int main() {
bi_initialize();
int k = 2;
bigint f1 = int_to_bi(1), f2 = int_to_bi(1), f3, tmp;
bigint zeros = int_to_bi(1000000000);
while (1) {
k++;
f3 = bi_add(f1, bi_copy(f2));
int mod = bi_int_mod(bi_copy(f3), 1000000000);
if (mod >= 100000000) {
if (is_pandigital(mod)) {
tmp = bi_copy(f3);
while (bi_compare(bi_copy(tmp), bi_copy(zeros)) > 0) {
tmp = bi_int_divide(tmp, 10);
}
if (is_pandigital(bi_to_int(tmp))) {
break;
}
}
}
f1 = f2;
f2 = f3;
}
bi_free(f2);
bi_free(f3);
bi_free(zeros);
printf("%d\n", k);
bi_terminate();
return 0;
}
/**
* @brief Use the Chinese Remainder Theorem to quickly perform RSA decrypts.
*
* @param ctx [in] The bigint session context.
* @param bi [in] The bigint to perform the exp/mod.
* @param dP [in] CRT's dP bigint
* @param dQ [in] CRT's dQ bigint
* @param p [in] CRT's p bigint
* @param q [in] CRT's q bigint
* @param qInv [in] CRT's qInv bigint
* @return The result of the CRT operation
*/
bigint * ICACHE_FLASH_ATTR bi_crt(BI_CTX *ctx, bigint *bi,
bigint *dP, bigint *dQ,
bigint *p, bigint *q, bigint *qInv)
{
bigint *m1, *m2, *h;
/* Montgomery has a condition the 0 < x, y < m and these products violate
* that condition. So disable Montgomery when using CRT */
#if defined(CONFIG_BIGINT_MONTGOMERY)
ctx->use_classical = 1;
#endif
ctx->mod_offset = BIGINT_P_OFFSET;
m1 = bi_mod_power(ctx, bi_copy(bi), dP);
ctx->mod_offset = BIGINT_Q_OFFSET;
m2 = bi_mod_power(ctx, bi, dQ);
h = bi_subtract(ctx, bi_add(ctx, m1, p), bi_copy(m2), NULL);
h = bi_multiply(ctx, h, qInv);
ctx->mod_offset = BIGINT_P_OFFSET;
h = bi_residue(ctx, h);
#if defined(CONFIG_BIGINT_MONTGOMERY)
ctx->use_classical = 0; /* reset for any further operation */
#endif
return bi_add(ctx, m2, bi_multiply(ctx, q, h));
}
/**
* Use the Chinese Remainder Theorem to quickly perform RSA decrypts.
* This should really be in bigint.c (and was at one stage), but needs
* access to the RSA_CTX context...
*/
static bigint *bi_crt(const RSA_CTX *rsa, bigint *bi)
{
BI_CTX *ctx = rsa->bi_ctx;
bigint *m1, *m2, *h;
/* Montgomery has a condition the 0 < x, y < m and these products violate
* that condition. So disable Montgomery when using CRT */
#if defined(CONFIG_BIGINT_MONTGOMERY)
ctx->use_classical = 1;
#endif
ctx->mod_offset = BIGINT_P_OFFSET;
m1 = bi_mod_power(ctx, bi_copy(bi), rsa->dP);
ctx->mod_offset = BIGINT_Q_OFFSET;
m2 = bi_mod_power(ctx, bi, rsa->dQ);
h = bi_subtract(ctx, bi_add(ctx, m1, rsa->p), bi_copy(m2), NULL);
h = bi_multiply(ctx, h, rsa->qInv);
ctx->mod_offset = BIGINT_P_OFFSET;
h = bi_residue(ctx, h);
#if defined(CONFIG_BIGINT_MONTGOMERY)
ctx->use_classical = 0; /* reset for any further operation */
#endif
return bi_add(ctx, m2, bi_multiply(ctx, rsa->q, h));
}
/**************************************************************************
* RSA tests
*
* Use the results from openssl to verify PKCS1 etc
**************************************************************************/
static int RSA_test(void)
{
int res = 1;
const char *plaintext = /* 128 byte hex number */
"1234567890abbbbbbbbbbbbbbbccccccccccccccdddddddddddddeeeeeeeeee2"
"1aaaaaaaaaabbbbbbbbbbbbbbbccccccccccccccdddddddddddddeeeeeeeee2\012";
uint8_t enc_data[128], dec_data[128];
RSA_CTX *rsa_ctx = NULL;
BI_CTX *bi_ctx;
bigint *plaintext_bi;
bigint *enc_data_bi, *dec_data_bi;
uint8_t enc_data2[128], dec_data2[128];
int len;
uint8_t *buf;
/* extract the private key elements */
len = get_file("./axTLS.key_1024", &buf);
if (asn1_get_private_key(buf, len, &rsa_ctx) < 0)
{
goto end;
}
free(buf);
dump_frame("original data",(char *)plaintext, strlen(plaintext));
bi_ctx = rsa_ctx->bi_ctx;
plaintext_bi = bi_import(bi_ctx,
(const uint8_t *)plaintext, strlen(plaintext));
/* basic rsa encrypt */
enc_data_bi = RSA_public(rsa_ctx, plaintext_bi);
bi_export(bi_ctx, bi_copy(enc_data_bi), enc_data, sizeof(enc_data));
dump_frame("encrypt data",(char *)enc_data, sizeof(enc_data));
/* basic rsa decrypt */
dec_data_bi = RSA_private(rsa_ctx, enc_data_bi);
bi_export(bi_ctx, dec_data_bi, dec_data, sizeof(dec_data));
dump_frame("decrypt data",(char *)dec_data, sizeof(dec_data));
if (memcmp(dec_data, plaintext, strlen(plaintext)))
{
printf("Error: DECRYPT #1 failed\n");
goto end;
}
RSA_encrypt(rsa_ctx, (const uint8_t *)"abc", 3, enc_data2, 0);
RSA_decrypt(rsa_ctx, enc_data2, dec_data2, 1);
if (memcmp("abc", dec_data2, 3))
{
printf("Error: ENCRYPT/DECRYPT #2 failed\n");
goto end;
}
RSA_free(rsa_ctx);
res = 0;
printf("All RSA tests passed\n");
end:
return res;
}
/*
* Karatsuba improves on regular multiplication due to only 3 multiplications
* being done instead of 4. The additional additions/subtractions are O(N)
* rather than O(N^2) and so for big numbers it saves on a few operations
*/
static bigint * ICACHE_FLASH_ATTR karatsuba(BI_CTX *ctx, bigint *bia, bigint *bib, int is_square)
{
bigint *x0, *x1;
bigint *p0, *p1, *p2;
int m;
if (is_square)
{
m = (bia->size + 1)/2;
}
else
{
m = (max(bia->size, bib->size) + 1)/2;
}
x0 = bi_clone(ctx, bia);
x0->size = m;
x1 = bi_clone(ctx, bia);
comp_right_shift(x1, m);
bi_free(ctx, bia);
/* work out the 3 partial products */
if (is_square)
{
p0 = bi_square(ctx, bi_copy(x0));
p2 = bi_square(ctx, bi_copy(x1));
p1 = bi_square(ctx, bi_add(ctx, x0, x1));
}
else /* normal multiply */
{
bigint *y0, *y1;
y0 = bi_clone(ctx, bib);
y0->size = m;
y1 = bi_clone(ctx, bib);
comp_right_shift(y1, m);
bi_free(ctx, bib);
p0 = bi_multiply(ctx, bi_copy(x0), bi_copy(y0));
p2 = bi_multiply(ctx, bi_copy(x1), bi_copy(y1));
p1 = bi_multiply(ctx, bi_add(ctx, x0, x1), bi_add(ctx, y0, y1));
}
p1 = bi_subtract(ctx,
bi_subtract(ctx, p1, bi_copy(p2), NULL), bi_copy(p0), NULL);
comp_left_shift(p1, m);
comp_left_shift(p2, 2*m);
return bi_add(ctx, p1, bi_add(ctx, p0, p2));
}
int main() {
bi_initialize();
int a, b, n;
int max_number, prod;
for (a = -999; a < 1000; ++a) {
for (b = -999; b < 1000; ++b) {
n = 0;
for (;;) {
bigint a_ = int_to_bi(a);
bigint b_ = int_to_bi(b);
bigint n_ = int_to_bi(n);
bigint n2 = bi_multiply( bi_copy( n_ ), bi_copy( n_ ) );
bigint an = bi_multiply(bi_copy(a_),bi_copy(n_));
bigint num = bi_add(bi_copy(n2), bi_copy(an));
bigint num2 = bi_add(bi_copy(num), bi_copy(b_));
int should_break = 0;
if (bi_is_probable_prime(bi_copy(num2), 99)) {
++n;
} else {
if (n > max_number) {
max_number = n;
prod = a * b;
}
should_break = 1;
}
bi_free(num);
bi_free(num2);
bi_free(a_);
bi_free(b_);
bi_free(n_);
bi_free(n2);
bi_free(an);
if (should_break) break;
}
}
}
printf("%d\n", prod);
bi_terminate();
return 0;
}
int main() {
bi_initialize();
bigint sum = int_to_bi(1);
bigint last = int_to_bi(1);
int i, j;
for (i = 1; i <= (SIZE-1)/2; ++i) {
for (j = 0; j < 4; ++j) {
last = bi_add(last, bi_int_multiply(int_to_bi(i), 2));
sum = bi_add(sum, bi_copy(last));
}
}
bi_print(stdout, sum);
printf("\n");
bi_free(last);
bi_terminate();
return 0;
}
/*
* Work out g1, g3, g5, g7... etc for the sliding-window algorithm
*/
static void ICACHE_FLASH_ATTR precompute_slide_window(BI_CTX *ctx, int window, bigint *g1) {
int k = 1, i;
bigint *g2;
for (i = 0; i < window - 1; i++) { /* compute 2^(window-1) */
k <<= 1;
}
ctx->g = (bigint **)os_malloc(k * sizeof(bigint *));
ctx->g[0] = bi_clone(ctx, g1);
bi_permanent(ctx->g[0]);
g2 = bi_residue(ctx, bi_square(ctx, ctx->g[0])); /* g^2 */
for (i = 1; i < k; i++) {
ctx->g[i] = bi_residue(ctx, bi_multiply(ctx, ctx->g[i - 1], bi_copy(g2)));
bi_permanent(ctx->g[i]);
}
bi_free(ctx, g2);
ctx->window = k;
}
int main() {
bi_initialize();
bigint last = int_to_bi(1);
int i, j;
int number_of_primes = 0;
for (i = 1;; ++i) {
for (j = 0; j < 4; ++j) {
last = bi_add(last, bi_int_multiply(int_to_bi(i), 2));
if (j != 3 && bi_is_probable_prime(bi_copy(last), 4)) {
++number_of_primes;
}
}
if ((double)number_of_primes / (4*i+1) < 0.1) {
printf("%d\n", i*2+1);
break;
}
#ifdef DEBUG
printf("%d/%d on iteration %d ~%f\n", number_of_primes, (4*i+1), i, (float)number_of_primes/(4*i+1));
#endif
}
bi_free(last);
bi_terminate();
return 0;
}
/**
* @brief Does both division and modulo calculations.
*
* Used extensively when doing classical reduction.
* @param ctx [in] The bigint session context.
* @param u [in] A bigint which is the numerator.
* @param v [in] Either the denominator or the modulus depending on the mode.
* @param is_mod [n] Determines if this is a normal division (0) or a reduction
* (1).
* @return The result of the division/reduction.
*/
bigint * ICACHE_FLASH_ATTR bi_divide(BI_CTX *ctx, bigint *u, bigint *v, int is_mod)
{
int n = v->size, m = u->size-n;
int j = 0, orig_u_size = u->size;
uint8_t mod_offset = ctx->mod_offset;
comp d;
bigint *quotient, *tmp_u;
comp q_dash;
check(u);
check(v);
/* if doing reduction and we are < mod, then return mod */
if (is_mod && bi_compare(v, u) > 0)
{
bi_free(ctx, v);
return u;
}
quotient = alloc(ctx, m+1);
tmp_u = alloc(ctx, n+1);
v = trim(v); /* make sure we have no leading 0's */
d = (comp)((long_comp)COMP_RADIX/(V1+1));
/* clear things to start with */
memset(quotient->comps, 0, ((quotient->size)*COMP_BYTE_SIZE));
/* normalise */
if (d > 1)
{
u = bi_int_multiply(ctx, u, d);
if (is_mod)
{
v = ctx->bi_normalised_mod[mod_offset];
}
else
{
v = bi_int_multiply(ctx, v, d);
}
}
if (orig_u_size == u->size) /* new digit position u0 */
{
more_comps(u, orig_u_size + 1);
}
do
{
/* get a temporary short version of u */
memcpy(tmp_u->comps, &u->comps[u->size-n-1-j], (n+1)*COMP_BYTE_SIZE);
/* calculate q' */
if (U(0) == V1)
{
q_dash = COMP_RADIX-1;
}
else
{
q_dash = (comp)(((long_comp)U(0)*COMP_RADIX + U(1))/V1);
if (v->size > 1 && V2)
{
/* we are implementing the following:
if (V2*q_dash > (((U(0)*COMP_RADIX + U(1) -
q_dash*V1)*COMP_RADIX) + U(2))) ... */
comp inner = (comp)((long_comp)COMP_RADIX*U(0) + U(1) -
(long_comp)q_dash*V1);
if ((long_comp)V2*q_dash > (long_comp)inner*COMP_RADIX + U(2))
{
q_dash--;
}
}
}
/* multiply and subtract */
if (q_dash)
{
int is_negative;
tmp_u = bi_subtract(ctx, tmp_u,
bi_int_multiply(ctx, bi_copy(v), q_dash), &is_negative);
more_comps(tmp_u, n+1);
Q(j) = q_dash;
/* add back */
if (is_negative)
{
Q(j)--;
tmp_u = bi_add(ctx, tmp_u, bi_copy(v));
/* lop off the carry */
tmp_u->size--;
v->size--;
}
}
else
{
Q(j) = 0;
}
/* copy back to u */
memcpy(&u->comps[u->size-n-1-j], tmp_u->comps, (n+1)*COMP_BYTE_SIZE);
} while (++j <= m);
bi_free(ctx, tmp_u);
bi_free(ctx, v);
if (is_mod) /* get the remainder */
{
bi_free(ctx, quotient);
return bi_int_divide(ctx, trim(u), d);
}
else /* get the quotient */
{
bi_free(ctx, u);
return trim(quotient);
}
}
int main(int argc, char *argv[])
{
#ifdef CONFIG_SSL_CERT_VERIFICATION
RSA_CTX *rsa_ctx = NULL;
BI_CTX *ctx;
bigint *bi_data, *bi_res;
float diff;
int res = 1;
struct timeval tv_old, tv_new;
const char *plaintext;
uint8_t compare[MAX_KEY_BYTE_SIZE];
int i, max_biggie = 10; /* really crank performance */
int len;
uint8_t *buf;
/**
* 512 bit key
*/
plaintext = /* 64 byte number */
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^";
len = get_file("../ssl/test/axTLS.key_512", &buf);
asn1_get_private_key(buf, len, &rsa_ctx);
ctx = rsa_ctx->bi_ctx;
bi_data = bi_import(ctx, (uint8_t *)plaintext, strlen(plaintext));
bi_res = RSA_public(rsa_ctx, bi_data);
bi_data = bi_res; /* reuse again */
gettimeofday(&tv_old, NULL);
for (i = 0; i < max_biggie; i++)
{
bi_res = RSA_private(rsa_ctx, bi_copy(bi_data));
if (i < max_biggie-1)
{
bi_free(ctx, bi_res);
}
}
gettimeofday(&tv_new, NULL);
bi_free(ctx, bi_data);
diff = (tv_new.tv_sec-tv_old.tv_sec)*1000 +
(tv_new.tv_usec-tv_old.tv_usec)/1000;
printf("512 bit decrypt time: %.2fms\n", diff/max_biggie);
TTY_FLUSH();
bi_export(ctx, bi_res, compare, 64);
RSA_free(rsa_ctx);
free(buf);
if (memcmp(plaintext, compare, 64) != 0)
goto end;
/**
* 1024 bit key
*/
plaintext = /* 128 byte number */
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^"
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^";
len = get_file("../ssl/test/axTLS.key_1024", &buf);
rsa_ctx = NULL;
asn1_get_private_key(buf, len, &rsa_ctx);
ctx = rsa_ctx->bi_ctx;
bi_data = bi_import(ctx, (uint8_t *)plaintext, strlen(plaintext));
bi_res = RSA_public(rsa_ctx, bi_data);
bi_data = bi_res; /* reuse again */
gettimeofday(&tv_old, NULL);
for (i = 0; i < max_biggie; i++)
{
bi_res = RSA_private(rsa_ctx, bi_copy(bi_data));
if (i < max_biggie-1)
{
bi_free(ctx, bi_res);
}
}
gettimeofday(&tv_new, NULL);
bi_free(ctx, bi_data);
diff = (tv_new.tv_sec-tv_old.tv_sec)*1000 +
(tv_new.tv_usec-tv_old.tv_usec)/1000;
printf("1024 bit decrypt time: %.2fms\n", diff/max_biggie);
TTY_FLUSH();
bi_export(ctx, bi_res, compare, 128);
RSA_free(rsa_ctx);
free(buf);
if (memcmp(plaintext, compare, 128) != 0)
goto end;
/**
* 2048 bit key
*/
plaintext = /* 256 byte number */
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^"
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^"
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^"
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^";
len = get_file("../ssl/test/axTLS.key_2048", &buf);
rsa_ctx = NULL;
asn1_get_private_key(buf, len, &rsa_ctx);
ctx = rsa_ctx->bi_ctx;
bi_data = bi_import(ctx, (uint8_t *)plaintext, strlen(plaintext));
bi_res = RSA_public(rsa_ctx, bi_data);
bi_data = bi_res; /* reuse again */
gettimeofday(&tv_old, NULL);
for (i = 0; i < max_biggie; i++)
{
bi_res = RSA_private(rsa_ctx, bi_copy(bi_data));
if (i < max_biggie-1)
{
bi_free(ctx, bi_res);
}
}
gettimeofday(&tv_new, NULL);
bi_free(ctx, bi_data);
diff = (tv_new.tv_sec-tv_old.tv_sec)*1000 +
(tv_new.tv_usec-tv_old.tv_usec)/1000;
printf("2048 bit decrypt time: %.2fms\n", diff/max_biggie);
TTY_FLUSH();
bi_export(ctx, bi_res, compare, 256);
RSA_free(rsa_ctx);
free(buf);
if (memcmp(plaintext, compare, 256) != 0)
goto end;
/**
* 4096 bit key
*/
plaintext = /* 512 byte number */
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^"
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^"
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^"
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^"
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^"
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^"
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^"
"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ*^";
len = get_file("../ssl/test/axTLS.key_4096", &buf);
rsa_ctx = NULL;
asn1_get_private_key(buf, len, &rsa_ctx);
ctx = rsa_ctx->bi_ctx;
bi_data = bi_import(ctx, (uint8_t *)plaintext, strlen(plaintext));
gettimeofday(&tv_old, NULL);
bi_res = RSA_public(rsa_ctx, bi_data);
gettimeofday(&tv_new, NULL);
diff = (tv_new.tv_sec-tv_old.tv_sec)*1000 +
(tv_new.tv_usec-tv_old.tv_usec)/1000;
printf("4096 bit encrypt time: %.2fms\n", diff);
TTY_FLUSH();
bi_data = bi_res; /* reuse again */
gettimeofday(&tv_old, NULL);
for (i = 0; i < max_biggie; i++)
{
bi_res = RSA_private(rsa_ctx, bi_copy(bi_data));
if (i < max_biggie-1)
{
bi_free(ctx, bi_res);
}
}
gettimeofday(&tv_new, NULL);
bi_free(ctx, bi_data);
diff = (tv_new.tv_sec-tv_old.tv_sec)*1000 +
(tv_new.tv_usec-tv_old.tv_usec)/1000;
printf("4096 bit decrypt time: %.2fms\n", diff/max_biggie);
TTY_FLUSH();
bi_export(ctx, bi_res, compare, 512);
RSA_free(rsa_ctx);
free(buf);
if (memcmp(plaintext, compare, 512) != 0)
goto end;
/* done */
printf("Bigint performance testing complete\n");
res = 0;
end:
return res;
#else
return 0;
#endif
}
int main() {
bi_initialize();
bigint sum = int_to_bi(0);
int a,b,c,d,e,f,g,h,i,j;
int n;
for (a=9;a>0;--a) {
for (b=9;b>=0;--b) {
if (b==a) continue;
for (c=9;c>=0;--c) {
if (c==a||c==b) continue;
for (d=9;d>=0;--d) {
if (d==a||d==b||d==c) continue;
for (e=9;e>=0;--e) {
if (e==a||e==b||e==c||e==d) continue;
for (f=9;f>=0;--f) {
if (f==a||f==b||f==c||f==d||f==e) continue;
for (g=9;g>=0;--g) {
if (g==a||g==b||g==c||g==d||g==e||g==f) continue;
for (h=9;h>=0;--h) {
if (h==a||h==b||h==c||h==d||h==e||h==f||h==g) continue;
for (i=9;i>=0;--i) {
if (i==a||i==b||i==c||i==d||i==e||i==f||i==g||i==h) continue;
for (j=9;j>=0;--j) {
if (j==a||j==b||j==c||j==d||j==e||j==f||j==g||j==h||j==i) continue;
if ((b * 100 + c * 10 + d) % 2 == 0)
if ((c * 100 + d * 10 + e) % 3 == 0)
if ((d * 100 + e * 10 + f) % 5 == 0)
if ((e * 100 + f * 10 + g) % 7 == 0)
if ((f * 100 + g * 10 + h) % 11 == 0)
if ((g * 100 + h * 10 + i) % 13 == 0)
if ((h * 100 + i * 10 + j) % 17 == 0) {
n =
b * 100000000 +
c * 10000000 +
d * 1000000 +
e * 100000 +
f * 10000 +
g * 1000 +
h * 100 +
i * 10 +
j * 1;
sum = bi_add(sum, int_to_bi(n));
sum = bi_add(sum, bi_int_multiply(int_to_bi(1000000000), a));
#ifdef DEBUG
printf("%d%d%d%d%d%d%d%d%d%d\n", a,b,c,d,e,f,g,h,i,j);
bi_print(stdout,bi_copy(sum));
printf("\n");
#endif
}
}
}
}
}
}
}
}
}
}
}
bi_print(stdout,sum);
printf("\n");
bi_terminate();
return 0;
}