From 94ba242c330268b8bdd1cf8a0e694a2102b49e2d Mon Sep 17 00:00:00 2001 From: Adam Ierymenko Date: Tue, 16 Jul 2019 16:09:14 -0500 Subject: [PATCH] Nist P-384 guts and glory --- make-linux.mk | 1 - node/C25519.cpp | 17 +- node/C25519.hpp | 15 +- node/ECC384.cpp | 1430 +++++++++++++++++++++++++++++++++++++++++++++ node/ECC384.hpp | 74 +++ node/Identity.hpp | 12 +- objects.mk | 1 + selftest.cpp | 38 +- 8 files changed, 1557 insertions(+), 31 deletions(-) create mode 100644 node/ECC384.cpp create mode 100644 node/ECC384.hpp diff --git a/make-linux.mk b/make-linux.mk index d0745fe9a..a84786918 100644 --- a/make-linux.mk +++ b/make-linux.mk @@ -14,7 +14,6 @@ DEFS?= LDLIBS?= DESTDIR?= - include objects.mk ONE_OBJS+=osdep/LinuxEthernetTap.o ONE_OBJS+=osdep/LinuxNetLink.o diff --git a/node/C25519.cpp b/node/C25519.cpp index 4384f8fd8..0bea59e9d 100644 --- a/node/C25519.cpp +++ b/node/C25519.cpp @@ -2687,7 +2687,7 @@ void ge25519_scalarmult_base(ge25519_p3 *r, const sc25519 *s) } } -void get_hram(unsigned char *hram, const unsigned char *sm, const unsigned char *pk, unsigned char *playground, unsigned long long smlen) +void get_hram(unsigned char *hram, const unsigned char *sm, const unsigned char *pk, unsigned char *playground, unsigned long smlen) { unsigned long long i; @@ -2778,13 +2778,22 @@ void C25519::sign(const C25519::Private &myPrivate,const C25519::Public &myPubli #endif } -bool C25519::verify(const C25519::Public &their,const void *msg,unsigned int len,const void *signature) +bool C25519::verify(const C25519::Public &their,const void *msg,unsigned int len,const void *signature,const unsigned int siglen) { - const unsigned char *const sig = (const unsigned char *)signature; + if (siglen < 64) return false; + + const unsigned char *sig = (const unsigned char *)signature; unsigned char digest[64]; // we sign the first 32 bytes of SHA-512(msg) + unsigned char sigtmp[96]; SHA512::hash(digest,msg,len); - if (!Utils::secureEq(sig + 64,digest,32)) + + if ((siglen == 96)&&(!Utils::secureEq(sig+64,digest,32))) { return false; + } else if (siglen == 64) { + memcpy(sigtmp,sig,64); + memcpy(sigtmp+64,digest,32); + sig = sigtmp; + } unsigned char t2[32]; ge25519 get1, get2; diff --git a/node/C25519.hpp b/node/C25519.hpp index 640aedf55..c87df9c20 100644 --- a/node/C25519.hpp +++ b/node/C25519.hpp @@ -125,6 +125,11 @@ public: /** * Sign a message with a sender's key pair * + * Note that this generates a 96-byte signature that contains an extra 32 bytes + * of hash data. This data is included for historical reasons and is optional. The + * verify function here will take the first 64 bytes only (normal ed25519 signature) + * or a 96-byte length signature with the extra input hash data. + * * @param myPrivate My private key * @param myPublic My public key * @param msg Message to sign @@ -150,10 +155,11 @@ public: * @param their Public key to verify against * @param msg Message to verify signature integrity against * @param len Length of message in bytes - * @param signature 96-byte signature + * @param signature Signature bytes + * @param siglen Length of signature in bytes * @return True if signature is valid and the message is authentic and unmodified */ - static bool verify(const Public &their,const void *msg,unsigned int len,const void *signature); + static bool verify(const Public &their,const void *msg,unsigned int len,const void *signature,const unsigned int siglen); /** * Verify a message's signature @@ -164,10 +170,7 @@ public: * @param signature 96-byte signature * @return True if signature is valid and the message is authentic and unmodified */ - static inline bool verify(const Public &their,const void *msg,unsigned int len,const Signature &signature) - { - return verify(their,msg,len,signature.data); - } + static inline bool verify(const Public &their,const void *msg,unsigned int len,const Signature &signature) { return verify(their,msg,len,signature.data,96); } private: // derive first 32 bytes of kp.pub from first 32 bytes of kp.priv diff --git a/node/ECC384.cpp b/node/ECC384.cpp new file mode 100644 index 000000000..44c8778f1 --- /dev/null +++ b/node/ECC384.cpp @@ -0,0 +1,1430 @@ +/* + * ZeroTier One - Network Virtualization Everywhere + * Copyright (C) 2011-2019 ZeroTier, Inc. https://www.zerotier.com/ + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see . + * + * -- + * + * You can be released from the requirements of the license by purchasing + * a commercial license. Buying such a license is mandatory as soon as you + * develop commercial closed-source software that incorporates or links + * directly against ZeroTier software without disclosing the source code + * of your own application. + */ + +#include +#include +#include +#include + +#include "Constants.hpp" +#include "ECC384.hpp" +#include "Utils.hpp" + +namespace ZeroTier { + +namespace { +////////////////////////////////////////////////////////////////////////////// +// This is EASY-ECC by Kenneth MacKay +// https://github.com/esxgx/easy-ecc +// This code is under the BSD 2-clause license, not ZeroTier's license +////////////////////////////////////////////////////////////////////////////// + +////////////////////////////////////////////////////////////////////////////// +// ecc.h from easy-ecc +////////////////////////////////////////////////////////////////////////////// + +#define secp128r1 16 +#define secp192r1 24 +#define secp256r1 32 +#define secp384r1 48 + +//#ifndef ECC_CURVE +// #define ECC_CURVE secp256r1 +//#endif +#define ECC_CURVE secp384r1 + +//#if (ECC_CURVE != secp128r1 && ECC_CURVE != secp192r1 && ECC_CURVE != secp256r1 && ECC_CURVE != secp384r1) +// #error "Must define ECC_CURVE to one of the available curves" +//#endif + +#define ECC_BYTES ECC_CURVE + +////////////////////////////////////////////////////////////////////////////// +// ecc.c from easy-ecc +////////////////////////////////////////////////////////////////////////////// + +//#include "ecc.h" +//#include + +#define NUM_ECC_DIGITS (ECC_BYTES/8) +#define MAX_TRIES 16 + +typedef unsigned int uint; + +#if defined(__SIZEOF_INT128__) || ((__clang_major__ * 100 + __clang_minor__) >= 302) + #define SUPPORTS_INT128 1 +#else + #define SUPPORTS_INT128 0 +#endif + +#if SUPPORTS_INT128 +typedef unsigned __int128 uint128_t; +#else +typedef struct +{ + uint64_t m_low; + uint64_t m_high; +} uint128_t; +#endif + +typedef struct EccPoint +{ + uint64_t x[NUM_ECC_DIGITS]; + uint64_t y[NUM_ECC_DIGITS]; +} EccPoint; + +#define CONCAT1(a, b) a##b +#define CONCAT(a, b) CONCAT1(a, b) + +#define Curve_P_16 {0xFFFFFFFFFFFFFFFF, 0xFFFFFFFDFFFFFFFF} +#define Curve_P_24 {0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFFFFFFFFFEull, 0xFFFFFFFFFFFFFFFFull} +#define Curve_P_32 {0xFFFFFFFFFFFFFFFFull, 0x00000000FFFFFFFFull, 0x0000000000000000ull, 0xFFFFFFFF00000001ull} +#define Curve_P_48 {0x00000000FFFFFFFF, 0xFFFFFFFF00000000, 0xFFFFFFFFFFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF} + +#define Curve_B_16 {0xD824993C2CEE5ED3, 0xE87579C11079F43D} +#define Curve_B_24 {0xFEB8DEECC146B9B1ull, 0x0FA7E9AB72243049ull, 0x64210519E59C80E7ull} +#define Curve_B_32 {0x3BCE3C3E27D2604Bull, 0x651D06B0CC53B0F6ull, 0xB3EBBD55769886BCull, 0x5AC635D8AA3A93E7ull} +#define Curve_B_48 {0x2A85C8EDD3EC2AEF, 0xC656398D8A2ED19D, 0x0314088F5013875A, 0x181D9C6EFE814112, 0x988E056BE3F82D19, 0xB3312FA7E23EE7E4} + +#define Curve_G_16 { \ + {0x0C28607CA52C5B86, 0x161FF7528B899B2D}, \ + {0xC02DA292DDED7A83, 0xCF5AC8395BAFEB13}} + +#define Curve_G_24 { \ + {0xF4FF0AFD82FF1012ull, 0x7CBF20EB43A18800ull, 0x188DA80EB03090F6ull}, \ + {0x73F977A11E794811ull, 0x631011ED6B24CDD5ull, 0x07192B95FFC8DA78ull}} + +#define Curve_G_32 { \ + {0xF4A13945D898C296ull, 0x77037D812DEB33A0ull, 0xF8BCE6E563A440F2ull, 0x6B17D1F2E12C4247ull}, \ + {0xCBB6406837BF51F5ull, 0x2BCE33576B315ECEull, 0x8EE7EB4A7C0F9E16ull, 0x4FE342E2FE1A7F9Bull}} + +#define Curve_G_48 { \ + {0x3A545E3872760AB7, 0x5502F25DBF55296C, 0x59F741E082542A38, 0x6E1D3B628BA79B98, 0x8EB1C71EF320AD74, 0xAA87CA22BE8B0537}, \ + {0x7A431D7C90EA0E5F, 0x0A60B1CE1D7E819D, 0xE9DA3113B5F0B8C0, 0xF8F41DBD289A147C, 0x5D9E98BF9292DC29, 0x3617DE4A96262C6F}} + +#define Curve_N_16 {0x75A30D1B9038A115, 0xFFFFFFFE00000000} +#define Curve_N_24 {0x146BC9B1B4D22831ull, 0xFFFFFFFF99DEF836ull, 0xFFFFFFFFFFFFFFFFull} +#define Curve_N_32 {0xF3B9CAC2FC632551ull, 0xBCE6FAADA7179E84ull, 0xFFFFFFFFFFFFFFFFull, 0xFFFFFFFF00000000ull} +#define Curve_N_48 {0xECEC196ACCC52973, 0x581A0DB248B0A77A, 0xC7634D81F4372DDF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF} + +static uint64_t curve_p[NUM_ECC_DIGITS] = CONCAT(Curve_P_, ECC_CURVE); +static uint64_t curve_b[NUM_ECC_DIGITS] = CONCAT(Curve_B_, ECC_CURVE); +static EccPoint curve_G = CONCAT(Curve_G_, ECC_CURVE); +static uint64_t curve_n[NUM_ECC_DIGITS] = CONCAT(Curve_N_, ECC_CURVE); + +#if 0 +#if (defined(_WIN32) || defined(_WIN64)) +/* Windows */ + +#define WIN32_LEAN_AND_MEAN +#include +#include + +static int getRandomNumber(uint64_t *p_vli) +{ + HCRYPTPROV l_prov; + if(!CryptAcquireContext(&l_prov, NULL, NULL, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT)) + { + return 0; + } + + CryptGenRandom(l_prov, ECC_BYTES, (BYTE *)p_vli); + CryptReleaseContext(l_prov, 0); + + return 1; +} + +#else /* _WIN32 */ + +/* Assume that we are using a POSIX-like system with /dev/urandom or /dev/random. */ +#include +#include +#include + +#ifndef O_CLOEXEC + #define O_CLOEXEC 0 +#endif + +static int getRandomNumber(uint64_t *p_vli) +{ + 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_vli; + size_t l_left = ECC_BYTES; + 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; +} + +#endif /* _WIN32 */ +#endif + +// Use ZeroTier's secure PRNG +static inline int getRandomNumber(uint64_t *p_vli) +{ + Utils::getSecureRandom(p_vli,ECC_BYTES); + return 1; +} + +static inline void vli_clear(uint64_t *p_vli) +{ + uint i; + for(i=0; i= 0 && p_vli[i] == 0; --i) + { + } + + return (i + 1); +} + +/* Counts the number of bits required for p_vli. */ +static inline uint vli_numBits(uint64_t *p_vli) +{ + uint i; + uint64_t l_digit; + + uint l_numDigits = vli_numDigits(p_vli); + if(l_numDigits == 0) + { + return 0; + } + + l_digit = p_vli[l_numDigits - 1]; + for(i=0; l_digit; ++i) + { + l_digit >>= 1; + } + + return ((l_numDigits - 1) * 64 + i); +} + +/* Sets p_dest = p_src. */ +static inline void vli_set(uint64_t *p_dest, uint64_t *p_src) +{ + uint i; + for(i=0; i= 0; --i) + { + if(p_left[i] > p_right[i]) + { + return 1; + } + else if(p_left[i] < p_right[i]) + { + return -1; + } + } + return 0; +} + +/* Computes p_result = p_in << c, returning carry. Can modify in place (if p_result == p_in). 0 < p_shift < 64. */ +static inline uint64_t vli_lshift(uint64_t *p_result, uint64_t *p_in, uint p_shift) +{ + uint64_t l_carry = 0; + uint i; + for(i = 0; i < NUM_ECC_DIGITS; ++i) + { + uint64_t l_temp = p_in[i]; + p_result[i] = (l_temp << p_shift) | l_carry; + l_carry = l_temp >> (64 - p_shift); + } + + return l_carry; +} + +/* Computes p_vli = p_vli >> 1. */ +static inline void vli_rshift1(uint64_t *p_vli) +{ + uint64_t *l_end = p_vli; + uint64_t l_carry = 0; + + p_vli += NUM_ECC_DIGITS; + while(p_vli-- > l_end) + { + uint64_t l_temp = *p_vli; + *p_vli = (l_temp >> 1) | l_carry; + l_carry = l_temp << 63; + } +} + +/* Computes p_result = p_left + p_right, returning carry. Can modify in place. */ +static inline uint64_t vli_add(uint64_t *p_result, uint64_t *p_left, uint64_t *p_right) +{ + uint64_t l_carry = 0; + uint i; + for(i=0; i p_left[i]); + } + p_result[i] = l_diff; + } + return l_borrow; +} + +#if SUPPORTS_INT128 + +/* Computes p_result = p_left * p_right. */ +static inline void vli_mult(uint64_t *p_result, uint64_t *p_left, uint64_t *p_right) +{ + uint128_t r01 = 0; + uint64_t r2 = 0; + + uint i, k; + + /* Compute each digit of p_result in sequence, maintaining the carries. */ + for(k=0; k < NUM_ECC_DIGITS*2 - 1; ++k) + { + uint l_min = (k < NUM_ECC_DIGITS ? 0 : (k + 1) - NUM_ECC_DIGITS); + for(i=l_min; i<=k && i> 64) | (((uint128_t)r2) << 64); + r2 = 0; + } + + p_result[NUM_ECC_DIGITS*2 - 1] = (uint64_t)r01; +} + +/* Computes p_result = p_left^2. */ +static inline void vli_square(uint64_t *p_result, uint64_t *p_left) +{ + uint128_t r01 = 0; + uint64_t r2 = 0; + + uint i, k; + for(k=0; k < NUM_ECC_DIGITS*2 - 1; ++k) + { + uint l_min = (k < NUM_ECC_DIGITS ? 0 : (k + 1) - NUM_ECC_DIGITS); + for(i=l_min; i<=k && i<=k-i; ++i) + { + uint128_t l_product = (uint128_t)p_left[i] * p_left[k-i]; + if(i < k-i) + { + r2 += l_product >> 127; + l_product *= 2; + } + r01 += l_product; + r2 += (r01 < l_product); + } + p_result[k] = (uint64_t)r01; + r01 = (r01 >> 64) | (((uint128_t)r2) << 64); + r2 = 0; + } + + p_result[NUM_ECC_DIGITS*2 - 1] = (uint64_t)r01; +} + +#else /* #if SUPPORTS_INT128 */ + +static inline uint128_t mul_64_64(uint64_t p_left, uint64_t p_right) +{ + uint128_t l_result; + + uint64_t a0 = p_left & 0xffffffffull; + uint64_t a1 = p_left >> 32; + uint64_t b0 = p_right & 0xffffffffull; + uint64_t b1 = p_right >> 32; + + uint64_t m0 = a0 * b0; + uint64_t m1 = a0 * b1; + uint64_t m2 = a1 * b0; + uint64_t m3 = a1 * b1; + + m2 += (m0 >> 32); + m2 += m1; + if(m2 < m1) + { // overflow + m3 += 0x100000000ull; + } + + l_result.m_low = (m0 & 0xffffffffull) | (m2 << 32); + l_result.m_high = m3 + (m2 >> 32); + + return l_result; +} + +static inline uint128_t add_128_128(uint128_t a, uint128_t b) +{ + uint128_t l_result; + l_result.m_low = a.m_low + b.m_low; + l_result.m_high = a.m_high + b.m_high + (l_result.m_low < a.m_low); + return l_result; +} + +static inline void vli_mult(uint64_t *p_result, uint64_t *p_left, uint64_t *p_right) +{ + uint128_t r01 = {0, 0}; + uint64_t r2 = 0; + + uint i, k; + + /* Compute each digit of p_result in sequence, maintaining the carries. */ + for(k=0; k < NUM_ECC_DIGITS*2 - 1; ++k) + { + uint l_min = (k < NUM_ECC_DIGITS ? 0 : (k + 1) - NUM_ECC_DIGITS); + for(i=l_min; i<=k && i> 63; + l_product.m_high = (l_product.m_high << 1) | (l_product.m_low >> 63); + l_product.m_low <<= 1; + } + r01 = add_128_128(r01, l_product); + r2 += (r01.m_high < l_product.m_high); + } + p_result[k] = r01.m_low; + r01.m_low = r01.m_high; + r01.m_high = r2; + r2 = 0; + } + + p_result[NUM_ECC_DIGITS*2 - 1] = r01.m_low; +} + +#endif /* SUPPORTS_INT128 */ + + +/* Computes p_result = (p_left + p_right) % p_mod. + Assumes that p_left < p_mod and p_right < p_mod, p_result != p_mod. */ +static inline void vli_modAdd(uint64_t *p_result, uint64_t *p_left, uint64_t *p_right, uint64_t *p_mod) +{ + uint64_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); + } +} + +/* Computes p_result = (p_left - p_right) % p_mod. + Assumes that p_left < p_mod and p_right < p_mod, p_result != p_mod. */ +static inline void vli_modSub(uint64_t *p_result, uint64_t *p_left, uint64_t *p_right, uint64_t *p_mod) +{ + uint64_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); + } +} + +#if ECC_CURVE == secp128r1 + +/* Computes p_result = p_product % curve_p. + See algorithm 5 and 6 from http://www.isys.uni-klu.ac.at/PDF/2001-0126-MT.pdf */ +static void vli_mmod_fast(uint64_t *p_result, uint64_t *p_product) +{ + uint64_t l_tmp[NUM_ECC_DIGITS]; + int l_carry; + + vli_set(p_result, p_product); + + l_tmp[0] = p_product[2]; + l_tmp[1] = (p_product[3] & 0x1FFFFFFFFull) | (p_product[2] << 33); + l_carry = vli_add(p_result, p_result, l_tmp); + + l_tmp[0] = (p_product[2] >> 31) | (p_product[3] << 33); + l_tmp[1] = (p_product[3] >> 31) | ((p_product[2] & 0xFFFFFFFF80000000ull) << 2); + l_carry += vli_add(p_result, p_result, l_tmp); + + l_tmp[0] = (p_product[2] >> 62) | (p_product[3] << 2); + l_tmp[1] = (p_product[3] >> 62) | ((p_product[2] & 0xC000000000000000ull) >> 29) | (p_product[3] << 35); + l_carry += vli_add(p_result, p_result, l_tmp); + + l_tmp[0] = (p_product[3] >> 29); + l_tmp[1] = ((p_product[3] & 0xFFFFFFFFE0000000ull) << 4); + l_carry += vli_add(p_result, p_result, l_tmp); + + l_tmp[0] = (p_product[3] >> 60); + l_tmp[1] = (p_product[3] & 0xFFFFFFFE00000000ull); + l_carry += vli_add(p_result, p_result, l_tmp); + + l_tmp[0] = 0; + l_tmp[1] = ((p_product[3] & 0xF000000000000000ull) >> 27); + 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 ECC_CURVE == 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 */ +static void vli_mmod_fast(uint64_t *p_result, uint64_t *p_product) +{ + uint64_t l_tmp[NUM_ECC_DIGITS]; + int l_carry; + + 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); + } +} + +#elif ECC_CURVE == secp256r1 + +/* Computes p_result = p_product % curve_p + from http://www.nsa.gov/ia/_files/nist-routines.pdf */ +static void vli_mmod_fast(uint64_t *p_result, uint64_t *p_product) +{ + uint64_t l_tmp[NUM_ECC_DIGITS]; + 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_lshift(l_tmp, l_tmp, 1); + 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_lshift(l_tmp, l_tmp, 1); + 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); + } + } +} + +#elif ECC_CURVE == secp384r1 + +static inline void omega_mult(uint64_t *p_result, uint64_t *p_right) +{ + uint64_t l_tmp[NUM_ECC_DIGITS]; + uint64_t l_carry, l_diff; + + /* Multiply by (2^128 + 2^96 - 2^32 + 1). */ + vli_set(p_result, p_right); /* 1 */ + l_carry = vli_lshift(l_tmp, p_right, 32); + p_result[1 + NUM_ECC_DIGITS] = l_carry + vli_add(p_result + 1, p_result + 1, l_tmp); /* 2^96 + 1 */ + p_result[2 + NUM_ECC_DIGITS] = vli_add(p_result + 2, p_result + 2, p_right); /* 2^128 + 2^96 + 1 */ + l_carry += vli_sub(p_result, p_result, l_tmp); /* 2^128 + 2^96 - 2^32 + 1 */ + l_diff = p_result[NUM_ECC_DIGITS] - l_carry; + if(l_diff > p_result[NUM_ECC_DIGITS]) + { /* Propagate borrow if necessary. */ + uint i; + for(i = 1 + NUM_ECC_DIGITS; ; ++i) + { + --p_result[i]; + if(p_result[i] != (uint64_t)-1) + { + break; + } + } + } + p_result[NUM_ECC_DIGITS] = l_diff; +} + +/* Computes p_result = p_product % curve_p + see PDF "Comparing Elliptic Curve Cryptography and RSA on 8-bit CPUs" + section "Curve-Specific Optimizations" */ +static inline void vli_mmod_fast(uint64_t *p_result, uint64_t *p_product) +{ + uint64_t l_tmp[2*NUM_ECC_DIGITS]; + + while(!vli_isZero(p_product + NUM_ECC_DIGITS)) /* While c1 != 0 */ + { + uint64_t l_carry = 0; + uint i; + + vli_clear(l_tmp); + vli_clear(l_tmp + NUM_ECC_DIGITS); + omega_mult(l_tmp, p_product + NUM_ECC_DIGITS); /* tmp = w * c1 */ + vli_clear(p_product + NUM_ECC_DIGITS); /* p = c0 */ + + /* (c1, c0) = c0 + w * c1 */ + for(i=0; i 0) + { + vli_sub(p_product, p_product, curve_p); + } + vli_set(p_result, p_product); +} + +#endif + +/* Computes p_result = (p_left * p_right) % curve_p. */ +static inline void vli_modMult_fast(uint64_t *p_result, uint64_t *p_left, uint64_t *p_right) +{ + uint64_t l_product[2 * NUM_ECC_DIGITS]; + vli_mult(l_product, p_left, p_right); + vli_mmod_fast(p_result, l_product); +} + +/* Computes p_result = p_left^2 % curve_p. */ +static inline void vli_modSquare_fast(uint64_t *p_result, uint64_t *p_left) +{ + uint64_t l_product[2 * NUM_ECC_DIGITS]; + vli_square(l_product, p_left); + vli_mmod_fast(p_result, l_product); +} + +#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 */ +static inline void vli_modInv(uint64_t *p_result, uint64_t *p_input, uint64_t *p_mod) +{ + uint64_t a[NUM_ECC_DIGITS], b[NUM_ECC_DIGITS], u[NUM_ECC_DIGITS], v[NUM_ECC_DIGITS]; + uint64_t l_carry; + int 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[NUM_ECC_DIGITS-1] |= 0x8000000000000000ull; + } + } + 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[NUM_ECC_DIGITS-1] |= 0x8000000000000000ull; + } + } + 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[NUM_ECC_DIGITS-1] |= 0x8000000000000000ull; + } + } + 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[NUM_ECC_DIGITS-1] |= 0x8000000000000000ull; + } + } + } + + vli_set(p_result, u); +} + +/* ------ Point operations ------ */ + +/* Returns 1 if p_point is the point at infinity, 0 otherwise. */ +static inline int 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 */ +static inline void EccPoint_double_jacobian(uint64_t *X1, uint64_t *Y1, uint64_t *Z1) +{ + /* t1 = X, t2 = Y, t3 = Z */ + uint64_t t4[NUM_ECC_DIGITS]; + uint64_t t5[NUM_ECC_DIGITS]; + + 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(Z1, X1, Z1, curve_p); /* 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)) + { + uint64_t l_carry = vli_add(X1, X1, curve_p); + vli_rshift1(X1); + X1[NUM_ECC_DIGITS-1] |= l_carry << 63; + } + else + { + vli_rshift1(X1); + } + /* t1 = 3/2*(x1^2 - z1^4) = B */ + + vli_modSquare_fast(Z1, X1); /* t3 = B^2 */ + vli_modSub(Z1, Z1, t5, curve_p); /* t3 = B^2 - A */ + vli_modSub(Z1, Z1, t5, curve_p); /* t3 = B^2 - 2A = x3 */ + vli_modSub(t5, t5, Z1, curve_p); /* t5 = A - x3 */ + vli_modMult_fast(X1, X1, t5); /* t1 = B * (A - x3) */ + vli_modSub(t4, X1, t4, curve_p); /* t4 = B * (A - x3) - y1^4 = y3 */ + + vli_set(X1, Z1); + vli_set(Z1, Y1); + vli_set(Y1, t4); +} + +/* Modify (x1, y1) => (x1 * z^2, y1 * z^3) */ +static inline void apply_z(uint64_t *X1, uint64_t *Y1, uint64_t *Z) +{ + uint64_t t1[NUM_ECC_DIGITS]; + + 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 inline void XYcZ_initial_double(uint64_t *X1, uint64_t *Y1, uint64_t *X2, uint64_t *Y2, uint64_t *p_initialZ) +{ + uint64_t z[NUM_ECC_DIGITS]; + + 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 inline void XYcZ_add(uint64_t *X1, uint64_t *Y1, uint64_t *X2, uint64_t *Y2) +{ + /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ + uint64_t t5[NUM_ECC_DIGITS]; + + vli_modSub(t5, X2, X1, curve_p); /* 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(Y2, Y2, Y1, curve_p); /* t4 = y2 - y1 */ + vli_modSquare_fast(t5, Y2); /* t5 = (y2 - y1)^2 = D */ + + vli_modSub(t5, t5, X1, curve_p); /* t5 = D - B */ + vli_modSub(t5, t5, X2, curve_p); /* t5 = D - B - C = x3 */ + vli_modSub(X2, X2, X1, curve_p); /* t3 = C - B */ + vli_modMult_fast(Y1, Y1, X2); /* t2 = y1*(C - B) */ + vli_modSub(X2, X1, t5, curve_p); /* t3 = B - x3 */ + vli_modMult_fast(Y2, Y2, X2); /* t4 = (y2 - y1)*(B - x3) */ + vli_modSub(Y2, Y2, Y1, curve_p); /* t4 = y3 */ + + vli_set(X2, t5); +} + +/* Input P = (x1, y1, Z), Q = (x2, y2, Z) + Output P + Q = (x3, y3, Z3), P - Q = (x3', y3', Z3) + or P => P - Q, Q => P + Q +*/ +static inline void XYcZ_addC(uint64_t *X1, uint64_t *Y1, uint64_t *X2, uint64_t *Y2) +{ + /* t1 = X1, t2 = Y1, t3 = X2, t4 = Y2 */ + uint64_t t5[NUM_ECC_DIGITS]; + uint64_t t6[NUM_ECC_DIGITS]; + uint64_t t7[NUM_ECC_DIGITS]; + + vli_modSub(t5, X2, X1, curve_p); /* 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(Y2, Y2, Y1, curve_p); /* t4 = y2 - y1 */ + + vli_modSub(t6, X2, X1, curve_p); /* 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(X2, X2, t6, curve_p); /* t3 = x3 */ + + vli_modSub(t7, X1, X2, curve_p); /* t7 = B - x3 */ + vli_modMult_fast(Y2, Y2, t7); /* t4 = (y2 - y1)*(B - x3) */ + vli_modSub(Y2, Y2, Y1, curve_p); /* t4 = y3 */ + + vli_modSquare_fast(t7, t5); /* t7 = (y2 + y1)^2 = F */ + vli_modSub(t7, t7, t6, curve_p); /* t7 = x3' */ + vli_modSub(t6, t7, X1, curve_p); /* t6 = x3' - B */ + vli_modMult_fast(t6, t6, t5); /* t6 = (y2 + y1)*(x3' - B) */ + vli_modSub(Y1, t6, Y1, curve_p); /* t2 = y3' */ + + vli_set(X1, t7); +} + +static inline void EccPoint_mult(EccPoint *p_result, EccPoint *p_point, uint64_t *p_scalar, uint64_t *p_initialZ) +{ + /* R0 and R1 */ + uint64_t Rx[2][NUM_ECC_DIGITS]; + uint64_t Ry[2][NUM_ECC_DIGITS]; + uint64_t z[NUM_ECC_DIGITS]; + + int i, 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 = vli_numBits(p_scalar) - 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(z, Rx[1], Rx[0], curve_p); /* 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]); +} + +static inline void ecc_bytes2native(uint64_t p_native[NUM_ECC_DIGITS], const uint8_t p_bytes[ECC_BYTES]) +{ + unsigned i; + for(i=0; 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]; + } +} + +/* Compute a = sqrt(a) (mod curve_p). */ +static inline void mod_sqrt(uint64_t a[NUM_ECC_DIGITS]) +{ + unsigned i; + uint64_t p1[NUM_ECC_DIGITS] = {1}; + uint64_t l_result[NUM_ECC_DIGITS] = {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) - 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); +} + +static inline void ecc_point_decompress(EccPoint *p_point, const uint8_t p_compressed[ECC_BYTES+1]) +{ + uint64_t _3[NUM_ECC_DIGITS] = {3}; /* -a = 3 */ + ecc_bytes2native(p_point->x, p_compressed+1); + + vli_modSquare_fast(p_point->y, p_point->x); /* y = x^2 */ + vli_modSub(p_point->y, p_point->y, _3, curve_p); /* y = x^2 - 3 */ + vli_modMult_fast(p_point->y, p_point->y, p_point->x); /* y = x^3 - 3x */ + vli_modAdd(p_point->y, p_point->y, curve_b, curve_p); /* y = x^3 - 3x + b */ + + mod_sqrt(p_point->y); + + if((p_point->y[0] & 0x01) != (p_compressed[0] & 0x01)) + { + vli_sub(p_point->y, curve_p, p_point->y); + } +} + +static inline int ecc_make_key(uint8_t p_publicKey[ECC_BYTES+1], uint8_t p_privateKey[ECC_BYTES]) +{ + uint64_t l_private[NUM_ECC_DIGITS]; + EccPoint l_public; + unsigned l_tries = 0; + + do + { + if(!getRandomNumber(l_private) || (l_tries++ >= MAX_TRIES)) + { + return 0; + } + if(vli_isZero(l_private)) + { + continue; + } + + /* Make sure the private key is in the range [1, n-1]. + For the supported curves, n is always large enough that we only need to subtract once at most. */ + if(vli_cmp(curve_n, l_private) != 1) + { + vli_sub(l_private, l_private, curve_n); + } + + EccPoint_mult(&l_public, &curve_G, l_private, NULL); + } while(EccPoint_isZero(&l_public)); + + ecc_native2bytes(p_privateKey, l_private); + ecc_native2bytes(p_publicKey + 1, l_public.x); + p_publicKey[0] = 2 + (l_public.y[0] & 0x01); + return 1; +} + +static inline int ecdh_shared_secret(const uint8_t p_publicKey[ECC_BYTES+1], const uint8_t p_privateKey[ECC_BYTES], uint8_t p_secret[ECC_BYTES]) +{ + EccPoint l_public; + uint64_t l_private[NUM_ECC_DIGITS]; + uint64_t l_random[NUM_ECC_DIGITS]; + + if(!getRandomNumber(l_random)) + { + return 0; + } + + ecc_point_decompress(&l_public, p_publicKey); + ecc_bytes2native(l_private, p_privateKey); + + EccPoint l_product; + EccPoint_mult(&l_product, &l_public, l_private, l_random); + + ecc_native2bytes(p_secret, l_product.x); + + return !EccPoint_isZero(&l_product); +} + +/* -------- ECDSA code -------- */ + +/* Computes p_result = (p_left * p_right) % p_mod. */ +static inline void vli_modMult(uint64_t *p_result, uint64_t *p_left, uint64_t *p_right, uint64_t *p_mod) +{ + uint64_t l_product[2 * NUM_ECC_DIGITS]; + uint64_t l_modMultiple[2 * NUM_ECC_DIGITS]; + uint l_digitShift, l_bitShift; + uint l_productBits; + uint l_modBits = vli_numBits(p_mod); + + vli_mult(l_product, p_left, p_right); + l_productBits = vli_numBits(l_product + NUM_ECC_DIGITS); + if(l_productBits) + { + l_productBits += NUM_ECC_DIGITS * 64; + } + else + { + l_productBits = vli_numBits(l_product); + } + + if(l_productBits < l_modBits) + { /* l_product < p_mod. */ + vli_set(p_result, l_product); + return; + } + + /* Shift p_mod by (l_leftBits - l_modBits). This multiplies p_mod by the largest + power of two possible while still resulting in a number less than p_left. */ + vli_clear(l_modMultiple); + vli_clear(l_modMultiple + NUM_ECC_DIGITS); + l_digitShift = (l_productBits - l_modBits) / 64; + l_bitShift = (l_productBits - l_modBits) % 64; + if(l_bitShift) + { + l_modMultiple[l_digitShift + NUM_ECC_DIGITS] = vli_lshift(l_modMultiple + l_digitShift, p_mod, l_bitShift); + } + else + { + vli_set(l_modMultiple + l_digitShift, p_mod); + } + + /* Subtract all multiples of p_mod to get the remainder. */ + vli_clear(p_result); + p_result[0] = 1; /* Use p_result as a temp var to store 1 (for subtraction) */ + while(l_productBits > NUM_ECC_DIGITS * 64 || vli_cmp(l_modMultiple, p_mod) >= 0) + { + int l_cmp = vli_cmp(l_modMultiple + NUM_ECC_DIGITS, l_product + NUM_ECC_DIGITS); + if(l_cmp < 0 || (l_cmp == 0 && vli_cmp(l_modMultiple, l_product) <= 0)) + { + if(vli_sub(l_product, l_product, l_modMultiple)) + { /* borrow */ + vli_sub(l_product + NUM_ECC_DIGITS, l_product + NUM_ECC_DIGITS, p_result); + } + vli_sub(l_product + NUM_ECC_DIGITS, l_product + NUM_ECC_DIGITS, l_modMultiple + NUM_ECC_DIGITS); + } + uint64_t l_carry = (l_modMultiple[NUM_ECC_DIGITS] & 0x01) << 63; + vli_rshift1(l_modMultiple + NUM_ECC_DIGITS); + vli_rshift1(l_modMultiple); + l_modMultiple[NUM_ECC_DIGITS-1] |= l_carry; + + --l_productBits; + } + vli_set(p_result, l_product); +} + +static inline uint umax(uint a, uint b) +{ + return (a > b ? a : b); +} + +static inline int ecdsa_sign(const uint8_t p_privateKey[ECC_BYTES], const uint8_t p_hash[ECC_BYTES], uint8_t p_signature[ECC_BYTES*2]) +{ + uint64_t k[NUM_ECC_DIGITS]; + uint64_t l_tmp[NUM_ECC_DIGITS]; + uint64_t l_s[NUM_ECC_DIGITS]; + EccPoint p; + unsigned l_tries = 0; + + do + { + if(!getRandomNumber(k) || (l_tries++ >= MAX_TRIES)) + { + return 0; + } + if(vli_isZero(k)) + { + continue; + } + + if(vli_cmp(curve_n, k) != 1) + { + vli_sub(k, k, curve_n); + } + + /* tmp = k * G */ + EccPoint_mult(&p, &curve_G, k, NULL); + + /* r = x1 (mod n) */ + if(vli_cmp(curve_n, p.x) != 1) + { + vli_sub(p.x, p.x, curve_n); + } + } while(vli_isZero(p.x)); + + ecc_native2bytes(p_signature, p.x); + + ecc_bytes2native(l_tmp, p_privateKey); + vli_modMult(l_s, p.x, l_tmp, curve_n); /* s = r*d */ + ecc_bytes2native(l_tmp, p_hash); + vli_modAdd(l_s, l_tmp, l_s, curve_n); /* s = e + r*d */ + vli_modInv(k, k, curve_n); /* k = 1 / k */ + vli_modMult(l_s, l_s, k, curve_n); /* s = (e + r*d) / k */ + ecc_native2bytes(p_signature + ECC_BYTES, l_s); + + return 1; +} + +static inline int ecdsa_verify(const uint8_t p_publicKey[ECC_BYTES+1], const uint8_t p_hash[ECC_BYTES], const uint8_t p_signature[ECC_BYTES*2]) +{ + uint64_t u1[NUM_ECC_DIGITS], u2[NUM_ECC_DIGITS]; + uint64_t z[NUM_ECC_DIGITS]; + EccPoint l_public, l_sum; + uint64_t rx[NUM_ECC_DIGITS]; + uint64_t ry[NUM_ECC_DIGITS]; + uint64_t tx[NUM_ECC_DIGITS]; + uint64_t ty[NUM_ECC_DIGITS]; + uint64_t tz[NUM_ECC_DIGITS]; + + uint64_t l_r[NUM_ECC_DIGITS], l_s[NUM_ECC_DIGITS]; + + ecc_point_decompress(&l_public, p_publicKey); + ecc_bytes2native(l_r, p_signature); + ecc_bytes2native(l_s, p_signature + ECC_BYTES); + + if(vli_isZero(l_r) || vli_isZero(l_s)) + { /* r, s must not be 0. */ + return 0; + } + + if(vli_cmp(curve_n, l_r) != 1 || vli_cmp(curve_n, l_s) != 1) + { /* r, s must be < n. */ + return 0; + } + + /* Calculate u1 and u2. */ + vli_modInv(z, l_s, curve_n); /* Z = s^-1 */ + ecc_bytes2native(u1, p_hash); + vli_modMult(u1, u1, z, curve_n); /* u1 = e/s */ + vli_modMult(u2, l_r, z, curve_n); /* 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(z, l_sum.x, tx, curve_p); /* 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] = {NULL, &curve_G, &l_public, &l_sum}; + uint l_numBits = umax(vli_numBits(u1), vli_numBits(u2)); + + 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; + + int i; + for(i = l_numBits - 2; i >= 0; --i) + { + EccPoint_double_jacobian(rx, ry, z); + + int l_index = (!!vli_testBit(u1, i)) | ((!!vli_testBit(u2, i)) << 1); + EccPoint *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(tz, rx, tx, curve_p); /* 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(vli_cmp(curve_n, rx) != 1) + { + vli_sub(rx, rx, curve_n); + } + + /* Accept only if v == r. */ + return (vli_cmp(rx, l_r) == 0); +} + +////////////////////////////////////////////////////////////////////////////// + +////////////////////////////////////////////////////////////////////////////// +////////////////////////////////////////////////////////////////////////////// +} // anonymous namespace + +void ECC384GenerateKey(uint8_t pub[ZT_ECC384_PUBLIC_KEY_SIZE],uint8_t priv[ZT_ECC384_PRIVATE_KEY_SIZE]) +{ + if (!ecc_make_key(pub,priv)) { + fprintf(stderr,"FATAL: ecdsa_make_key() failed!" ZT_EOL_S); + abort(); + } +} + +void ECC384ECDSASign(const uint8_t priv[ZT_ECC384_PRIVATE_KEY_SIZE],const uint8_t hash[ZT_ECC384_SIGNATURE_HASH_SIZE],uint8_t sig[ZT_ECC384_SIGNATURE_SIZE]) +{ + if (!ecdsa_sign(priv,hash,sig)) { + fprintf(stderr,"FATAL: ecdsa_sign() failed!" ZT_EOL_S); + abort(); + } +} + +bool ECC384ECDSAVerify(const uint8_t pub[ZT_ECC384_PUBLIC_KEY_SIZE],const uint8_t hash[ZT_ECC384_SIGNATURE_HASH_SIZE],const uint8_t sig[ZT_ECC384_SIGNATURE_SIZE]) +{ + return (ecdsa_verify(pub,hash,sig) != 0); +} + +bool ECC384ECDH(const uint8_t theirPub[ZT_ECC384_PUBLIC_KEY_SIZE],const uint8_t ourPriv[ZT_ECC384_PRIVATE_KEY_SIZE],uint8_t secret[ZT_ECC384_SHARED_SECRET_SIZE]) +{ + return (ecdh_shared_secret(theirPub,ourPriv,secret) != 0); +} + +} // namespace ZeroTier diff --git a/node/ECC384.hpp b/node/ECC384.hpp new file mode 100644 index 000000000..40ce3a145 --- /dev/null +++ b/node/ECC384.hpp @@ -0,0 +1,74 @@ +/* + * ZeroTier One - Network Virtualization Everywhere + * Copyright (C) 2011-2019 ZeroTier, Inc. https://www.zerotier.com/ + * + * This program is free software: you can redistribute it and/or modify + * it under the terms of the GNU General Public License as published by + * the Free Software Foundation, either version 3 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program. If not, see . + * + * -- + * + * You can be released from the requirements of the license by purchasing + * a commercial license. Buying such a license is mandatory as soon as you + * develop commercial closed-source software that incorporates or links + * directly against ZeroTier software without disclosing the source code + * of your own application. + */ + +// This is glue code to ease the use of the NIST P-384 elliptic curve. + +// Note that some of the code inside ECC384.cpp is third party code and +// is under the BSD 2-clause license rather than ZeroTier's license. + +#ifndef ZT_ECC384_HPP +#define ZT_ECC384_HPP + +#include "Constants.hpp" + +/** + * Size of a (point compressed) P-384 public key + */ +#define ZT_ECC384_PUBLIC_KEY_SIZE 49 + +/** + * Size of a P-384 private key + */ +#define ZT_ECC384_PRIVATE_KEY_SIZE 48 + +/** + * Size of the hash that should be signed using P-384 + */ +#define ZT_ECC384_SIGNATURE_HASH_SIZE 48 + +/** + * Size of a P-384 signature + */ +#define ZT_ECC384_SIGNATURE_SIZE 96 + +/** + * Size of shared secret generated by ECDH key agreement + */ +#define ZT_ECC384_SHARED_SECRET_SIZE 48 + +namespace ZeroTier { + +void ECC384GenerateKey(uint8_t pub[ZT_ECC384_PUBLIC_KEY_SIZE],uint8_t priv[ZT_ECC384_PRIVATE_KEY_SIZE]); + +void ECC384ECDSASign(const uint8_t priv[ZT_ECC384_PRIVATE_KEY_SIZE],const uint8_t hash[ZT_ECC384_SIGNATURE_HASH_SIZE],uint8_t sig[ZT_ECC384_SIGNATURE_SIZE]); + +bool ECC384ECDSAVerify(const uint8_t pub[ZT_ECC384_PUBLIC_KEY_SIZE],const uint8_t hash[ZT_ECC384_SIGNATURE_HASH_SIZE],const uint8_t sig[ZT_ECC384_SIGNATURE_SIZE]); + +bool ECC384ECDH(const uint8_t theirPub[ZT_ECC384_PUBLIC_KEY_SIZE],const uint8_t ourPriv[ZT_ECC384_PRIVATE_KEY_SIZE],uint8_t secret[ZT_ECC384_SHARED_SECRET_SIZE]); + +} // namespace ZeroTier + +#endif diff --git a/node/Identity.hpp b/node/Identity.hpp index f559bcc5d..ee55028cf 100644 --- a/node/Identity.hpp +++ b/node/Identity.hpp @@ -159,12 +159,7 @@ public: * @param siglen Length of signature in bytes * @return True if signature validates and data integrity checks */ - inline bool verify(const void *data,unsigned int len,const void *signature,unsigned int siglen) const - { - if (siglen != ZT_C25519_SIGNATURE_LEN) - return false; - return C25519::verify(_publicKey,data,len,signature); - } + inline bool verify(const void *data,unsigned int len,const void *signature,unsigned int siglen) const { return C25519::verify(_publicKey,data,len,signature,siglen); } /** * Verify a message signature against this identity @@ -174,10 +169,7 @@ public: * @param signature Signature * @return True if signature validates and data integrity checks */ - inline bool verify(const void *data,unsigned int len,const C25519::Signature &signature) const - { - return C25519::verify(_publicKey,data,len,signature); - } + inline bool verify(const void *data,unsigned int len,const C25519::Signature &signature) const { return C25519::verify(_publicKey,data,len,signature); } /** * Shortcut method to perform key agreement with another identity diff --git a/objects.mk b/objects.mk index eb348dca2..cab07490d 100644 --- a/objects.mk +++ b/objects.mk @@ -3,6 +3,7 @@ CORE_OBJS=\ node/Capability.o \ node/CertificateOfMembership.o \ node/CertificateOfOwnership.o \ + node/ECC384.o \ node/Identity.o \ node/IncomingPacket.o \ node/InetAddress.o \ diff --git a/selftest.cpp b/selftest.cpp index 77c06cc03..b63bf4bde 100644 --- a/selftest.cpp +++ b/selftest.cpp @@ -50,6 +50,7 @@ #include "node/Dictionary.hpp" #include "node/SHA512.hpp" #include "node/C25519.hpp" +#include "node/ECC384.hpp" #include "node/Poly1305.hpp" #include "node/CertificateOfMembership.hpp" #include "node/Node.hpp" @@ -305,18 +306,35 @@ static int testCrypto() ::free((void *)bb); } - /* - for(unsigned int d=8;d<=10;++d) { - for(int k=0;k<8;++k) { - std::cout << "[crypto] computeSalsa2012Sha512ProofOfWork(" << d << ",\"foobarbaz\",9) == "; std::cout.flush(); - unsigned char result[16]; - uint64_t start = OSUtils::now(); - IncomingPacket::computeSalsa2012Sha512ProofOfWork(d,"foobarbaz",9,result); - uint64_t end = OSUtils::now(); - std::cout << Utils::hex(result,16) << " -- valid: " << IncomingPacket::testSalsa2012Sha512ProofOfWorkResult(d,"foobarbaz",9,result) << ", " << (end - start) << "ms" << std::endl; + std::cout << "[crypto] Testing ECC384 (NIST P-384)..." << std::endl; + { + uint8_t p384pub[ZT_ECC384_PUBLIC_KEY_SIZE],p384priv[ZT_ECC384_PRIVATE_KEY_SIZE],p384sig[ZT_ECC384_SIGNATURE_SIZE],p384hash[ZT_ECC384_SIGNATURE_HASH_SIZE]; + char p384hex[256]; + ECC384GenerateKey(p384pub,p384priv); + std::cout << "[crypto] Public Key: " << Utils::hex(p384pub,sizeof(p384pub),p384hex) << std::endl; + Utils::getSecureRandom(p384hash,sizeof(p384hash)); + ECC384ECDSASign(p384priv,p384hash,p384sig); + if (!ECC384ECDSAVerify(p384pub,p384hash,p384sig)) { + std::cout << "[crypto] Signature: FAILED (verify good signature)" << std::endl; + return -1; } + ++p384sig[0]; + if (ECC384ECDSAVerify(p384pub,p384hash,p384sig)) { + std::cout << "[crypto] Signature: FAILED (verify bad signature)" << std::endl; + return -1; + } + --p384sig[0]; + std::cout << "[crypto] Signature: " << Utils::hex(p384sig,sizeof(p384sig),p384hex) << std::endl; + uint8_t p384pub2[ZT_ECC384_PUBLIC_KEY_SIZE],p384priv2[ZT_ECC384_PRIVATE_KEY_SIZE],p384sec[ZT_ECC384_SHARED_SECRET_SIZE],p384sec2[ZT_ECC384_SHARED_SECRET_SIZE]; + ECC384GenerateKey(p384pub2,p384priv2); + ECC384ECDH(p384pub,p384priv2,p384sec); + ECC384ECDH(p384pub2,p384priv,p384sec2); + if (memcmp(p384sec,p384sec2,ZT_ECC384_SHARED_SECRET_SIZE)) { + std::cout << "[crypto] ECDH Agree: FAILED (secrets do not match)" << std::endl; + return -1; + } + std::cout << "[crypto] ECDH Agree: " << Utils::hex(p384sec,sizeof(p384sec),p384hex) << std::endl; } - */ std::cout << "[crypto] Testing C25519 and Ed25519 against test vectors... "; std::cout.flush(); for(int k=0;k