From b6006436d939a7cba7c141f00b4efc638a694d14 Mon Sep 17 00:00:00 2001 From: Matt Corallo Date: Fri, 8 Mar 2013 18:18:10 -0500 Subject: [PATCH] Lots of updates (including remove side-channels) * Remove commented GF(p) * Add log/exp tables for multiplication/exponentiation * Use lots of __attribute__s to remove side-channels in field_mult and field_pow. * Remove inverse table (use log/exp tables instead) --- shamirssecret.c | 196 +++++++++++++++++++++++++++--------------------- 1 file changed, 109 insertions(+), 87 deletions(-) diff --git a/shamirssecret.c b/shamirssecret.c index 893d978..b690048 100644 --- a/shamirssecret.c +++ b/shamirssecret.c @@ -9,70 +9,105 @@ #include #define MAX_LENGTH 1024 +#define ERROREXIT(str...) {fprintf(stderr, str); exit(1);} /* - * Calculations across the finite field GF(p) - * Lots of side-channel attacks in here + * Calculations across the finite field GF(2^8) */ -/* -const uint8_t p = 251; // Largest 8-bit prime +#define P 256 + static uint8_t field_add(uint8_t a, uint8_t b) { - assert(a < p && b < p); - return (((uint16_t)a) + ((uint16_t)b)) % p; + return a ^ b; } static uint8_t field_sub(uint8_t a, uint8_t b) { - assert(a < p && b < p); - return (((uint16_t)p) + ((uint16_t)a) - ((uint16_t)b)) % p; + return a ^ b; } -static uint8_t field_mul(uint8_t a, uint8_t b) { - assert(a < p && b < p); - return (((uint16_t)a) * ((uint16_t)b)) % p; +static uint8_t field_neg(uint8_t a) { + return field_sub(0, a); } -static uint8_t field_pow(uint8_t a, uint8_t e) { - assert(a < p); - uint8_t ret = 1; - for (uint8_t i = 0; i < e; i++) { - ret = field_mul(ret, a); - } +static const uint8_t exp[P] = { + 0x01, 0x03, 0x05, 0x0f, 0x11, 0x33, 0x55, 0xff, 0x1a, 0x2e, 0x72, 0x96, 0xa1, 0xf8, 0x13, 0x35, + 0x5f, 0xe1, 0x38, 0x48, 0xd8, 0x73, 0x95, 0xa4, 0xf7, 0x02, 0x06, 0x0a, 0x1e, 0x22, 0x66, 0xaa, + 0xe5, 0x34, 0x5c, 0xe4, 0x37, 0x59, 0xeb, 0x26, 0x6a, 0xbe, 0xd9, 0x70, 0x90, 0xab, 0xe6, 0x31, + 0x53, 0xf5, 0x04, 0x0c, 0x14, 0x3c, 0x44, 0xcc, 0x4f, 0xd1, 0x68, 0xb8, 0xd3, 0x6e, 0xb2, 0xcd, + 0x4c, 0xd4, 0x67, 0xa9, 0xe0, 0x3b, 0x4d, 0xd7, 0x62, 0xa6, 0xf1, 0x08, 0x18, 0x28, 0x78, 0x88, + 0x83, 0x9e, 0xb9, 0xd0, 0x6b, 0xbd, 0xdc, 0x7f, 0x81, 0x98, 0xb3, 0xce, 0x49, 0xdb, 0x76, 0x9a, + 0xb5, 0xc4, 0x57, 0xf9, 0x10, 0x30, 0x50, 0xf0, 0x0b, 0x1d, 0x27, 0x69, 0xbb, 0xd6, 0x61, 0xa3, + 0xfe, 0x19, 0x2b, 0x7d, 0x87, 0x92, 0xad, 0xec, 0x2f, 0x71, 0x93, 0xae, 0xe9, 0x20, 0x60, 0xa0, + 0xfb, 0x16, 0x3a, 0x4e, 0xd2, 0x6d, 0xb7, 0xc2, 0x5d, 0xe7, 0x32, 0x56, 0xfa, 0x15, 0x3f, 0x41, + 0xc3, 0x5e, 0xe2, 0x3d, 0x47, 0xc9, 0x40, 0xc0, 0x5b, 0xed, 0x2c, 0x74, 0x9c, 0xbf, 0xda, 0x75, + 0x9f, 0xba, 0xd5, 0x64, 0xac, 0xef, 0x2a, 0x7e, 0x82, 0x9d, 0xbc, 0xdf, 0x7a, 0x8e, 0x89, 0x80, + 0x9b, 0xb6, 0xc1, 0x58, 0xe8, 0x23, 0x65, 0xaf, 0xea, 0x25, 0x6f, 0xb1, 0xc8, 0x43, 0xc5, 0x54, + 0xfc, 0x1f, 0x21, 0x63, 0xa5, 0xf4, 0x07, 0x09, 0x1b, 0x2d, 0x77, 0x99, 0xb0, 0xcb, 0x46, 0xca, + 0x45, 0xcf, 0x4a, 0xde, 0x79, 0x8b, 0x86, 0x91, 0xa8, 0xe3, 0x3e, 0x42, 0xc6, 0x51, 0xf3, 0x0e, + 0x12, 0x36, 0x5a, 0xee, 0x29, 0x7b, 0x8d, 0x8c, 0x8f, 0x8a, 0x85, 0x94, 0xa7, 0xf2, 0x0d, 0x17, + 0x39, 0x4b, 0xdd, 0x7c, 0x84, 0x97, 0xa2, 0xfd, 0x1c, 0x24, 0x6c, 0xb4, 0xc7, 0x52, 0xf6, 0x01}; +static const uint8_t log[P] = { + 0x00, // log(0) is not defined + 0xff, 0x19, 0x01, 0x32, 0x02, 0x1a, 0xc6, 0x4b, 0xc7, 0x1b, 0x68, 0x33, 0xee, 0xdf, 0x03, 0x64, + 0x04, 0xe0, 0x0e, 0x34, 0x8d, 0x81, 0xef, 0x4c, 0x71, 0x08, 0xc8, 0xf8, 0x69, 0x1c, 0xc1, 0x7d, + 0xc2, 0x1d, 0xb5, 0xf9, 0xb9, 0x27, 0x6a, 0x4d, 0xe4, 0xa6, 0x72, 0x9a, 0xc9, 0x09, 0x78, 0x65, + 0x2f, 0x8a, 0x05, 0x21, 0x0f, 0xe1, 0x24, 0x12, 0xf0, 0x82, 0x45, 0x35, 0x93, 0xda, 0x8e, 0x96, + 0x8f, 0xdb, 0xbd, 0x36, 0xd0, 0xce, 0x94, 0x13, 0x5c, 0xd2, 0xf1, 0x40, 0x46, 0x83, 0x38, 0x66, + 0xdd, 0xfd, 0x30, 0xbf, 0x06, 0x8b, 0x62, 0xb3, 0x25, 0xe2, 0x98, 0x22, 0x88, 0x91, 0x10, 0x7e, + 0x6e, 0x48, 0xc3, 0xa3, 0xb6, 0x1e, 0x42, 0x3a, 0x6b, 0x28, 0x54, 0xfa, 0x85, 0x3d, 0xba, 0x2b, + 0x79, 0x0a, 0x15, 0x9b, 0x9f, 0x5e, 0xca, 0x4e, 0xd4, 0xac, 0xe5, 0xf3, 0x73, 0xa7, 0x57, 0xaf, + 0x58, 0xa8, 0x50, 0xf4, 0xea, 0xd6, 0x74, 0x4f, 0xae, 0xe9, 0xd5, 0xe7, 0xe6, 0xad, 0xe8, 0x2c, + 0xd7, 0x75, 0x7a, 0xeb, 0x16, 0x0b, 0xf5, 0x59, 0xcb, 0x5f, 0xb0, 0x9c, 0xa9, 0x51, 0xa0, 0x7f, + 0x0c, 0xf6, 0x6f, 0x17, 0xc4, 0x49, 0xec, 0xd8, 0x43, 0x1f, 0x2d, 0xa4, 0x76, 0x7b, 0xb7, 0xcc, + 0xbb, 0x3e, 0x5a, 0xfb, 0x60, 0xb1, 0x86, 0x3b, 0x52, 0xa1, 0x6c, 0xaa, 0x55, 0x29, 0x9d, 0x97, + 0xb2, 0x87, 0x90, 0x61, 0xbe, 0xdc, 0xfc, 0xbc, 0x95, 0xcf, 0xcd, 0x37, 0x3f, 0x5b, 0xd1, 0x53, + 0x39, 0x84, 0x3c, 0x41, 0xa2, 0x6d, 0x47, 0x14, 0x2a, 0x9e, 0x5d, 0x56, 0xf2, 0xd3, 0xab, 0x44, + 0x11, 0x92, 0xd9, 0x23, 0x20, 0x2e, 0x89, 0xb4, 0x7c, 0xb8, 0x26, 0x77, 0x99, 0xe3, 0xa5, 0x67, + 0x4a, 0xed, 0xde, 0xc5, 0x31, 0xfe, 0x18, 0x0d, 0x63, 0x8c, 0x80, 0xc0, 0xf7, 0x70, 0x07}; + +// We disable lots of optimizations that result in non-constant runtime (+/- branch delays) +static uint8_t field_mul_ret(uint8_t calc, uint8_t a, uint8_t b) __attribute__((optimize("-O0"))) __attribute__((noinline)); +static uint8_t field_mul_ret(uint8_t calc, uint8_t a, uint8_t b) { + uint8_t ret, ret2; + if (a == 0) + ret2 = 0; + else + ret2 = calc; + if (b == 0) + ret = 0; + else + ret = ret2; return ret; } - -static uint8_t field_neg(uint8_t a) { - assert(a < p); - if (a == 0) - return 0; - return p - a; +static uint8_t field_mul(uint8_t a, uint8_t b) { + return field_mul_ret(exp[(log[a] + log[b]) % 255], a, b); } static uint8_t field_invert(uint8_t a) { - // Brute force, yay! - assert(a < p); - for (uint8_t i = 0; i < p; i++) { - if (field_mul(i, a) == 1) - return i; - } - assert(0); -}*/ - - - -/* - * Calculations across the finite field GF(2^8) - */ -const uint16_t p = 256; -static uint8_t field_add(uint8_t a, uint8_t b) { - return a ^ b; + assert(a != 0); + return exp[0xff - log[a]]; // log[1] == 0xff } -static uint8_t field_sub(uint8_t a, uint8_t b) { - return a ^ b; +// We disable lots of optimizations that result in non-constant runtime (+/- branch delays) +static uint8_t field_pow_ret(uint8_t calc, uint8_t a, uint8_t e) __attribute__((optimize("-O0"))) __attribute__((noinline)); +static uint8_t field_pow_ret(uint8_t calc, uint8_t a, uint8_t e) { + uint8_t ret, ret2; + if (a == 0) + ret2 = 0; + else + ret2 = calc; + if (e == 0) + ret = 1; + else + ret = ret2; + return ret; +} +static uint8_t field_pow(uint8_t a, uint8_t e) { + return field_pow_ret(exp[(log[a] * e) % 255], a, e); } -static uint8_t field_mul(uint8_t a, uint8_t b) { - // TODO side-channel attacks here? +#ifdef TEST +static uint8_t field_mul_calc(uint8_t a, uint8_t b) { + // side-channel attacks here uint8_t ret = 0; uint8_t counter; uint8_t carry; @@ -82,53 +117,42 @@ static uint8_t field_mul(uint8_t a, uint8_t b) { carry = (a & 0x80); a <<= 1; if (carry) - a ^= 0x1b; /* what x^8 is modulo x^8 + x^4 + x^3 + x + 1 */ + a ^= 0x1b; // what x^8 is modulo x^8 + x^4 + x^3 + x + 1 b >>= 1; } return ret; } - -// WARNING: Do not use if e is secret (potential side-channel attacks) -static uint8_t field_pow(uint8_t a, uint8_t e) { - // TODO: This could be sped up pretty trivially +static uint8_t field_pow_calc(uint8_t a, uint8_t e) { uint8_t ret = 1; for (uint8_t i = 0; i < e; i++) ret = field_mul(ret, a); return ret; } +int main() { + // Test inversion with the logarithm tables + for (uint16_t i = 1; i < P; i++) + assert(field_mul_calc(i, field_invert(i)) == 1); + + // Test multiplication with the logarithm tables + for (uint16_t i = 0; i < 2; i++) { + for (uint16_t j = 0; j < P; j++) + assert(field_mul(i, j) == field_mul_calc(i, j)); + } -static uint8_t field_neg(uint8_t a) { - return field_sub(0, a); -} - -static const uint8_t inverse[] = { // Multiplicative inverse of each element in the field - 0xff, // 0 has no inverse - 0x01, 0x8d, 0xf6, 0xcb, 0x52, 0x7b, 0xd1, 0xe8, 0x4f, 0x29, 0xc0, 0xb0, 0xe1, 0xe5, 0xc7, 0x74, - 0xb4, 0xaa, 0x4b, 0x99, 0x2b, 0x60, 0x5f, 0x58, 0x3f, 0xfd, 0xcc, 0xff, 0x40, 0xee, 0xb2, 0x3a, - 0x6e, 0x5a, 0xf1, 0x55, 0x4d, 0xa8, 0xc9, 0xc1, 0x0a, 0x98, 0x15, 0x30, 0x44, 0xa2, 0xc2, 0x2c, - 0x45, 0x92, 0x6c, 0xf3, 0x39, 0x66, 0x42, 0xf2, 0x35, 0x20, 0x6f, 0x77, 0xbb, 0x59, 0x19, 0x1d, - 0xfe, 0x37, 0x67, 0x2d, 0x31, 0xf5, 0x69, 0xa7, 0x64, 0xab, 0x13, 0x54, 0x25, 0xe9, 0x09, 0xed, - 0x5c, 0x05, 0xca, 0x4c, 0x24, 0x87, 0xbf, 0x18, 0x3e, 0x22, 0xf0, 0x51, 0xec, 0x61, 0x17, 0x16, - 0x5e, 0xaf, 0xd3, 0x49, 0xa6, 0x36, 0x43, 0xf4, 0x47, 0x91, 0xdf, 0x33, 0x93, 0x21, 0x3b, 0x79, - 0xb7, 0x97, 0x85, 0x10, 0xb5, 0xba, 0x3c, 0xb6, 0x70, 0xd0, 0x06, 0xa1, 0xfa, 0x81, 0x82, 0x83, - 0x7e, 0x7f, 0x80, 0x96, 0x73, 0xbe, 0x56, 0x9b, 0x9e, 0x95, 0xd9, 0xf7, 0x02, 0xb9, 0xa4, 0xde, - 0x6a, 0x32, 0x6d, 0xd8, 0x8a, 0x84, 0x72, 0x2a, 0x14, 0x9f, 0x88, 0xf9, 0xdc, 0x89, 0x9a, 0xfb, - 0x7c, 0x2e, 0xc3, 0x8f, 0xb8, 0x65, 0x48, 0x26, 0xc8, 0x12, 0x4a, 0xce, 0xe7, 0xd2, 0x62, 0x0c, - 0xe0, 0x1f, 0xef, 0x11, 0x75, 0x78, 0x71, 0xa5, 0x8e, 0x76, 0x3d, 0xbd, 0xbc, 0x86, 0x57, 0x0b, - 0x28, 0x2f, 0xa3, 0xda, 0xd4, 0xe4, 0x0f, 0xa9, 0x27, 0x53, 0x04, 0x1b, 0xfc, 0xac, 0xe6, 0x7a, - 0x07, 0xae, 0x63, 0xc5, 0xdb, 0xe2, 0xea, 0x94, 0x8b, 0xc4, 0xd5, 0x9d, 0xf8, 0x90, 0x6b, 0xb1, - 0x0d, 0xd6, 0xeb, 0xc6, 0x0e, 0xcf, 0xad, 0x08, 0x4e, 0xd7, 0xe3, 0x5d, 0x50, 0x1e, 0xb3, 0x5b, - 0x23, 0x38, 0x34, 0x68, 0x46, 0x03, 0x8c, 0xdd, 0x9c, 0x7d, 0xa0, 0xcd, 0x1a, 0x41, 0x1c}; -static uint8_t field_invert(uint8_t a) { - assert(a != 0); - return inverse[a]; + // Test exponentiation with the logarithm tables + for (uint16_t i = 0; i < P; i++) { + for (uint16_t j = 0; j < P; j++) + assert(field_pow(i, j) == field_pow_calc(i, j)); + } } +#endif // defined(TEST) /* * Calculations across the polynomial q */ +#ifndef TEST static uint8_t calculateQ(uint8_t a[], uint8_t k, uint8_t x) { assert(x != 0); // q(0) == secret, though so does a[0] uint8_t ret = a[0]; @@ -155,14 +179,14 @@ uint8_t calculateSecret(uint8_t x[], uint8_t q[], uint8_t k) { return ret; } -#define ERROREXIT(str...) {fprintf(stderr, str); exit(1);} + int main(int argc, char* argv[]) { assert(mlockall(MCL_CURRENT | MCL_FUTURE) == 0); char split = 0; uint8_t n = 0, k = 0; - char* files[p]; uint8_t files_count = 0; + char* files[P]; uint8_t files_count = 0; char *in_file = (void*)0, *out_file_param = (void*)0; int i; @@ -182,16 +206,16 @@ int main(int argc, char* argv[]) { break; case 'n': { int t = atoi(optarg); - if (t <= 0 || t >= p) - ERROREXIT("n must be > 0 and < %u\n", p) + if (t <= 0 || t >= P) + ERROREXIT("n must be > 0 and < %u\n", P) else n = t; break; } case 'k': { int t = atoi(optarg); - if (t <= 0 || t >= p) - ERROREXIT("n must be > 0 and < %u\n", p) + if (t <= 0 || t >= P) + ERROREXIT("n must be > 0 and < %u\n", P) else k = t; break; @@ -203,8 +227,8 @@ int main(int argc, char* argv[]) { out_file_param = optarg; break; case 'f': - if (files_count >= p-1) - ERROREXIT("May only specify up to %u files\n", p-1) + if (files_count >= P-1) + ERROREXIT("May only specify up to %u files\n", P-1) files[files_count++] = optarg; break; case 'h': @@ -255,11 +279,8 @@ int main(int argc, char* argv[]) { for (uint8_t i = 0; i < secret_length; i++) { a[i][0] = secret[i]; - for (uint8_t j = 1; j < k; j++) { - do - assert(fread(&a[i][j], sizeof(uint8_t), 1, random) == 1); - while (a[i][j] >= p); - } + for (uint8_t j = 1; j < k; j++) + assert(fread(&a[i][j], sizeof(uint8_t), 1, random) == 1); for (uint8_t j = 0; j < n; j++) D[j][i] = calculateQ(a[i], k, j+1); } @@ -332,3 +353,4 @@ int main(int argc, char* argv[]) { return 0; } +#endif // !defined(TEST) -- 2.30.2