#include <sys/mman.h>
#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;
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];
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;
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;
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':
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);
}
return 0;
}
+#endif // !defined(TEST)
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