final int[] polynomial = {0x000000c9, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000008};
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static final int[] coeff_b = {0x4a3205fd, 0x512f7874, 0x1481eb10, 0xb8c953ca, 0x0a601907, 0x00000002};
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static final int[] base_x = {0xe8343e36, 0xd4994637, 0xa0991168, 0x86a2d57e, 0xf0eba162, 0x00000003};
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static final int[] base_y = {0x797324f1, 0xb11c5c0c, 0xa2cdd545, 0x71a0094f, 0xd51fbc6c, 0x00000000};
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static final int[] base_order = {0xa4234c33, 0x77e70c12, 0x000292fe, 0x00000000, 0x00000000, 0x00000004};
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/*************************************************************************************************/
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/* Private / static functions: */
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/* some basic bit-manipulation routines that act on bit-vectors follow */
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static int bitvec_get_bit(final int[] x, final int idx) {
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return (int) ((((((long) x[idx / 32] & 0xffffffffL) >> (idx & 31)) & 1)));
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}
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static void bitvec_clr_bit(final int[] x, final int idx) {
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x[idx / 32] &= ~(1 << (idx & 31));
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}
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static void bitvec_copy(int[] x, int[] y) {
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int i;
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for (i = 0; i < BITVEC_NWORDS; ++i) {
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x[i] = y[i];
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}
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}
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static void bitvec_swap(int[] x, int[] y) {
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int[] tmp = new int[BITVEC_NWORDS];
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bitvec_copy(tmp, x);
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bitvec_copy(x, y);
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bitvec_copy(y, tmp);
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}
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/* fast version of equality test */
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static boolean bitvec_equal(final int[] x, final int[] y) {
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int i;
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for (i = 0; i < BITVEC_NWORDS; ++i) {
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if (x[i] != y[i]) {
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return false;
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}
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}
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return true;
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}
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static void bitvec_set_zero(int[] x) {
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int i;
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for (i = 0; i < BITVEC_NWORDS; ++i) {
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x[i] = 0;
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}
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}
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/* fast implementation */
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static boolean bitvec_is_zero(final int[] x) {
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int i = 0;
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while (i < BITVEC_NWORDS) {
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if (x[i] != 0) {
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break;
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}
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i += 1;
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}
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return (i == BITVEC_NWORDS);
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}
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/* return the number of the highest one-bit + 1 */
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static int bitvec_degree(final int[] x) {
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int i = BITVEC_NWORDS * 32;
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/* Start at the back of the vector (MSB) */
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int y = BITVEC_NWORDS;
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/* Skip empty / zero words */
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while ((i > 0)
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&& (x[--y] == 0)) {
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i -= 32;
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}
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/* Run through rest if count is not multiple of bitsize of DTYPE */
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if (i != 0) {
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int u32mask = ((int) 1 << 31);
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while (((x[y]) & u32mask) == 0) {
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u32mask = (int) (((long) u32mask & 0xffffffffL) >> 1);
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i -= 1;
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}
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}
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return i;
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}
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/* left-shift by 'count' digits */
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static void bitvec_lshift(int[] x, final int[] y, int nbits) {
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int nwords = (nbits / 32);
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/* Shift whole words first if nwords > 0 */
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int i, j;
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for (i = 0; i < nwords; ++i) {
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/* Zero-initialize from least-significant word until offset reached */
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x[i] = 0;
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}
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j = 0;
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/* Copy to x output */
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while (i < BITVEC_NWORDS) {
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x[i] = y[j];
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i += 1;
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j += 1;
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}
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/* Shift the rest if count was not multiple of bitsize of DTYPE */
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nbits &= 31;
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if (nbits != 0) {
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/* Left shift rest */
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for (i = (BITVEC_NWORDS - 1); i > 0; --i) {
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x[i] = (int) (((long) (x[i]) << nbits) | (((long) x[i - 1] & 0xffffffffL) >> (32 - nbits)));
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}
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x[0] = (int) ((long) (x[0]) << nbits);
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}
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}
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/*************************************************************************************************/
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/*
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* Code that does arithmetic on bit-vectors in the Galois Field
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* GF(2^CURVE_DEGREE).
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*/
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/*************************************************************************************************/
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static void gf2field_set_one(int[] x) {
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/* Set first word to one */
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x[0] = 1;
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/* .. and the rest to zero */
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int i;
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for (i = 1; i < BITVEC_NWORDS; ++i) {
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x[i] = 0;
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}
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}
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/* fastest check if x == 1 */
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static boolean gf2field_is_one(int[] x) {
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/* Check if first word == 1 */
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if (x[0] != 1) {
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return false;
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}
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/* ...and if rest of words == 0 */
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int i;
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for (i = 1; i < BITVEC_NWORDS; ++i) {
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if (x[i] != 0) {
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break;
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}
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}
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return (i == BITVEC_NWORDS);
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}
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/* galois field(2^m) addition is modulo 2, so XOR is used instead - 'z := a + b' */
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static void gf2field_add(int[] z, final int[] x, final int[] y) {
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int i;
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for (i = 0; i < BITVEC_NWORDS; ++i) {
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z[i] = (x[i] ^ y[i]);
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}
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}
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/* increment element */
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static void gf2field_inc(int[] x) {
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x[0] ^= 1;
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}
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/* field multiplication 'z := (x * y)' */
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static void gf2field_mul(int[] z, final int[] x, final int[] y) {
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int i;
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int[] tmp = new int[BITVEC_NWORDS];
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assert (z != y);
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bitvec_copy(tmp, x);
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/* LSB set? Then start with x */
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if (bitvec_get_bit(y, 0) != 0) {
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bitvec_copy(z, x);
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} else /* .. or else start with zero */ {
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bitvec_set_zero(z);
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}
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/* Then add 2^i * x for the rest */
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for (i = 1; i < CURVE_DEGREE; ++i) {
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/* lshift 1 - doubling the value of tmp */
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bitvec_lshift(tmp, tmp, 1);
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/* Modulo reduction polynomial if degree(tmp) > CURVE_DEGREE */
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if (bitvec_get_bit(tmp, CURVE_DEGREE) != 0) {
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gf2field_add(tmp, tmp, polynomial);
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}
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/* Add 2^i * tmp if this factor in y is non-zero */
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if (bitvec_get_bit(y, i) != 0) {
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gf2field_add(z, z, tmp);
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}
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}
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}
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/* field inversion 'z := 1/x' */
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static void gf2field_inv(int[] z, final int[] x) {
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int[] u = new int[BITVEC_NWORDS];
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int[] v = new int[BITVEC_NWORDS];
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int[] g = new int[BITVEC_NWORDS];
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int[] h = new int[BITVEC_NWORDS];
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int i;
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bitvec_copy(u, x);
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bitvec_copy(v, polynomial);
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bitvec_set_zero(g);
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gf2field_set_one(z);
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while (!gf2field_is_one(u)) {
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i = (bitvec_degree(u) - bitvec_degree(v));
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if (i < 0) {
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bitvec_swap(u, v);
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bitvec_swap(g, z);
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i = -i;
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}
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bitvec_lshift(h, v, i);
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gf2field_add(u, u, h);
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bitvec_lshift(h, g, i);
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gf2field_add(z, z, h);
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}
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}
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/*************************************************************************************************/
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/*
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* The following code takes care of Galois-Field arithmetic.
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* Elliptic curve points are represented by pairs (x,y) of bitvec_t.
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* It is assumed that curve coefficient 'a' is {0,1}
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* This is the case for all NIST binary curves.
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* Coefficient 'b' is given in 'coeff_b'.
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* '(base_x, base_y)' is a point that generates a large prime order group.
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*/
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/*************************************************************************************************/
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static void gf2point_copy(int[] x1, int[] y1, final int[] x2, final int[] y2) {
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bitvec_copy(x1, x2);
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bitvec_copy(y1, y2);
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}
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static void gf2point_set_zero(int[] x, int[] y) {
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bitvec_set_zero(x);
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bitvec_set_zero(y);
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}
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static boolean gf2point_is_zero(final int[] x, final int[] y) {
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return (bitvec_is_zero(x)
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&& bitvec_is_zero(y));
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}
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/* double the point (x,y) */
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static void gf2point_double(int[] x, int[] y) {
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/* iff P = O (zero or infinity): 2 * P = P */
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if (bitvec_is_zero(x)) {
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bitvec_set_zero(y);
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} else {
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int[] l = new int[BITVEC_NWORDS];
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gf2field_inv(l, x);
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gf2field_mul(l, l, y);
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gf2field_add(l, l, x);
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gf2field_mul(y, x, x);
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gf2field_mul(x, l, l);
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gf2field_inc(l);
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gf2field_add(x, x, l);
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gf2field_mul(l, l, x);
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gf2field_add(y, y, l);
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}
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}
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/* add two points together (x1, y1) := (x1, y1) + (x2, y2) */
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static void gf2point_add(int[] x1, int[] y1, final int[] x2, final int[] y2) {
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if (!gf2point_is_zero(x2, y2)) {
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if (gf2point_is_zero(x1, y1)) {
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gf2point_copy(x1, y1, x2, y2);
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} else {
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if (bitvec_equal(x1, x2)) {
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if (bitvec_equal(y1, y2)) {
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gf2point_double(x1, y1);
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} else {
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gf2point_set_zero(x1, y1);
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}
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} else {
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/* Arithmetic with temporary variables */
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int[] a = new int[BITVEC_NWORDS];
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int[] b = new int[BITVEC_NWORDS];
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int[] c = new int[BITVEC_NWORDS];
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int[] d = new int[BITVEC_NWORDS];
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gf2field_add(a, y1, y2);
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gf2field_add(b, x1, x2);
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gf2field_inv(c, b);
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gf2field_mul(c, c, a);
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gf2field_mul(d, c, c);
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gf2field_add(d, d, c);
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gf2field_add(d, d, b);
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gf2field_inc(d);
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gf2field_add(x1, x1, d);
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gf2field_mul(a, x1, c);
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gf2field_add(a, a, d);
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gf2field_add(y1, y1, a);
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bitvec_copy(x1, d);
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}
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}
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}
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}
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/* point multiplication via double-and-add algorithm */
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static void gf2point_mul(int[] x, int[] y, final int[] exp) {
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int[] tmpx = new int[BITVEC_NWORDS];
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int[] tmpy = new int[BITVEC_NWORDS];
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int i;
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int nbits = bitvec_degree(exp);
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gf2point_set_zero(tmpx, tmpy);
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for (i = (nbits - 1); i >= 0; --i) {
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gf2point_double(tmpx, tmpy);
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if (bitvec_get_bit(exp, i) != 0) {
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gf2point_add(tmpx, tmpy, x, y);
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}
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}
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gf2point_copy(x, y, tmpx, tmpy);
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}
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/* check if y^2 + x*y = x^3 + a*x^2 + coeff_b holds */
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static boolean gf2point_on_curve(final int[] x, final int[] y) {
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int[] a = new int[BITVEC_NWORDS];
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int[] b = new int[BITVEC_NWORDS];
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if (gf2point_is_zero(x, y)) {
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return false;
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} else {
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gf2field_mul(a, x, x);
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gf2field_mul(b, a, x);
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gf2field_add(a, a, b);
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gf2field_add(a, a, coeff_b);
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gf2field_mul(b, y, y);
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gf2field_add(a, a, b);
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gf2field_mul(b, x, y);
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return bitvec_equal(a, b);
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}
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}
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// helper needed for C->Java conversion (Java cant cast pointers)
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static int[] bytes_to_int(byte[] bytes, int offset) {
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int[] value = new int[BITVEC_NWORDS];
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int byteptr = offset;
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for (int i = 0; i < BITVEC_NWORDS; i++) {
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value[i] = ((bytes[byteptr++] & 0xff)) | ((bytes[byteptr++] & 0xff) << 8) | ((bytes[byteptr++] & 0xff) << 16) | ((bytes[byteptr++] & 0xff) << 24);
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}
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return value;
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}
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// helper needed for C->Java conversion (Java cant cast pointers)
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static void ints_to_bytes(byte[] bytes, int[] ints, int offset) {
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int byteptr = offset;
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for (int i = 0; i < BITVEC_NWORDS; i++) {
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bytes[byteptr++] = (byte) (ints[i] & 0x000000ff);
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bytes[byteptr++] = (byte) ((ints[i] & 0x0000ff00) >> 8);
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bytes[byteptr++] = (byte) ((ints[i] & 0x00ff0000) >> 16);
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bytes[byteptr++] = (byte) ((ints[i] & 0xff000000) >> 24);
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}
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}
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/*************************************************************************************************/
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/*
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* Elliptic Curve Diffie-Hellman key exchange protocol.
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*/
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/*************************************************************************************************/
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/* NOTE: private should contain random data a-priori! */
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static boolean ecdh_generate_keys(byte[] public_key, byte[] private_key) {
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int[] private_key_int32 = bytes_to_int(private_key, 0);
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int[] public_key_int32_1 = bytes_to_int(public_key, 0);
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int[] public_key_int32_2 = bytes_to_int(public_key, BITVEC_NBYTES);
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/* Get copy of "base" point 'G' */
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gf2point_copy(public_key_int32_1, public_key_int32_2, base_x, base_y);
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/* Abort key generation if random number is too small */
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if (bitvec_degree(private_key_int32) < (CURVE_DEGREE / 2)) {
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return false;
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} else {
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/* Clear bits > CURVE_DEGREE in highest word to satisfy constraint 1 <= exp < n. */
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int nbits = bitvec_degree(base_order);
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int i;
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for (i = (nbits - 1); i < (BITVEC_NWORDS * 32); ++i) {
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bitvec_clr_bit(private_key_int32, i);
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}
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/* Multiply base-point with scalar (private-key) */
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gf2point_mul(public_key_int32_1, public_key_int32_2, private_key_int32);
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ints_to_bytes(public_key, public_key_int32_1, 0);
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ints_to_bytes(public_key, public_key_int32_2, BITVEC_NBYTES);
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return true;
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}
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}
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static boolean ecdh_shared_secret(byte[] private_key, byte[] others_pub, byte[] output) {
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int[] private_key_int32 = bytes_to_int(private_key, 0);
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int[] others_pub_int32_1 = bytes_to_int(others_pub, 0);
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int[] others_pub_int32_2 = bytes_to_int(others_pub, BITVEC_NBYTES);
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/* Do some basic validation of other party's public key */
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if (!gf2point_is_zero(others_pub_int32_1, others_pub_int32_2)
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&& gf2point_on_curve(others_pub_int32_1, others_pub_int32_2)) {
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/* Copy other side's public key to output */
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int i;
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for (i = 0; i < (BITVEC_NBYTES * 2); ++i) {
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output[i] = others_pub[i];
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}
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/* Clear bits > CURVE_DEGREE in highest word to satisfy constraint 1 <= exp < n. */
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int nbits = bitvec_degree(base_order);
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for (i = (nbits - 1); i < (BITVEC_NWORDS * 32); ++i) {
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bitvec_clr_bit(private_key_int32, i);
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}
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/* Multiply other side's public key with own private key */
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int[] output_int32_1 = bytes_to_int(output, 0);
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int[] output_int32_2 = bytes_to_int(output, BITVEC_NBYTES);
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gf2point_mul(output_int32_1, output_int32_2, private_key_int32);
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ints_to_bytes(output, output_int32_1, 0);
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ints_to_bytes(output, output_int32_2, BITVEC_NBYTES);
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return true;
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} else {
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return false;
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}
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}
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// these are wrappers around the above C-style methods for Gadgetbridge to use
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public static byte[] ecdh_generate_public(byte[] privateEC) {
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byte[] pubKey = new byte[ECC_PUB_KEY_SIZE];
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if (ecdh_generate_keys(pubKey, privateEC)) {
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return pubKey;
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}
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return null;
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}
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public static byte[] ecdh_generate_shared(byte[] privateEC, byte[] remotePublicEC) {
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byte[] sharedKey = new byte[ECC_PUB_KEY_SIZE];
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if (ecdh_shared_secret(privateEC, remotePublicEC, sharedKey)) {
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return sharedKey;
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}
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return null;
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}
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}
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