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;
}
void DH_generate_key(DH_CTX *dh_ctx)
{
BI_CTX *bi_ctx = bi_initialize();
int len = dh_ctx->len;
bigint *p = bi_import(bi_ctx, dh_ctx->p, len); //p modulus
bigint *g = bi_import(bi_ctx, dh_ctx->g, dh_ctx->glen); //generator
bigint *x, *gx;
bi_permanent(g);
//generate private key X
get_random_NZ(len, dh_ctx->x);
x = bi_import(bi_ctx, dh_ctx->x, len);
bi_permanent(x);
//calculate public key gx = g^x mod p
bi_set_mod(bi_ctx, p, BIGINT_M_OFFSET);
bi_ctx->mod_offset = BIGINT_M_OFFSET;
gx = bi_mod_power(bi_ctx, g, x);
bi_permanent(gx);
bi_export(bi_ctx, x, dh_ctx->x, len);
bi_export(bi_ctx, gx, dh_ctx->gx, len);
bi_depermanent(g);
bi_depermanent(x);
bi_depermanent(gx);
bi_free(bi_ctx, g);
bi_free(bi_ctx, x);
bi_free(bi_ctx, gx);
bi_free_mod(bi_ctx, BIGINT_M_OFFSET);
bi_terminate(bi_ctx);
}
/**
* Free up any RSA context resources.
*/
void RSA_free(RSA_CTX *rsa_ctx) {
BI_CTX *bi_ctx;
if (rsa_ctx == NULL) /* deal with ptrs that are null */
return;
bi_ctx = rsa_ctx->bi_ctx;
bi_depermanent(rsa_ctx->e);
bi_free(bi_ctx, rsa_ctx->e);
bi_free_mod(rsa_ctx->bi_ctx, BIGINT_M_OFFSET);
if (rsa_ctx->d) {
bi_depermanent(rsa_ctx->d);
bi_free(bi_ctx, rsa_ctx->d);
bi_depermanent(rsa_ctx->dP);
bi_depermanent(rsa_ctx->dQ);
bi_depermanent(rsa_ctx->qInv);
bi_free(bi_ctx, rsa_ctx->dP);
bi_free(bi_ctx, rsa_ctx->dQ);
bi_free(bi_ctx, rsa_ctx->qInv);
bi_free_mod(rsa_ctx->bi_ctx, BIGINT_P_OFFSET);
bi_free_mod(rsa_ctx->bi_ctx, BIGINT_Q_OFFSET);
}
bi_terminate(bi_ctx);
free(rsa_ctx);
}
/**
* Free up any RSA context resources.
*/
void ICACHE_FLASH_ATTR RSA_free(RSA_CTX *rsa_ctx)
{
BI_CTX *bi_ctx;
if (rsa_ctx == NULL) /* deal with ptrs that are null */
return;
bi_ctx = rsa_ctx->bi_ctx;
bi_depermanent(rsa_ctx->e);
bi_free(bi_ctx, rsa_ctx->e);
bi_free_mod(rsa_ctx->bi_ctx, BIGINT_M_OFFSET);
if (rsa_ctx->d)
{
bi_depermanent(rsa_ctx->d);
bi_free(bi_ctx, rsa_ctx->d);
#ifdef CONFIG_BIGINT_CRT
bi_depermanent(rsa_ctx->dP);
bi_depermanent(rsa_ctx->dQ);
bi_depermanent(rsa_ctx->qInv);
bi_free(bi_ctx, rsa_ctx->dP);
bi_free(bi_ctx, rsa_ctx->dQ);
bi_free(bi_ctx, rsa_ctx->qInv);
bi_free_mod(rsa_ctx->bi_ctx, BIGINT_P_OFFSET);
bi_free_mod(rsa_ctx->bi_ctx, BIGINT_Q_OFFSET);
#endif
}
bi_terminate(bi_ctx);
os_free(rsa_ctx);
}
void DH_compute_key(DH_CTX *dh_ctx)
{
BI_CTX *bi_ctx = bi_initialize();
int len = dh_ctx->len;
bigint *p = bi_import(bi_ctx, dh_ctx->p, len); //p modulus
bigint *x = bi_import(bi_ctx, dh_ctx->x, len); //private key
bigint *gy = bi_import(bi_ctx, dh_ctx->gy, len); //public key(peer)
bigint *k; //negotiated(session) key
bi_permanent(x);
bi_permanent(gy);
//calculate session key k = gy^x mod p
bi_set_mod(bi_ctx, p, BIGINT_M_OFFSET);
bi_ctx->mod_offset = BIGINT_M_OFFSET;
k = bi_mod_power(bi_ctx, gy, x);
bi_permanent(k);
bi_export(bi_ctx, k, dh_ctx->k, len);
bi_depermanent(x);
bi_depermanent(gy);
bi_depermanent(k);
bi_free(bi_ctx, x);
bi_free(bi_ctx, gy);
bi_free(bi_ctx, k);
bi_free_mod(bi_ctx, BIGINT_M_OFFSET);
bi_terminate(bi_ctx);
}
static bigint * ICACHE_FLASH_ATTR regular_multiply(BI_CTX *ctx, bigint *bia, bigint *bib,
int inner_partial, int outer_partial)
{
int i = 0, j;
int n = bia->size;
int t = bib->size;
bigint *biR = alloc(ctx, n + t);
comp *sr = biR->comps;
comp *sa = bia->comps;
comp *sb = bib->comps;
check(bia);
check(bib);
/* clear things to start with */
memset(biR->comps, 0, ((n+t)*COMP_BYTE_SIZE));
do
{
long_comp tmp;
comp carry = 0;
int r_index = i;
j = 0;
if (outer_partial && outer_partial-i > 0 && outer_partial < n)
{
r_index = outer_partial-1;
j = outer_partial-i-1;
}
do
{
if (inner_partial && r_index >= inner_partial)
{
break;
}
tmp = sr[r_index] + ((long_comp)sa[j])*sb[i] + carry;
sr[r_index++] = (comp)tmp; /* downsize */
carry = tmp >> COMP_BIT_SIZE;
} while (++j < n);
sr[r_index] = carry;
} while (++i < t);
bi_free(ctx, bia);
bi_free(ctx, bib);
return trim(biR);
}
/*
* 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));
}
/**
* @brief Used when cleaning various bigints at the end of a session.
* @param ctx [in] The bigint session context.
* @param mod_offset [in] The offset to use.
* @see bi_set_mod().
*/
void ICACHE_FLASH_ATTR bi_free_mod(BI_CTX *ctx, int mod_offset) {
bi_depermanent(ctx->bi_mod[mod_offset]);
bi_free(ctx, ctx->bi_mod[mod_offset]);
#if defined (CONFIG_BIGINT_MONTGOMERY)
bi_depermanent(ctx->bi_RR_mod_m[mod_offset]);
bi_depermanent(ctx->bi_R_mod_m[mod_offset]);
bi_free(ctx, ctx->bi_RR_mod_m[mod_offset]);
bi_free(ctx, ctx->bi_R_mod_m[mod_offset]);
#elif defined(CONFIG_BIGINT_BARRETT)
bi_depermanent(ctx->bi_mu[mod_offset]);
bi_free(ctx, ctx->bi_mu[mod_offset]);
#endif
bi_depermanent(ctx->bi_normalised_mod[mod_offset]);
bi_free(ctx, ctx->bi_normalised_mod[mod_offset]);
}
// Initialize B object by placing all Raws into one Bi
// Called on B construction
void b_init(B *b) {
unsigned int i, index;
// Destruct existing clusters
for(i=0; i<b->nclust; i++) {
bi_free(b->bi[i]);
}
b->nclust=0;
// Add the one cluster and initialize its "birth" information
b_add_bi(b, bi_new(b->nraw));
strcpy(b->bi[0]->birth_type, "I");
b->bi[0]->birth_pval = 0.0;
b->bi[0]->birth_fold = 1.0;
b->bi[0]->birth_e = b->reads;
b->nalign = 0;
b->nshroud = 0;
// Add all raws to that cluster
for (index=0; index<b->nraw; index++) {
bi_add_raw(b->bi[0], b->raw[index]);
}
bi_census(b->bi[0]);
bi_assign_center(b->bi[0]); // Makes cluster center sequence
}
/**
* @brief Take a bigint and convert it into a byte sequence.
*
* This is useful after a decrypt operation.
* @param ctx [in] The bigint session context.
* @param x [in] The bigint to be converted.
* @param data [out] The converted data as a byte stream.
* @param size [in] The maximum size of the byte stream. Unused bytes will be
* zeroed.
*/
void ICACHE_FLASH_ATTR bi_export(BI_CTX *ctx, bigint *x, uint8_t *data, int size)
{
int i, j, k = size-1;
check(x);
memset(data, 0, size); /* ensure all leading 0's are cleared */
for (i = 0; i < x->size; i++)
{
for (j = 0; j < COMP_BYTE_SIZE; j++)
{
comp mask = 0xff << (j*8);
int num = (x->comps[i] & mask) >> (j*8);
data[k--] = num;
if (k < 0)
{
goto buf_done;
}
}
}
buf_done:
bi_free(ctx, x);
}
/**
* @brief Perform a subtraction operation between two bigints.
* @param ctx [in] The bigint session context.
* @param bia [in] A bigint.
* @param bib [in] Another bigint.
* @param is_negative [out] If defined, indicates that the result was negative.
* is_negative may be null.
* @return The result of the subtraction. The result is always positive.
*/
bigint * ICACHE_FLASH_ATTR bi_subtract(BI_CTX *ctx,
bigint *bia, bigint *bib, int *is_negative)
{
int n = bia->size;
comp *pa, *pb, carry = 0;
check(bia);
check(bib);
more_comps(bib, n);
pa = bia->comps;
pb = bib->comps;
do
{
comp sl, rl, cy1;
sl = *pa - *pb++;
rl = sl - carry;
cy1 = sl > *pa;
carry = cy1 | (rl > sl);
*pa++ = rl;
} while (--n != 0);
if (is_negative) /* indicate a negative result */
{
*is_negative = carry;
}
bi_free(ctx, trim(bib)); /* put bib back to the way it was */
return trim(bia);
}
static PGPError
Teardown (PGPPipeline *myself)
{
DefModContext *context;
PGPContextRef cdkContext;
pgpAssertAddrValid( myself, PGPPipeline );
cdkContext = myself->cdkContext;
pgpAssert (myself);
pgpAssert (myself->magic == DEFMODMAGIC);
context = (DefModContext *)myself->priv;
pgpAssert (context);
if (context->tail)
context->tail->teardown (context->tail);
bi_free (context->zbcontext); /* Free bits data structures */
ct_free (context->ztcontext); /* Free code tree buffers */
lm_free (context->zdcontext); /* Free longest match buffers */
byteFifoDestroy (context->fifo);
pgpClearMemory( context, sizeof (*context));
pgpContextMemFree( cdkContext, context);
return kPGPError_NoErr;
}
/**
* @brief Perform an addition operation between two bigints.
* @param ctx [in] The bigint session context.
* @param bia [in] A bigint.
* @param bib [in] Another bigint.
* @return The result of the addition.
*/
bigint * ICACHE_FLASH_ATTR bi_add(BI_CTX *ctx, bigint *bia, bigint *bib)
{
int n;
comp carry = 0;
comp *pa, *pb;
check(bia);
check(bib);
n = max(bia->size, bib->size);
more_comps(bia, n+1);
more_comps(bib, n);
pa = bia->comps;
pb = bib->comps;
do
{
comp sl, rl, cy1;
sl = *pa + *pb++;
rl = sl + carry;
cy1 = sl < *pa;
carry = cy1 | (rl < sl);
*pa++ = rl;
} while (--n != 0);
*pa = carry; /* do overflow */
bi_free(ctx, bib);
return trim(bia);
}
/* from DAAUtil */
bi_ptr project_into_group_gamma( bi_ptr base, TSS_DAA_PK_internal *issuer_pk) {
bi_t exponent; bi_new( exponent);
bi_ptr capital_gamma = issuer_pk->capitalGamma;
bi_ptr rho = issuer_pk->rho;
bi_ptr zeta = bi_new_ptr();
if( capital_gamma == NULL ||
rho == NULL ||
zeta == NULL) return NULL;
// exponent = capital_gamma - 1
bi_sub( exponent, capital_gamma, bi_1);
// exponent = exponent / rho
bi_div( exponent, exponent, rho);
// zeta = ( base ^ exponent) % capital_gamma
LogDebug("project_into_group_gamma: rho [%ld]:%s",
bi_nbin_size( rho), bi_2_hex_char( rho));
LogDebug("project_into_group_gamma: base[%ld]:%s",
bi_nbin_size( base), bi_2_hex_char( base));
LogDebug("project_into_group_gamma: exponent [%ld]:%s",
bi_nbin_size( exponent), bi_2_hex_char( exponent));
LogDebug("project_into_group_gamma: capitalGamma[%ld]:%s",
bi_nbin_size( capital_gamma),
bi_2_hex_char( capital_gamma));
bi_mod_exp( zeta, base, exponent, capital_gamma);
LogDebug("project_into_group_gamma: result:%s", bi_2_hex_char( zeta));
bi_free( exponent);
return zeta;
}
/**
* @brief Perform a modular exponentiation using a temporary modulus.
*
* We need this function to check the signatures of certificates. The modulus
* of this function is temporary as it's just used for authentication.
* @param ctx [in] The bigint session context.
* @param bi [in] The bigint to perform the exp/mod.
* @param bim [in] The temporary modulus.
* @param biexp [in] The bigint exponent.
* @return The result of the mod exponentiation operation
* @see bi_set_mod().
*/
bigint *ICACHE_FLASH_ATTR bi_mod_power2(BI_CTX *ctx, bigint *bi, bigint *bim, bigint *biexp) {
bigint *biR, *tmp_biR;
/* Set up a temporary bigint context and transfer what we need between
* them. We need to do this since we want to keep the original modulus
* which is already in this context. This operation is only called when
* doing peer verification, and so is not expensive :-) */
BI_CTX *tmp_ctx = bi_initialize();
bi_set_mod(tmp_ctx, bi_clone(tmp_ctx, bim), BIGINT_M_OFFSET);
tmp_biR = bi_mod_power(tmp_ctx,
bi_clone(tmp_ctx, bi),
bi_clone(tmp_ctx, biexp));
biR = bi_clone(ctx, tmp_biR);
bi_free(tmp_ctx, tmp_biR);
bi_free_mod(tmp_ctx, BIGINT_M_OFFSET);
bi_terminate(tmp_ctx);
bi_free(ctx, bi);
bi_free(ctx, bim);
bi_free(ctx, biexp);
return biR;
}
inline bi_ptr apply_challenge( bi_ptr value, bi_ptr delta, bi_ptr c, bi_ptr capital_gamma) {
bi_ptr delta_tilde = bi_new_ptr();
bi_t c_negate;
if( delta_tilde == NULL) return NULL;
bi_new( c_negate);
bi_set( c_negate, c);
bi_negate( c_negate);
// delta_tilde = ( delta ^ (-c)) % capital_gamma
bi_mod_exp( delta_tilde, delta, c_negate, capital_gamma);
bi_free( c_negate);
// delta_tilde = (delta_tilde * value) % capital_gamma
return bi_mod( delta_tilde, bi_mul( delta_tilde, delta_tilde, value), capital_gamma);
}
/*
* Perform the actual square operion. It takes into account overflow.
*/
static bigint *ICACHE_FLASH_ATTR regular_square(BI_CTX *ctx, bigint *bi) {
int t = bi->size;
int i = 0, j;
bigint *biR = alloc(ctx, t * 2 + 1);
comp *w = biR->comps;
comp *x = bi->comps;
long_comp carry;
os_memset(w, 0, biR->size * COMP_BYTE_SIZE);
do {
long_comp tmp = w[2 * i] + (long_comp)x[i] * x[i];
w[2 * i] = (comp)tmp;
carry = tmp >> COMP_BIT_SIZE;
for (j = i + 1; j < t; j++) {
uint8_t c = 0;
long_comp xx = (long_comp)x[i] * x[j];
if ((COMP_MAX - xx) < xx) {
c = 1;
}
tmp = (xx << 1);
if ((COMP_MAX - tmp) < w[i + j]) {
c = 1;
}
tmp += w[i + j];
if ((COMP_MAX - tmp) < carry) {
c = 1;
}
tmp += carry;
w[i + j] = (comp)tmp;
carry = tmp >> COMP_BIT_SIZE;
if (c) {
carry += COMP_RADIX;
}
}
tmp = w[i + t] + carry;
w[i + t] = (comp)tmp;
w[i + t + 1] = tmp >> COMP_BIT_SIZE;
} while (++i < t);
bi_free(ctx, bi);
return trim(biR);
}
/**
* @brief Close the bigint context and free any resources.
*
* Free up any used memory - a check is done if all objects were not
* properly freed.
* @param ctx [in] The bigint session context.
*/
void ICACHE_FLASH_ATTR bi_terminate(BI_CTX *ctx) {
bi_depermanent(ctx->bi_radix);
bi_free(ctx, ctx->bi_radix);
if (ctx->active_count != 0) {
#ifdef CONFIG_SSL_FULL_MODE
ssl_printf("bi_terminate: there were %d un-freed bigints\n",
ctx->active_count);
#endif
return; /* wujg : org ---> abort(); */
}
bi_clear_cache(ctx);
os_free(ctx);
}
/**
* @brief Close the bigint context and free any resources.
*
* Free up any used memory - a check is done if all objects were not
* properly freed.
* @param ctx [in] The bigint session context.
*/
void bi_terminate(BI_CTX *ctx)
{
bi_depermanent(ctx->bi_radix);
bi_free(ctx, ctx->bi_radix);
if (ctx->active_count != 0) {
#ifdef CONFIG_SSL_FULL_MODE
printf("bi_terminate: there were %d un-freed bigints\n",
ctx->active_count);
#endif
abort();
}
bi_clear_cache(ctx);
free(ctx);
}
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;
}
/**
* Free an X.509 object's resources.
*/
void x509_free(X509_CTX *x509_ctx)
{
X509_CTX *next;
int i;
if (x509_ctx == NULL) /* if already null, then don't bother */
return;
for (i = 0; i < X509_NUM_DN_TYPES; i++)
{
free(x509_ctx->ca_cert_dn[i]);
free(x509_ctx->cert_dn[i]);
}
free(x509_ctx->signature);
#ifdef CONFIG_SSL_CERT_VERIFICATION
if (x509_ctx->digest)
{
bi_free(x509_ctx->rsa_ctx->bi_ctx, x509_ctx->digest);
}
if (x509_ctx->fingerprint)
{
free(x509_ctx->fingerprint);
}
if (x509_ctx->spki_sha256)
{
free(x509_ctx->spki_sha256);
}
if (x509_ctx->subject_alt_dnsnames)
{
for (i = 0; x509_ctx->subject_alt_dnsnames[i]; ++i)
free(x509_ctx->subject_alt_dnsnames[i]);
free(x509_ctx->subject_alt_dnsnames);
}
#endif
RSA_free(x509_ctx->rsa_ctx);
next = x509_ctx->next;
free(x509_ctx);
x509_free(next); /* clear the chain */
}
/*
* 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;
}
/**
* Perform a multiply between a bigint an an (unsigned) integer
*/
static bigint *ICACHE_FLASH_ATTR bi_int_multiply(BI_CTX *ctx, bigint *bia, comp b) {
int j = 0, n = bia->size;
bigint *biR = alloc(ctx, n + 1);
comp carry = 0;
comp *r = biR->comps;
comp *a = bia->comps;
check(bia);
/* clear things to start with */
os_memset(r, 0, ((n + 1)*COMP_BYTE_SIZE));
do {
long_comp tmp = *r + (long_comp)a[j] * b + carry;
*r++ = (comp)tmp; /* downsize */
carry = (comp)(tmp >> COMP_BIT_SIZE);
} while (++j < n);
*r = carry;
bi_free(ctx, bia);
return trim(biR);
}
static bool process_block(const struct bp_block *block, int64_t fpos)
{
struct blkinfo *bi = bi_new();
bu256_copy(&bi->hash, &block->sha256);
bp_block_copy_hdr(&bi->hdr, block);
bi->n_file = 0;
bi->n_pos = fpos;
struct blkdb_reorg reorg;
if (!blkdb_add(&db, bi, &reorg)) {
fprintf(plog, "brd: blkdb add fail\n");
goto err_out;
}
/* FIXME: support reorg */
assert(reorg.conn == 1);
assert(reorg.disconn == 0);
/* if best chain, mark TX's as spent */
if (bu256_equal(&db.best_chain->hash, &bi->hdr.sha256)) {
if (!spend_block(&uset, block, bi->height)) {
char hexstr[BU256_STRSZ];
bu256_hex(hexstr, &bi->hdr.sha256);
fprintf(plog,
"brd: block spend fail %u %s\n",
bi->height, hexstr);
/* FIXME: bad record is now in blkdb */
goto err_out;
}
}
return true;
err_out:
bi_free(bi);
return false;
}
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 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;
}
static bool blkdb_read_rec(struct blkdb *db, const struct p2p_message *msg)
{
struct blkinfo *bi;
struct const_buffer buf = { msg->data, msg->hdr.data_len };
if (strncmp(msg->hdr.command, "rec", 12))
return false;
bi = bi_new();
if (!bi)
return false;
/* deserialize record */
if (!deser_u256(&bi->hash, &buf))
goto err_out;
if (!deser_bp_block(&bi->hdr, &buf))
goto err_out;
/* verify that provided hash matches block header, as an additional
* self-verification step
*/
bp_block_calc_sha256(&bi->hdr);
if (!bu256_equal(&bi->hash, &bi->hdr.sha256))
goto err_out;
/* verify block may be added to chain, then add it */
struct blkdb_reorg dummy;
if (!blkdb_connect(db, bi, &dummy))
goto err_out;
return true;
err_out:
bi_free(bi);
return false;
}
/**
* @brief Perform a modular exponentiation.
*
* This function requires bi_set_mod() to have been called previously. This is
* one of the optimisations used for performance.
* @param ctx [in] The bigint session context.
* @param bi [in] The bigint on which to perform the mod power operation.
* @param biexp [in] The bigint exponent.
* @return The result of the mod exponentiation operation
* @see bi_set_mod().
*/
bigint * ICACHE_FLASH_ATTR bi_mod_power(BI_CTX *ctx, bigint *bi, bigint *biexp)
{
int i = find_max_exp_index(biexp), j, window_size = 1;
bigint *biR = int_to_bi(ctx, 1);
#if defined(CONFIG_BIGINT_MONTGOMERY)
uint8_t mod_offset = ctx->mod_offset;
if (!ctx->use_classical)
{
/* preconvert */
bi = bi_mont(ctx,
bi_multiply(ctx, bi, ctx->bi_RR_mod_m[mod_offset])); /* x' */
bi_free(ctx, biR);
biR = ctx->bi_R_mod_m[mod_offset]; /* A */
}
#endif
check(bi);
check(biexp);
#ifdef CONFIG_BIGINT_SLIDING_WINDOW
for (j = i; j > 32; j /= 5) /* work out an optimum size */
window_size++;
/* work out the slide constants */
precompute_slide_window(ctx, window_size, bi);
#else /* just one constant */
ctx->g = (bigint **)SSL_MALLOC(sizeof(bigint *));
ctx->g[0] = bi_clone(ctx, bi);
ctx->window = 1;
bi_permanent(ctx->g[0]);
#endif
/* if sliding-window is off, then only one bit will be done at a time and
* will reduce to standard left-to-right exponentiation */
do
{
if (exp_bit_is_one(biexp, i))
{
int l = i-window_size+1;
int part_exp = 0;
if (l < 0) /* LSB of exponent will always be 1 */
l = 0;
else
{
while (exp_bit_is_one(biexp, l) == 0)
l++; /* go back up */
}
/* build up the section of the exponent */
for (j = i; j >= l; j--)
{
biR = bi_residue(ctx, bi_square(ctx, biR));
if (exp_bit_is_one(biexp, j))
part_exp++;
if (j != l)
part_exp <<= 1;
}
part_exp = (part_exp-1)/2; /* adjust for array */
biR = bi_residue(ctx, bi_multiply(ctx, biR, ctx->g[part_exp]));
i = l-1;
}
else /* square it */
{
biR = bi_residue(ctx, bi_square(ctx, biR));
i--;
}
} while (i >= 0);
/* cleanup */
for (i = 0; i < ctx->window; i++)
{
bi_depermanent(ctx->g[i]);
bi_free(ctx, ctx->g[i]);
}
SSL_FREE(ctx->g);
bi_free(ctx, bi);
bi_free(ctx, biexp);
#if defined CONFIG_BIGINT_MONTGOMERY
return ctx->use_classical ? biR : bi_mont(ctx, biR); /* convert back */
#else /* CONFIG_BIGINT_CLASSICAL or CONFIG_BIGINT_BARRETT */
return biR;
#endif
}
/**
* @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);
}
}
/**
* Do some basic checks on the certificate chain.
*
* Certificate verification consists of a number of checks:
* - The date of the certificate is after the start date.
* - The date of the certificate is before the finish date.
* - A root certificate exists in the certificate store.
* - That the certificate(s) are not self-signed.
* - The certificate chain is valid.
* - The signature of the certificate is valid.
*/
int x509_verify(const CA_CERT_CTX *ca_cert_ctx, const X509_CTX *cert)
{
int ret = X509_OK, i = 0;
bigint *cert_sig;
X509_CTX *next_cert = NULL;
BI_CTX *ctx = NULL;
bigint *mod = NULL, *expn = NULL;
int match_ca_cert = 0;
struct timeval tv;
uint8_t is_self_signed = 0;
if (cert == NULL)
{
ret = X509_VFY_ERROR_NO_TRUSTED_CERT;
goto end_verify;
}
/* a self-signed certificate that is not in the CA store - use this
to check the signature */
if (asn1_compare_dn(cert->ca_cert_dn, cert->cert_dn) == 0)
{
is_self_signed = 1;
ctx = cert->rsa_ctx->bi_ctx;
mod = cert->rsa_ctx->m;
expn = cert->rsa_ctx->e;
}
gettimeofday(&tv, NULL);
/* check the not before date */
if (tv.tv_sec < cert->not_before)
{
ret = X509_VFY_ERROR_NOT_YET_VALID;
goto end_verify;
}
/* check the not after date */
if (tv.tv_sec > cert->not_after)
{
ret = X509_VFY_ERROR_EXPIRED;
goto end_verify;
}
next_cert = cert->next;
/* last cert in the chain - look for a trusted cert */
if (next_cert == NULL)
{
if (ca_cert_ctx != NULL)
{
/* go thu the CA store */
while (i < CONFIG_X509_MAX_CA_CERTS && ca_cert_ctx->cert[i])
{
if (asn1_compare_dn(cert->ca_cert_dn,
ca_cert_ctx->cert[i]->cert_dn) == 0)
{
/* use this CA certificate for signature verification */
match_ca_cert = 1;
ctx = ca_cert_ctx->cert[i]->rsa_ctx->bi_ctx;
mod = ca_cert_ctx->cert[i]->rsa_ctx->m;
expn = ca_cert_ctx->cert[i]->rsa_ctx->e;
break;
}
i++;
}
}
/* couldn't find a trusted cert (& let self-signed errors
be returned) */
if (!match_ca_cert && !is_self_signed)
{
ret = X509_VFY_ERROR_NO_TRUSTED_CERT;
goto end_verify;
}
}
else if (asn1_compare_dn(cert->ca_cert_dn, next_cert->cert_dn) != 0)
{
/* check the chain */
ret = X509_VFY_ERROR_INVALID_CHAIN;
goto end_verify;
}
else /* use the next certificate in the chain for signature verify */
{
ctx = next_cert->rsa_ctx->bi_ctx;
mod = next_cert->rsa_ctx->m;
expn = next_cert->rsa_ctx->e;
}
/* cert is self signed */
if (!match_ca_cert && is_self_signed)
{
ret = X509_VFY_ERROR_SELF_SIGNED;
goto end_verify;
}
/* check the signature */
cert_sig = sig_verify(ctx, cert->signature, cert->sig_len,
bi_clone(ctx, mod), bi_clone(ctx, expn));
if (cert_sig && cert->digest)
{
if (bi_compare(cert_sig, cert->digest) != 0)
ret = X509_VFY_ERROR_BAD_SIGNATURE;
bi_free(ctx, cert_sig);
}
else
{
ret = X509_VFY_ERROR_BAD_SIGNATURE;
}
if (ret)
goto end_verify;
/* go down the certificate chain using recursion. */
if (next_cert != NULL)
{
ret = x509_verify(ca_cert_ctx, next_cert);
}
end_verify:
return ret;
}