feat: rsa 32bits (16 bits msg no padding)

rsa64/primes.c

@@ -1,49 +1,47 @@
 #include "rsa.h"
 
-uint32_t get_random_bytes(int fd) {
+uint16_t get_random_bytes(int fd) {
-	uint32_t ret;
+	uint16_t ret;
-	if (read(fd, &ret, sizeof(uint32_t)) == -1) {
+	if (read(fd, &ret, sizeof(uint16_t)) == -1) {
 		exit(1);
 	}
 	return ret;
 }
 
-// nn pow e mod mm
+// n pow e mod m
-uint32_t pow_mod(uint32_t nn, uint32_t e, uint32_t mm) {
+uint64_t pow_mod(uint64_t n, uint64_t e, uint64_t m) {
-	uint64_t x = nn;
-	uint64_t m = mm;
 	uint64_t y = 1;
 
 	while (e > 1) {
-		if (e % 2) {
+		if (e & 1) {
-			y *= x;
+			y = (y * n) % m;
-			e -= 1;
-			y = y % m;
 		}
-		x *= x;
+		n = (n * n) % m;
-		e /= 2;
+		e = e >> 1;
-		x = x % m;
 	}
-	return (uint32_t)(x * y % m);
+	return (n * y) % m;
 }
 
-bool is_prime(uint32_t n, uint32_t k_max, int fd) {
+bool is_prime(uint16_t n, size_t k_max, int fd) {
-	uint32_t a = get_random_bytes(fd);
+	uint16_t a = get_random_bytes(fd);
-	uint32_t d = n - 1;
+	//	a &= 0xFFFF;
-	uint32_t s = 0;
+	uint16_t d = n - 1;
+	uint16_t s = 0;
 
 	while ((d & 1) == 0) {
 		s++;
 		d = d >> 1;
 	}
 
-	for (uint32_t k = 0; k < k_max; k++) {
+	for (size_t k = 0; k < k_max; k++) {
+		a = 0;
 		while (a < 2 || a > (n - 2)) {
 			a = get_random_bytes(fd);
+		//a &= 0xFFFF;
 		}
-		uint32_t x = pow_mod(a, d, n);
+		uint16_t x = pow_mod(a, d, n);
-		uint32_t y;
+		uint16_t y;
-		for (uint32_t i = 0; i < s; i++) {
+		for (uint16_t i = 0; i < s; i++) {
 			y = pow_mod(x, 2, n);
 			if (y == 1 && x != 1 && x != n - 1)
 				return false;
@@ -56,22 +54,25 @@ bool is_prime(uint32_t n, uint32_t k_max, int fd) {
 	return true;
 }
 
-uint32_t generate_prime_fd(int fd) {
+uint16_t generate_prime_fd(int fd) {
-	uint32_t n = get_random_bytes(fd);
+	uint16_t n = get_random_bytes(fd);
-	n |= 1 << 31;
+	n |= 1 << 15;
 	n |= 1;
+	//n &= 0xFFFF;
 
-	while (n % 65537 == 0 || !is_prime(n, 128, fd)) {
+	while (/*n % 3 == 0 ||*/ !is_prime(n, 16, fd)) {
 		n = get_random_bytes(fd);
-		n |= 1 << 31;
+		n |= 1 << 15;
 		n |= 1;
+		//n &= 0xFFFF;
 	}
 	return n;
 }
 
-uint32_t generate_prime() {
+uint16_t generate_prime() {
 	int fd = open("/dev/urandom", O_RDONLY);
-	uint32_t n = generate_prime_fd(fd);
+	uint16_t n = generate_prime_fd(fd);
 	close(fd);
 	return n;
 }
+

rsa64/rsa.c

@@ -3,20 +3,73 @@
 rsa_t rsa_init(size_t len, bigint_t *primes) {
 	rsa_t rsa;
 
-	printf("Generating two primes of length %d bits\n", RSA_BLOCK_SIZE / 2);
+//	printf("Generating two primes of length %d bits\n", RSA_BLOCK_SIZE / 2);
 	//printf("Generating p...\n");
 	rsa.p = bigint_prime(len / 2, primes);
-	printf("p = %lu\n", ((uint64_t)rsa.p.data[1] << 32) + (uint64_t)rsa.p.data[0]);
+//	printf("p = %lu\n", ((uint64_t)rsa.p.data[1] << 32) + (uint64_t)rsa.p.data[0]);
 //printf("p = %u\n", rsa.p.data[0]);
 	//printf("Generating q...\n");
 	rsa.q = bigint_prime(len / 2, primes);
-	printf("q = %lu\n", ((uint64_t)rsa.q.data[1] << 32) + (uint64_t)rsa.q.data[0]);
+//	printf("q = %lu\n", ((uint64_t)rsa.q.data[1] << 32) + (uint64_t)rsa.q.data[0]);
 	//printf("q = %u\n", rsa.q.data[0]);
 
 
 	return rsa;
 }
 
+int64_t euler(int64_t r0, int64_t r1) {
+	int64_t s0 = 1;
+	int64_t s1 = 0;
+	int64_t t0 = 0;
+	int64_t t1 = 1;
+	int64_t q0 = 0;
+
+	//printf(""
+	//printf("|% 20d|% 20ld|% 20ld|% 20ld|\n", 0, r0, s0, t0);
+	//printf("|% 20d|% 20ld|% 20ld|% 20ld|\n", 0, r1, s1, t1);
+
+	while (r1 != 0) {
+		q0 = r0 / r1;
+		int64_t tmp = r0 % r1;
+		r0 = r1;
+		r1 = tmp;
+		tmp = s0 - q0 * s1;
+		s0 = s1;
+		s1 = tmp;
+		tmp = t0 - q0 * t1;
+		t0 = t1;
+		t1 = tmp;
+		//printf("|% 20ld|% 20ld|% 20ld|% 20ld|\n", q0, r1, s1, t1);
+	}
+	return s0;
+}
+
+int64_t euler2(int64_t r0, int64_t r1) {
+	int64_t s0 = 1;
+	int64_t s1 = 0;
+	int64_t t0 = 0;
+	int64_t t1 = 1;
+	int64_t q0 = 0;
+
+	//printf(""
+	printf("|% 20d|% 20ld|% 20ld|% 20ld|\n", 0, r0, s0, t0);
+	printf("|% 20d|% 20ld|% 20ld|% 20ld|\n", 0, r1, s1, t1);
+
+	while (r1 != 0) {
+		q0 = r0 / r1;
+		int64_t tmp = r0 % r1;
+		r0 = r1;
+		r1 = tmp;
+		tmp = s0 - q0 * s1;
+		s0 = s1;
+		s1 = tmp;
+		tmp = t0 - q0 * t1;
+		t0 = t1;
+		t1 = tmp;
+		printf("|% 20ld|% 20ld|% 20ld|% 20ld|\n", q0, r1, s1, t1);
+	}
+	return t0;
+}
 rsa_t rsa_generate_keys(size_t block_size) {
 	size_t len = block_size / sizeof(uint32_t) / 8;
 	bigint_t *primes = (bigint_t *)protected_malloc(3245 * sizeof(bigint_t));
@@ -40,10 +93,100 @@ rsa_t rsa_generate_keys(size_t block_size) {
 	bigint_destroy(rsa.p);
 	bigint_destroy(rsa.q);
 
-	for (int i = 0; i < 100; i++) {
+	//int64_t p = 56843;//(uint64_t)generate_prime();
-		printf("%u\n", generate_prime());
+	//int64_t q = 61861;//(uint64_t)generate_prime();
+	//int64_t p = 36671;
+	//int64_t q = 53939;
+	//int64_t p = 57313;
+	//int64_t q = 51329;
+	//int64_t p = 39901;
+	//int64_t q = 43391;
+
+//	int fd2 = open("/dev/urandom", O_RDONLY);
+	for (int try = 0; try < 1000; try++) {
+
+	if (try % 100 == 0)
+		printf("try: %d\n", try);
+	int64_t p = (uint64_t)generate_prime();
+	int64_t q = (uint64_t)generate_prime();
+	//p = 63761;
+	//q = 65003;
+	int64_t ln = (p - 1) * (q - 1);
+	int64_t e = 11317;
+	//e = 11;
+
+	while (ln % e == 0 || p == q) {
+		p = generate_prime();
+		q = generate_prime();
+		ln = (p - 1) * (q - 1);
 	}
 
+	if (q > p) {
+		uint64_t tmp = p;
+		p = q;
+		q = tmp;
+	}
+	int64_t n = p * q;
+
+	int64_t r0 = e;
+	int64_t r1 = ln;
+	int64_t s0 = 1;
+	int64_t s1 = 0;
+	int64_t t0 = 0;
+	int64_t t1 = 1;
+	int64_t q0 = 0;
+
+	while (r1 != 0) {
+		q0 = r0 / r1;
+		int64_t tmp = r0 % r1;
+		r0 = r1;
+		r1 = tmp;
+		tmp = s0 - q0 * s1;
+		s0 = s1;
+		s1 = tmp;
+		tmp = t0 - q0 * t1;
+		t0 = t1;
+		t1 = tmp;
+	}
+
+	int64_t d = euler(e, ln) + ln;
+	if (d > n) {
+		d -= ln;
+	}
+
+/*	printf("p: %ld\n", p);
+	printf("q: %ld\n", q);
+	printf("ln: %ld\n", ln);
+	printf("n: %ld\n", n);
+	printf("d: %ld\n", d);
+	printf("e: %ld\n", e);
+	printf("d * e %% ln = %ld\n", (d*e)%ln);*/
+	for (uint64_t m = 0; m < 16384; m++) {
+		//uint64_t m = get_random_bytes(fd2);
+		uint64_t c = pow_mod(m, e, n);
+		uint64_t m2 = pow_mod(c, d, n);
+		if (m != m2) {
+			printf("ERROR try: %d\nround: n/a\nmsg: %ld\ncypher: %ld\ndecrypted: %ld\nd: %ld\ne: %ld\np: %lu\nq: %lu\nn: %lu\n", try, m, c, m2, d, e, p, q, n);
+			break;
+		}
+	}
+	//int64_t m = 42;
+	/*
+	for (int64_t m = 41; m < 43; m++) {
+	int64_t c = pow_mod(m, e, n);
+	int64_t m2 = pow_mod(c, d, n);
+	if (d < 0) {
+		int64_t c2 = euler(c, n);
+		printf("c2: %ld\n", c2);
+		printf("c2 * c %% n = %ld\n", ((c2 + n)*c)%n);
+		printf("c2 * c %% n = %ld\n", ((c2)*c)%n);
+		m2 = pow_mod(c2 + n, -d, n);
+	}
+	printf("message: %ld\n", m);
+	printf("cypher: %ld\n", c);
+	printf("decrypted: %ld\n", m2);
+	}*/
+	}
 	return rsa;
 }
 

rsa64/rsa.h

@@ -54,7 +54,9 @@ void array_bitwise_right_shift(uint32_t *a, size_t len);
 void array_bitwise_right_shift(uint32_t *a, size_t len);
 void array_decrement(uint32_t *a, size_t len);
 
-uint32_t generate_prime();
+uint16_t generate_prime();
+uint64_t pow_mod(uint64_t nn, uint64_t e, uint64_t mm);
+uint16_t get_random_bytes(int fd);
 
 #endif