/* Copyright 2014, Kenneth MacKay. Licensed under the BSD 2-clause license. */

#include "uECC.h"

#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 64

#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 { \
    {0x59F2815B16F81798ull, 0x029BFCDB2DCE28D9ull, 0x55A06295CE870B07ull, 0x79BE667EF9DCBBACull}, \
    {0x9C47D08FFB10D4B8ull, 0xFD17B448A6855419ull, 0x5DA4FBFC0E1108A8ull, 0x483ADA7726A3C465ull}}

#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 {0xBFD25E8CD0364141ull, 0xBAAEDCE6AF48A03Bull, \
                   0xFFFFFFFFFFFFFFFEull, 0xFFFFFFFFFFFFFFFFull}

#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 const uECC_word_t curve_p[uECC_WORDS] = uECC_CONCAT(Curve_P_, uECC_CURVE);
static const uECC_word_t curve_b[uECC_WORDS] = uECC_CONCAT(Curve_B_, uECC_CURVE);
static const EccPoint curve_G = uECC_CONCAT(Curve_G_, uECC_CURVE);
static const 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(const uECC_word_t *p_left, const uECC_word_t *p_right);
static cmpresult_t vli_equal(const uECC_word_t *p_left, const 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,
                           const uECC_word_t *p_left,
                           const uECC_word_t *p_right);
static uECC_word_t vli_sub(uECC_word_t *p_result,
                           const uECC_word_t *p_left,
                           const uECC_word_t *p_right);
static void vli_mult(uECC_word_t *p_result, const uECC_word_t *p_left, const uECC_word_t *p_right);
static void vli_modAdd(uECC_word_t *p_result,
                       const uECC_word_t *p_left,
                       const uECC_word_t *p_right,
                       const uECC_word_t *p_mod);
static void vli_modSub(uECC_word_t *p_result,
                       const uECC_word_t *p_left,
                       const uECC_word_t *p_right,
                       const 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,
                             const uECC_word_t *p_left,
                             const uECC_word_t *p_right);
static void vli_modInv(uECC_word_t *p_result, const uECC_word_t *p_input, const uECC_word_t *p_mod);
#if uECC_SQUARE_FUNC
static void vli_square(uECC_word_t *p_result, const uECC_word_t *p_left);
static void vli_modSquare_fast(uECC_word_t *p_result, const uECC_word_t *p_left);
#endif

#if (defined(_WIN32) || defined(_WIN64))
/* Windows */

#define WIN32_LEAN_AND_MEAN
#include <windows.h>
#include <wincrypt.h>

static int default_RNG(uint8_t *dest, unsigned size) {
    HCRYPTPROV prov;
    if (!CryptAcquireContext(&prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT)) {
        return 0;
    }

    CryptGenRandom(prov, size, (BYTE *)dest);
    CryptReleaseContext(prov, 0);
    return 1;
}

#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 *dest, unsigned size) {
    int fd = open("/dev/urandom", O_RDONLY | O_CLOEXEC);
    if (fd == -1) {
        fd = open("/dev/random", O_RDONLY | O_CLOEXEC);
        if (fd == -1) {
            return 0;
        }
    }
    
    char *ptr = (char *)dest;
    size_t left = size;
    while (left > 0) {
        ssize_t bytes_read = read(fd, ptr, left);
        if (bytes_read <= 0) { // read failed
            close(fd);
            return 0;
        }
        left -= bytes_read;
        ptr += bytes_read;
    }
    
    close(fd);
    return 1;
}

#else /* Some other platform */

static int default_RNG(uint8_t *dest, unsigned size) {
    return 0;
}

#endif

static uECC_RNG_Function g_rng_function = &default_RNG;

void uECC_set_rng(uECC_RNG_Function rng_function) {
    g_rng_function = rng_function;
}

#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 *vli) {
    wordcount_t i;
    for (i = 0; i < uECC_WORDS; ++i) {
        vli[i] = 0;
    }
}
#endif

/* Returns 1 if vli == 0, 0 otherwise. */
#if !asm_isZero
static uECC_word_t vli_isZero(const uECC_word_t *vli) {
    wordcount_t i;
    for (i = 0; i < uECC_WORDS; ++i) {
        if (vli[i]) {
            return 0;
        }
    }
    return 1;
}
#endif

/* Returns nonzero if bit 'bit' of vli is set. */
#if !asm_testBit
static uECC_word_t vli_testBit(const uECC_word_t *vli, bitcount_t bit) {
    return (vli[bit >> uECC_WORD_BITS_SHIFT] & ((uECC_word_t)1 << (bit & uECC_WORD_BITS_MASK)));
}
#endif

/* Counts the number of words in vli. */
#if !asm_numBits
static wordcount_t vli_numDigits(const uECC_word_t *vli, wordcount_t max_words) {
    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 = max_words - 1; i >= 0 && vli[i] == 0; --i) {
    }

    return (i + 1);
}

/* Counts the number of bits required to represent vli. */
static bitcount_t vli_numBits(const uECC_word_t *vli, wordcount_t max_words) {
    uECC_word_t i;
    uECC_word_t digit;
    
    wordcount_t num_digits = vli_numDigits(vli, max_words);
    if (num_digits == 0) {
        return 0;
    }

    digit = vli[num_digits - 1];
    for (i = 0; digit; ++i) {
        digit >>= 1;
    }
    
    return (((bitcount_t)(num_digits - 1) << uECC_WORD_BITS_SHIFT) + i);
}
#endif /* !asm_numBits */

/* Sets dest = src. */
#if !asm_set
static void vli_set(uECC_word_t *dest, const uECC_word_t *src) {
    wordcount_t i;
    for (i = 0; i < uECC_WORDS; ++i) {
        dest[i] = src[i];
    }
}
#endif

/* Returns sign of left - right. */
#if !asm_cmp
static cmpresult_t vli_cmp(const uECC_word_t *left, const uECC_word_t *right) {
    swordcount_t i;
    for (i = uECC_WORDS - 1; i >= 0; --i) {
        if (left[i] > right[i]) {
            return 1;
        } else if (left[i] < right[i]) {
            return -1;
        }
    }
    return 0;
}
#endif

static cmpresult_t vli_equal(const uECC_word_t *left, const uECC_word_t *right) {
    uECC_word_t result = 0;
    swordcount_t i;
    for (i = uECC_WORDS - 1; i >= 0; --i) {
        result |= (left[i] ^ right[i]);
    }
    return (result == 0);
}

/* Computes vli = vli >> 1. */
#if !asm_rshift1
static void vli_rshift1(uECC_word_t *vli) {
    uECC_word_t *end = vli;
    uECC_word_t carry = 0;
    
    vli += uECC_WORDS;
    while (vli-- > end) {
        uECC_word_t temp = *vli;
        *vli = (temp >> 1) | carry;
        carry = temp << (uECC_WORD_BITS - 1);
    }
}
#endif

/* Computes result = left + right, returning carry. Can modify in place. */
#if !asm_add
static uECC_word_t vli_add(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) {
    uECC_word_t carry = 0;
    wordcount_t i;
    for (i = 0; i < uECC_WORDS; ++i) {
        uECC_word_t sum = left[i] + right[i] + carry;
        if (sum != left[i]) {
            carry = (sum < left[i]);
        }
        result[i] = sum;
    }
    return carry;
}
#endif

/* Computes result = left - right, returning borrow. Can modify in place. */
#if !asm_sub
static uECC_word_t vli_sub(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) {
    uECC_word_t borrow = 0;
    wordcount_t i;
    for (i = 0; i < uECC_WORDS; ++i) {
        uECC_word_t diff = left[i] - right[i] - borrow;
        if (diff != left[i]) {
            borrow = (diff > left[i]);
        }
        result[i] = diff;
    }
    return borrow;
}
#endif

#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

#if !asm_mult
static void vli_mult(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) {
    uECC_word_t r0 = 0;
    uECC_word_t r1 = 0;
    uECC_word_t r2 = 0;
    wordcount_t i, k;
    
    /* Compute each digit of result in sequence, maintaining the carries. */
    for (k = 0; k < uECC_WORDS; ++k) {
        for (i = 0; i <= k; ++i) {
            muladd(left[i], right[k - i], &r0, &r1, &r2);
        }
        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(left[i], right[k - i], &r0, &r1, &r2);
        }
        result[k] = r0;
        r0 = r1;
        r1 = r2;
        r2 = 0;
    }
    result[uECC_WORDS * 2 - 1] = r0;
}
#endif

#if uECC_SQUARE_FUNC

#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
}

static void vli_square(uECC_word_t *result, const uECC_word_t *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 min = (k < uECC_WORDS ? 0 : (k + 1) - uECC_WORDS);
        for (i = min; i <= k && i <= k - i; ++i) {
            if (i < k-i) {
                mul2add(left[i], left[k - i], &r0, &r1, &r2);
            } else {
                muladd(left[i], left[k - i], &r0, &r1, &r2);
            }
        }
        result[k] = r0;
        r0 = r1;
        r1 = r2;
        r2 = 0;
    }
    
    result[uECC_WORDS * 2 - 1] = r0;
}
#endif

#else /* uECC_SQUARE_FUNC */

#define vli_square(result, left, size) vli_mult((result), (left), (left), (size))
    
#endif /* uECC_SQUARE_FUNC */


/* Computes result = (left + right) % mod.
   Assumes that left < mod and right < mod, and that result does not overlap mod. */
#if !asm_modAdd
static void vli_modAdd(uECC_word_t *result,
                       const uECC_word_t *left,
                       const uECC_word_t *right,
                       const uECC_word_t *mod) {
    uECC_word_t carry = vli_add(result, left, right);
    if (carry || vli_cmp(result, mod) >= 0) {
        /* result > mod (result = mod + remainder), so subtract mod to get remainder. */
        vli_sub(result, result, mod);
    }
}
#endif

/* Computes result = (left - right) % mod.
   Assumes that left < mod and right < mod, and that result does not overlap mod. */
#if !asm_modSub
static void vli_modSub(uECC_word_t *result,
                       const uECC_word_t *left,
                       const uECC_word_t *right,
                       const uECC_word_t *mod) {
    uECC_word_t l_borrow = vli_sub(result, left, right);
    if (l_borrow) {
        /* In this case, result == -diff == (max int) - diff. Since -x % d == d - x,
           we can get the correct result from result + mod (with overflow). */
        vli_add(result, result, mod);
    }
}
#endif

#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 result, const uECC_word_t * RESTRICT right);

/* Computes result = 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 result, uECC_word_t *RESTRICT product) {
    uECC_word_t tmp[2 * uECC_WORDS];
    uECC_word_t carry;
    
    vli_clear(tmp);
    vli_clear(tmp + uECC_WORDS);
    
    omega_mult(tmp, product + uECC_WORDS); /* (Rq, q) = q * c */
    
    carry = vli_add(result, product, tmp); /* (C, r) = r + q       */
    vli_clear(product);
    omega_mult(product, tmp + uECC_WORDS); /* Rq*c */
    carry += vli_add(result, result, product); /* (C1, r) = r + Rq*c */
    
    while (carry > 0) {
        --carry;
        vli_sub(result, result, curve_p);
    }
    if (vli_cmp(result, curve_p) > 0) {
        vli_sub(result, result, curve_p);
    }
}

#endif

#if uECC_CURVE == uECC_secp160r1

#if uECC_WORD_SIZE == 1
static void omega_mult(uint8_t * RESTRICT result, const uint8_t * RESTRICT right) {
    uint8_t carry;
    uint8_t i;
    
    /* Multiply by (2^31 + 1). */
    vli_set(result + 4, right); /* 2^32 */
    vli_rshift1(result + 4); /* 2^31 */
    result[3] = right[0] << 7; /* get last bit from shift */
    
    carry = vli_add(result, result, right); /* 2^31 + 1 */
    for (i = uECC_WORDS; carry; ++i) {
        uint16_t sum = (uint16_t)result[i] + carry;
        result[i] = (uint8_t)sum;
        carry = sum >> 8;
    }
}
#elif uECC_WORD_SIZE == 4
static void omega_mult(uint32_t * RESTRICT result, const uint32_t * RESTRICT right) {
    uint32_t carry;
    unsigned i;
    
    /* Multiply by (2^31 + 1). */
    vli_set(result + 1, right); /* 2^32 */
    vli_rshift1(result + 1); /* 2^31 */
    result[0] = right[0] << 31; /* get last bit from shift */
    
    carry = vli_add(result, result, right); /* 2^31 + 1 */
    for (i = uECC_WORDS; carry; ++i) {
        uint64_t sum = (uint64_t)result[i] + carry;
        result[i] = (uint32_t)sum;
        carry = sum >> 32;
    }
}
#endif /* uECC_WORD_SIZE */

#elif uECC_CURVE == uECC_secp192r1

/* Computes result = 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 result, uint8_t *RESTRICT product) {
    uint8_t tmp[uECC_WORDS];
    uint8_t carry;
    
    vli_set(result, product);
    
    vli_set(tmp, &product[24]);
    carry = vli_add(result, result, tmp);
    
    tmp[0] = tmp[1] = tmp[2] = tmp[3] = tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0;
    tmp[8] = product[24]; tmp[9] = product[25]; tmp[10] = product[26]; tmp[11] = product[27];
    tmp[12] = product[28]; tmp[13] = product[29]; tmp[14] = product[30]; tmp[15] = product[31];
    tmp[16] = product[32]; tmp[17] = product[33]; tmp[18] = product[34]; tmp[19] = product[35];
    tmp[20] = product[36]; tmp[21] = product[37]; tmp[22] = product[38]; tmp[23] = product[39];
    carry += vli_add(result, result, tmp);
    
    tmp[0] = tmp[8] = product[40];
    tmp[1] = tmp[9] = product[41];
    tmp[2] = tmp[10] = product[42];
    tmp[3] = tmp[11] = product[43];
    tmp[4] = tmp[12] = product[44];
    tmp[5] = tmp[13] = product[45];
    tmp[6] = tmp[14] = product[46];
    tmp[7] = tmp[15] = product[47];
    tmp[16] = tmp[17] = tmp[18] = tmp[19] = tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
    carry += vli_add(result, result, tmp);
    
    while (carry || vli_cmp(curve_p, result) != 1) {
        carry -= vli_sub(result, result, curve_p);
    }
}
#elif uECC_WORD_SIZE == 4
static void vli_mmod_fast(uint32_t *RESTRICT result, uint32_t *RESTRICT product) {
    uint32_t tmp[uECC_WORDS];
    int carry;
    
    vli_set(result, product);
    
    vli_set(tmp, &product[6]);
    carry = vli_add(result, result, tmp);
    
    tmp[0] = tmp[1] = 0;
    tmp[2] = product[6];
    tmp[3] = product[7];
    tmp[4] = product[8];
    tmp[5] = product[9];
    carry += vli_add(result, result, tmp);
    
    tmp[0] = tmp[2] = product[10];
    tmp[1] = tmp[3] = product[11];
    tmp[4] = tmp[5] = 0;
    carry += vli_add(result, result, tmp);
    
    while (carry || vli_cmp(curve_p, result) != 1) {
        carry -= vli_sub(result, result, curve_p);
    }
}
#else
static void vli_mmod_fast(uint64_t *RESTRICT result, uint64_t *RESTRICT product) {
    uint64_t tmp[uECC_WORDS];
    int carry;
    
    vli_set(result, product);
    
    vli_set(tmp, &product[3]);
    carry = vli_add(result, result, tmp);
    
    tmp[0] = 0;
    tmp[1] = product[3];
    tmp[2] = product[4];
    carry += vli_add(result, result, tmp);
    
    tmp[0] = tmp[1] = product[5];
    tmp[2] = 0;
    carry += vli_add(result, result, tmp);
    
    while (carry || vli_cmp(curve_p, result) != 1) {
        carry -= vli_sub(result, result, curve_p);
    }
}
#endif /* uECC_WORD_SIZE */

#elif uECC_CURVE == uECC_secp256r1

/* Computes result = 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 result, uint8_t *RESTRICT product) {
    uint8_t tmp[uECC_BYTES];
    int8_t carry;
    
    /* t */
    vli_set(result, product);
    
    /* s1 */
    tmp[0] = tmp[1] = tmp[2] = tmp[3] = 0;
    tmp[4] = tmp[5] = tmp[6] = tmp[7] = 0;
    tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0;
    tmp[12] = product[44]; tmp[13] = product[45]; tmp[14] = product[46]; tmp[15] = product[47];
    tmp[16] = product[48]; tmp[17] = product[49]; tmp[18] = product[50]; tmp[19] = product[51];
    tmp[20] = product[52]; tmp[21] = product[53]; tmp[22] = product[54]; tmp[23] = product[55];
    tmp[24] = product[56]; tmp[25] = product[57]; tmp[26] = product[58]; tmp[27] = product[59];
    tmp[28] = product[60]; tmp[29] = product[61]; tmp[30] = product[62]; tmp[31] = product[63];
    carry = vli_add(tmp, tmp, tmp);
    carry += vli_add(result, result, tmp);
    
    /* s2 */
    tmp[12] = product[48]; tmp[13] = product[49]; tmp[14] = product[50]; tmp[15] = product[51];
    tmp[16] = product[52]; tmp[17] = product[53]; tmp[18] = product[54]; tmp[19] = product[55];
    tmp[20] = product[56]; tmp[21] = product[57]; tmp[22] = product[58]; tmp[23] = product[59];
    tmp[24] = product[60]; tmp[25] = product[61]; tmp[26] = product[62]; tmp[27] = product[63];
    tmp[28] = tmp[29] = tmp[30] = tmp[31] = 0;
    carry += vli_add(tmp, tmp, tmp);
    carry += vli_add(result, result, tmp);
    
    /* s3 */
    tmp[0] = product[32]; tmp[1] = product[33]; tmp[2] = product[34]; tmp[3] = product[35];
    tmp[4] = product[36]; tmp[5] = product[37]; tmp[6] = product[38]; tmp[7] = product[39];
    tmp[8] = product[40]; tmp[9] = product[41]; tmp[10] = product[42]; tmp[11] = product[43];
    tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0;
    tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0;
    tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
    tmp[24] = product[56]; tmp[25] = product[57]; tmp[26] = product[58]; tmp[27] = product[59];
    tmp[28] = product[60]; tmp[29] = product[61]; tmp[30] = product[62]; tmp[31] = product[63];
    carry += vli_add(result, result, tmp);
    
    /* s4 */
    tmp[0] = product[36]; tmp[1] = product[37]; tmp[2] = product[38]; tmp[3] = product[39];
    tmp[4] = product[40]; tmp[5] = product[41]; tmp[6] = product[42]; tmp[7] = product[43];
    tmp[8] = product[44]; tmp[9] = product[45]; tmp[10] = product[46]; tmp[11] = product[47];
    tmp[12] = product[52]; tmp[13] = product[53]; tmp[14] = product[54]; tmp[15] = product[55];
    tmp[16] = product[56]; tmp[17] = product[57]; tmp[18] = product[58]; tmp[19] = product[59];
    tmp[20] = product[60]; tmp[21] = product[61]; tmp[22] = product[62]; tmp[23] = product[63];
    tmp[24] = product[52]; tmp[25] = product[53]; tmp[26] = product[54]; tmp[27] = product[55];
    tmp[28] = product[32]; tmp[29] = product[33]; tmp[30] = product[34]; tmp[31] = product[35];
    carry += vli_add(result, result, tmp);
    
    /* d1 */
    tmp[0] = product[44]; tmp[1] = product[45]; tmp[2] = product[46]; tmp[3] = product[47];
    tmp[4] = product[48]; tmp[5] = product[49]; tmp[6] = product[50]; tmp[7] = product[51];
    tmp[8] = product[52]; tmp[9] = product[53]; tmp[10] = product[54]; tmp[11] = product[55];
    tmp[12] = tmp[13] = tmp[14] = tmp[15] = 0;
    tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0;
    tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
    tmp[24] = product[32]; tmp[25] = product[33]; tmp[26] = product[34]; tmp[27] = product[35];
    tmp[28] = product[40]; tmp[29] = product[41]; tmp[30] = product[42]; tmp[31] = product[43];
    carry -= vli_sub(result, result, tmp);
    
    /* d2 */
    tmp[0] = product[48]; tmp[1] = product[49]; tmp[2] = product[50]; tmp[3] = product[51];
    tmp[4] = product[52]; tmp[5] = product[53]; tmp[6] = product[54]; tmp[7] = product[55];
    tmp[8] = product[56]; tmp[9] = product[57]; tmp[10] = product[58]; tmp[11] = product[59];
    tmp[12] = product[60]; tmp[13] = product[61]; tmp[14] = product[62]; tmp[15] = product[63];
    tmp[16] = tmp[17] = tmp[18] = tmp[19] = 0;
    tmp[20] = tmp[21] = tmp[22] = tmp[23] = 0;
    tmp[24] = product[36]; tmp[25] = product[37]; tmp[26] = product[38]; tmp[27] = product[39];
    tmp[28] = product[44]; tmp[29] = product[45]; tmp[30] = product[46]; tmp[31] = product[47];
    carry -= vli_sub(result, result, tmp);
    
    /* d3 */
    tmp[0] = product[52]; tmp[1] = product[53]; tmp[2] = product[54]; tmp[3] = product[55];
    tmp[4] = product[56]; tmp[5] = product[57]; tmp[6] = product[58]; tmp[7] = product[59];
    tmp[8] = product[60]; tmp[9] = product[61]; tmp[10] = product[62]; tmp[11] = product[63];
    tmp[12] = product[32]; tmp[13] = product[33]; tmp[14] = product[34]; tmp[15] = product[35];
    tmp[16] = product[36]; tmp[17] = product[37]; tmp[18] = product[38]; tmp[19] = product[39];
    tmp[20] = product[40]; tmp[21] = product[41]; tmp[22] = product[42]; tmp[23] = product[43];
    tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0;
    tmp[28] = product[48]; tmp[29] = product[49]; tmp[30] = product[50]; tmp[31] = product[51];
    carry -= vli_sub(result, result, tmp);
    
    /* d4 */
    tmp[0] = product[56]; tmp[1] = product[57]; tmp[2] = product[58]; tmp[3] = product[59];
    tmp[4] = product[60]; tmp[5] = product[61]; tmp[6] = product[62]; tmp[7] = product[63];
    tmp[8] = tmp[9] = tmp[10] = tmp[11] = 0;
    tmp[12] = product[36]; tmp[13] = product[37]; tmp[14] = product[38]; tmp[15] = product[39];
    tmp[16] = product[40]; tmp[17] = product[41]; tmp[18] = product[42]; tmp[19] = product[43];
    tmp[20] = product[44]; tmp[21] = product[45]; tmp[22] = product[46]; tmp[23] = product[47];
    tmp[24] = tmp[25] = tmp[26] = tmp[27] = 0;
    tmp[28] = product[52]; tmp[29] = product[53]; tmp[30] = product[54]; tmp[31] = product[55];
    carry -= vli_sub(result, result, tmp);
    
    if (carry < 0) {
        do {
            carry += vli_add(result, result, curve_p);
        } while (carry < 0);
    } else {
        while (carry || vli_cmp(curve_p, result) != 1) {
            carry -= vli_sub(result, result, curve_p);
        }
    }
}
#elif uECC_WORD_SIZE == 4
static void vli_mmod_fast(uint32_t *RESTRICT result, uint32_t *RESTRICT product) {
    uint32_t tmp[uECC_WORDS];
    int carry;
    
    /* t */
    vli_set(result, product);
    
    /* s1 */
    tmp[0] = tmp[1] = tmp[2] = 0;
    tmp[3] = product[11];
    tmp[4] = product[12];
    tmp[5] = product[13];
    tmp[6] = product[14];
    tmp[7] = product[15];
    carry = vli_add(tmp, tmp, tmp);
    carry += vli_add(result, result, tmp);
    
    /* s2 */
    tmp[3] = product[12];
    tmp[4] = product[13];
    tmp[5] = product[14];
    tmp[6] = product[15];
    tmp[7] = 0;
    carry += vli_add(tmp, tmp, tmp);
    carry += vli_add(result, result, tmp);
    
    /* s3 */
    tmp[0] = product[8];
    tmp[1] = product[9];
    tmp[2] = product[10];
    tmp[3] = tmp[4] = tmp[5] = 0;
    tmp[6] = product[14];
    tmp[7] = product[15];
    carry += vli_add(result, result, tmp);
    
    /* s4 */
    tmp[0] = product[9];
    tmp[1] = product[10];
    tmp[2] = product[11];
    tmp[3] = product[13];
    tmp[4] = product[14];
    tmp[5] = product[15];
    tmp[6] = product[13];
    tmp[7] = product[8];
    carry += vli_add(result, result, tmp);
    
    /* d1 */
    tmp[0] = product[11];
    tmp[1] = product[12];
    tmp[2] = product[13];
    tmp[3] = tmp[4] = tmp[5] = 0;
    tmp[6] = product[8];
    tmp[7] = product[10];
    carry -= vli_sub(result, result, tmp);
    
    /* d2 */
    tmp[0] = product[12];
    tmp[1] = product[13];
    tmp[2] = product[14];
    tmp[3] = product[15];
    tmp[4] = tmp[5] = 0;
    tmp[6] = product[9];
    tmp[7] = product[11];
    carry -= vli_sub(result, result, tmp);
    
    /* d3 */
    tmp[0] = product[13];
    tmp[1] = product[14];
    tmp[2] = product[15];
    tmp[3] = product[8];
    tmp[4] = product[9];
    tmp[5] = product[10];
    tmp[6] = 0;
    tmp[7] = product[12];
    carry -= vli_sub(result, result, tmp);
    
    /* d4 */
    tmp[0] = product[14];
    tmp[1] = product[15];
    tmp[2] = 0;
    tmp[3] = product[9];
    tmp[4] = product[10];
    tmp[5] = product[11];
    tmp[6] = 0;
    tmp[7] = product[13];
    carry -= vli_sub(result, result, tmp);
    
    if (carry < 0) {
        do {
            carry += vli_add(result, result, curve_p);
        } while (carry < 0);
    } else {
        while (carry || vli_cmp(curve_p, result) != 1) {
            carry -= vli_sub(result, result, curve_p);
        }
    }
}
#else
static void vli_mmod_fast(uint64_t *RESTRICT result, uint64_t *RESTRICT product) {
    uint64_t tmp[uECC_WORDS];
    int carry;
    
    /* t */
    vli_set(result, product);
    
    /* s1 */
    tmp[0] = 0;
    tmp[1] = product[5] & 0xffffffff00000000ull;
    tmp[2] = product[6];
    tmp[3] = product[7];
    carry = vli_add(tmp, tmp, tmp);
    carry += vli_add(result, result, tmp);
    
    /* s2 */
    tmp[1] = product[6] << 32;
    tmp[2] = (product[6] >> 32) | (product[7] << 32);
    tmp[3] = product[7] >> 32;
    carry += vli_add(tmp, tmp, tmp);
    carry += vli_add(result, result, tmp);
    
    /* s3 */
    tmp[0] = product[4];
    tmp[1] = product[5] & 0xffffffff;
    tmp[2] = 0;
    tmp[3] = product[7];
    carry += vli_add(result, result, tmp);
    
    /* s4 */
    tmp[0] = (product[4] >> 32) | (product[5] << 32);
    tmp[1] = (product[5] >> 32) | (product[6] & 0xffffffff00000000ull);
    tmp[2] = product[7];
    tmp[3] = (product[6] >> 32) | (product[4] << 32);
    carry += vli_add(result, result, tmp);
    
    /* d1 */
    tmp[0] = (product[5] >> 32) | (product[6] << 32);
    tmp[1] = (product[6] >> 32);
    tmp[2] = 0;
    tmp[3] = (product[4] & 0xffffffff) | (product[5] << 32);
    carry -= vli_sub(result, result, tmp);
    
    /* d2 */
    tmp[0] = product[6];
    tmp[1] = product[7];
    tmp[2] = 0;
    tmp[3] = (product[4] >> 32) | (product[5] & 0xffffffff00000000ull);
    carry -= vli_sub(result, result, tmp);
    
    /* d3 */
    tmp[0] = (product[6] >> 32) | (product[7] << 32);
    tmp[1] = (product[7] >> 32) | (product[4] << 32);
    tmp[2] = (product[4] >> 32) | (product[5] << 32);
    tmp[3] = (product[6] << 32);
    carry -= vli_sub(result, result, tmp);
    
    /* d4 */
    tmp[0] = product[7];
    tmp[1] = product[4] & 0xffffffff00000000ull;
    tmp[2] = product[5];
    tmp[3] = product[6] & 0xffffffff00000000ull;
    carry -= vli_sub(result, result, tmp);
    
    if (carry < 0) {
        do {
            carry += vli_add(result, result, curve_p);
        } while (carry < 0);
    } else {
        while (carry || vli_cmp(curve_p, result) != 1) {
            carry -= vli_sub(result, result, curve_p);
        }
    }
}
#endif /* uECC_WORD_SIZE */

#elif uECC_CURVE == uECC_secp256k1

#if uECC_WORD_SIZE == 1
static void omega_mult(uint8_t * RESTRICT result, const uint8_t * RESTRICT 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, right[0], &r0, &r1, &r2);
    result[0] = r0;
    r0 = r1;
    r1 = r2;
    /* r2 is still 0 */
    
    for (k = 1; k < uECC_WORDS; ++k) {
        muladd(0x03, right[k - 1], &r0, &r1, &r2);
        muladd(0xD1, right[k], &r0, &r1, &r2);
        result[k] = r0;
        r0 = r1;
        r1 = r2;
        r2 = 0;
    }
    muladd(0x03, right[uECC_WORDS - 1], &r0, &r1, &r2);
    result[uECC_WORDS] = r0;
    result[uECC_WORDS + 1] = r1;

    result[4 + uECC_WORDS] = vli_add(result + 4, result + 4, right); /* add the 2^32 multiple */
}
#elif uECC_WORD_SIZE == 4
static void omega_mult(uint32_t * RESTRICT result, const uint32_t * RESTRICT right) {
    /* Multiply by (2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1). */
    uint32_t carry = 0;
    wordcount_t k;
    
    for (k = 0; k < uECC_WORDS; ++k) {
        uint64_t p = (uint64_t)0x3D1 * right[k] + carry;
        result[k] = (p & 0xffffffff);
        carry = p >> 32;
    }
    result[uECC_WORDS] = carry;
    
    result[1 + uECC_WORDS] = vli_add(result + 1, result + 1, right); /* add the 2^32 multiple */
}
#else
static void omega_mult(uint64_t * RESTRICT result, const uint64_t * RESTRICT 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, right[k], &r0, &r1, &r2);
        result[k] = r0;
        r0 = r1;
        r1 = r2;
        r2 = 0;
    }
    result[uECC_WORDS] = r0;
}
#endif /* uECC_WORD_SIZE */

#endif /* uECC_CURVE */
#endif /* !asm_mmod_fast */

/* Computes result = (left * right) % curve_p. */
static void vli_modMult_fast(uECC_word_t *result,
                             const uECC_word_t *left,
                             const uECC_word_t *right) {
    uECC_word_t product[2 * uECC_WORDS];
    vli_mult(product, left, right);
    vli_mmod_fast(result, product);
}

#if uECC_SQUARE_FUNC

/* Computes result = left^2 % curve_p. */
static void vli_modSquare_fast(uECC_word_t *result, const uECC_word_t *left) {
    uECC_word_t product[2 * uECC_WORDS];
    vli_square(product, left);
    vli_mmod_fast(result, product);
}

#else /* uECC_SQUARE_FUNC */

#define vli_modSquare_fast(result, left) vli_modMult_fast((result), (left), (left))
    
#endif /* uECC_SQUARE_FUNC */


#define EVEN(vli) (!(vli[0] & 1))
/* Computes result = (1 / input) % mod. All VLIs are the same size.
   See "From Euclid's GCD to Montgomery Multiplication to the Great Divide"
   https://labs.oracle.com/techrep/2001/smli_tr-2001-95.pdf */
#if !asm_modInv
static void vli_modInv(uECC_word_t *result, const uECC_word_t *input, const uECC_word_t *mod) {
    uECC_word_t a[uECC_WORDS], b[uECC_WORDS], u[uECC_WORDS], v[uECC_WORDS];
    uECC_word_t carry;
    cmpresult_t cmpResult;
    
    if (vli_isZero(input)) {
        vli_clear(result);
        return;
    }

    vli_set(a, input);
    vli_set(b, mod);
    vli_clear(u);
    u[0] = 1;
    vli_clear(v);
    while ((cmpResult = vli_cmp(a, b)) != 0) {
        carry = 0;
        if (EVEN(a)) {
            vli_rshift1(a);
            if (!EVEN(u)) {
                carry = vli_add(u, u, mod);
            }
            vli_rshift1(u);
            if (carry) {
                u[uECC_WORDS - 1] |= HIGH_BIT_SET;
            }
        } else if (EVEN(b)) {
            vli_rshift1(b);
            if (!EVEN(v)) {
                carry = vli_add(v, v, mod);
            }
            vli_rshift1(v);
            if (carry) {
                v[uECC_WORDS - 1] |= HIGH_BIT_SET;
            }
        } else if (cmpResult > 0) {
            vli_sub(a, a, b);
            vli_rshift1(a);
            if (vli_cmp(u, v) < 0) {
                vli_add(u, u, mod);
            }
            vli_sub(u, u, v);
            if (!EVEN(u)) {
                carry = vli_add(u, u, mod);
            }
            vli_rshift1(u);
            if (carry) {
                u[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, mod);
            }
            vli_sub(v, v, u);
            if (!EVEN(v)) {
                carry = vli_add(v, v, mod);
            }
            vli_rshift1(v);
            if (carry) {
                v[uECC_WORDS - 1] |= HIGH_BIT_SET;
            }
        }
    }
    vli_set(result, u);
}
#endif /* !asm_modInv */

/* ------ Point operations ------ */

/* Returns 1 if 'point' is the point at infinity, 0 otherwise. */
static cmpresult_t EccPoint_isZero(const EccPoint *point) {
    return (vli_isZero(point->x) && vli_isZero(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 carry = vli_add(Y1, Y1, curve_p);
        vli_rshift1(Y1);
        Y1[uECC_WORDS - 1] |= 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,
                    const 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 initial_Z) {
    uECC_word_t z[uECC_WORDS];
    if (initial_Z) {
        vli_set(z, initial_Z);
    } else {
        vli_clear(z);
        z[0] = 1;
    }

    vli_set(X2, X1);
    vli_set(Y2, Y1);

    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 result,
                          const EccPoint * RESTRICT point,
                          const uECC_word_t * RESTRICT scalar,
                          const uECC_word_t * RESTRICT initialZ,
                          bitcount_t 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], point->x);
    vli_set(Ry[1], point->y);

    XYcZ_initial_double(Rx[1], Ry[1], Rx[0], Ry[0], initialZ);

    for (i = numBits - 2; i > 0; --i) {
        nb = !vli_testBit(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(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, point->x); /* xP * Yb * (X1 - X0) */
    vli_modInv(z, z, curve_p);          /* 1 / (xP * Yb * (X1 - X0)) */
    vli_modMult_fast(z, z, 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(result->x, Rx[0]);
    vli_set(result->y, Ry[0]);
}

static int EccPoint_compute_public_key(EccPoint *result, const uECC_word_t *private) {
    /* Make sure the private key is in the range [1, n-1]. */
    if (vli_isZero(private)) {
        return 0;
    }

#if uECC_CURVE != uECC_secp160r1
    if (vli_cmp(curve_n, private) != 1) {
        return 0;
    }
#endif

    /* Compute the public point */
    EccPoint_mult(result, &curve_G, private, 0, vli_numBits(private, uECC_WORDS));
    if (EccPoint_isZero(result)) {
        return 0;
    }
    return 1;
}

/* 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 dest, const uint8_t * RESTRICT src) {
    uint8_t i;
    for (i = 0; i < uECC_BYTES; ++i) {
        dest[i] = 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 *bytes, const uint32_t *native) {
    unsigned i;
    for (i = 0; i < uECC_WORDS; ++i) {
        uint8_t *digit = bytes + 4 * (uECC_WORDS - 1 - i);
        digit[0] = native[i] >> 24;
        digit[1] = native[i] >> 16;
        digit[2] = native[i] >> 8;
        digit[3] = native[i];
    }
}

static void vli_bytesToNative(uint32_t *native, const uint8_t *bytes) {
    unsigned i;
    for (i = 0; i < uECC_WORDS; ++i) {
        const uint8_t *digit = bytes + 4 * (uECC_WORDS - 1 - i);
        native[i] = ((uint32_t)digit[0] << 24) | ((uint32_t)digit[1] << 16) |
                    ((uint32_t)digit[2] << 8) | (uint32_t)digit[3];
    }
}

#else

static void vli_nativeToBytes(uint8_t *bytes, const uint64_t *native) {
    unsigned i;
    for (i = 0; i < uECC_WORDS; ++i) {
        uint8_t *digit = bytes + 8 * (uECC_WORDS - 1 - i);
        digit[0] = native[i] >> 56;
        digit[1] = native[i] >> 48;
        digit[2] = native[i] >> 40;
        digit[3] = native[i] >> 32;
        digit[4] = native[i] >> 24;
        digit[5] = native[i] >> 16;
        digit[6] = native[i] >> 8;
        digit[7] = native[i];
    }
}

static void vli_bytesToNative(uint64_t *native, const uint8_t *bytes) {
    unsigned i;
    for (i = 0; i < uECC_WORDS; ++i) {
        const uint8_t *digit = bytes + 8 * (uECC_WORDS - 1 - i);
        native[i] = ((uint64_t)digit[0] << 56) | ((uint64_t)digit[1] << 48) |
                    ((uint64_t)digit[2] << 40) | ((uint64_t)digit[3] << 32) |
                    ((uint64_t)digit[4] << 24) | ((uint64_t)digit[5] << 16) |
                    ((uint64_t)digit[6] << 8) | (uint64_t)digit[7];
    }
}

#endif /* uECC_WORD_SIZE */

int uECC_make_key(uint8_t public_key[uECC_BYTES*2], uint8_t private_key[uECC_BYTES]) {
    uECC_word_t private[uECC_WORDS];
    uECC_word_t tries = 0;
    EccPoint public;

    while (1) {
        if (!g_rng_function((uint8_t *)private, sizeof(private)) || (tries++ >= MAX_TRIES)) {
            return 0;
        }
        if (EccPoint_compute_public_key(&public, private)) {
            break;
        }
    }

    vli_nativeToBytes(private_key, private);
    vli_nativeToBytes(public_key, public.x);
    vli_nativeToBytes(public_key + uECC_BYTES, public.y);
    return 1;
}

int uECC_shared_secret(const uint8_t public_key[uECC_BYTES*2],
                       const uint8_t private_key[uECC_BYTES],
                       uint8_t secret[uECC_BYTES]) {
    EccPoint public;
    EccPoint product;
    uECC_word_t private[uECC_WORDS];
    uECC_word_t random[uECC_WORDS];
    uECC_word_t *initial_Z = 0;
    uECC_word_t tries;
    
    // Try to get a random initial Z value to improve protection against side-channel
    // attacks. If the RNG fails every time (eg it was not defined), we continue so that
    // uECC_shared_secret() can still work without an RNG defined.
    for (tries = 0; tries < MAX_TRIES; ++tries) {
        if (g_rng_function((uint8_t *)random, sizeof(random)) && !vli_isZero(random)) {
            initial_Z = random;
            break;
        }
    }
    
    vli_bytesToNative(private, private_key);
    vli_bytesToNative(public.x, public_key);
    vli_bytesToNative(public.y, public_key + uECC_BYTES);
    
    EccPoint_mult(&product, &public, private, initial_Z, vli_numBits(private, uECC_WORDS));
    vli_nativeToBytes(secret, product.x);
    return !EccPoint_isZero(&product);
}

void uECC_compress(const uint8_t public_key[uECC_BYTES*2], uint8_t compressed[uECC_BYTES+1]) {
    wordcount_t i;
    for (i = 0; i < uECC_BYTES; ++i) {
        compressed[i+1] = public_key[i];
    }
    compressed[0] = 2 + (public_key[uECC_BYTES * 2 - 1] & 0x01);
}

/* Computes result = x^3 + ax + b. result must not overlap x. */
static void curve_x_side(uECC_word_t * RESTRICT result, const uECC_word_t * RESTRICT x) {
#if (uECC_CURVE == uECC_secp256k1)
    vli_modSquare_fast(result, x); /* r = x^2 */
    vli_modMult_fast(result, result, x); /* r = x^3 */
    vli_modAdd(result, result, curve_b, curve_p); /* r = x^3 + b */
#else
    uECC_word_t _3[uECC_WORDS] = {3}; /* -a = 3 */

    vli_modSquare_fast(result, x); /* r = x^2 */
    vli_modSub_fast(result, result, _3); /* r = x^2 - 3 */
    vli_modMult_fast(result, result, x); /* r = x^3 - 3x */
    vli_modAdd(result, result, curve_b, curve_p); /* r = x^3 - 3x + b */
#endif
}

void uECC_decompress(const uint8_t compressed[uECC_BYTES+1], uint8_t public_key[uECC_BYTES*2]) {
    EccPoint point;
    vli_bytesToNative(point.x, compressed + 1);
    curve_x_side(point.y, point.x);
    mod_sqrt(point.y);
    
    if ((point.y[0] & 0x01) != (compressed[0] & 0x01)) {
        vli_sub(point.y, curve_p, point.y);
    }
    
    vli_nativeToBytes(public_key, point.x);
    vli_nativeToBytes(public_key + uECC_BYTES, point.y);
}

int uECC_valid_public_key(const uint8_t public_key[uECC_BYTES*2]) {
    uECC_word_t tmp1[uECC_WORDS];
    uECC_word_t tmp2[uECC_WORDS];
    EccPoint public;
    vli_bytesToNative(public.x, public_key);
    vli_bytesToNative(public.y, public_key + uECC_BYTES);
    
    // The point at infinity is invalid.
    if (EccPoint_isZero(&public)) {
        return 0;
    }
    
    // x and y must be smaller than p.
    if (vli_cmp(curve_p, public.x) != 1 || vli_cmp(curve_p, public.y) != 1) {
        return 0;
    }
    
    vli_modSquare_fast(tmp1, public.y); /* tmp1 = y^2 */
    curve_x_side(tmp2, public.x); /* tmp2 = x^3 + ax + b */
    
    /* Make sure that y^2 == x^3 + ax + b */
    return (vli_cmp(tmp1, tmp2) == 0);
}

int uECC_compute_public_key(const uint8_t private_key[uECC_BYTES],
                            uint8_t public_key[uECC_BYTES * 2]) {
    uECC_word_t private[uECC_WORDS];
    EccPoint public;

    vli_bytesToNative(private, private_key);

    if (!EccPoint_compute_public_key(&public, private)) {
        return 0;
    }

    vli_nativeToBytes(public_key, public.x);
    vli_nativeToBytes(public_key + uECC_BYTES, public.y);
    return 1;
}

int uECC_bytes(void) {
    return uECC_BYTES;
}

int uECC_curve(void) {
    return uECC_CURVE;
}

/* -------- ECDSA code -------- */

#if (uECC_CURVE == uECC_secp160r1)
static void vli_clear_n(uECC_word_t *vli) {
    vli_clear(vli);
    vli[uECC_N_WORDS - 1] = 0;
}

static uECC_word_t vli_isZero_n(const uECC_word_t *vli) {
    if (vli[uECC_N_WORDS - 1]) {
        return 0;
    }
    return vli_isZero(vli);
}

static void vli_set_n(uECC_word_t *dest, const uECC_word_t *src) {
    vli_set(dest, src);
    dest[uECC_N_WORDS - 1] = src[uECC_N_WORDS - 1];
}

static cmpresult_t vli_cmp_n(const uECC_word_t *left, const uECC_word_t *right) {
    if (left[uECC_N_WORDS - 1] > right[uECC_N_WORDS - 1]) {
        return 1;
    } else if (left[uECC_N_WORDS - 1] < right[uECC_N_WORDS - 1]) {
        return -1;
    }
    return vli_cmp(left, right);
}

static void vli_rshift1_n(uECC_word_t *vli) {
    vli_rshift1(vli);
    vli[uECC_N_WORDS - 2] |= vli[uECC_N_WORDS - 1] << (uECC_WORD_BITS - 1);
    vli[uECC_N_WORDS - 1] = vli[uECC_N_WORDS - 1] >> 1;
}

static uECC_word_t vli_add_n(uECC_word_t *result,
                             const uECC_word_t *left,
                             const uECC_word_t *right) {
    uECC_word_t carry = vli_add(result, left, right);
    uECC_word_t sum = left[uECC_N_WORDS - 1] + right[uECC_N_WORDS - 1] + carry;
    if (sum != left[uECC_N_WORDS - 1]) {
        carry = (sum < left[uECC_N_WORDS - 1]);
    }
    result[uECC_N_WORDS - 1] = sum;
    return carry;
}

static uECC_word_t vli_sub_n(uECC_word_t *result,
                             const uECC_word_t *left,
                             const uECC_word_t *right) {
    uECC_word_t borrow = vli_sub(result, left, right);
    uECC_word_t diff = left[uECC_N_WORDS - 1] - right[uECC_N_WORDS - 1] - borrow;
    if (diff != left[uECC_N_WORDS - 1]) {
        borrow = (diff > left[uECC_N_WORDS - 1]);
    }
    result[uECC_N_WORDS - 1] = diff;
    return borrow;
}

#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) {
    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;
}
#define muladd_exists 1
#endif

static void vli_mult_n(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) {
    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 min = (k < uECC_N_WORDS ? 0 : (k + 1) - uECC_N_WORDS);
        wordcount_t max = (k < uECC_N_WORDS ? k : uECC_N_WORDS - 1);
        for (i = min; i <= max; ++i) {
            muladd(left[i], right[k - i], &r0, &r1, &r2);
        }
        result[k] = r0;
        r0 = r1;
        r1 = r2;
        r2 = 0;
    }
    result[uECC_N_WORDS * 2 - 1] = r0;
}

static void vli_modAdd_n(uECC_word_t *result,
                         const uECC_word_t *left,
                         const uECC_word_t *right,
                         const uECC_word_t *mod) {
    uECC_word_t carry = vli_add_n(result, left, right);
    if (carry || vli_cmp_n(result, mod) >= 0) {
        vli_sub_n(result, result, mod);
    }
}

static void vli_modInv_n(uECC_word_t *result, const uECC_word_t *input, const uECC_word_t *mod) {
    uECC_word_t a[uECC_N_WORDS], b[uECC_N_WORDS], u[uECC_N_WORDS], v[uECC_N_WORDS];
    uECC_word_t carry;
    cmpresult_t cmpResult;
    
    if (vli_isZero_n(input)) {
        vli_clear_n(result);
        return;
    }

    vli_set_n(a, input);
    vli_set_n(b, mod);
    vli_clear_n(u);
    u[0] = 1;
    vli_clear_n(v);
    while ((cmpResult = vli_cmp_n(a, b)) != 0) {
        carry = 0;
        if (EVEN(a)) {
            vli_rshift1_n(a);
            if (!EVEN(u)) {
                carry = vli_add_n(u, u, mod);
            }
            vli_rshift1_n(u);
            if (carry) {
                u[uECC_N_WORDS - 1] |= HIGH_BIT_SET;
            }
        } else if (EVEN(b)) {
            vli_rshift1_n(b);
            if (!EVEN(v)) {
                carry = vli_add_n(v, v, mod);
            }
            vli_rshift1_n(v);
            if (carry) {
                v[uECC_N_WORDS - 1] |= HIGH_BIT_SET;
            }
        } else if (cmpResult > 0) {
            vli_sub_n(a, a, b);
            vli_rshift1_n(a);
            if (vli_cmp_n(u, v) < 0) {
                vli_add_n(u, u, mod);
            }
            vli_sub_n(u, u, v);
            if (!EVEN(u)) {
                carry = vli_add_n(u, u, mod);
            }
            vli_rshift1_n(u);
            if (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, mod);
            }
            vli_sub_n(v, v, u);
            if (!EVEN(v)) {
                carry = vli_add_n(v, v, mod);
            }
            vli_rshift1_n(v);
            if (carry) {
                v[uECC_N_WORDS - 1] |= HIGH_BIT_SET;
            }
        }
    }
    vli_set_n(result, u);
}

static void vli2_rshift1_n(uECC_word_t *vli) {
    vli_rshift1_n(vli);
    vli[uECC_N_WORDS - 1] |= vli[uECC_N_WORDS] << (uECC_WORD_BITS - 1);
    vli_rshift1_n(vli + uECC_N_WORDS);
}

static uECC_word_t vli2_sub_n(uECC_word_t *result,
                              const uECC_word_t *left,
                              const uECC_word_t *right) {
    uECC_word_t borrow = 0;
    wordcount_t i;
    for (i = 0; i < uECC_N_WORDS * 2; ++i) {
        uECC_word_t diff = left[i] - right[i] - borrow;
        if (diff != left[i]) {
            borrow = (diff > left[i]);
        }
        result[i] = diff;
    }
    return borrow;
}

/* Computes result = (left * right) % curve_n. */
static void vli_modMult_n(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) {
    bitcount_t i;
    uECC_word_t product[2 * uECC_N_WORDS];
    uECC_word_t modMultiple[2 * uECC_N_WORDS];
    uECC_word_t tmp[2 * uECC_N_WORDS];
    uECC_word_t *v[2] = {tmp, product};
    uECC_word_t index = 1;
    
    vli_mult_n(product, left, right);
    vli_clear_n(modMultiple);
    vli_set(modMultiple + uECC_N_WORDS + 1, curve_n);
    vli_rshift1(modMultiple + uECC_N_WORDS + 1);
    modMultiple[2 * uECC_N_WORDS - 1] |= HIGH_BIT_SET;
    modMultiple[uECC_N_WORDS] = HIGH_BIT_SET;
    
    for (i = 0;
         i <= ((((bitcount_t)uECC_N_WORDS) << uECC_WORD_BITS_SHIFT) + (uECC_WORD_BITS - 1));
         ++i) {
        uECC_word_t borrow = vli2_sub_n(v[1 - index], v[index], modMultiple);
        index = !(index ^ borrow); /* Swap the index if there was no borrow */
        vli2_rshift1_n(modMultiple);
    }
    vli_set_n(result, v[index]);
}

#else

#define vli_modInv_n vli_modInv
#define vli_modAdd_n vli_modAdd

static void vli2_rshift1(uECC_word_t *vli) {
    vli_rshift1(vli);
    vli[uECC_WORDS - 1] |= vli[uECC_WORDS] << (uECC_WORD_BITS - 1);
    vli_rshift1(vli + uECC_WORDS);
}

static uECC_word_t vli2_sub(uECC_word_t *result,
                            const uECC_word_t *left,
                            const uECC_word_t *right) {
    uECC_word_t borrow = 0;
    wordcount_t i;
    for (i = 0; i < uECC_WORDS * 2; ++i) {
        uECC_word_t diff = left[i] - right[i] - borrow;
        if (diff != left[i]) {
            borrow = (diff > left[i]);
        }
        result[i] = diff;
    }
    return borrow;
}

/* Computes result = (left * right) % curve_n. */
static void vli_modMult_n(uECC_word_t *result, const uECC_word_t *left, const uECC_word_t *right) {
    uECC_word_t product[2 * uECC_WORDS];
    uECC_word_t modMultiple[2 * uECC_WORDS];
    uECC_word_t tmp[2 * uECC_WORDS];
    uECC_word_t *v[2] = {tmp, product};
    
    vli_mult(product, left, right);
    vli_set(modMultiple + uECC_WORDS, curve_n); /* works if curve_n has its highest bit set */
    vli_clear(modMultiple);
    
    bitcount_t i;
    uECC_word_t index = 1;
    for (i = 0; i <= uECC_BYTES * 8; ++i) {
        uECC_word_t borrow = vli2_sub(v[1 - index], v[index], modMultiple);
        index = !(index ^ borrow); /* Swap the index if there was no borrow */
        vli2_rshift1(modMultiple);
    }
    vli_set(result, v[index]);
}
#endif /* (uECC_CURVE != uECC_secp160r1) */

// 0 < k < curve_n
static int uECC_sign_with_k(const uint8_t private_key[uECC_BYTES],
                            const uint8_t hash[uECC_BYTES],
                            uECC_word_t k[uECC_N_WORDS],
                            uint8_t signature[uECC_BYTES*2]) {
    uECC_word_t tmp[uECC_N_WORDS];
    uECC_word_t s[uECC_N_WORDS];
    uECC_word_t *k2[2] = {tmp, s};
    EccPoint p;
    uECC_word_t carry;
    uECC_word_t tries;

#if (uECC_CURVE == uECC_secp160r1)
    /* Make sure that we don't leak timing information about k.
       See http://eprint.iacr.org/2011/232.pdf */
    vli_add_n(tmp, k, curve_n);
    carry = (tmp[uECC_WORDS] & 0x02);
    vli_add_n(s, tmp, curve_n);

    /* p = k * G */
    EccPoint_mult(&p, &curve_G, k2[!carry], 0, (uECC_BYTES * 8) + 2);
#else
    /* Make sure that we don't leak timing information about k.
       See http://eprint.iacr.org/2011/232.pdf */
    carry = vli_add(tmp, k, curve_n);
    vli_add(s, tmp, curve_n);

    /* p = k * G */
    EccPoint_mult(&p, &curve_G, k2[!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
    if (vli_isZero(p.x)) {
        return 0;
    }
    
    // Attempt to get a random number to prevent side channel analysis of k.
    // If the RNG fails every time (eg it was not defined), we continue so that
    // deterministic signing can still work (with reduced security) without
    // an RNG defined.
    carry = 0; // use to signal that the RNG succeeded at least once.
    for (tries = 0; tries < MAX_TRIES; ++tries) {
        if (!g_rng_function((uint8_t *)tmp, sizeof(tmp))) {
            continue;
        }
        carry = 1;
        if (!vli_isZero(tmp)) {
            break;
        }
    }
    if (!carry) {
        vli_clear(tmp);
        tmp[0] = 1;
    }
    
    /* 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, tmp); /* k' = rand * k */
    vli_modInv_n(k, k, curve_n); /* k = 1 / k' */
    vli_modMult_n(k, k, tmp); /* k = 1 / k */
    
    vli_nativeToBytes(signature, p.x); /* store r */
    
    tmp[uECC_N_WORDS - 1] = 0;
    vli_bytesToNative(tmp, private_key); /* tmp = d */
    s[uECC_N_WORDS - 1] = 0;
    vli_set(s, p.x);
    vli_modMult_n(s, tmp, s); /* s = r*d */

    vli_bytesToNative(tmp, hash);
    vli_modAdd_n(s, 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]) {
        return 0;
    }
#endif
    vli_nativeToBytes(signature + uECC_BYTES, s);
    return 1;
}

int uECC_sign(const uint8_t private_key[uECC_BYTES],
              const uint8_t hash[uECC_BYTES],
              uint8_t signature[uECC_BYTES*2]) {
    uECC_word_t k[uECC_N_WORDS];
    uECC_word_t tmp[uECC_N_WORDS];
    uECC_word_t s[uECC_N_WORDS];
    uECC_word_t *k2[2] = {tmp, s};
    EccPoint p;
    uECC_word_t tries;
    
    for (tries = 0; tries < MAX_TRIES; ++tries) {
        if(!g_rng_function((uint8_t *)k, sizeof(k))) {
            return 0;
        }
    #if (uECC_CURVE == uECC_secp160r1)
        k[uECC_WORDS] &= 0x01;
    #endif
        
        if (vli_isZero(k) || vli_cmp_n(curve_n, k) != 1) {
            continue;
        }
        if (uECC_sign_with_k(private_key, hash, k, signature)) {
            return 1;
        }
    }
    return 0;
}

static bitcount_t smax(bitcount_t a, bitcount_t b) {
    return (a > b ? a : b);
}

int uECC_verify(const uint8_t public_key[uECC_BYTES*2],
                const uint8_t hash[uECC_BYTES],
                const uint8_t signature[uECC_BYTES*2]) {
    uECC_word_t u1[uECC_N_WORDS], u2[uECC_N_WORDS];
    uECC_word_t z[uECC_N_WORDS];
    EccPoint public, 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];
    
    const EccPoint *points[4];
    const EccPoint *point;
    bitcount_t numBits;
    bitcount_t i;

    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(public.x, public_key);
    vli_bytesToNative(public.y, public_key + uECC_BYTES);
    vli_bytesToNative(r, signature);
    vli_bytesToNative(s, 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, hash);
    vli_modMult_n(u1, u1, z); /* u1 = e/s */
    vli_modMult_n(u2, r, z); /* u2 = r/s */
    
    /* Calculate sum = G + Q. */
    vli_set(sum.x, public.x);
    vli_set(sum.y, public.y);
    vli_set(tx, curve_G.x);
    vli_set(ty, curve_G.y);
    vli_modSub_fast(z, sum.x, tx); /* Z = x2 - x1 */
    XYcZ_add(tx, ty, sum.x, sum.y);
    vli_modInv(z, z, curve_p); /* Z = 1/Z */
    apply_z(sum.x, sum.y, z);
    
    /* Use Shamir's trick to calculate u1*G + u2*Q */
    points[0] = 0;
    points[1] = &curve_G;
    points[2] = &public;
    points[3] = &sum;
    numBits = smax(vli_numBits(u1, uECC_N_WORDS), vli_numBits(u2, uECC_N_WORDS));
    
    point = points[(!!vli_testBit(u1, numBits - 1)) | ((!!vli_testBit(u2, numBits - 1)) << 1)];
    vli_set(rx, point->x);
    vli_set(ry, point->y);
    vli_clear(z);
    z[0] = 1;

    for (i = numBits - 2; i >= 0; --i) {
        uECC_word_t index;
        EccPoint_double_jacobian(rx, ry, z);
        
        index = (!!vli_testBit(u1, i)) | ((!!vli_testBit(u2, i)) << 1);
        point = points[index];
        if (point) {
            vli_set(tx, point->x);
            vli_set(ty, 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_equal(rx, r);
}