-/*
- * Copyright (c) 2009 Chris K Cockrum <ckc@cockrum.net>
- *
- * Copyright (c) 2013 Jens Trillmann <jtrillma@tzi.de>
- * Copyright (c) 2013 Marc Müller-Weinhardt <muewei@tzi.de>
- * Copyright (c) 2013 Lars Schmertmann <lars@tzi.de>
- * Copyright (c) 2013 Hauke Mehrtens <hauke@hauke-m.de>
- *
- * Permission is hereby granted, free of charge, to any person obtaining a copy
- * of this software and associated documentation files (the "Software"), to deal
- * in the Software without restriction, including without limitation the rights
- * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
- * copies of the Software, and to permit persons to whom the Software is
- * furnished to do so, subject to the following conditions:
- *
- * The above copyright notice and this permission notice shall be included in
- * all copies or substantial portions of the Software.
- *
- * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
- * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
- * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
- * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
- * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
- * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
- * THE SOFTWARE.
- *
- *
- * This implementation is based in part on the paper Implementation of an
- * Elliptic Curve Cryptosystem on an 8-bit Microcontroller [0] by
- * Chris K Cockrum <ckc@cockrum.net>.
- *
- * [0]: http://cockrum.net/Implementation_of_ECC_on_an_8-bit_microcontroller.pdf
- *
- * This is a efficient ECC implementation on the secp256r1 curve for 32 Bit CPU
- * architectures. It provides basic operations on the secp256r1 curve and support
- * for ECDH and ECDSA.
- */
-
-//big number functions
+/* Copyright 2014, Kenneth MacKay. Licensed under the BSD 2-clause license. */
+
#include "ecc.h"
-#include <string.h>
-
-static uint32_t add( const uint32_t *x, const uint32_t *y, uint32_t *result, uint8_t length){
- uint64_t d = 0; //carry
- int v = 0;
- for(v = 0;v<length;v++){
- //printf("%02x + %02x + %01x = ", x[v], y[v], d);
- d += (uint64_t) x[v] + (uint64_t) y[v];
- //printf("%02x\n", d);
- result[v] = d;
- d = d>>32; //save carry
- }
-
- return (uint32_t)d;
+
+#ifndef uECC_PLATFORM
+ #if __AVR__
+ #define uECC_PLATFORM uECC_avr
+ #elif defined(__thumb2__) || defined(_M_ARMT) /* I think MSVC only supports Thumb-2 targets */
+ #define uECC_PLATFORM uECC_arm_thumb2
+ #elif defined(__thumb__)
+ #define uECC_PLATFORM uECC_arm_thumb
+ #elif defined(__arm__) || defined(_M_ARM)
+ #define uECC_PLATFORM uECC_arm
+ #elif defined(__i386__) || defined(_M_IX86) || defined(_X86_) || defined(__I86__)
+ #define uECC_PLATFORM uECC_x86
+ #elif defined(__amd64__) || defined(_M_X64)
+ #define uECC_PLATFORM uECC_x86_64
+ #else
+ #define uECC_PLATFORM uECC_arch_other
+ #endif
+#endif
+
+#ifndef uECC_WORD_SIZE
+ #if uECC_PLATFORM == uECC_avr
+ #define uECC_WORD_SIZE 1
+ #elif (uECC_PLATFORM == uECC_x86_64)
+ #define uECC_WORD_SIZE 8
+ #else
+ #define uECC_WORD_SIZE 4
+ #endif
+#endif
+
+#if (uECC_CURVE == uECC_secp160r1) && (uECC_WORD_SIZE == 8)
+ #undef uECC_WORD_SIZE
+ #define uECC_WORD_SIZE 4
+ #if (uECC_PLATFORM == uECC_x86_64)
+ #undef uECC_PLATFORM
+ #define uECC_PLATFORM uECC_x86
+ #endif
+#endif
+
+#if (uECC_WORD_SIZE != 1) && (uECC_WORD_SIZE != 4) && (uECC_WORD_SIZE != 8)
+ #error "Unsupported value for uECC_WORD_SIZE"
+#endif
+
+#if (uECC_ASM && (uECC_PLATFORM == uECC_avr) && (uECC_WORD_SIZE != 1))
+ #pragma message ("uECC_WORD_SIZE must be 1 when using AVR asm")
+ #undef uECC_WORD_SIZE
+ #define uECC_WORD_SIZE 1
+#endif
+
+#if (uECC_ASM && (uECC_PLATFORM == uECC_arm || uECC_PLATFORM == uECC_arm_thumb) && (uECC_WORD_SIZE != 4))
+ #pragma message ("uECC_WORD_SIZE must be 4 when using ARM asm")
+ #undef uECC_WORD_SIZE
+ #define uECC_WORD_SIZE 4
+#endif
+
+#if __STDC_VERSION__ >= 199901L
+ #define RESTRICT restrict
+#else
+ #define RESTRICT
+#endif
+
+#if defined(__SIZEOF_INT128__) || ((__clang_major__ * 100 + __clang_minor__) >= 302)
+ #define SUPPORTS_INT128 1
+#else
+ #define SUPPORTS_INT128 0
+#endif
+
+#define MAX_TRIES 16
+
+#if (uECC_WORD_SIZE == 1)
+
+typedef uint8_t uECC_word_t;
+typedef uint16_t uECC_dword_t;
+typedef uint8_t wordcount_t;
+typedef int8_t swordcount_t;
+typedef int16_t bitcount_t;
+typedef int8_t cmpresult_t;
+
+#define HIGH_BIT_SET 0x80
+#define uECC_WORD_BITS 8
+#define uECC_WORD_BITS_SHIFT 3
+#define uECC_WORD_BITS_MASK 0x07
+
+#define uECC_WORDS_1 20
+#define uECC_WORDS_2 24
+#define uECC_WORDS_3 32
+#define uECC_WORDS_4 32
+
+#define uECC_N_WORDS_1 21
+#define uECC_N_WORDS_2 24
+#define uECC_N_WORDS_3 32
+#define uECC_N_WORDS_4 32
+
+#define Curve_P_1 {0xFF, 0xFF, 0xFF, 0x7F, 0xFF, 0xFF, 0xFF, 0xFF, \
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
+ 0xFF, 0xFF, 0xFF, 0xFF}
+#define Curve_P_2 {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
+ 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF}
+#define Curve_P_3 {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
+ 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, \
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \
+ 0x01, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF}
+#define Curve_P_4 {0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, \
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF}
+
+#define Curve_B_1 {0x45, 0xFA, 0x65, 0xC5, 0xAD, 0xD4, 0xD4, 0x81, \
+ 0x9F, 0xF8, 0xAC, 0x65, 0x8B, 0x7A, 0xBD, 0x54, \
+ 0xFC, 0xBE, 0x97, 0x1C}
+#define Curve_B_2 {0xB1, 0xB9, 0x46, 0xC1, 0xEC, 0xDE, 0xB8, 0xFE, \
+ 0x49, 0x30, 0x24, 0x72, 0xAB, 0xE9, 0xA7, 0x0F, \
+ 0xE7, 0x80, 0x9C, 0xE5, 0x19, 0x05, 0x21, 0x64}
+#define Curve_B_3 {0x4B, 0x60, 0xD2, 0x27, 0x3E, 0x3C, 0xCE, 0x3B, \
+ 0xF6, 0xB0, 0x53, 0xCC, 0xB0, 0x06, 0x1D, 0x65, \
+ 0xBC, 0x86, 0x98, 0x76, 0x55, 0xBD, 0xEB, 0xB3, \
+ 0xE7, 0x93, 0x3A, 0xAA, 0xD8, 0x35, 0xC6, 0x5A}
+#define Curve_B_4 {0x07, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, \
+ 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}
+
+#define Curve_G_1 { \
+ {0x82, 0xFC, 0xCB, 0x13, 0xB9, 0x8B, 0xC3, 0x68, \
+ 0x89, 0x69, 0x64, 0x46, 0x28, 0x73, 0xF5, 0x8E, \
+ 0x68, 0xB5, 0x96, 0x4A}, \
+ {0x32, 0xFB, 0xC5, 0x7A, 0x37, 0x51, 0x23, 0x04, \
+ 0x12, 0xC9, 0xDC, 0x59, 0x7D, 0x94, 0x68, 0x31, \
+ 0x55, 0x28, 0xA6, 0x23}}
+
+#define Curve_G_2 { \
+ {0x12, 0x10, 0xFF, 0x82, 0xFD, 0x0A, 0xFF, 0xF4, \
+ 0x00, 0x88, 0xA1, 0x43, 0xEB, 0x20, 0xBF, 0x7C, \
+ 0xF6, 0x90, 0x30, 0xB0, 0x0E, 0xA8, 0x8D, 0x18}, \
+ {0x11, 0x48, 0x79, 0x1E, 0xA1, 0x77, 0xF9, 0x73, \
+ 0xD5, 0xCD, 0x24, 0x6B, 0xED, 0x11, 0x10, 0x63, \
+ 0x78, 0xDA, 0xC8, 0xFF, 0x95, 0x2B, 0x19, 0x07}}
+
+#define Curve_G_3 { \
+ {0x96, 0xC2, 0x98, 0xD8, 0x45, 0x39, 0xA1, 0xF4, \
+ 0xA0, 0x33, 0xEB, 0x2D, 0x81, 0x7D, 0x03, 0x77, \
+ 0xF2, 0x40, 0xA4, 0x63, 0xE5, 0xE6, 0xBC, 0xF8, \
+ 0x47, 0x42, 0x2C, 0xE1, 0xF2, 0xD1, 0x17, 0x6B}, \
+ {0xF5, 0x51, 0xBF, 0x37, 0x68, 0x40, 0xB6, 0xCB, \
+ 0xCE, 0x5E, 0x31, 0x6B, 0x57, 0x33, 0xCE, 0x2B, \
+ 0x16, 0x9E, 0x0F, 0x7C, 0x4A, 0xEB, 0xE7, 0x8E, \
+ 0x9B, 0x7F, 0x1A, 0xFE, 0xE2, 0x42, 0xE3, 0x4F}}
+
+#define Curve_G_4 { \
+ {0x98, 0x17, 0xF8, 0x16, 0x5B, 0x81, 0xF2, 0x59, \
+ 0xD9, 0x28, 0xCE, 0x2D, 0xDB, 0xFC, 0x9B, 0x02, \
+ 0x07, 0x0B, 0x87, 0xCE, 0x95, 0x62, 0xA0, 0x55, \
+ 0xAC, 0xBB, 0xDC, 0xF9, 0x7E, 0x66, 0xBE, 0x79}, \
+ {0xB8, 0xD4, 0x10, 0xFB, 0x8F, 0xD0, 0x47, 0x9C, \
+ 0x19, 0x54, 0x85, 0xA6, 0x48, 0xB4, 0x17, 0xFD, \
+ 0xA8, 0x08, 0x11, 0x0E, 0xFC, 0xFB, 0xA4, 0x5D, \
+ 0x65, 0xC4, 0xA3, 0x26, 0x77, 0xDA, 0x3A, 0x48}}
+
+#define Curve_N_1 {0x57, 0x22, 0x75, 0xCA, 0xD3, 0xAE, 0x27, 0xF9, \
+ 0xC8, 0xF4, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, \
+ 0x00, 0x00, 0x00, 0x00, 0x01}
+#define Curve_N_2 {0x31, 0x28, 0xD2, 0xB4, 0xB1, 0xC9, 0x6B, 0x14, \
+ 0x36, 0xF8, 0xDE, 0x99, 0xFF, 0xFF, 0xFF, 0xFF, \
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF}
+#define Curve_N_3 {0x51, 0x25, 0x63, 0xFC, 0xC2, 0xCA, 0xB9, 0xF3, \
+ 0x84, 0x9E, 0x17, 0xA7, 0xAD, 0xFA, 0xE6, 0xBC, \
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
+ 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF}
+#define Curve_N_4 {0x41, 0x41, 0x36, 0xD0, 0x8C, 0x5E, 0xD2, 0xBF, \
+ 0x3B, 0xA0, 0x48, 0xAF, 0xE6, 0xDC, 0xAE, 0xBA, \
+ 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, \
+ 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF}
+
+#elif (uECC_WORD_SIZE == 4)
+
+typedef uint32_t uECC_word_t;
+typedef uint64_t uECC_dword_t;
+typedef unsigned wordcount_t;
+typedef int swordcount_t;
+typedef int bitcount_t;
+typedef int cmpresult_t;
+
+#define HIGH_BIT_SET 0x80000000
+#define uECC_WORD_BITS 32
+#define uECC_WORD_BITS_SHIFT 5
+#define uECC_WORD_BITS_MASK 0x01F
+
+#define uECC_WORDS_1 5
+#define uECC_WORDS_2 6
+#define uECC_WORDS_3 8
+#define uECC_WORDS_4 8
+
+#define uECC_N_WORDS_1 6
+#define uECC_N_WORDS_2 6
+#define uECC_N_WORDS_3 8
+#define uECC_N_WORDS_4 8
+
+#define Curve_P_1 {0x7FFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
+#define Curve_P_2 {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
+#define Curve_P_3 {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0x00000000, 0x00000000, 0x00000001, 0xFFFFFFFF}
+#define Curve_P_4 {0xFFFFFC2F, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
+
+#define Curve_B_1 {0xC565FA45, 0x81D4D4AD, 0x65ACF89F, 0x54BD7A8B, 0x1C97BEFC}
+#define Curve_B_2 {0xC146B9B1, 0xFEB8DEEC, 0x72243049, 0x0FA7E9AB, 0xE59C80E7, 0x64210519}
+#define Curve_B_3 {0x27D2604B, 0x3BCE3C3E, 0xCC53B0F6, 0x651D06B0, 0x769886BC, 0xB3EBBD55, 0xAA3A93E7, 0x5AC635D8}
+#define Curve_B_4 {0x00000007, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000}
+
+#define Curve_G_1 { \
+ {0x13CBFC82, 0x68C38BB9, 0x46646989, 0x8EF57328, 0x4A96B568}, \
+ {0x7AC5FB32, 0x04235137, 0x59DCC912, 0x3168947D, 0x23A62855}}
+
+#define Curve_G_2 { \
+ {0x82FF1012, 0xF4FF0AFD, 0x43A18800, 0x7CBF20EB, 0xB03090F6, 0x188DA80E}, \
+ {0x1E794811, 0x73F977A1, 0x6B24CDD5, 0x631011ED, 0xFFC8DA78, 0x07192B95}}
+
+#define Curve_G_3 { \
+ {0xD898C296, 0xF4A13945, 0x2DEB33A0, 0x77037D81, 0x63A440F2, 0xF8BCE6E5, 0xE12C4247, 0x6B17D1F2}, \
+ {0x37BF51F5, 0xCBB64068, 0x6B315ECE, 0x2BCE3357, 0x7C0F9E16, 0x8EE7EB4A, 0xFE1A7F9B, 0x4FE342E2}}
+
+#define Curve_G_4 { \
+ {0x16F81798, 0x59F2815B, 0x2DCE28D9, 0x029BFCDB, 0xCE870B07, 0x55A06295, 0xF9DCBBAC, 0x79BE667E}, \
+ {0xFB10D4B8, 0x9C47D08F, 0xA6855419, 0xFD17B448, 0x0E1108A8, 0x5DA4FBFC, 0x26A3C465, 0x483ADA77}}
+
+#define Curve_N_1 {0xCA752257, 0xF927AED3, 0x0001F4C8, 0x00000000, 0x00000000, 0x00000001}
+#define Curve_N_2 {0xB4D22831, 0x146BC9B1, 0x99DEF836, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
+#define Curve_N_3 {0xFC632551, 0xF3B9CAC2, 0xA7179E84, 0xBCE6FAAD, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0xFFFFFFFF}
+#define Curve_N_4 {0xD0364141, 0xBFD25E8C, 0xAF48A03B, 0xBAAEDCE6, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}
+
+#elif (uECC_WORD_SIZE == 8)
+
+typedef uint64_t uECC_word_t;
+#if SUPPORTS_INT128
+typedef unsigned __int128 uECC_dword_t;
+#endif
+typedef unsigned wordcount_t;
+typedef int swordcount_t;
+typedef int bitcount_t;
+typedef int cmpresult_t;
+
+#define HIGH_BIT_SET 0x8000000000000000ull
+#define uECC_WORD_BITS 64
+#define uECC_WORD_BITS_SHIFT 6
+#define uECC_WORD_BITS_MASK 0x03F
+
+#define uECC_WORDS_1 3
+#define uECC_WORDS_2 3
+#define uECC_WORDS_3 4
+#define uECC_WORDS_4 4
+
+#define uECC_N_WORDS_1 3
+#define uECC_N_WORDS_2 3
+#define uECC_N_WORDS_3 4
+#define uECC_N_WORDS_4 4
+
+#define Curve_P_1 {0xFFFFFFFF7FFFFFFFull, 0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull}
+#define Curve_P_2 {0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFFFFFFFFFEull, 0xFFFFFFFFFFFFFFFFull}
+#define Curve_P_3 {0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull, 0x0000000000000000ull, 0xFFFFFFFF00000001ull}
+#define Curve_P_4 {0xFFFFFFFEFFFFFC2Full, 0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFFFFFFFFFFull}
+
+#define Curve_B_1 {0x81D4D4ADC565FA45ull, 0x54BD7A8B65ACF89Full, 0x000000001C97BEFCull}
+#define Curve_B_2 {0xFEB8DEECC146B9B1ull, 0x0FA7E9AB72243049ull, 0x64210519E59C80E7ull}
+#define Curve_B_3 {0x3BCE3C3E27D2604Bull, 0x651D06B0CC53B0F6ull, 0xB3EBBD55769886BCull, 0x5AC635D8AA3A93E7ull}
+#define Curve_B_4 {0x0000000000000007ull, 0x0000000000000000ull, 0x0000000000000000ull, 0x0000000000000000ull}
+
+#define Curve_G_1 { \
+ {0x68C38BB913CBFC82ull, 0x8EF5732846646989ull, 0x000000004A96B568ull}, \
+ {0x042351377AC5FB32ull, 0x3168947D59DCC912ull, 0x0000000023A62855ull}}
+
+#define Curve_G_2 { \
+ {0xF4FF0AFD82FF1012ull, 0x7CBF20EB43A18800ull, 0x188DA80EB03090F6ull}, \
+ {0x73F977A11E794811ull, 0x631011ED6B24CDD5ull, 0x07192B95FFC8DA78ull}}
+
+#define Curve_G_3 { \
+ {0xF4A13945D898C296ull, 0x77037D812DEB33A0ull, 0xF8BCE6E563A440F2ull, 0x6B17D1F2E12C4247ull}, \
+ {0xCBB6406837BF51F5ull, 0x2BCE33576B315ECEull, 0x8EE7EB4A7C0F9E16ull, 0x4FE342E2FE1A7F9Bull}}
+
+#define Curve_G_4 { \
+ {0x59F2815B16F81798, 0x029BFCDB2DCE28D9, 0x55A06295CE870B07, 0x79BE667EF9DCBBAC}, \
+ {0x9C47D08FFB10D4B8, 0xFD17B448A6855419, 0x5DA4FBFC0E1108A8, 0x483ADA7726A3C465}}
+
+#define Curve_N_1 {0xF927AED3CA752257ull, 0x000000000001F4C8ull, 0x0000000100000000ull}
+#define Curve_N_2 {0x146BC9B1B4D22831ull, 0xFFFFFFFF99DEF836ull, 0xFFFFFFFFFFFFFFFFull}
+#define Curve_N_3 {0xF3B9CAC2FC632551ull, 0xBCE6FAADA7179E84ull, 0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFF00000000ull}
+#define Curve_N_4 {0xBFD25E8CD0364141, 0xBAAEDCE6AF48A03B, 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF}
+
+#endif /* (uECC_WORD_SIZE == 8) */
+
+#define uECC_WORDS uECC_CONCAT(uECC_WORDS_, uECC_CURVE)
+#define uECC_N_WORDS uECC_CONCAT(uECC_N_WORDS_, uECC_CURVE)
+
+typedef struct EccPoint
+{
+ uECC_word_t x[uECC_WORDS];
+ uECC_word_t y[uECC_WORDS];
+} EccPoint;
+
+static uECC_word_t curve_p[uECC_WORDS] = uECC_CONCAT(Curve_P_, uECC_CURVE);
+static uECC_word_t curve_b[uECC_WORDS] = uECC_CONCAT(Curve_B_, uECC_CURVE);
+static EccPoint curve_G = uECC_CONCAT(Curve_G_, uECC_CURVE);
+static uECC_word_t curve_n[uECC_N_WORDS] = uECC_CONCAT(Curve_N_, uECC_CURVE);
+
+static void vli_clear(uECC_word_t *p_vli);
+static uECC_word_t vli_isZero(const uECC_word_t *p_vli);
+static uECC_word_t vli_testBit(const uECC_word_t *p_vli, bitcount_t p_bit);
+static bitcount_t vli_numBits(const uECC_word_t *p_vli, wordcount_t p_maxWords);
+static void vli_set(uECC_word_t *p_dest, const uECC_word_t *p_src);
+static cmpresult_t vli_cmp(uECC_word_t *p_left, uECC_word_t *p_right);
+static void vli_rshift1(uECC_word_t *p_vli);
+static uECC_word_t vli_add(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right);
+static uECC_word_t vli_sub(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right);
+static void vli_mult(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right);
+static void vli_modAdd(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right, uECC_word_t *p_mod);
+static void vli_modSub(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right, uECC_word_t *p_mod);
+static void vli_mmod_fast(uECC_word_t *RESTRICT p_result, uECC_word_t *RESTRICT p_product);
+static void vli_modMult_fast(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right);
+static void vli_modInv(uECC_word_t *p_result, uECC_word_t *p_input, uECC_word_t *p_mod);
+#if uECC_SQUARE_FUNC
+static void vli_square(uECC_word_t *p_result, uECC_word_t *p_left);
+static void vli_modSquare_fast(uECC_word_t *p_result, uECC_word_t *p_left);
+#endif
+// Function declarations to support the HAL shims
+int uECC_make_key_impl(uint8_t p_publicKey[uECC_BYTES*2], uint8_t p_privateKey[uECC_BYTES]);
+int uECC_shared_secret_impl(const uint8_t p_publicKey[uECC_BYTES*2], const uint8_t p_privateKey[uECC_BYTES], uint8_t p_secret[uECC_BYTES]);
+int uECC_sign_impl(const uint8_t p_privateKey[uECC_BYTES], const uint8_t p_hash[uECC_BYTES], uint8_t p_signature[uECC_BYTES*2]);
+int uECC_verify_impl(const uint8_t p_publicKey[uECC_BYTES*2], const uint8_t p_hash[uECC_BYTES], const uint8_t p_signature[uECC_BYTES*2]);
+int uECC_ecdhe_impl(const uint8_t p_public_key_in[uECC_BYTES*2], uint8_t p_public_key_out[uECC_BYTES*2], uint8_t p_secret[uECC_BYTES]);
+int uECC_get_pubkey_impl(const uint8_t p_key_handle[uECC_BYTES], uint8_t p_public_key[uECC_BYTES*2]);
+
+#if (defined(_WIN32) || defined(_WIN64))
+/* Windows */
+
+#define WIN32_LEAN_AND_MEAN
+#include <windows.h>
+#include <bcrypt.h>
+
+static int default_RNG(uint8_t *p_dest, unsigned p_size)
+{
+ if (!BCRYPT_SUCCESS(BCryptGenRandom(NULL, (PUCHAR)p_dest, p_size, BCRYPT_USE_SYSTEM_PREFERRED_RNG)))
+ {
+ return 0;
+ }
+
+ return 1;
}
-static uint32_t sub( const uint32_t *x, const uint32_t *y, uint32_t *result, uint8_t length){
- uint64_t d = 0;
- int v;
- for(v = 0;v < length; v++){
- d = (uint64_t) x[v] - (uint64_t) y[v] - d;
- result[v] = d & 0xFFFFFFFF;
- d = d>>32;
- d &= 0x1;
- }
- return (uint32_t)d;
+#elif defined(unix) || defined(__linux__) || defined(__unix__) || defined(__unix) || \
+ (defined(__APPLE__) && defined(__MACH__)) || defined(uECC_POSIX)
+
+/* Some POSIX-like system with /dev/urandom or /dev/random. */
+#include <sys/types.h>
+#include <fcntl.h>
+#include <unistd.h>
+
+#ifndef O_CLOEXEC
+ #define O_CLOEXEC 0
+#endif
+
+static int default_RNG(uint8_t *p_dest, unsigned p_size)
+{
+ int l_fd = open("/dev/urandom", O_RDONLY | O_CLOEXEC);
+ if(l_fd == -1)
+ {
+ l_fd = open("/dev/random", O_RDONLY | O_CLOEXEC);
+ if(l_fd == -1)
+ {
+ return 0;
+ }
+ }
+
+ char *l_ptr = (char *)p_dest;
+ size_t l_left = p_size;
+ while(l_left > 0)
+ {
+ int l_read = read(l_fd, l_ptr, l_left);
+ if(l_read <= 0)
+ { // read failed
+ close(l_fd);
+ return 0;
+ }
+ l_left -= l_read;
+ l_ptr += l_read;
+ }
+
+ close(l_fd);
+ return 1;
}
-static void rshiftby(const uint32_t *in, uint8_t in_size, uint32_t *out, uint8_t out_size, uint8_t shift) {
- int i;
+#else /* Some other platform */
- for (i = 0; i < (in_size - shift) && i < out_size; i++)
- out[i] = in[i + shift];
- for (/* reuse i */; i < out_size; i++)
- out[i] = 0;
+static int default_RNG(uint8_t *p_dest, unsigned p_size)
+{
+ return 0;
}
-//finite field functions
-//FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF
-static const uint32_t ecc_prime_m[8] = {0xffffffff, 0xffffffff, 0xffffffff, 0x00000000,
- 0x00000000, 0x00000000, 0x00000001, 0xffffffff};
+#endif
-
-/* This is added after an static byte addition if the answer has a carry in MSB*/
-static const uint32_t ecc_prime_r[8] = {0x00000001, 0x00000000, 0x00000000, 0xffffffff,
- 0xffffffff, 0xffffffff, 0xfffffffe, 0x00000000};
+///////////////////////////////////////////////////////
+// Functions to set the callbacks for crypto operations
+static uECC_RNG_Function g_rng = &default_RNG;
-// ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551
-static const uint32_t ecc_order_m[9] = {0xFC632551, 0xF3B9CAC2, 0xA7179E84, 0xBCE6FAAD,
- 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0xFFFFFFFF,
- 0x00000000};
+void uECC_set_rng(uECC_RNG_Function p_rng)
+{
+ g_rng = p_rng;
+}
-static const uint32_t ecc_order_r[8] = {0x039CDAAF, 0x0C46353D, 0x58E8617B, 0x43190552,
- 0x00000000, 0x00000000, 0xFFFFFFFF, 0x00000000};
+static uECC_make_key_Function g_make_key_cb = &uECC_make_key_impl;
-static const uint32_t ecc_order_mu[9] = {0xEEDF9BFE, 0x012FFD85, 0xDF1A6C21, 0x43190552,
- 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0x00000000,
- 0x00000001};
+void uECC_set_make_key_cb(uECC_make_key_Function p_make_key_cb)
+{
+ g_make_key_cb = p_make_key_cb;
+}
-static const uint8_t ecc_order_k = 8;
+static uECC_shared_secret_Function g_shared_secret_cb = &uECC_shared_secret_impl;
-const uint32_t ecc_g_point_x[8] = { 0xD898C296, 0xF4A13945, 0x2DEB33A0, 0x77037D81,
- 0x63A440F2, 0xF8BCE6E5, 0xE12C4247, 0x6B17D1F2};
-const uint32_t ecc_g_point_y[8] = { 0x37BF51F5, 0xCBB64068, 0x6B315ECE, 0x2BCE3357,
- 0x7C0F9E16, 0x8EE7EB4A, 0xFE1A7F9B, 0x4FE342E2};
+void uECC_set_shared_secret_cb(uECC_shared_secret_Function p_shared_secret_cb)
+{
+ g_shared_secret_cb = p_shared_secret_cb;
+}
+static uECC_sign_Function g_sign_cb = &uECC_sign_impl;
-static void setZero(uint32_t *A, const int length){
- memset(A, 0x0, length * sizeof(uint32_t));
+void uECC_set_sign_cb(uECC_sign_Function p_sign_cb)
+{
+ g_sign_cb = p_sign_cb;
}
-/*
- * copy one array to another
- */
-static void copy(const uint32_t *from, uint32_t *to, uint8_t length){
- memcpy(to, from, length * sizeof(uint32_t));
+static uECC_verify_Function g_verify_cb = &uECC_verify_impl;
+
+void uECC_set_verify_cb(uECC_verify_Function p_verify_cb)
+{
+ g_verify_cb = p_verify_cb;
}
-static int isSame(const uint32_t *A, const uint32_t *B, uint8_t length){
- return !memcmp(A, B, length * sizeof(uint32_t));
+static uECC_ecdhe_Function g_ecdhe_cb = &uECC_ecdhe_impl;
+
+void uECC_set_ecdhe_cb(uECC_ecdhe_Function p_ecdhe_cb)
+{
+ g_ecdhe_cb = p_ecdhe_cb;
}
-//is A greater than B?
-static int isGreater(const uint32_t *A, const uint32_t *B, uint8_t length){
- int i;
- for (i = length-1; i >= 0; --i)
- {
- if(A[i] > B[i])
- return 1;
- if(A[i] < B[i])
- return -1;
- }
- return 0;
+static uECC_get_pubkey_Function g_get_pubkey_cb = &uECC_get_pubkey_impl;
+
+void uECC_set_get_pubkey_cb(uECC_get_pubkey_Function p_get_pubkey_cb)
+{
+ g_get_pubkey_cb = p_get_pubkey_cb;
}
+///////////////////////////////////////////////////////
-static int fieldAdd(const uint32_t *x, const uint32_t *y, const uint32_t *reducer, uint32_t *result){
- if(add(x, y, result, arrayLength)){ //add prime if carry is still set!
- uint32_t tempas[8];
- setZero(tempas, 8);
- add(result, reducer, tempas, arrayLength);
- copy(tempas, result, arrayLength);
- }
- return 0;
+
+#ifdef __GNUC__ /* Only support GCC inline asm for now */
+ #if (uECC_ASM && (uECC_PLATFORM == uECC_avr))
+ #include "asm_avr.inc"
+ #endif
+
+ #if (uECC_ASM && (uECC_PLATFORM == uECC_arm || uECC_PLATFORM == uECC_arm_thumb || uECC_PLATFORM == uECC_arm_thumb2))
+ #include "asm_arm.inc"
+ #endif
+#endif
+
+#if !asm_clear
+static void vli_clear(uECC_word_t *p_vli)
+{
+ wordcount_t i;
+ for(i = 0; i < uECC_WORDS; ++i)
+ {
+ p_vli[i] = 0;
+ }
}
+#endif
-static int fieldSub(const uint32_t *x, const uint32_t *y, const uint32_t *modulus, uint32_t *result){
- if(sub(x, y, result, arrayLength)){ //add modulus if carry is set
- uint32_t tempas[8];
- setZero(tempas, 8);
- add(result, modulus, tempas, arrayLength);
- copy(tempas, result, arrayLength);
- }
- return 0;
+/* Returns 1 if p_vli == 0, 0 otherwise. */
+#if !asm_isZero
+static uECC_word_t vli_isZero(const uECC_word_t *p_vli)
+{
+ wordcount_t i;
+ for(i = 0; i < uECC_WORDS; ++i)
+ {
+ if(p_vli[i])
+ {
+ return 0;
+ }
+ }
+ return 1;
}
+#endif
-//finite Field multiplication
-//32bit * 32bit = 64bit
-static int fieldMult(const uint32_t *x, const uint32_t *y, uint32_t *result, uint8_t length){
- uint32_t temp[length * 2];
- setZero(temp, length * 2);
- setZero(result, length * 2);
- uint8_t k, n;
- uint64_t l;
- for (k = 0; k < length; k++){
- for (n = 0; n < length; n++){
- l = (uint64_t)x[n]*(uint64_t)y[k];
- temp[n+k] = l&0xFFFFFFFF;
- temp[n+k+1] = l>>32;
- add(&temp[n+k], &result[n+k], &result[n+k], (length * 2) - (n + k));
-
- setZero(temp, length * 2);
- }
- }
- return 0;
+/* Returns nonzero if bit p_bit of p_vli is set. */
+#if !asm_testBit
+static uECC_word_t vli_testBit(const uECC_word_t *p_vli, bitcount_t p_bit)
+{
+ return (p_vli[p_bit >> uECC_WORD_BITS_SHIFT] & ((uECC_word_t)1 << (p_bit & uECC_WORD_BITS_MASK)));
}
+#endif
-//TODO: maximum:
-//fffffffe00000002fffffffe0000000100000001fffffffe00000001fffffffe00000001fffffffefffffffffffffffffffffffe000000000000000000000001_16
-static void fieldModP(uint32_t *A, const uint32_t *B)
-{
- uint32_t tempm[8];
- uint32_t tempm2[8];
- uint8_t n;
- setZero(tempm, 8);
- setZero(tempm2, 8);
- /* A = T */
- copy(B,A,arrayLength);
-
- /* Form S1 */
- for(n=0;n<3;n++) tempm[n]=0;
- for(n=3;n<8;n++) tempm[n]=B[n+8];
-
- /* tempm2=T+S1 */
- fieldAdd(A,tempm,ecc_prime_r,tempm2);
- /* A=T+S1+S1 */
- fieldAdd(tempm2,tempm,ecc_prime_r,A);
- /* Form S2 */
- for(n=0;n<3;n++) tempm[n]=0;
- for(n=3;n<7;n++) tempm[n]=B[n+9];
- for(n=7;n<8;n++) tempm[n]=0;
- /* tempm2=T+S1+S1+S2 */
- fieldAdd(A,tempm,ecc_prime_r,tempm2);
- /* A=T+S1+S1+S2+S2 */
- fieldAdd(tempm2,tempm,ecc_prime_r,A);
- /* Form S3 */
- for(n=0;n<3;n++) tempm[n]=B[n+8];
- for(n=3;n<6;n++) tempm[n]=0;
- for(n=6;n<8;n++) tempm[n]=B[n+8];
- /* tempm2=T+S1+S1+S2+S2+S3 */
- fieldAdd(A,tempm,ecc_prime_r,tempm2);
- /* Form S4 */
- for(n=0;n<3;n++) tempm[n]=B[n+9];
- for(n=3;n<6;n++) tempm[n]=B[n+10];
- for(n=6;n<7;n++) tempm[n]=B[n+7];
- for(n=7;n<8;n++) tempm[n]=B[n+1];
- /* A=T+S1+S1+S2+S2+S3+S4 */
- fieldAdd(tempm2,tempm,ecc_prime_r,A);
- /* Form D1 */
- for(n=0;n<3;n++) tempm[n]=B[n+11];
- for(n=3;n<6;n++) tempm[n]=0;
- for(n=6;n<7;n++) tempm[n]=B[n+2];
- for(n=7;n<8;n++) tempm[n]=B[n+3];
- /* tempm2=T+S1+S1+S2+S2+S3+S4-D1 */
- fieldSub(A,tempm,ecc_prime_m,tempm2);
- /* Form D2 */
- for(n=0;n<4;n++) tempm[n]=B[n+12];
- for(n=4;n<6;n++) tempm[n]=0;
- for(n=6;n<7;n++) tempm[n]=B[n+3];
- for(n=7;n<8;n++) tempm[n]=B[n+4];
- /* A=T+S1+S1+S2+S2+S3+S4-D1-D2 */
- fieldSub(tempm2,tempm,ecc_prime_m,A);
- /* Form D3 */
- for(n=0;n<3;n++) tempm[n]=B[n+13];
- for(n=3;n<6;n++) tempm[n]=B[n+5];
- for(n=6;n<7;n++) tempm[n]=0;
- for(n=7;n<8;n++) tempm[n]=B[n+5];
- /* tempm2=T+S1+S1+S2+S2+S3+S4-D1-D2-D3 */
- fieldSub(A,tempm,ecc_prime_m,tempm2);
- /* Form D4 */
- for(n=0;n<2;n++) tempm[n]=B[n+14];
- for(n=2;n<3;n++) tempm[n]=0;
- for(n=3;n<6;n++) tempm[n]=B[n+6];
- for(n=6;n<7;n++) tempm[n]=0;
- for(n=7;n<8;n++) tempm[n]=B[n+6];
- /* A=T+S1+S1+S2+S2+S3+S4-D1-D2-D3-D4 */
- fieldSub(tempm2,tempm,ecc_prime_m,A);
- if(isGreater(A, ecc_prime_m, arrayLength) >= 0){
- fieldSub(A, ecc_prime_m, ecc_prime_m, tempm);
- copy(tempm, A, arrayLength);
- }
+/* Counts the number of words in p_vli. */
+#if !asm_numBits
+static wordcount_t vli_numDigits(const uECC_word_t *p_vli, wordcount_t p_maxWords)
+{
+ swordcount_t 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 = p_maxWords-1; i >= 0 && p_vli[i] == 0; --i)
+ {
+ }
+
+ return (i + 1);
}
-/**
- * calculate the result = A mod n.
- * n is the order of the eliptic curve.
- * A and result could point to the same value
- *
- * A: input value (max size * 4 bytes)
- * result: result of modulo calculation (max 36 bytes)
- * size: size of A
- *
- * This uses the Barrett modular reduction as described in the Handbook
- * of Applied Cryptography 14.42 Algorithm Barrett modular reduction,
- * see http://cacr.uwaterloo.ca/hac/about/chap14.pdf and
- * http://everything2.com/title/Barrett+Reduction
- *
- * b = 32 (bite size of the processor architecture)
- * mu (ecc_order_mu) was precomputed in a java program
- */
-static void fieldModO(const uint32_t *A, uint32_t *result, uint8_t length) {
- // This is used for value q1 and q3
- uint32_t q1_q3[9];
- // This is used for q2 and a temp var
- uint32_t q2_tmp[18];
-
- // return if the given value is smaller than the modulus
- if (length == arrayLength && isGreater(A, ecc_order_m, arrayLength) <= 0) {
- if (A != result)
- copy(A, result, length);
- return;
- }
+/* Counts the number of bits required to represent p_vli. */
+static bitcount_t vli_numBits(const uECC_word_t *p_vli, wordcount_t p_maxWords)
+{
+ uECC_word_t i;
+ uECC_word_t l_digit;
+
+ wordcount_t l_numDigits = vli_numDigits(p_vli, p_maxWords);
+ if(l_numDigits == 0)
+ {
+ return 0;
+ }
+
+ l_digit = p_vli[l_numDigits - 1];
+ for(i = 0; l_digit; ++i)
+ {
+ l_digit >>= 1;
+ }
+
+ return (((bitcount_t)(l_numDigits - 1) << uECC_WORD_BITS_SHIFT) + i);
+}
+#endif /* !asm_numBits */
+
+/* Sets p_dest = p_src. */
+#if !asm_set
+static void vli_set(uECC_word_t *p_dest, const uECC_word_t *p_src)
+{
+ wordcount_t i;
+ for(i=0; i<uECC_WORDS; ++i)
+ {
+ p_dest[i] = p_src[i];
+ }
+}
+#endif
+
+/* Returns sign of p_left - p_right. */
+#if !asm_cmp
+static cmpresult_t vli_cmp(uECC_word_t *p_left, uECC_word_t *p_right)
+{
+ swordcount_t i;
+ for(i = uECC_WORDS-1; i >= 0; --i)
+ {
+ if(p_left[i] > p_right[i])
+ {
+ return 1;
+ }
+ else if(p_left[i] < p_right[i])
+ {
+ return -1;
+ }
+ }
+ return 0;
+}
+#endif
- rshiftby(A, length, q1_q3, 9, ecc_order_k - 1);
+/* Computes p_vli = p_vli >> 1. */
+#if !asm_rshift1
+static void vli_rshift1(uECC_word_t *p_vli)
+{
+ uECC_word_t *l_end = p_vli;
+ uECC_word_t l_carry = 0;
+
+ p_vli += uECC_WORDS;
+ while(p_vli-- > l_end)
+ {
+ uECC_word_t l_temp = *p_vli;
+ *p_vli = (l_temp >> 1) | l_carry;
+ l_carry = l_temp << (uECC_WORD_BITS - 1);
+ }
+}
+#endif
- fieldMult(ecc_order_mu, q1_q3, q2_tmp, 9);
+/* Computes p_result = p_left + p_right, returning carry. Can modify in place. */
+#if !asm_add
+static uECC_word_t vli_add(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right)
+{
+ uECC_word_t l_carry = 0;
+ wordcount_t i;
+ for(i = 0; i < uECC_WORDS; ++i)
+ {
+ uECC_word_t l_sum = p_left[i] + p_right[i] + l_carry;
+ if(l_sum != p_left[i])
+ {
+ l_carry = (l_sum < p_left[i]);
+ }
+ p_result[i] = l_sum;
+ }
+ return l_carry;
+}
+#endif
- rshiftby(q2_tmp, 18, q1_q3, 8, ecc_order_k + 1);
+/* Computes p_result = p_left - p_right, returning borrow. Can modify in place. */
+#if !asm_sub
+static uECC_word_t vli_sub(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right)
+{
+ uECC_word_t l_borrow = 0;
+ wordcount_t i;
+ for(i = 0; i < uECC_WORDS; ++i)
+ {
+ uECC_word_t l_diff = p_left[i] - p_right[i] - l_borrow;
+ if(l_diff != p_left[i])
+ {
+ l_borrow = (l_diff > p_left[i]);
+ }
+ p_result[i] = l_diff;
+ }
+ return l_borrow;
+}
+#endif
- // r1 = first 9 blocks of A
+#if (!asm_mult || !asm_square || uECC_CURVE == uECC_secp256k1)
+static void muladd(uECC_word_t a, uECC_word_t b, uECC_word_t *r0, uECC_word_t *r1, uECC_word_t *r2)
+{
+#if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128
+ uint64_t a0 = a & 0xffffffffull;
+ uint64_t a1 = a >> 32;
+ uint64_t b0 = b & 0xffffffffull;
+ uint64_t b1 = b >> 32;
+
+ uint64_t i0 = a0 * b0;
+ uint64_t i1 = a0 * b1;
+ uint64_t i2 = a1 * b0;
+ uint64_t i3 = a1 * b1;
+
+ uint64_t p0, p1;
+
+ i2 += (i0 >> 32);
+ i2 += i1;
+ if(i2 < i1)
+ { // overflow
+ i3 += 0x100000000ull;
+ }
+
+ p0 = (i0 & 0xffffffffull) | (i2 << 32);
+ p1 = i3 + (i2 >> 32);
+
+ *r0 += p0;
+ *r1 += (p1 + (*r0 < p0));
+ *r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0));
+#else
+ uECC_dword_t p = (uECC_dword_t)a * b;
+ uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0;
+ r01 += p;
+ *r2 += (r01 < p);
+ *r1 = r01 >> uECC_WORD_BITS;
+ *r0 = (uECC_word_t)r01;
+#endif
+}
+#define muladd_exists 1
+#endif
- fieldMult(q1_q3, ecc_order_m, q2_tmp, 8);
+#if !asm_mult
+static void vli_mult(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right)
+{
+ uECC_word_t r0 = 0;
+ uECC_word_t r1 = 0;
+ uECC_word_t r2 = 0;
+
+ wordcount_t i, k;
+
+ /* Compute each digit of p_result in sequence, maintaining the carries. */
+ for(k = 0; k < uECC_WORDS; ++k)
+ {
+ for(i = 0; i <= k; ++i)
+ {
+ muladd(p_left[i], p_right[k-i], &r0, &r1, &r2);
+ }
+ p_result[k] = r0;
+ r0 = r1;
+ r1 = r2;
+ r2 = 0;
+ }
+ for(k = uECC_WORDS; k < uECC_WORDS*2 - 1; ++k)
+ {
+ for(i = (k + 1) - uECC_WORDS; i<uECC_WORDS; ++i)
+ {
+ muladd(p_left[i], p_right[k-i], &r0, &r1, &r2);
+ }
+ p_result[k] = r0;
+ r0 = r1;
+ r1 = r2;
+ r2 = 0;
+ }
+
+ p_result[uECC_WORDS*2 - 1] = r0;
+}
+#endif
- // r2 = first 9 blocks of q2_tmp
+#if uECC_SQUARE_FUNC
- sub(A, q2_tmp, result, 9);
+#if !asm_square
+static void mul2add(uECC_word_t a, uECC_word_t b, uECC_word_t *r0, uECC_word_t *r1, uECC_word_t *r2)
+{
+#if uECC_WORD_SIZE == 8 && !SUPPORTS_INT128
+ uint64_t a0 = a & 0xffffffffull;
+ uint64_t a1 = a >> 32;
+ uint64_t b0 = b & 0xffffffffull;
+ uint64_t b1 = b >> 32;
+
+ uint64_t i0 = a0 * b0;
+ uint64_t i1 = a0 * b1;
+ uint64_t i2 = a1 * b0;
+ uint64_t i3 = a1 * b1;
+
+ uint64_t p0, p1;
+
+ i2 += (i0 >> 32);
+ i2 += i1;
+ if(i2 < i1)
+ { // overflow
+ i3 += 0x100000000ull;
+ }
+
+ p0 = (i0 & 0xffffffffull) | (i2 << 32);
+ p1 = i3 + (i2 >> 32);
+
+ *r2 += (p1 >> 63);
+ p1 = (p1 << 1) | (p0 >> 63);
+ p0 <<= 1;
+
+ *r0 += p0;
+ *r1 += (p1 + (*r0 < p0));
+ *r2 += ((*r1 < p1) || (*r1 == p1 && *r0 < p0));
+#else
+ uECC_dword_t p = (uECC_dword_t)a * b;
+ uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0;
+ *r2 += (p >> (uECC_WORD_BITS * 2 - 1));
+ p *= 2;
+ r01 += p;
+ *r2 += (r01 < p);
+ *r1 = r01 >> uECC_WORD_BITS;
+ *r0 = (uECC_word_t)r01;
+#endif
+}
- while (isGreater(result, ecc_order_m, 9) >= 0)
- sub(result, ecc_order_m, result, 9);
+static void vli_square(uECC_word_t *p_result, uECC_word_t *p_left)
+{
+ uECC_word_t r0 = 0;
+ uECC_word_t r1 = 0;
+ uECC_word_t r2 = 0;
+
+ wordcount_t i, k;
+
+ for(k = 0; k < uECC_WORDS*2 - 1; ++k)
+ {
+ uECC_word_t l_min = (k < uECC_WORDS ? 0 : (k + 1) - uECC_WORDS);
+ for(i = l_min; i<=k && i<=k-i; ++i)
+ {
+ if(i < k-i)
+ {
+ mul2add(p_left[i], p_left[k-i], &r0, &r1, &r2);
+ }
+ else
+ {
+ muladd(p_left[i], p_left[k-i], &r0, &r1, &r2);
+ }
+ }
+ p_result[k] = r0;
+ r0 = r1;
+ r1 = r2;
+ r2 = 0;
+ }
+
+ p_result[uECC_WORDS*2 - 1] = r0;
}
+#endif
+
+#else /* uECC_SQUARE_FUNC */
-static int isOne(const uint32_t* A){
- uint8_t n;
- for(n=1;n<8;n++)
- if (A[n]!=0)
- break;
+#define vli_square(result, left, size) vli_mult((result), (left), (left), (size))
- if ((n==8)&&(A[0]==1))
- return 1;
- else
- return 0;
+#endif /* uECC_SQUARE_FUNC */
+
+
+/* Computes p_result = (p_left + p_right) % p_mod.
+ Assumes that p_left < p_mod and p_right < p_mod, p_result != p_mod. */
+#if !asm_modAdd
+static void vli_modAdd(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right, uECC_word_t *p_mod)
+{
+ uECC_word_t l_carry = vli_add(p_result, p_left, p_right);
+ if(l_carry || vli_cmp(p_result, p_mod) >= 0)
+ { /* p_result > p_mod (p_result = p_mod + remainder), so subtract p_mod to get remainder. */
+ vli_sub(p_result, p_result, p_mod);
+ }
}
+#endif
-static int isZero(const uint32_t* A){
- uint8_t n, r=0;
- for(n=0;n<8;n++){
- if (A[n] == 0) r++;
- }
- return r==8;
+/* Computes p_result = (p_left - p_right) % p_mod.
+ Assumes that p_left < p_mod and p_right < p_mod, p_result != p_mod. */
+#if !asm_modSub
+static void vli_modSub(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right, uECC_word_t *p_mod)
+{
+ uECC_word_t l_borrow = vli_sub(p_result, p_left, p_right);
+ if(l_borrow)
+ { /* In this case, p_result == -diff == (max int) - diff.
+ Since -x % d == d - x, we can get the correct result from p_result + p_mod (with overflow). */
+ vli_add(p_result, p_result, p_mod);
+ }
}
+#endif
-static void rshift(uint32_t* A){
- int n, i;
- uint32_t nOld = 0;
- for (i = 8; i--;)
- {
- n = A[i]&0x1;
- A[i] = A[i]>>1 | nOld<<31;
- nOld = n;
- }
+#if !asm_modSub_fast
+ #define vli_modSub_fast(result, left, right) vli_modSub((result), (left), (right), curve_p)
+#endif
+
+#if !asm_mmod_fast
+
+#if (uECC_CURVE == uECC_secp160r1 || uECC_CURVE == uECC_secp256k1)
+/* omega_mult() is defined farther below for the different curves / word sizes */
+static void omega_mult(uECC_word_t * RESTRICT p_result, uECC_word_t * RESTRICT p_right);
+
+/* Computes p_result = p_product % curve_p
+ see http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf page 354
+
+ Note that this only works if log2(omega) < log2(p)/2 */
+static void vli_mmod_fast(uECC_word_t *RESTRICT p_result, uECC_word_t *RESTRICT p_product)
+{
+ uECC_word_t l_tmp[2*uECC_WORDS];
+ uECC_word_t l_carry;
+
+ vli_clear(l_tmp);
+ vli_clear(l_tmp + uECC_WORDS);
+
+ omega_mult(l_tmp, p_product + uECC_WORDS); /* (Rq, q) = q * c */
+
+ l_carry = vli_add(p_result, p_product, l_tmp); /* (C, r) = r + q */
+ vli_clear(p_product);
+ omega_mult(p_product, l_tmp + uECC_WORDS); /* Rq*c */
+ l_carry += vli_add(p_result, p_result, p_product); /* (C1, r) = r + Rq*c */
+
+ while(l_carry > 0)
+ {
+ --l_carry;
+ vli_sub(p_result, p_result, curve_p);
+ }
+
+ if(vli_cmp(p_result, curve_p) > 0)
+ {
+ vli_sub(p_result, p_result, curve_p);
+ }
}
-static int fieldAddAndDivide(const uint32_t *x, const uint32_t *modulus, const uint32_t *reducer, uint32_t* result){
- uint32_t n = add(x, modulus, result, arrayLength);
- rshift(result);
- if(n){ //add prime if carry is still set!
- result[7] |= 0x80000000;//add the carry
- if (isGreater(result, modulus, arrayLength) == 1)
- {
- uint32_t tempas[8];
- setZero(tempas, 8);
- add(result, reducer, tempas, 8);
- copy(tempas, result, arrayLength);
- }
-
- }
- return 0;
+#endif
+
+#if uECC_CURVE == uECC_secp160r1
+
+#if uECC_WORD_SIZE == 1
+static void omega_mult(uint8_t * RESTRICT p_result, uint8_t * RESTRICT p_right)
+{
+ uint8_t l_carry;
+ uint8_t i;
+
+ /* Multiply by (2^31 + 1). */
+ vli_set(p_result + 4, p_right); /* 2^32 */
+ vli_rshift1(p_result + 4); /* 2^31 */
+ p_result[3] = p_right[0] << 7; /* get last bit from shift */
+
+ l_carry = vli_add(p_result, p_result, p_right); /* 2^31 + 1 */
+ for(i = uECC_WORDS; l_carry; ++i)
+ {
+ uint16_t l_sum = (uint16_t)p_result[i] + l_carry;
+ p_result[i] = (uint8_t)l_sum;
+ l_carry = l_sum >> 8;
+ }
+}
+#elif uECC_WORD_SIZE == 4
+static void omega_mult(uint32_t * RESTRICT p_result, uint32_t * RESTRICT p_right)
+{
+ uint32_t l_carry;
+ unsigned i;
+
+ /* Multiply by (2^31 + 1). */
+ vli_set(p_result + 1, p_right); /* 2^32 */
+ vli_rshift1(p_result + 1); /* 2^31 */
+ p_result[0] = p_right[0] << 31; /* get last bit from shift */
+
+ l_carry = vli_add(p_result, p_result, p_right); /* 2^31 + 1 */
+ for(i = uECC_WORDS; l_carry; ++i)
+ {
+ uint64_t l_sum = (uint64_t)p_result[i] + l_carry;
+ p_result[i] = (uint32_t)l_sum;
+ l_carry = l_sum >> 32;
+ }
}
+#endif /* uECC_WORD_SIZE */
-/*
- * Inverse A and output to B
- */
-static void fieldInv(const uint32_t *A, const uint32_t *modulus, const uint32_t *reducer, uint32_t *B){
- uint32_t u[8],v[8],x1[8],x2[8];
- uint32_t tempm[8];
- uint32_t tempm2[8];
- setZero(tempm, 8);
- setZero(tempm2, 8);
- setZero(u, 8);
- setZero(v, 8);
-
- uint8_t t;
- copy(A,u,arrayLength);
- copy(modulus,v,arrayLength);
- setZero(x1, 8);
- setZero(x2, 8);
- x1[0]=1;
- /* While u !=1 and v !=1 */
- while ((isOne(u) || isOne(v))==0) {
- while(!(u[0]&1)) { /* While u is even */
- rshift(u); /* divide by 2 */
- if (!(x1[0]&1)) /*ifx1iseven*/
- rshift(x1); /* Divide by 2 */
- else {
- fieldAddAndDivide(x1,modulus,reducer,tempm); /* tempm=x1+p */
- copy(tempm,x1,arrayLength); /* x1=tempm */
- //rshift(x1); /* Divide by 2 */
- }
- }
- while(!(v[0]&1)) { /* While v is even */
- rshift(v); /* divide by 2 */
- if (!(x2[0]&1)) /*ifx1iseven*/
- rshift(x2); /* Divide by 2 */
- else
- {
- fieldAddAndDivide(x2,modulus,reducer,tempm); /* tempm=x1+p */
- copy(tempm,x2,arrayLength); /* x1=tempm */
- //rshift(x2); /* Divide by 2 */
- }
-
- }
- t=sub(u,v,tempm,arrayLength); /* tempm=u-v */
- if (t==0) { /* If u > 0 */
- copy(tempm,u,arrayLength); /* u=u-v */
- fieldSub(x1,x2,modulus,tempm); /* tempm=x1-x2 */
- copy(tempm,x1,arrayLength); /* x1=x1-x2 */
- } else {
- sub(v,u,tempm,arrayLength); /* tempm=v-u */
- copy(tempm,v,arrayLength); /* v=v-u */
- fieldSub(x2,x1,modulus,tempm); /* tempm=x2-x1 */
- copy(tempm,x2,arrayLength); /* x2=x2-x1 */
- }
- }
- if (isOne(u)) {
- copy(x1,B,arrayLength);
- } else {
- copy(x2,B,arrayLength);
- }
+#elif uECC_CURVE == uECC_secp192r1
+
+/* 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 */
+#if uECC_WORD_SIZE == 1
+static void vli_mmod_fast(uint8_t *RESTRICT p_result, uint8_t *RESTRICT p_product)
+{
+ uint8_t l_tmp[uECC_WORDS];
+ uint8_t l_carry;
+
+ vli_set(p_result, p_product);
+
+ vli_set(l_tmp, &p_product[24]);
+ l_carry = vli_add(p_result, p_result, l_tmp);
+
+ l_tmp[0] = l_tmp[1] = l_tmp[2] = l_tmp[3] = l_tmp[4] = l_tmp[5] = l_tmp[6] = l_tmp[7] = 0;
+ l_tmp[8] = p_product[24]; l_tmp[9] = p_product[25]; l_tmp[10] = p_product[26]; l_tmp[11] = p_product[27];
+ l_tmp[12] = p_product[28]; l_tmp[13] = p_product[29]; l_tmp[14] = p_product[30]; l_tmp[15] = p_product[31];
+ l_tmp[16] = p_product[32]; l_tmp[17] = p_product[33]; l_tmp[18] = p_product[34]; l_tmp[19] = p_product[35];
+ l_tmp[20] = p_product[36]; l_tmp[21] = p_product[37]; l_tmp[22] = p_product[38]; l_tmp[23] = p_product[39];
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ l_tmp[0] = l_tmp[8] = p_product[40];
+ l_tmp[1] = l_tmp[9] = p_product[41];
+ l_tmp[2] = l_tmp[10] = p_product[42];
+ l_tmp[3] = l_tmp[11] = p_product[43];
+ l_tmp[4] = l_tmp[12] = p_product[44];
+ l_tmp[5] = l_tmp[13] = p_product[45];
+ l_tmp[6] = l_tmp[14] = p_product[46];
+ l_tmp[7] = l_tmp[15] = p_product[47];
+ l_tmp[16] = l_tmp[17] = l_tmp[18] = l_tmp[19] = l_tmp[20] = l_tmp[21] = l_tmp[22] = l_tmp[23] = 0;
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ while(l_carry || vli_cmp(curve_p, p_result) != 1)
+ {
+ l_carry -= vli_sub(p_result, p_result, curve_p);
+ }
+}
+#elif uECC_WORD_SIZE == 4
+static void vli_mmod_fast(uint32_t *RESTRICT p_result, uint32_t *RESTRICT p_product)
+{
+ uint32_t l_tmp[uECC_WORDS];
+ int l_carry;
+
+ vli_set(p_result, p_product);
+
+ vli_set(l_tmp, &p_product[6]);
+ l_carry = vli_add(p_result, p_result, l_tmp);
+
+ l_tmp[0] = l_tmp[1] = 0;
+ l_tmp[2] = p_product[6];
+ l_tmp[3] = p_product[7];
+ l_tmp[4] = p_product[8];
+ l_tmp[5] = p_product[9];
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ l_tmp[0] = l_tmp[2] = p_product[10];
+ l_tmp[1] = l_tmp[3] = p_product[11];
+ l_tmp[4] = l_tmp[5] = 0;
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ while(l_carry || vli_cmp(curve_p, p_result) != 1)
+ {
+ l_carry -= vli_sub(p_result, p_result, curve_p);
+ }
}
+#else
+static void vli_mmod_fast(uint64_t *RESTRICT p_result, uint64_t *RESTRICT p_product)
+{
+ uint64_t l_tmp[uECC_WORDS];
+ int l_carry;
-void static ec_double(const uint32_t *px, const uint32_t *py, uint32_t *Dx, uint32_t *Dy){
- uint32_t tempA[8];
- uint32_t tempB[8];
- uint32_t tempC[8];
- uint32_t tempD[16];
+ vli_set(p_result, p_product);
+
+ vli_set(l_tmp, &p_product[3]);
+ l_carry = vli_add(p_result, p_result, l_tmp);
+
+ l_tmp[0] = 0;
+ l_tmp[1] = p_product[3];
+ l_tmp[2] = p_product[4];
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ l_tmp[0] = l_tmp[1] = p_product[5];
+ l_tmp[2] = 0;
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ while(l_carry || vli_cmp(curve_p, p_result) != 1)
+ {
+ l_carry -= vli_sub(p_result, p_result, curve_p);
+ }
+}
+#endif /* uECC_WORD_SIZE */
+
+#elif uECC_CURVE == uECC_secp256r1
+
+/* Computes p_result = p_product % curve_p
+ from http://www.nsa.gov/ia/_files/nist-routines.pdf */
+#if uECC_WORD_SIZE == 1
+static void vli_mmod_fast(uint8_t *RESTRICT p_result, uint8_t *RESTRICT p_product)
+{
+ uint8_t l_tmp[uECC_BYTES];
+ int8_t l_carry;
+
+ /* t */
+ vli_set(p_result, p_product);
+
+ /* s1 */
+ l_tmp[0] = l_tmp[1] = l_tmp[2] = l_tmp[3] = 0;
+ l_tmp[4] = l_tmp[5] = l_tmp[6] = l_tmp[7] = 0;
+ l_tmp[8] = l_tmp[9] = l_tmp[10] = l_tmp[11] = 0;
+ l_tmp[12] = p_product[44]; l_tmp[13] = p_product[45]; l_tmp[14] = p_product[46]; l_tmp[15] = p_product[47];
+ l_tmp[16] = p_product[48]; l_tmp[17] = p_product[49]; l_tmp[18] = p_product[50]; l_tmp[19] = p_product[51];
+ l_tmp[20] = p_product[52]; l_tmp[21] = p_product[53]; l_tmp[22] = p_product[54]; l_tmp[23] = p_product[55];
+ l_tmp[24] = p_product[56]; l_tmp[25] = p_product[57]; l_tmp[26] = p_product[58]; l_tmp[27] = p_product[59];
+ l_tmp[28] = p_product[60]; l_tmp[29] = p_product[61]; l_tmp[30] = p_product[62]; l_tmp[31] = p_product[63];
+ l_carry = vli_add(l_tmp, l_tmp, l_tmp);
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ /* s2 */
+ l_tmp[12] = p_product[48]; l_tmp[13] = p_product[49]; l_tmp[14] = p_product[50]; l_tmp[15] = p_product[51];
+ l_tmp[16] = p_product[52]; l_tmp[17] = p_product[53]; l_tmp[18] = p_product[54]; l_tmp[19] = p_product[55];
+ l_tmp[20] = p_product[56]; l_tmp[21] = p_product[57]; l_tmp[22] = p_product[58]; l_tmp[23] = p_product[59];
+ l_tmp[24] = p_product[60]; l_tmp[25] = p_product[61]; l_tmp[26] = p_product[62]; l_tmp[27] = p_product[63];
+ l_tmp[28] = l_tmp[29] = l_tmp[30] = l_tmp[31] = 0;
+ l_carry += vli_add(l_tmp, l_tmp, l_tmp);
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ /* s3 */
+ l_tmp[0] = p_product[32]; l_tmp[1] = p_product[33]; l_tmp[2] = p_product[34]; l_tmp[3] = p_product[35];
+ l_tmp[4] = p_product[36]; l_tmp[5] = p_product[37]; l_tmp[6] = p_product[38]; l_tmp[7] = p_product[39];
+ l_tmp[8] = p_product[40]; l_tmp[9] = p_product[41]; l_tmp[10] = p_product[42]; l_tmp[11] = p_product[43];
+ l_tmp[12] = l_tmp[13] = l_tmp[14] = l_tmp[15] = 0;
+ l_tmp[16] = l_tmp[17] = l_tmp[18] = l_tmp[19] = 0;
+ l_tmp[20] = l_tmp[21] = l_tmp[22] = l_tmp[23] = 0;
+ l_tmp[24] = p_product[56]; l_tmp[25] = p_product[57]; l_tmp[26] = p_product[58]; l_tmp[27] = p_product[59];
+ l_tmp[28] = p_product[60]; l_tmp[29] = p_product[61]; l_tmp[30] = p_product[62]; l_tmp[31] = p_product[63];
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ /* s4 */
+ l_tmp[0] = p_product[36]; l_tmp[1] = p_product[37]; l_tmp[2] = p_product[38]; l_tmp[3] = p_product[39];
+ l_tmp[4] = p_product[40]; l_tmp[5] = p_product[41]; l_tmp[6] = p_product[42]; l_tmp[7] = p_product[43];
+ l_tmp[8] = p_product[44]; l_tmp[9] = p_product[45]; l_tmp[10] = p_product[46]; l_tmp[11] = p_product[47];
+ l_tmp[12] = p_product[52]; l_tmp[13] = p_product[53]; l_tmp[14] = p_product[54]; l_tmp[15] = p_product[55];
+ l_tmp[16] = p_product[56]; l_tmp[17] = p_product[57]; l_tmp[18] = p_product[58]; l_tmp[19] = p_product[59];
+ l_tmp[20] = p_product[60]; l_tmp[21] = p_product[61]; l_tmp[22] = p_product[62]; l_tmp[23] = p_product[63];
+ l_tmp[24] = p_product[52]; l_tmp[25] = p_product[53]; l_tmp[26] = p_product[54]; l_tmp[27] = p_product[55];
+ l_tmp[28] = p_product[32]; l_tmp[29] = p_product[33]; l_tmp[30] = p_product[34]; l_tmp[31] = p_product[35];
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ /* d1 */
+ l_tmp[0] = p_product[44]; l_tmp[1] = p_product[45]; l_tmp[2] = p_product[46]; l_tmp[3] = p_product[47];
+ l_tmp[4] = p_product[48]; l_tmp[5] = p_product[49]; l_tmp[6] = p_product[50]; l_tmp[7] = p_product[51];
+ l_tmp[8] = p_product[52]; l_tmp[9] = p_product[53]; l_tmp[10] = p_product[54]; l_tmp[11] = p_product[55];
+ l_tmp[12] = l_tmp[13] = l_tmp[14] = l_tmp[15] = 0;
+ l_tmp[16] = l_tmp[17] = l_tmp[18] = l_tmp[19] = 0;
+ l_tmp[20] = l_tmp[21] = l_tmp[22] = l_tmp[23] = 0;
+ l_tmp[24] = p_product[32]; l_tmp[25] = p_product[33]; l_tmp[26] = p_product[34]; l_tmp[27] = p_product[35];
+ l_tmp[28] = p_product[40]; l_tmp[29] = p_product[41]; l_tmp[30] = p_product[42]; l_tmp[31] = p_product[43];
+ l_carry -= vli_sub(p_result, p_result, l_tmp);
+
+ /* d2 */
+ l_tmp[0] = p_product[48]; l_tmp[1] = p_product[49]; l_tmp[2] = p_product[50]; l_tmp[3] = p_product[51];
+ l_tmp[4] = p_product[52]; l_tmp[5] = p_product[53]; l_tmp[6] = p_product[54]; l_tmp[7] = p_product[55];
+ l_tmp[8] = p_product[56]; l_tmp[9] = p_product[57]; l_tmp[10] = p_product[58]; l_tmp[11] = p_product[59];
+ l_tmp[12] = p_product[60]; l_tmp[13] = p_product[61]; l_tmp[14] = p_product[62]; l_tmp[15] = p_product[63];
+ l_tmp[16] = l_tmp[17] = l_tmp[18] = l_tmp[19] = 0;
+ l_tmp[20] = l_tmp[21] = l_tmp[22] = l_tmp[23] = 0;
+ l_tmp[24] = p_product[36]; l_tmp[25] = p_product[37]; l_tmp[26] = p_product[38]; l_tmp[27] = p_product[39];
+ l_tmp[28] = p_product[44]; l_tmp[29] = p_product[45]; l_tmp[30] = p_product[46]; l_tmp[31] = p_product[47];
+ l_carry -= vli_sub(p_result, p_result, l_tmp);
+
+ /* d3 */
+ l_tmp[0] = p_product[52]; l_tmp[1] = p_product[53]; l_tmp[2] = p_product[54]; l_tmp[3] = p_product[55];
+ l_tmp[4] = p_product[56]; l_tmp[5] = p_product[57]; l_tmp[6] = p_product[58]; l_tmp[7] = p_product[59];
+ l_tmp[8] = p_product[60]; l_tmp[9] = p_product[61]; l_tmp[10] = p_product[62]; l_tmp[11] = p_product[63];
+ l_tmp[12] = p_product[32]; l_tmp[13] = p_product[33]; l_tmp[14] = p_product[34]; l_tmp[15] = p_product[35];
+ l_tmp[16] = p_product[36]; l_tmp[17] = p_product[37]; l_tmp[18] = p_product[38]; l_tmp[19] = p_product[39];
+ l_tmp[20] = p_product[40]; l_tmp[21] = p_product[41]; l_tmp[22] = p_product[42]; l_tmp[23] = p_product[43];
+ l_tmp[24] = l_tmp[25] = l_tmp[26] = l_tmp[27] = 0;
+ l_tmp[28] = p_product[48]; l_tmp[29] = p_product[49]; l_tmp[30] = p_product[50]; l_tmp[31] = p_product[51];
+ l_carry -= vli_sub(p_result, p_result, l_tmp);
+
+ /* d4 */
+ l_tmp[0] = p_product[56]; l_tmp[1] = p_product[57]; l_tmp[2] = p_product[58]; l_tmp[3] = p_product[59];
+ l_tmp[4] = p_product[60]; l_tmp[5] = p_product[61]; l_tmp[6] = p_product[62]; l_tmp[7] = p_product[63];
+ l_tmp[8] = l_tmp[9] = l_tmp[10] = l_tmp[11] = 0;
+ l_tmp[12] = p_product[36]; l_tmp[13] = p_product[37]; l_tmp[14] = p_product[38]; l_tmp[15] = p_product[39];
+ l_tmp[16] = p_product[40]; l_tmp[17] = p_product[41]; l_tmp[18] = p_product[42]; l_tmp[19] = p_product[43];
+ l_tmp[20] = p_product[44]; l_tmp[21] = p_product[45]; l_tmp[22] = p_product[46]; l_tmp[23] = p_product[47];
+ l_tmp[24] = l_tmp[25] = l_tmp[26] = l_tmp[27] = 0;
+ l_tmp[28] = p_product[52]; l_tmp[29] = p_product[53]; l_tmp[30] = p_product[54]; l_tmp[31] = p_product[55];
+ l_carry -= vli_sub(p_result, p_result, l_tmp);
+
+ if(l_carry < 0)
+ {
+ do
+ {
+ l_carry += vli_add(p_result, p_result, curve_p);
+ } while(l_carry < 0);
+ }
+ else
+ {
+ while(l_carry || vli_cmp(curve_p, p_result) != 1)
+ {
+ l_carry -= vli_sub(p_result, p_result, curve_p);
+ }
+ }
+}
+#elif uECC_WORD_SIZE == 4
+static void vli_mmod_fast(uint32_t *RESTRICT p_result, uint32_t *RESTRICT p_product)
+{
+ uint32_t l_tmp[uECC_WORDS];
+ int l_carry;
+
+ /* t */
+ vli_set(p_result, p_product);
+
+ /* s1 */
+ l_tmp[0] = l_tmp[1] = l_tmp[2] = 0;
+ l_tmp[3] = p_product[11];
+ l_tmp[4] = p_product[12];
+ l_tmp[5] = p_product[13];
+ l_tmp[6] = p_product[14];
+ l_tmp[7] = p_product[15];
+ l_carry = vli_add(l_tmp, l_tmp, l_tmp);
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ /* s2 */
+ l_tmp[3] = p_product[12];
+ l_tmp[4] = p_product[13];
+ l_tmp[5] = p_product[14];
+ l_tmp[6] = p_product[15];
+ l_tmp[7] = 0;
+ l_carry += vli_add(l_tmp, l_tmp, l_tmp);
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ /* s3 */
+ l_tmp[0] = p_product[8];
+ l_tmp[1] = p_product[9];
+ l_tmp[2] = p_product[10];
+ l_tmp[3] = l_tmp[4] = l_tmp[5] = 0;
+ l_tmp[6] = p_product[14];
+ l_tmp[7] = p_product[15];
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ /* s4 */
+ l_tmp[0] = p_product[9];
+ l_tmp[1] = p_product[10];
+ l_tmp[2] = p_product[11];
+ l_tmp[3] = p_product[13];
+ l_tmp[4] = p_product[14];
+ l_tmp[5] = p_product[15];
+ l_tmp[6] = p_product[13];
+ l_tmp[7] = p_product[8];
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ /* d1 */
+ l_tmp[0] = p_product[11];
+ l_tmp[1] = p_product[12];
+ l_tmp[2] = p_product[13];
+ l_tmp[3] = l_tmp[4] = l_tmp[5] = 0;
+ l_tmp[6] = p_product[8];
+ l_tmp[7] = p_product[10];
+ l_carry -= vli_sub(p_result, p_result, l_tmp);
+
+ /* d2 */
+ l_tmp[0] = p_product[12];
+ l_tmp[1] = p_product[13];
+ l_tmp[2] = p_product[14];
+ l_tmp[3] = p_product[15];
+ l_tmp[4] = l_tmp[5] = 0;
+ l_tmp[6] = p_product[9];
+ l_tmp[7] = p_product[11];
+ l_carry -= vli_sub(p_result, p_result, l_tmp);
+
+ /* d3 */
+ l_tmp[0] = p_product[13];
+ l_tmp[1] = p_product[14];
+ l_tmp[2] = p_product[15];
+ l_tmp[3] = p_product[8];
+ l_tmp[4] = p_product[9];
+ l_tmp[5] = p_product[10];
+ l_tmp[6] = 0;
+ l_tmp[7] = p_product[12];
+ l_carry -= vli_sub(p_result, p_result, l_tmp);
+
+ /* d4 */
+ l_tmp[0] = p_product[14];
+ l_tmp[1] = p_product[15];
+ l_tmp[2] = 0;
+ l_tmp[3] = p_product[9];
+ l_tmp[4] = p_product[10];
+ l_tmp[5] = p_product[11];
+ l_tmp[6] = 0;
+ l_tmp[7] = p_product[13];
+ l_carry -= vli_sub(p_result, p_result, l_tmp);
+
+ if(l_carry < 0)
+ {
+ do
+ {
+ l_carry += vli_add(p_result, p_result, curve_p);
+ } while(l_carry < 0);
+ }
+ else
+ {
+ while(l_carry || vli_cmp(curve_p, p_result) != 1)
+ {
+ l_carry -= vli_sub(p_result, p_result, curve_p);
+ }
+ }
+}
+#else
+static void vli_mmod_fast(uint64_t *RESTRICT p_result, uint64_t *RESTRICT p_product)
+{
+ uint64_t l_tmp[uECC_WORDS];
+ int l_carry;
+
+ /* t */
+ vli_set(p_result, p_product);
+
+ /* s1 */
+ l_tmp[0] = 0;
+ l_tmp[1] = p_product[5] & 0xffffffff00000000ull;
+ l_tmp[2] = p_product[6];
+ l_tmp[3] = p_product[7];
+ l_carry = vli_add(l_tmp, l_tmp, l_tmp);
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ /* s2 */
+ l_tmp[1] = p_product[6] << 32;
+ l_tmp[2] = (p_product[6] >> 32) | (p_product[7] << 32);
+ l_tmp[3] = p_product[7] >> 32;
+ l_carry += vli_add(l_tmp, l_tmp, l_tmp);
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ /* s3 */
+ l_tmp[0] = p_product[4];
+ l_tmp[1] = p_product[5] & 0xffffffff;
+ l_tmp[2] = 0;
+ l_tmp[3] = p_product[7];
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ /* s4 */
+ l_tmp[0] = (p_product[4] >> 32) | (p_product[5] << 32);
+ l_tmp[1] = (p_product[5] >> 32) | (p_product[6] & 0xffffffff00000000ull);
+ l_tmp[2] = p_product[7];
+ l_tmp[3] = (p_product[6] >> 32) | (p_product[4] << 32);
+ l_carry += vli_add(p_result, p_result, l_tmp);
+
+ /* d1 */
+ l_tmp[0] = (p_product[5] >> 32) | (p_product[6] << 32);
+ l_tmp[1] = (p_product[6] >> 32);
+ l_tmp[2] = 0;
+ l_tmp[3] = (p_product[4] & 0xffffffff) | (p_product[5] << 32);
+ l_carry -= vli_sub(p_result, p_result, l_tmp);
+
+ /* d2 */
+ l_tmp[0] = p_product[6];
+ l_tmp[1] = p_product[7];
+ l_tmp[2] = 0;
+ l_tmp[3] = (p_product[4] >> 32) | (p_product[5] & 0xffffffff00000000ull);
+ l_carry -= vli_sub(p_result, p_result, l_tmp);
+
+ /* d3 */
+ l_tmp[0] = (p_product[6] >> 32) | (p_product[7] << 32);
+ l_tmp[1] = (p_product[7] >> 32) | (p_product[4] << 32);
+ l_tmp[2] = (p_product[4] >> 32) | (p_product[5] << 32);
+ l_tmp[3] = (p_product[6] << 32);
+ l_carry -= vli_sub(p_result, p_result, l_tmp);
+
+ /* d4 */
+ l_tmp[0] = p_product[7];
+ l_tmp[1] = p_product[4] & 0xffffffff00000000ull;
+ l_tmp[2] = p_product[5];
+ l_tmp[3] = p_product[6] & 0xffffffff00000000ull;
+ l_carry -= vli_sub(p_result, p_result, l_tmp);
+
+ if(l_carry < 0)
+ {
+ do
+ {
+ l_carry += vli_add(p_result, p_result, curve_p);
+ } while(l_carry < 0);
+ }
+ else
+ {
+ while(l_carry || vli_cmp(curve_p, p_result) != 1)
+ {
+ l_carry -= vli_sub(p_result, p_result, curve_p);
+ }
+ }
+}
+#endif /* uECC_WORD_SIZE */
+
+#elif uECC_CURVE == uECC_secp256k1
+
+#if uECC_WORD_SIZE == 1
+static void omega_mult(uint8_t * RESTRICT p_result, uint8_t * RESTRICT p_right)
+{
+ /* Multiply by (2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
+ uECC_word_t r0 = 0;
+ uECC_word_t r1 = 0;
+ uECC_word_t r2 = 0;
+
+ wordcount_t k;
+
+ /* Multiply by (2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
+ muladd(0xD1, p_right[0], &r0, &r1, &r2);
+ p_result[0] = r0;
+ r0 = r1;
+ r1 = r2;
+ /* r2 is still 0 */
+
+ for(k = 1; k < uECC_WORDS; ++k)
+ {
+ muladd(0x03, p_right[k-1], &r0, &r1, &r2);
+ muladd(0xD1, p_right[k], &r0, &r1, &r2);
+ p_result[k] = r0;
+ r0 = r1;
+ r1 = r2;
+ r2 = 0;
+ }
+
+ muladd(0x03, p_right[uECC_WORDS-1], &r0, &r1, &r2);
+ p_result[uECC_WORDS] = r0;
+ p_result[uECC_WORDS + 1] = r1;
+
+ p_result[4 + uECC_WORDS] = vli_add(p_result + 4, p_result + 4, p_right); /* add the 2^32 multiple */
+}
+#elif uECC_WORD_SIZE == 4
+static void omega_mult(uint32_t * RESTRICT p_result, uint32_t * RESTRICT p_right)
+{
+ /* Multiply by (2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
+ uint32_t l_carry = 0;
+ wordcount_t k;
+
+ for(k = 0; k < uECC_WORDS; ++k)
+ {
+ uint64_t p = (uint64_t)0x3D1 * p_right[k] + l_carry;
+ p_result[k] = (p & 0xffffffff);
+ l_carry = p >> 32;
+ }
+ p_result[uECC_WORDS] = l_carry;
+
+ p_result[1 + uECC_WORDS] = vli_add(p_result + 1, p_result + 1, p_right); /* add the 2^32 multiple */
+}
+#else
+static void omega_mult(uint64_t * RESTRICT p_result, uint64_t * RESTRICT p_right)
+{
+ uECC_word_t r0 = 0;
+ uECC_word_t r1 = 0;
+ uECC_word_t r2 = 0;
+
+ wordcount_t k;
+
+ /* Multiply by (2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
+ for(k = 0; k < uECC_WORDS; ++k)
+ {
+ muladd(0x1000003D1ull, p_right[k], &r0, &r1, &r2);
+ p_result[k] = r0;
+ r0 = r1;
+ r1 = r2;
+ r2 = 0;
+ }
+
+ p_result[uECC_WORDS] = r0;
+}
+#endif /* uECC_WORD_SIZE */
+
+#endif /* uECC_CURVE */
+#endif /* !asm_mmod_fast */
+
+/* Computes p_result = (p_left * p_right) % curve_p. */
+static void vli_modMult_fast(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right)
+{
+ uECC_word_t l_product[2 * uECC_WORDS];
+ vli_mult(l_product, p_left, p_right);
+ vli_mmod_fast(p_result, l_product);
+}
+
+#if uECC_SQUARE_FUNC
+
+/* Computes p_result = p_left^2 % curve_p. */
+static void vli_modSquare_fast(uECC_word_t *p_result, uECC_word_t *p_left)
+{
+ uECC_word_t l_product[2 * uECC_WORDS];
+ vli_square(l_product, p_left);
+ vli_mmod_fast(p_result, l_product);
+}
+
+#else /* uECC_SQUARE_FUNC */
+
+#define vli_modSquare_fast(result, left) vli_modMult_fast((result), (left), (left))
+
+#endif /* uECC_SQUARE_FUNC */
- if(isZero(px) && isZero(py)){
- copy(px, Dx,arrayLength);
- copy(py, Dy,arrayLength);
- return;
- }
- fieldMult(px, px, tempD, arrayLength);
- fieldModP(tempA, tempD);
- setZero(tempB, 8);
- tempB[0] = 0x00000001;
- fieldSub(tempA, tempB, ecc_prime_m, tempC); //tempC = (qx^2-1)
- tempB[0] = 0x00000003;
- fieldMult(tempC, tempB, tempD, arrayLength);
- fieldModP(tempA, tempD);//tempA = 3*(qx^2-1)
- fieldAdd(py, py, ecc_prime_r, tempB); //tempB = 2*qy
- fieldInv(tempB, ecc_prime_m, ecc_prime_r, tempC); //tempC = 1/(2*qy)
- fieldMult(tempA, tempC, tempD, arrayLength); //tempB = lambda = (3*(qx^2-1))/(2*qy)
- fieldModP(tempB, tempD);
-
- fieldMult(tempB, tempB, tempD, arrayLength); //tempC = lambda^2
- fieldModP(tempC, tempD);
- fieldSub(tempC, px, ecc_prime_m, tempA); //lambda^2 - Px
- fieldSub(tempA, px, ecc_prime_m, Dx); //lambda^2 - Px - Qx
-
- fieldSub(px, Dx, ecc_prime_m, tempA); //tempA = qx-dx
- fieldMult(tempB, tempA, tempD, arrayLength); //tempC = lambda * (qx-dx)
- fieldModP(tempC, tempD);
- fieldSub(tempC, py, ecc_prime_m, Dy); //Dy = lambda * (qx-dx) - px
-}
-
-void static ec_add(const uint32_t *px, const uint32_t *py, const uint32_t *qx, const uint32_t *qy, uint32_t *Sx, uint32_t *Sy){
- uint32_t tempA[8];
- uint32_t tempB[8];
- uint32_t tempC[8];
- uint32_t tempD[16];
-
- if(isZero(px) && isZero(py)){
- copy(qx, Sx,arrayLength);
- copy(qy, Sy,arrayLength);
- return;
- } else if(isZero(qx) && isZero(qy)) {
- copy(px, Sx,arrayLength);
- copy(py, Sy,arrayLength);
- return;
+#define EVEN(vli) (!(vli[0] & 1))
+/* Computes p_result = (1 / p_input) % p_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 */
+#if !asm_modInv
+static void vli_modInv(uECC_word_t *p_result, uECC_word_t *p_input, uECC_word_t *p_mod)
+{
+ uECC_word_t a[uECC_WORDS], b[uECC_WORDS], u[uECC_WORDS], v[uECC_WORDS];
+ uECC_word_t l_carry;
+ cmpresult_t l_cmpResult;
+
+ if(vli_isZero(p_input))
+ {
+ vli_clear(p_result);
+ return;
+ }
+
+ vli_set(a, p_input);
+ vli_set(b, p_mod);
+ vli_clear(u);
+ u[0] = 1;
+ vli_clear(v);
+ while((l_cmpResult = vli_cmp(a, b)) != 0)
+ {
+ l_carry = 0;
+ if(EVEN(a))
+ {
+ vli_rshift1(a);
+ if(!EVEN(u))
+ {
+ l_carry = vli_add(u, u, p_mod);
+ }
+ vli_rshift1(u);
+ if(l_carry)
+ {
+ u[uECC_WORDS-1] |= HIGH_BIT_SET;
+ }
+ }
+ else if(EVEN(b))
+ {
+ vli_rshift1(b);
+ if(!EVEN(v))
+ {
+ l_carry = vli_add(v, v, p_mod);
+ }
+ vli_rshift1(v);
+ if(l_carry)
+ {
+ v[uECC_WORDS-1] |= HIGH_BIT_SET;
+ }
+ }
+ else if(l_cmpResult > 0)
+ {
+ vli_sub(a, a, b);
+ vli_rshift1(a);
+ if(vli_cmp(u, v) < 0)
+ {
+ vli_add(u, u, p_mod);
+ }
+ vli_sub(u, u, v);
+ if(!EVEN(u))
+ {
+ l_carry = vli_add(u, u, p_mod);
+ }
+ vli_rshift1(u);
+ if(l_carry)
+ {
+ u[uECC_WORDS-1] |= HIGH_BIT_SET;
+ }
+ }
+ else
+ {
+ vli_sub(b, b, a);
+ vli_rshift1(b);
+ if(vli_cmp(v, u) < 0)
+ {
+ vli_add(v, v, p_mod);
+ }
+ vli_sub(v, v, u);
+ if(!EVEN(v))
+ {
+ l_carry = vli_add(v, v, p_mod);
+ }
+ vli_rshift1(v);
+ if(l_carry)
+ {
+ v[uECC_WORDS-1] |= HIGH_BIT_SET;
+ }
+ }
+ }
+
+ vli_set(p_result, u);
+}
+#endif /* !asm_modInv */
+
+/* ------ Point operations ------ */
+
+/* Returns 1 if p_point is the point at infinity, 0 otherwise. */
+static cmpresult_t EccPoint_isZero(EccPoint *p_point)
+{
+ return (vli_isZero(p_point->x) && vli_isZero(p_point->y));
+}
+
+/* Point multiplication algorithm using Montgomery's ladder with co-Z coordinates.
+From http://eprint.iacr.org/2011/338.pdf
+*/
+
+/* Double in place */
+#if (uECC_CURVE == uECC_secp256k1)
+static void EccPoint_double_jacobian(uECC_word_t * RESTRICT X1, uECC_word_t * RESTRICT Y1, uECC_word_t * RESTRICT Z1)
+{
+ /* t1 = X, t2 = Y, t3 = Z */
+ uECC_word_t t4[uECC_WORDS];
+ uECC_word_t t5[uECC_WORDS];
+
+ if(vli_isZero(Z1))
+ {
+ return;
+ }
+
+ vli_modSquare_fast(t5, Y1); /* t5 = y1^2 */
+ vli_modMult_fast(t4, X1, t5); /* t4 = x1*y1^2 = A */
+ vli_modSquare_fast(X1, X1); /* t1 = x1^2 */
+ vli_modSquare_fast(t5, t5); /* t5 = y1^4 */
+ vli_modMult_fast(Z1, Y1, Z1); /* t3 = y1*z1 = z3 */
+
+ vli_modAdd(Y1, X1, X1, curve_p); /* t2 = 2*x1^2 */
+ vli_modAdd(Y1, Y1, X1, curve_p); /* t2 = 3*x1^2 */
+ if(vli_testBit(Y1, 0))
+ {
+ uECC_word_t l_carry = vli_add(Y1, Y1, curve_p);
+ vli_rshift1(Y1);
+ Y1[uECC_WORDS-1] |= l_carry << (uECC_WORD_BITS - 1);
+ }
+ else
+ {
+ vli_rshift1(Y1);
+ }
+ /* t2 = 3/2*(x1^2) = B */
+
+ vli_modSquare_fast(X1, Y1); /* t1 = B^2 */
+ vli_modSub(X1, X1, t4, curve_p); /* t1 = B^2 - A */
+ vli_modSub(X1, X1, t4, curve_p); /* t1 = B^2 - 2A = x3 */
+
+ vli_modSub(t4, t4, X1, curve_p); /* t4 = A - x3 */
+ vli_modMult_fast(Y1, Y1, t4); /* t2 = B * (A - x3) */
+ vli_modSub(Y1, Y1, t5, curve_p); /* t2 = B * (A - x3) - y1^4 = y3 */
+}
+#else
+static void EccPoint_double_jacobian(uECC_word_t * RESTRICT X1, uECC_word_t * RESTRICT Y1, uECC_word_t * RESTRICT Z1)
+{
+ /* t1 = X, t2 = Y, t3 = Z */
+ uECC_word_t t4[uECC_WORDS];
+ uECC_word_t t5[uECC_WORDS];
+
+ if(vli_isZero(Z1))
+ {
+ return;
+ }
+
+ vli_modSquare_fast(t4, Y1); /* t4 = y1^2 */
+ vli_modMult_fast(t5, X1, t4); /* t5 = x1*y1^2 = A */
+ vli_modSquare_fast(t4, t4); /* t4 = y1^4 */
+ vli_modMult_fast(Y1, Y1, Z1); /* t2 = y1*z1 = z3 */
+ vli_modSquare_fast(Z1, Z1); /* t3 = z1^2 */
+
+ vli_modAdd(X1, X1, Z1, curve_p); /* t1 = x1 + z1^2 */
+ vli_modAdd(Z1, Z1, Z1, curve_p); /* t3 = 2*z1^2 */
+ vli_modSub_fast(Z1, X1, Z1); /* t3 = x1 - z1^2 */
+ vli_modMult_fast(X1, X1, Z1); /* t1 = x1^2 - z1^4 */
+
+ vli_modAdd(Z1, X1, X1, curve_p); /* t3 = 2*(x1^2 - z1^4) */
+ vli_modAdd(X1, X1, Z1, curve_p); /* t1 = 3*(x1^2 - z1^4) */
+ if(vli_testBit(X1, 0))
+ {
+ uECC_word_t l_carry = vli_add(X1, X1, curve_p);
+ vli_rshift1(X1);
+ X1[uECC_WORDS-1] |= l_carry << (uECC_WORD_BITS - 1);
+ }
+ else
+ {
+ vli_rshift1(X1);
+ }
+ /* t1 = 3/2*(x1^2 - z1^4) = B */
+
+ vli_modSquare_fast(Z1, X1); /* t3 = B^2 */
+ vli_modSub_fast(Z1, Z1, t5); /* t3 = B^2 - A */
+ vli_modSub_fast(Z1, Z1, t5); /* t3 = B^2 - 2A = x3 */
+ vli_modSub_fast(t5, t5, Z1); /* t5 = A - x3 */
+ vli_modMult_fast(X1, X1, t5); /* t1 = B * (A - x3) */
+ vli_modSub_fast(t4, X1, t4); /* t4 = B * (A - x3) - y1^4 = y3 */
+
+ vli_set(X1, Z1);
+ vli_set(Z1, Y1);
+ vli_set(Y1, t4);
+}
+#endif
+
+/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */
+static void apply_z(uECC_word_t * RESTRICT X1, uECC_word_t * RESTRICT Y1, uECC_word_t * RESTRICT Z)
+{
+ uECC_word_t t1[uECC_WORDS];
+
+ vli_modSquare_fast(t1, Z); /* z^2 */
+ vli_modMult_fast(X1, X1, t1); /* x1 * z^2 */
+ vli_modMult_fast(t1, t1, Z); /* z^3 */
+ vli_modMult_fast(Y1, Y1, t1); /* y1 * z^3 */
+}
+
+/* P = (x1, y1) => 2P, (x2, y2) => P' */
+static void XYcZ_initial_double(uECC_word_t * RESTRICT X1, uECC_word_t * RESTRICT Y1,
+ uECC_word_t * RESTRICT X2, uECC_word_t * RESTRICT Y2, const uECC_word_t * RESTRICT p_initialZ)
+{
+ uECC_word_t z[uECC_WORDS];
+
+ vli_set(X2, X1);
+ vli_set(Y2, Y1);
+
+ vli_clear(z);
+ z[0] = 1;
+ if(p_initialZ)
+ {
+ vli_set(z, p_initialZ);
+ }
+
+ apply_z(X1, Y1, z);
+
+ EccPoint_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(uECC_word_t * RESTRICT X1, uECC_word_t * RESTRICT Y1, uECC_word_t * RESTRICT X2, uECC_word_t * RESTRICT Y2)
+{
+ /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
+ uECC_word_t t5[uECC_WORDS];
+
+ vli_modSub_fast(t5, X2, X1); /* t5 = x2 - x1 */
+ vli_modSquare_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */
+ vli_modMult_fast(X1, X1, t5); /* t1 = x1*A = B */
+ vli_modMult_fast(X2, X2, t5); /* t3 = x2*A = C */
+ vli_modSub_fast(Y2, Y2, Y1); /* t4 = y2 - y1 */
+ vli_modSquare_fast(t5, Y2); /* t5 = (y2 - y1)^2 = D */
+
+ vli_modSub_fast(t5, t5, X1); /* t5 = D - B */
+ vli_modSub_fast(t5, t5, X2); /* t5 = D - B - C = x3 */
+ vli_modSub_fast(X2, X2, X1); /* t3 = C - B */
+ vli_modMult_fast(Y1, Y1, X2); /* t2 = y1*(C - B) */
+ vli_modSub_fast(X2, X1, t5); /* t3 = B - x3 */
+ vli_modMult_fast(Y2, Y2, X2); /* t4 = (y2 - y1)*(B - x3) */
+ vli_modSub_fast(Y2, Y2, Y1); /* 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_addC(uECC_word_t * RESTRICT X1, uECC_word_t * RESTRICT Y1, uECC_word_t * RESTRICT X2, uECC_word_t * RESTRICT Y2)
+{
+ /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */
+ uECC_word_t t5[uECC_WORDS];
+ uECC_word_t t6[uECC_WORDS];
+ uECC_word_t t7[uECC_WORDS];
+
+ vli_modSub_fast(t5, X2, X1); /* t5 = x2 - x1 */
+ vli_modSquare_fast(t5, t5); /* t5 = (x2 - x1)^2 = A */
+ vli_modMult_fast(X1, X1, t5); /* t1 = x1*A = B */
+ vli_modMult_fast(X2, X2, t5); /* t3 = x2*A = C */
+ vli_modAdd(t5, Y2, Y1, curve_p); /* t4 = y2 + y1 */
+ vli_modSub_fast(Y2, Y2, Y1); /* t4 = y2 - y1 */
+
+ vli_modSub_fast(t6, X2, X1); /* t6 = C - B */
+ vli_modMult_fast(Y1, Y1, t6); /* t2 = y1 * (C - B) */
+ vli_modAdd(t6, X1, X2, curve_p); /* t6 = B + C */
+ vli_modSquare_fast(X2, Y2); /* t3 = (y2 - y1)^2 */
+ vli_modSub_fast(X2, X2, t6); /* t3 = x3 */
+
+ vli_modSub_fast(t7, X1, X2); /* t7 = B - x3 */
+ vli_modMult_fast(Y2, Y2, t7); /* t4 = (y2 - y1)*(B - x3) */
+ vli_modSub_fast(Y2, Y2, Y1); /* t4 = y3 */
+
+ vli_modSquare_fast(t7, t5); /* t7 = (y2 + y1)^2 = F */
+ vli_modSub_fast(t7, t7, t6); /* t7 = x3' */
+ vli_modSub_fast(t6, t7, X1); /* t6 = x3' - B */
+ vli_modMult_fast(t6, t6, t5); /* t6 = (y2 + y1)*(x3' - B) */
+ vli_modSub_fast(Y1, t6, Y1); /* t2 = y3' */
+
+ vli_set(X1, t7);
+}
+
+static void EccPoint_mult(EccPoint * RESTRICT p_result, EccPoint * RESTRICT p_point,
+ const uECC_word_t * RESTRICT p_scalar, const uECC_word_t * RESTRICT p_initialZ, bitcount_t p_numBits)
+{
+ /* R0 and R1 */
+ uECC_word_t Rx[2][uECC_WORDS];
+ uECC_word_t Ry[2][uECC_WORDS];
+ uECC_word_t z[uECC_WORDS];
+
+ bitcount_t i;
+ uECC_word_t nb;
+
+ vli_set(Rx[1], p_point->x);
+ vli_set(Ry[1], p_point->y);
+
+ XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], p_initialZ);
+
+ for(i = p_numBits - 2; i > 0; --i)
+ {
+ nb = !vli_testBit(p_scalar, i);
+ XYcZ_addC(Rx[1-nb], Ry[1-nb], Rx[nb], Ry[nb]);
+ XYcZ_add(Rx[nb], Ry[nb], Rx[1-nb], Ry[1-nb]);
+ }
+
+ nb = !vli_testBit(p_scalar, 0);
+ XYcZ_addC(Rx[1-nb], Ry[1-nb], Rx[nb], Ry[nb]);
+
+ /* Find final 1/Z value. */
+ vli_modSub_fast(z, Rx[1], Rx[0]); /* X1 - X0 */
+ vli_modMult_fast(z, z, Ry[1-nb]); /* Yb * (X1 - X0) */
+ vli_modMult_fast(z, z, p_point->x); /* xP * Yb * (X1 - X0) */
+ vli_modInv(z, z, curve_p); /* 1 / (xP * Yb * (X1 - X0)) */
+ vli_modMult_fast(z, z, p_point->y); /* yP / (xP * Yb * (X1 - X0)) */
+ vli_modMult_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(p_result->x, Rx[0]);
+ vli_set(p_result->y, Ry[0]);
+}
+
+/* Compute a = sqrt(a) (mod curve_p). */
+static void mod_sqrt(uECC_word_t *a)
+{
+ bitcount_t i;
+ uECC_word_t p1[uECC_WORDS] = {1};
+ uECC_word_t l_result[uECC_WORDS] = {1};
+
+ /* Since curve_p == 3 (mod 4) for all supported curves, we can
+ compute sqrt(a) = a^((curve_p + 1) / 4) (mod curve_p). */
+ vli_add(p1, curve_p, p1); /* p1 = curve_p + 1 */
+ for(i = vli_numBits(p1, uECC_WORDS) - 1; i > 1; --i)
+ {
+ vli_modSquare_fast(l_result, l_result);
+ if(vli_testBit(p1, i))
+ {
+ vli_modMult_fast(l_result, l_result, a);
+ }
+ }
+ vli_set(a, l_result);
+}
+
+#if uECC_WORD_SIZE == 1
+
+static void vli_nativeToBytes(uint8_t * RESTRICT p_dest, const uint8_t * RESTRICT p_src)
+{
+ uint8_t i;
+ for(i=0; i<uECC_BYTES; ++i)
+ {
+ p_dest[i] = p_src[(uECC_BYTES - 1) - i];
+ }
+}
+
+#define vli_bytesToNative(dest, src) vli_nativeToBytes((dest), (src))
+
+#elif uECC_WORD_SIZE == 4
+
+static void vli_nativeToBytes(uint8_t *p_bytes, const uint32_t *p_native)
+{
+ unsigned i;
+ for(i=0; i<uECC_WORDS; ++i)
+ {
+ uint8_t *p_digit = p_bytes + 4 * (uECC_WORDS - 1 - i);
+ p_digit[0] = p_native[i] >> 24;
+ p_digit[1] = p_native[i] >> 16;
+ p_digit[2] = p_native[i] >> 8;
+ p_digit[3] = p_native[i];
+ }
+}
+
+static void vli_bytesToNative(uint32_t *p_native, const uint8_t *p_bytes)
+{
+ unsigned i;
+ for(i=0; i<uECC_WORDS; ++i)
+ {
+ const uint8_t *p_digit = p_bytes + 4 * (uECC_WORDS - 1 - i);
+ p_native[i] = ((uint32_t)p_digit[0] << 24) | ((uint32_t)p_digit[1] << 16) | ((uint32_t)p_digit[2] << 8) | (uint32_t)p_digit[3];
+ }
+}
+
+#else
+
+static void vli_nativeToBytes(uint8_t *p_bytes, const uint64_t *p_native)
+{
+ unsigned i;
+ for(i=0; i<uECC_WORDS; ++i)
+ {
+ uint8_t *p_digit = p_bytes + 8 * (uECC_WORDS - 1 - i);
+ p_digit[0] = p_native[i] >> 56;
+ p_digit[1] = p_native[i] >> 48;
+ p_digit[2] = p_native[i] >> 40;
+ p_digit[3] = p_native[i] >> 32;
+ p_digit[4] = p_native[i] >> 24;
+ p_digit[5] = p_native[i] >> 16;
+ p_digit[6] = p_native[i] >> 8;
+ p_digit[7] = p_native[i];
+ }
+}
+
+static void vli_bytesToNative(uint64_t *p_native, const uint8_t *p_bytes)
+{
+ unsigned i;
+ for(i=0; i<uECC_WORDS; ++i)
+ {
+ const uint8_t *p_digit = p_bytes + 8 * (uECC_WORDS - 1 - i);
+ p_native[i] = ((uint64_t)p_digit[0] << 56) | ((uint64_t)p_digit[1] << 48) | ((uint64_t)p_digit[2] << 40) | ((uint64_t)p_digit[3] << 32) |
+ ((uint64_t)p_digit[4] << 24) | ((uint64_t)p_digit[5] << 16) | ((uint64_t)p_digit[6] << 8) | (uint64_t)p_digit[7];
+ }
+}
+
+#endif /* uECC_WORD_SIZE */
+
+// Safe calls to the callback functions
+int uECC_make_key(uint8_t p_publicKey[uECC_BYTES*2], uint8_t p_privateKey[uECC_BYTES])
+{
+ // Check for a valid function pointer
+ if (g_make_key_cb != NULL)
+ {
+ return g_make_key_cb(p_publicKey, p_privateKey);
+ }
+ else
+ {
+ return uECC_make_key_impl(p_publicKey, p_privateKey);
+ }
+}
+
+int uECC_shared_secret(const uint8_t p_publicKey[uECC_BYTES*2], const uint8_t p_privateKey[uECC_BYTES], uint8_t p_secret[uECC_BYTES])
+{
+ // Check for a valid function pointer
+ if (g_shared_secret_cb != NULL)
+ {
+ return g_shared_secret_cb(p_publicKey, p_privateKey, p_secret);
+ }
+ else
+ {
+ return uECC_shared_secret_impl(p_publicKey, p_privateKey, p_secret);
+ }
+}
+
+int uECC_sign(const uint8_t p_privateKey[uECC_BYTES], const uint8_t p_hash[uECC_BYTES], uint8_t p_signature[uECC_BYTES*2])
+{
+ // Check for a valid function pointer
+ if (g_sign_cb != NULL)
+ {
+ return g_sign_cb(p_privateKey, p_hash, p_signature);
+ }
+ else
+ {
+ return uECC_sign_impl(p_privateKey, p_hash, p_signature);
+ }
+}
+
+int uECC_verify(const uint8_t p_publicKey[uECC_BYTES*2], const uint8_t p_hash[uECC_BYTES], const uint8_t p_signature[uECC_BYTES*2])
+{
+ // Check for a valid function pointer
+ if (g_verify_cb != NULL)
+ {
+ return g_verify_cb(p_publicKey, p_hash, p_signature);
+ }
+ else
+ {
+ return uECC_verify_impl(p_publicKey, p_hash, p_signature);
}
+}
- if(isSame(px, qx, arrayLength)){
- if(!isSame(py, qy, arrayLength)){
- setZero(Sx, 8);
- setZero(Sy, 8);
- return;
- } else {
- ec_double(px, py, Sx, Sy);
- return;
- }
+int uECC_ecdhe(const uint8_t p_public_key_in[uECC_BYTES*2], uint8_t p_public_key_out[uECC_BYTES*2], uint8_t p_secret[uECC_BYTES])
+{
+ // Check for a valid function pointer
+ if (g_ecdhe_cb != NULL)
+ {
+ return g_ecdhe_cb(p_public_key_in, p_public_key_out, p_secret);
+ }
+ else
+ {
+ return uECC_ecdhe_impl(p_public_key_in, p_public_key_out, p_secret);
}
+}
- fieldSub(py, qy, ecc_prime_m, tempA);
- fieldSub(px, qx, ecc_prime_m, tempB);
- fieldInv(tempB, ecc_prime_m, ecc_prime_r, tempB);
- fieldMult(tempA, tempB, tempD, arrayLength);
- fieldModP(tempC, tempD); //tempC = lambda
-
- fieldMult(tempC, tempC, tempD, arrayLength); //tempA = lambda^2
- fieldModP(tempA, tempD);
- fieldSub(tempA, px, ecc_prime_m, tempB); //lambda^2 - Px
- fieldSub(tempB, qx, ecc_prime_m, Sx); //lambda^2 - Px - Qx
-
- fieldSub(qx, Sx, ecc_prime_m, tempB);
- fieldMult(tempC, tempB, tempD, arrayLength);
- fieldModP(tempC, tempD);
- fieldSub(tempC, qy, ecc_prime_m, Sy);
-}
-
-void ecc_ec_mult(const uint32_t *px, const uint32_t *py, const uint32_t *secret, uint32_t *resultx, uint32_t *resulty){
- uint32_t Qx[8];
- uint32_t Qy[8];
- setZero(Qx, 8);
- setZero(Qy, 8);
-
- uint32_t tempx[8];
- uint32_t tempy[8];
-
- int i;
- for (i = 256;i--;){
- ec_double(Qx, Qy, tempx, tempy);
- copy(tempx, Qx,arrayLength);
- copy(tempy, Qy,arrayLength);
- if (((secret[i / 32]) & ((uint32_t)1 << (i % 32)))) {
- ec_add(Qx, Qy, px, py, tempx, tempy); //eccAdd
- copy(tempx, Qx,arrayLength);
- copy(tempy, Qy,arrayLength);
- }
+int uECC_get_pubkey(const uint8_t p_key_handle[uECC_BYTES], uint8_t p_public_key[uECC_BYTES*2])
+{
+ // Check for a valid function pointer
+ if (g_get_pubkey_cb != NULL)
+ {
+ return g_get_pubkey_cb(p_key_handle, p_public_key);
+ }
+ else
+ {
+ return uECC_get_pubkey_impl(p_key_handle, p_public_key);
}
- copy(Qx, resultx,arrayLength);
- copy(Qy, resulty,arrayLength);
-}
-
-/**
- * Calculate the ecdsa signature.
- *
- * For a description of this algorithm see
- * https://en.wikipedia.org/wiki/Elliptic_Curve_DSA#Signature_generation_algorithm
- *
- * input:
- * d: private key on the curve secp256r1 (32 bytes)
- * e: hash to sign (32 bytes)
- * k: random data, this must be changed for every signature (32 bytes)
- *
- * output:
- * r: r value of the signature (36 bytes)
- * s: s value of the signature (36 bytes)
- *
- * return:
- * 0: everything is ok
- * -1: can not create signature, try again with different k.
- */
-int ecc_ecdsa_sign(const uint32_t *d, const uint32_t *e, const uint32_t *k, uint32_t *r, uint32_t *s)
-{
- uint32_t tmp1[16];
- uint32_t tmp2[9];
- uint32_t tmp3[9];
-
- if (isZero(k))
- return -1;
-
- // 4. Calculate the curve point (x_1, y_1) = k * G.
- ecc_ec_mult(ecc_g_point_x, ecc_g_point_y, k, r, tmp1);
-
- // 5. Calculate r = x_1 \pmod{n}.
- fieldModO(r, r, 8);
-
- // 5. If r = 0, go back to step 3.
- if (isZero(r))
- return -1;
-
- // 6. Calculate s = k^{-1}(z + r d_A) \pmod{n}.
- // 6. r * d
- fieldMult(r, d, tmp1, arrayLength);
- fieldModO(tmp1, tmp2, 16);
-
- // 6. z + (r d)
- tmp1[8] = add(e, tmp2, tmp1, 8);
- fieldModO(tmp1, tmp3, 9);
-
- // 6. k^{-1}
- fieldInv(k, ecc_order_m, ecc_order_r, tmp2);
-
- // 6. (k^{-1}) (z + (r d))
- fieldMult(tmp2, tmp3, tmp1, arrayLength);
- fieldModO(tmp1, s, 16);
-
- // 6. If s = 0, go back to step 3.
- if (isZero(s))
- return -1;
+}
+int uECC_ecdhe_impl(const uint8_t p_public_key_in[uECC_BYTES*2], uint8_t p_public_key_out[uECC_BYTES*2], uint8_t p_secret[uECC_BYTES])
+{
return 0;
}
-/**
- * Verifies a ecdsa signature.
- *
- * For a description of this algorithm see
- * https://en.wikipedia.org/wiki/Elliptic_Curve_DSA#Signature_verification_algorithm
- *
- * input:
- * x: x coordinate of the public key (32 bytes)
- * y: y coordinate of the public key (32 bytes)
- * e: hash to verify the signature of (32 bytes)
- * r: r value of the signature (32 bytes)
- * s: s value of the signature (32 bytes)
- *
- * return:
- * 0: signature is ok
- * -1: signature check failed the signature is invalid
- */
-int ecc_ecdsa_validate(const uint32_t *x, const uint32_t *y, const uint32_t *e, const uint32_t *r, const uint32_t *s)
+int uECC_get_pubkey_impl(const uint8_t p_key_handle[uECC_BYTES], uint8_t p_public_key[uECC_BYTES*2])
{
- uint32_t w[8];
- uint32_t tmp[16];
- uint32_t u1[9];
- uint32_t u2[9];
- uint32_t tmp1_x[8];
- uint32_t tmp1_y[8];
- uint32_t tmp2_x[8];
- uint32_t tmp2_y[8];
- uint32_t tmp3_x[8];
- uint32_t tmp3_y[8];
+ return 0;
+}
- // 3. Calculate w = s^{-1} \pmod{n}
- fieldInv(s, ecc_order_m, ecc_order_r, w);
+int uECC_make_key_impl(uint8_t p_publicKey[uECC_BYTES*2], uint8_t p_privateKey[uECC_BYTES])
+{
+ EccPoint l_public;
+ uECC_word_t l_private[uECC_WORDS];
+ uECC_word_t l_tries = 0;
+
+ do
+ {
+ repeat:
+ if(!g_rng((uint8_t *)l_private, sizeof(l_private)) || (l_tries++ >= MAX_TRIES))
+ {
+ return 0;
+ }
+ if(vli_isZero(l_private))
+ {
+ goto repeat;
+ }
+
+ /* Make sure the private key is in the range [1, n-1]. */
+ #if uECC_CURVE != uECC_secp160r1
+ if(vli_cmp(curve_n, l_private) != 1)
+ {
+ goto repeat;
+ }
+ #endif
+
+ EccPoint_mult(&l_public, &curve_G, l_private, 0, vli_numBits(l_private, uECC_WORDS));
+ } while(EccPoint_isZero(&l_public));
+
+ vli_nativeToBytes(p_privateKey, l_private);
+ vli_nativeToBytes(p_publicKey, l_public.x);
+ vli_nativeToBytes(p_publicKey + uECC_BYTES, l_public.y);
+ return 1;
+}
- // 4. Calculate u_1 = zw \pmod{n}
- fieldMult(e, w, tmp, arrayLength);
- fieldModO(tmp, u1, 16);
+int uECC_shared_secret_impl(const uint8_t p_publicKey[uECC_BYTES*2], const uint8_t p_privateKey[uECC_BYTES], uint8_t p_secret[uECC_BYTES])
+{
+ EccPoint l_public;
+ uECC_word_t l_private[uECC_WORDS];
+ uECC_word_t l_random[uECC_WORDS];
- // 4. Calculate u_2 = rw \pmod{n}
- fieldMult(r, w, tmp, arrayLength);
- fieldModO(tmp, u2, 16);
+ g_rng((uint8_t *)l_random, sizeof(l_random));
- // 5. Calculate the curve point (x_1, y_1) = u_1 * G + u_2 * Q_A.
- // tmp1 = u_1 * G
- ecc_ec_mult(ecc_g_point_x, ecc_g_point_y, u1, tmp1_x, tmp1_y);
+ vli_bytesToNative(l_private, p_privateKey);
+ vli_bytesToNative(l_public.x, p_publicKey);
+ vli_bytesToNative(l_public.y, p_publicKey + uECC_BYTES);
- // tmp2 = u_2 * Q_A
- ecc_ec_mult(x, y, u2, tmp2_x, tmp2_y);
+ EccPoint l_product;
+ EccPoint_mult(&l_product, &l_public, l_private, (vli_isZero(l_random) ? 0: l_random), vli_numBits(l_private, uECC_WORDS));
- // tmp3 = tmp1 + tmp2
- ec_add(tmp1_x, tmp1_y, tmp2_x, tmp2_y, tmp3_x, tmp3_y);
- // TODO: this u_1 * G + u_2 * Q_A could be optimiced with Straus's algorithm.
+ vli_nativeToBytes(p_secret, l_product.x);
- return isSame(tmp3_x, r, arrayLength) ? 0 : -1;
+ return !EccPoint_isZero(&l_product);
}
-int ecc_is_valid_key(const uint32_t * priv_key)
+void uECC_compress(const uint8_t p_publicKey[uECC_BYTES*2], uint8_t p_compressed[uECC_BYTES+1])
{
- return isGreater(ecc_order_m, priv_key, arrayLength) == 1;
+ wordcount_t i;
+ for(i=0; i<uECC_BYTES; ++i)
+ {
+ p_compressed[i+1] = p_publicKey[i];
+ }
+ p_compressed[0] = 2 + (p_publicKey[uECC_BYTES * 2 - 1] & 0x01);
}
-/*
- * This exports the low level functions so the tests can use them.
- * In real use the compiler is now bale to optimice the code better.
- */
-#ifdef TEST_INCLUDE
-uint32_t ecc_add( const uint32_t *x, const uint32_t *y, uint32_t *result, uint8_t length)
+void uECC_decompress(const uint8_t p_compressed[uECC_BYTES+1], uint8_t p_publicKey[uECC_BYTES*2])
{
- return add(x, y, result, length);
+ EccPoint l_point;
+ vli_bytesToNative(l_point.x, p_compressed + 1);
+
+#if (uECC_CURVE == uECC_secp256k1)
+ vli_modSquare_fast(l_point.y, l_point.x); /* r = x^2 */
+ vli_modMult_fast(l_point.y, l_point.y, l_point.x); /* r = x^3 */
+ vli_modAdd(l_point.y, l_point.y, curve_b, curve_p); /* r = x^3 + b */
+#else
+ uECC_word_t _3[uECC_WORDS] = {3}; /* -a = 3 */
+
+ vli_modSquare_fast(l_point.y, l_point.x); /* y = x^2 */
+ vli_modSub_fast(l_point.y, l_point.y, _3); /* y = x^2 - 3 */
+ vli_modMult_fast(l_point.y, l_point.y, l_point.x); /* y = x^3 - 3x */
+ vli_modAdd(l_point.y, l_point.y, curve_b, curve_p); /* y = x^3 - 3x + b */
+#endif
+
+ mod_sqrt(l_point.y);
+
+ if((l_point.y[0] & 0x01) != (p_compressed[0] & 0x01))
+ {
+ vli_sub(l_point.y, curve_p, l_point.y);
+ }
+
+ vli_nativeToBytes(p_publicKey, l_point.x);
+ vli_nativeToBytes(p_publicKey + uECC_BYTES, l_point.y);
}
-uint32_t ecc_sub( const uint32_t *x, const uint32_t *y, uint32_t *result, uint8_t length)
+
+/* -------- ECDSA code -------- */
+
+#if (uECC_CURVE == uECC_secp160r1)
+static void vli_clear_n(uECC_word_t *p_vli)
{
- return sub(x, y, result, length);
+ vli_clear(p_vli);
+ p_vli[uECC_N_WORDS - 1] = 0;
}
-int ecc_fieldAdd(const uint32_t *x, const uint32_t *y, const uint32_t *reducer, uint32_t *result)
+
+static uECC_word_t vli_isZero_n(const uECC_word_t *p_vli)
{
- return fieldAdd(x, y, reducer, result);
+ if(p_vli[uECC_N_WORDS - 1])
+ {
+ return 0;
+ }
+ return vli_isZero(p_vli);
}
-int ecc_fieldSub(const uint32_t *x, const uint32_t *y, const uint32_t *modulus, uint32_t *result)
+
+static void vli_set_n(uECC_word_t *p_dest, const uECC_word_t *p_src)
{
- return fieldSub(x, y, modulus, result);
+ vli_set(p_dest, p_src);
+ p_dest[uECC_N_WORDS-1] = p_src[uECC_N_WORDS-1];
}
-int ecc_fieldMult(const uint32_t *x, const uint32_t *y, uint32_t *result, uint8_t length)
+
+static cmpresult_t vli_cmp_n(uECC_word_t *p_left, uECC_word_t *p_right)
{
- return fieldMult(x, y, result, length);
+ if(p_left[uECC_N_WORDS-1] > p_right[uECC_N_WORDS-1])
+ {
+ return 1;
+ }
+ else if(p_left[uECC_N_WORDS-1] < p_right[uECC_N_WORDS-1])
+ {
+ return -1;
+ }
+ return vli_cmp(p_left, p_right);
}
-void ecc_fieldModP(uint32_t *A, const uint32_t *B)
+
+static void vli_rshift1_n(uECC_word_t *p_vli)
{
- fieldModP(A, B);
+ vli_rshift1(p_vli);
+ p_vli[uECC_N_WORDS-2] |= p_vli[uECC_N_WORDS-1] << (uECC_WORD_BITS - 1);
+ p_vli[uECC_N_WORDS-1] = p_vli[uECC_N_WORDS-1] >> 1;
}
-void ecc_fieldModO(const uint32_t *A, uint32_t *result, uint8_t length)
+
+static uECC_word_t vli_add_n(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right)
{
- fieldModO(A, result, length);
+ uECC_word_t l_carry = vli_add(p_result, p_left, p_right);
+ uECC_word_t l_sum = p_left[uECC_N_WORDS-1] + p_right[uECC_N_WORDS-1] + l_carry;
+ if(l_sum != p_left[uECC_N_WORDS-1])
+ {
+ l_carry = (l_sum < p_left[uECC_N_WORDS-1]);
+ }
+ p_result[uECC_N_WORDS-1] = l_sum;
+ return l_carry;
}
-void ecc_fieldInv(const uint32_t *A, const uint32_t *modulus, const uint32_t *reducer, uint32_t *B)
+
+static uECC_word_t vli_sub_n(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right)
{
- fieldInv(A, modulus, reducer, B);
+ uECC_word_t l_borrow = vli_sub(p_result, p_left, p_right);
+ uECC_word_t l_diff = p_left[uECC_N_WORDS-1] - p_right[uECC_N_WORDS-1] - l_borrow;
+ if(l_diff != p_left[uECC_N_WORDS-1])
+ {
+ l_borrow = (l_diff > p_left[uECC_N_WORDS-1]);
+ }
+ p_result[uECC_N_WORDS-1] = l_diff;
+ return l_borrow;
}
-void ecc_copy(const uint32_t *from, uint32_t *to, uint8_t length)
+
+#if !muladd_exists
+static void muladd(uECC_word_t a, uECC_word_t b, uECC_word_t *r0, uECC_word_t *r1, uECC_word_t *r2)
{
- copy(from, to, length);
+ uECC_dword_t p = (uECC_dword_t)a * b;
+ uECC_dword_t r01 = ((uECC_dword_t)(*r1) << uECC_WORD_BITS) | *r0;
+ r01 += p;
+ *r2 += (r01 < p);
+ *r1 = r01 >> uECC_WORD_BITS;
+ *r0 = (uECC_word_t)r01;
}
-int ecc_isSame(const uint32_t *A, const uint32_t *B, uint8_t length)
+#define muladd_exists 1
+#endif
+
+static void vli_mult_n(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right)
{
- return isSame(A, B, length);
+ uECC_word_t r0 = 0;
+ uECC_word_t r1 = 0;
+ uECC_word_t r2 = 0;
+
+ wordcount_t i, k;
+ for(k = 0; k < uECC_N_WORDS*2 - 1; ++k)
+ {
+ wordcount_t l_min = (k < uECC_N_WORDS ? 0 : (k + 1) - uECC_N_WORDS);
+ wordcount_t l_max = (k < uECC_N_WORDS ? k : uECC_N_WORDS-1);
+ for(i = l_min; i <= l_max; ++i)
+ {
+ muladd(p_left[i], p_right[k-i], &r0, &r1, &r2);
+ }
+ p_result[k] = r0;
+ r0 = r1;
+ r1 = r2;
+ r2 = 0;
+ }
+
+ p_result[uECC_N_WORDS*2 - 1] = r0;
}
-void ecc_setZero(uint32_t *A, const int length)
+
+static void vli_modAdd_n(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right, uECC_word_t *p_mod)
{
- setZero(A, length);
+ uECC_word_t l_carry = vli_add_n(p_result, p_left, p_right);
+ if(l_carry || vli_cmp_n(p_result, p_mod) >= 0)
+ {
+ vli_sub_n(p_result, p_result, p_mod);
+ }
}
-int ecc_isOne(const uint32_t* A)
+
+static void vli_modInv_n(uECC_word_t *p_result, uECC_word_t *p_input, uECC_word_t *p_mod)
{
- return isOne(A);
+ uECC_word_t a[uECC_N_WORDS], b[uECC_N_WORDS], u[uECC_N_WORDS], v[uECC_N_WORDS];
+ uECC_word_t l_carry;
+ cmpresult_t l_cmpResult;
+
+ if(vli_isZero_n(p_input))
+ {
+ vli_clear_n(p_result);
+ return;
+ }
+
+ vli_set_n(a, p_input);
+ vli_set_n(b, p_mod);
+ vli_clear_n(u);
+ u[0] = 1;
+ vli_clear_n(v);
+ while((l_cmpResult = vli_cmp_n(a, b)) != 0)
+ {
+ l_carry = 0;
+ if(EVEN(a))
+ {
+ vli_rshift1_n(a);
+ if(!EVEN(u)) l_carry = vli_add_n(u, u, p_mod);
+ vli_rshift1_n(u);
+ if(l_carry) u[uECC_N_WORDS-1] |= HIGH_BIT_SET;
+ }
+ else if(EVEN(b))
+ {
+ vli_rshift1_n(b);
+ if(!EVEN(v)) l_carry = vli_add_n(v, v, p_mod);
+ vli_rshift1_n(v);
+ if(l_carry) v[uECC_N_WORDS-1] |= HIGH_BIT_SET;
+ }
+ else if(l_cmpResult > 0)
+ {
+ vli_sub_n(a, a, b);
+ vli_rshift1_n(a);
+ if(vli_cmp_n(u, v) < 0) vli_add_n(u, u, p_mod);
+ vli_sub_n(u, u, v);
+ if(!EVEN(u)) l_carry = vli_add_n(u, u, p_mod);
+ vli_rshift1_n(u);
+ if(l_carry) u[uECC_N_WORDS-1] |= HIGH_BIT_SET;
+ }
+ else
+ {
+ vli_sub_n(b, b, a);
+ vli_rshift1_n(b);
+ if(vli_cmp_n(v, u) < 0) vli_add_n(v, v, p_mod);
+ vli_sub_n(v, v, u);
+ if(!EVEN(v)) l_carry = vli_add_n(v, v, p_mod);
+ vli_rshift1_n(v);
+ if(l_carry) v[uECC_N_WORDS-1] |= HIGH_BIT_SET;
+ }
+ }
+
+ vli_set_n(p_result, u);
}
-void ecc_rshift(uint32_t* A)
+
+static void vli2_rshift1_n(uECC_word_t *p_vli)
{
- rshift(A);
+ vli_rshift1_n(p_vli);
+ p_vli[uECC_N_WORDS-1] |= p_vli[uECC_N_WORDS] << (uECC_WORD_BITS - 1);
+ vli_rshift1_n(p_vli + uECC_N_WORDS);
}
-int ecc_isGreater(const uint32_t *A, const uint32_t *B, uint8_t length)
+
+static uECC_word_t vli2_sub_n(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right)
{
- return isGreater(A, B , length);
+ uECC_word_t l_borrow = 0;
+ wordcount_t i;
+ for(i=0; i<uECC_N_WORDS*2; ++i)
+ {
+ uECC_word_t l_diff = p_left[i] - p_right[i] - l_borrow;
+ if(l_diff != p_left[i])
+ {
+ l_borrow = (l_diff > p_left[i]);
+ }
+ p_result[i] = l_diff;
+ }
+ return l_borrow;
}
-void ecc_ec_add(const uint32_t *px, const uint32_t *py, const uint32_t *qx, const uint32_t *qy, uint32_t *Sx, uint32_t *Sy)
+/* Computes p_result = (p_left * p_right) % curve_n. */
+static void vli_modMult_n(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right)
{
- ec_add(px, py, qx, qy, Sx, Sy);
+ uECC_word_t l_product[2 * uECC_N_WORDS];
+ uECC_word_t l_modMultiple[2 * uECC_N_WORDS];
+ uECC_word_t l_tmp[2 * uECC_N_WORDS];
+ uECC_word_t *v[2] = {l_tmp, l_product};
+
+ vli_mult_n(l_product, p_left, p_right);
+ vli_clear_n(l_modMultiple);
+ vli_set(l_modMultiple + uECC_N_WORDS + 1, curve_n);
+ vli_rshift1(l_modMultiple + uECC_N_WORDS + 1);
+ l_modMultiple[2 * uECC_N_WORDS - 1] |= HIGH_BIT_SET;
+ l_modMultiple[uECC_N_WORDS] = HIGH_BIT_SET;
+
+ bitcount_t i;
+ uECC_word_t l_index = 1;
+ for(i=0; i<=((((bitcount_t)uECC_N_WORDS) << uECC_WORD_BITS_SHIFT) + (uECC_WORD_BITS - 1)); ++i)
+ {
+ uECC_word_t l_borrow = vli2_sub_n(v[1-l_index], v[l_index], l_modMultiple);
+ l_index = !(l_index ^ l_borrow); /* Swap the index if there was no borrow */
+ vli2_rshift1_n(l_modMultiple);
+ }
+
+ vli_set_n(p_result, v[l_index]);
}
-void ecc_ec_double(const uint32_t *px, const uint32_t *py, uint32_t *Dx, uint32_t *Dy)
+
+#else
+
+#define vli_modInv_n vli_modInv
+#define vli_modAdd_n vli_modAdd
+
+static void vli2_rshift1(uECC_word_t *p_vli)
+{
+ vli_rshift1(p_vli);
+ p_vli[uECC_WORDS-1] |= p_vli[uECC_WORDS] << (uECC_WORD_BITS - 1);
+ vli_rshift1(p_vli + uECC_WORDS);
+}
+
+static uECC_word_t vli2_sub(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right)
{
- ec_double(px, py, Dx, Dy);
+ uECC_word_t l_borrow = 0;
+ wordcount_t i;
+ for(i=0; i<uECC_WORDS*2; ++i)
+ {
+ uECC_word_t l_diff = p_left[i] - p_right[i] - l_borrow;
+ if(l_diff != p_left[i])
+ {
+ l_borrow = (l_diff > p_left[i]);
+ }
+ p_result[i] = l_diff;
+ }
+ return l_borrow;
}
-#endif /* TEST_INCLUDE */
+/* Computes p_result = (p_left * p_right) % curve_n. */
+static void vli_modMult_n(uECC_word_t *p_result, uECC_word_t *p_left, uECC_word_t *p_right)
+{
+ uECC_word_t l_product[2 * uECC_WORDS];
+ uECC_word_t l_modMultiple[2 * uECC_WORDS];
+ uECC_word_t l_tmp[2 * uECC_WORDS];
+ uECC_word_t *v[2] = {l_tmp, l_product};
+
+ vli_mult(l_product, p_left, p_right);
+ vli_set(l_modMultiple + uECC_WORDS, curve_n); /* works if curve_n has its highest bit set */
+ vli_clear(l_modMultiple);
+
+ bitcount_t i;
+ uECC_word_t l_index = 1;
+ for(i=0; i<=uECC_BYTES * 8; ++i)
+ {
+ uECC_word_t l_borrow = vli2_sub(v[1-l_index], v[l_index], l_modMultiple);
+ l_index = !(l_index ^ l_borrow); /* Swap the index if there was no borrow */
+ vli2_rshift1(l_modMultiple);
+ }
+
+ vli_set(p_result, v[l_index]);
+}
+#endif /* (uECC_CURVE != uECC_secp160r1) */
+
+int uECC_sign_impl(const uint8_t p_privateKey[uECC_BYTES], const uint8_t p_hash[uECC_BYTES], uint8_t p_signature[uECC_BYTES*2])
+{
+ uECC_word_t k[uECC_N_WORDS];
+ uECC_word_t l_tmp[uECC_N_WORDS];
+ uECC_word_t s[uECC_N_WORDS];
+ uECC_word_t *k2[2] = {l_tmp, s};
+ EccPoint p;
+ uECC_word_t l_tries = 0;
+
+ do
+ {
+ repeat:
+ if(!g_rng((uint8_t *)k, sizeof(k)) || (l_tries++ >= MAX_TRIES))
+ {
+ return 0;
+ }
+
+ if(vli_isZero(k))
+ {
+ goto repeat;
+ }
+
+ #if (uECC_CURVE == uECC_secp160r1)
+ k[uECC_WORDS] &= 0x01;
+ if(vli_cmp_n(curve_n, k) != 1)
+ {
+ goto repeat;
+ }
+
+ /* make sure that we don't leak timing information about k. See http://eprint.iacr.org/2011/232.pdf */
+ vli_add_n(l_tmp, k, curve_n);
+ uECC_word_t l_carry = (l_tmp[uECC_WORDS] & 0x02);
+ vli_add_n(s, l_tmp, curve_n);
+
+ /* p = k * G */
+ EccPoint_mult(&p, &curve_G, k2[!l_carry], 0, (uECC_BYTES * 8) + 2);
+ #else
+ if(vli_cmp(curve_n, k) != 1)
+ {
+ goto repeat;
+ }
+
+ /* make sure that we don't leak timing information about k. See http://eprint.iacr.org/2011/232.pdf */
+ uECC_word_t l_carry = vli_add(l_tmp, k, curve_n);
+ vli_add(s, l_tmp, curve_n);
+
+ /* p = k * G */
+ EccPoint_mult(&p, &curve_G, k2[!l_carry], 0, (uECC_BYTES * 8) + 1);
+
+ /* r = x1 (mod n) */
+ if(vli_cmp(curve_n, p.x) != 1)
+ {
+ vli_sub(p.x, p.x, curve_n);
+ }
+ #endif
+ } while(vli_isZero(p.x));
+
+ l_tries = 0;
+ do
+ {
+ if(!g_rng((uint8_t *)l_tmp, sizeof(l_tmp)) || (l_tries++ >= MAX_TRIES))
+ {
+ return 0;
+ }
+ } while(vli_isZero(l_tmp));
+
+ /* Prevent side channel analysis of vli_modInv() to determine
+ bits of k / the private key by premultiplying by a random number */
+ vli_modMult_n(k, k, l_tmp); /* k' = rand * k */
+ vli_modInv_n(k, k, curve_n); /* k = 1 / k' */
+ vli_modMult_n(k, k, l_tmp); /* k = 1 / k */
+
+ vli_nativeToBytes(p_signature, p.x); /* store r */
+
+ l_tmp[uECC_N_WORDS-1] = 0;
+ vli_bytesToNative(l_tmp, p_privateKey); /* tmp = d */
+ s[uECC_N_WORDS-1] = 0;
+ vli_set(s, p.x);
+ vli_modMult_n(s, l_tmp, s); /* s = r*d */
+
+ vli_bytesToNative(l_tmp, p_hash);
+ vli_modAdd_n(s, l_tmp, s, curve_n); /* s = e + r*d */
+ vli_modMult_n(s, s, k); /* s = (e + r*d) / k */
+#if (uECC_CURVE == uECC_secp160r1)
+ if(s[uECC_N_WORDS-1])
+ {
+ goto repeat;
+ }
+#endif
+ vli_nativeToBytes(p_signature + uECC_BYTES, s);
+
+ return 1;
+}
+
+static bitcount_t smax(bitcount_t a, bitcount_t b)
+{
+ return (a > b ? a : b);
+}
+
+int uECC_verify_impl(const uint8_t p_publicKey[uECC_BYTES*2], const uint8_t p_hash[uECC_BYTES], const uint8_t p_signature[uECC_BYTES*2])
+{
+ uECC_word_t u1[uECC_N_WORDS], u2[uECC_N_WORDS];
+ uECC_word_t z[uECC_N_WORDS];
+ EccPoint l_public, l_sum;
+ uECC_word_t rx[uECC_WORDS];
+ uECC_word_t ry[uECC_WORDS];
+ uECC_word_t tx[uECC_WORDS];
+ uECC_word_t ty[uECC_WORDS];
+ uECC_word_t tz[uECC_WORDS];
+
+ uECC_word_t r[uECC_N_WORDS], s[uECC_N_WORDS];
+ r[uECC_N_WORDS-1] = 0;
+ s[uECC_N_WORDS-1] = 0;
+
+ vli_bytesToNative(l_public.x, p_publicKey);
+ vli_bytesToNative(l_public.y, p_publicKey + uECC_BYTES);
+ vli_bytesToNative(r, p_signature);
+ vli_bytesToNative(s, p_signature + uECC_BYTES);
+
+ if(vli_isZero(r) || vli_isZero(s))
+ { /* r, s must not be 0. */
+ return 0;
+ }
+
+#if (uECC_CURVE != uECC_secp160r1)
+ if(vli_cmp(curve_n, r) != 1 || vli_cmp(curve_n, s) != 1)
+ { /* r, s must be < n. */
+ return 0;
+ }
+#endif
+
+ /* Calculate u1 and u2. */
+ vli_modInv_n(z, s, curve_n); /* Z = s^-1 */
+ u1[uECC_N_WORDS-1] = 0;
+ vli_bytesToNative(u1, p_hash);
+ vli_modMult_n(u1, u1, z); /* u1 = e/s */
+ vli_modMult_n(u2, r, z); /* u2 = r/s */
+
+ /* Calculate l_sum = G + Q. */
+ vli_set(l_sum.x, l_public.x);
+ vli_set(l_sum.y, l_public.y);
+ vli_set(tx, curve_G.x);
+ vli_set(ty, curve_G.y);
+ vli_modSub_fast(z, l_sum.x, tx); /* Z = x2 - x1 */
+ XYcZ_add(tx, ty, l_sum.x, l_sum.y);
+ vli_modInv(z, z, curve_p); /* Z = 1/Z */
+ apply_z(l_sum.x, l_sum.y, z);
+
+ /* Use Shamir's trick to calculate u1*G + u2*Q */
+ EccPoint *l_points[4] = {0, &curve_G, &l_public, &l_sum};
+ bitcount_t l_numBits = smax(vli_numBits(u1, uECC_N_WORDS), vli_numBits(u2, uECC_N_WORDS));
+
+ EccPoint *l_point = l_points[(!!vli_testBit(u1, l_numBits-1)) | ((!!vli_testBit(u2, l_numBits-1)) << 1)];
+ vli_set(rx, l_point->x);
+ vli_set(ry, l_point->y);
+ vli_clear(z);
+ z[0] = 1;
+
+ bitcount_t i;
+ for(i = l_numBits - 2; i >= 0; --i)
+ {
+ EccPoint_double_jacobian(rx, ry, z);
+
+ uECC_word_t l_index = (!!vli_testBit(u1, i)) | ((!!vli_testBit(u2, i)) << 1);
+ l_point = l_points[l_index];
+ if(l_point)
+ {
+ vli_set(tx, l_point->x);
+ vli_set(ty, l_point->y);
+ apply_z(tx, ty, z);
+ vli_modSub_fast(tz, rx, tx); /* Z = x2 - x1 */
+ XYcZ_add(tx, ty, rx, ry);
+ vli_modMult_fast(z, z, tz);
+ }
+ }
+
+ vli_modInv(z, z, curve_p); /* Z = 1/Z */
+ apply_z(rx, ry, z);
+
+ /* v = x1 (mod n) */
+#if (uECC_CURVE != uECC_secp160r1)
+ if(vli_cmp(curve_n, rx) != 1)
+ {
+ vli_sub(rx, rx, curve_n);
+ }
+#endif
+
+ /* Accept only if v == r. */
+ return (vli_cmp(rx, r) == 0);
+}
projects / platform / upstream / iotivity.git / blobdiff