/* Division */
Rational bignum_div(Bignum _n, Bignum _m)
{
mpz_t n, m, tmp;
*n = *theBIGNUM(_n);
*m = *theBIGNUM(_m);
mpz_init(tmp);
mpz_mod(tmp, n, m);
/* Divided evenly */
if (mpz_sgn(tmp) == 0) {
mpz_cdiv_q(tmp, n, m);
return make_bignum(tmp);
} else {
mpz_t q;
ratio_t r;
mpz_gcd(tmp, n, m);
r = malloc(sizeof(struct ratio_t));
mpz_cdiv_q(q, n, tmp);
r->numerator = make_bignum(q);
mpz_cdiv_q(q, m, tmp);
r->denominator = make_bignum(q);
return make_ratio(r);
}
}
int main (int argc, char *argv[]) {
mpz_t c, m1, m2, pc, q1, q2, e, d1, d2, phi1, phi2, tmp1, tmp2,
key1, key2;
FILE *fp, *fp1;
char chars[3];
//initializations
mpz_inits(c, m1, m2, pc, q1, q2, e, d1, d2, phi1, phi2, tmp1, tmp2,
key1, key2, NULL);
//Welcome!
printf("Begin task 4 / 5...\n");
printf("*******************************\n");
printf("Welcome to fun with big numbers\n");
printf("Lets do some decryption\n");
printf("*******************************\n");
//Get needed input from file
fp = fopen("p4in.txt", "r");
gmp_fscanf(fp, "%Zd\n%Zd\n%Zd\n%Zd", &key1, &key2, &pc, &c);
gmp_printf("key1=%Zd\n\nkey2=%Zd\n\nCommon factor=%Zd\n\ncipher=%Zd\n\n",
key1, key2, pc, c);
fclose(fp);
//setup calculating needed values
mpz_cdiv_q(q1, key1, pc);
mpz_cdiv_q(q2, key2, pc);
mpz_set_ui(e, 65537);
mpz_sub_ui(tmp1, pc, 1);
mpz_sub_ui(tmp2, q1, 1);
mpz_mul(phi1, tmp1, tmp2);
mpz_sub_ui(tmp2, q2, 1);
mpz_mul(phi2, tmp1, tmp2);
mpz_invert(d1, e, phi1);
mpz_invert(d2, e, phi2);
//Lets try and decrypt
decrypt(&m1, c, d1, key1);
decrypt(&m2, c, d2, key2);
fp = fopen("p4out.txt", "w");
gmp_fprintf(fp, "%Zx\n%Zx\n", m1, m2);
fclose(fp);
mpz_clears(c, m1, m2, pc, q1, q2, e, d1, d2, phi1, phi2, tmp1, tmp2,
key1, key2, NULL);
fp = fopen("p4out.txt", "r");
chars[2] = 0;
while (fscanf(fp, "%c%c", chars, chars + 1) > 0){
printf("%c", (int)strtol(chars, NULL, 16));
}
fclose(fp);
return 0;
}
/* q = a / b */
static int
wrap_nettle_mpi_div(bigint_t q, const bigint_t a, const bigint_t b)
{
mpz_cdiv_q(TOMPZ(q), TOMPZ(a), TOMPZ(b));
return 0;
}
void make_headers(void)
{
mpz_t newk, oldk, thing, div;
mpz_init(newk);
mpz_init(thing);
mpz_ui_pow_ui(thing, 2, M);
mpz_init_set(div, thing);
mpz_init_set_ui(oldk, 3);
int size = SIZE;
for(int i = 0; i <= LEVELS; i++)
{
mpz_set_ui(newk, 0);
int r = 1;
int n;
while(mpz_get_ui(newk) < 3)
{
r++;
double bottom = mpz_get_d(oldk);
n = floor(((M+1)*log(2.0) + log((double) r))/log(bottom));
mpz_pow_ui(thing, oldk, n);
mpz_cdiv_q(newk, thing, div);
}
headers[i].chunksize = n;
headers[i].K = mpz_get_ui(oldk);
mpz_set(oldk,newk);
headers[i].size = size;
size = ceil((double)size/n);
}
fwrite(headers, sizeof(header), LEVELS + 1, output);
mpz_clear(oldk);
mpz_clear(div);
mpz_clear(thing);
mpz_clear(newk);
}
/*
* It is a function that performs Extended Euclid
* input: mpz_t of a, b, s and t
* output: variable a as the GCD and give s and t values
*/
void extendedEuclid(mpz_t a, mpz_t b, mpz_t s, mpz_t t){
mpz_t q, r, r1, r2,s1,s2,t1,t2, temp;
mpz_init(q);
mpz_init(r1);
mpz_init(r2);
mpz_init(temp);
mpz_set(r1, a);
mpz_set(r2, b);
mpz_init_set_str(r, "1", 10); //to prevent r from inheriting other value
mpz_init_set_str(s1, "1", 10);
mpz_init_set_str(s2, "0", 10);
mpz_init_set_str(t1, "0", 10);
mpz_init_set_str(t2, "1", 10);
while(mpz_cmp_ui(r2,0) != 0){
mpz_cdiv_q(q, r1, r2);
mpz_cdiv_r(r, r1, r2);
mpz_mul(temp, q, s2);
mpz_sub(s, s1, temp);
mpz_mul(temp, q, t2);
mpz_sub(t, t1, temp);
mpz_set(r1, r2);
mpz_set(r2, r);
mpz_set(s1, s2);
mpz_set(s2, s);
mpz_set(t1, t2);
mpz_set(t2, t);
}
mpz_set(s, s1);
mpz_set(t, t1);
mpz_set(a, r1);
}
/*
* Step 3 of bleichenbacher's algorithm : search space reduction
*/
int b98_update_boundaries(struct bleichenbacher_98_t *b98)
{
mpz_t min_r, max_r;
mpz_init(min_r);
mpz_mul(min_r, b98->a, b98->s );
mpz_sub(min_r, min_r, b98->max_range);
mpz_cdiv_q (min_r, min_r, b98->n);
if (!mpz_sgn(min_r))
mpz_add_ui(min_r, min_r, 1);
mpz_init(max_r);
mpz_mul(max_r, b98->b, b98->s );
mpz_sub(max_r, max_r, b98->min_range);
mpz_fdiv_q (max_r, max_r, b98->n);
if (mpz_cmp(min_r, max_r) > 0)
{
mpz_set(min_r, b98->r);
mpz_set(max_r, b98->r);
}
b98_update_a(b98->a, min_r, b98->s, b98->min_range, b98->max_range, b98->n );
b98_update_b(b98->b, max_r, b98->s, b98->min_range, b98->max_range, b98->n );
mpz_clear(min_r);
mpz_clear(max_r);
return 0x00;
}
static PyObject *
Pygmpy_c_div(PyObject *self, PyObject *args)
{
PyObject *x, *y;
PympzObject *q, *tempx, *tempy;
if (PyTuple_GET_SIZE(args) != 2) {
TYPE_ERROR("c_div() requires 'mpz','mpz' arguments");
return NULL;
}
x = PyTuple_GET_ITEM(args, 0);
y = PyTuple_GET_ITEM(args, 1);
if (!(q = Pympz_new()))
return NULL;
if (CHECK_MPZANY(x) && CHECK_MPZANY(y)) {
if (mpz_sgn(Pympz_AS_MPZ(y)) == 0) {
ZERO_ERROR("c_div() division by 0");
Py_DECREF((PyObject*)q);
return NULL;
}
mpz_cdiv_q(q->z, Pympz_AS_MPZ(x), Pympz_AS_MPZ(y));
}
else {
tempx = Pympz_From_Integer(x);
tempy = Pympz_From_Integer(y);
if (!tempx || !tempy) {
TYPE_ERROR("c_div() requires 'mpz','mpz' arguments");
Py_XDECREF((PyObject*)tempx);
Py_XDECREF((PyObject*)tempy);
Py_DECREF((PyObject*)q);
return NULL;
}
if (mpz_sgn(Pympz_AS_MPZ(tempy)) == 0) {
ZERO_ERROR("c_div() division by 0");
Py_DECREF((PyObject*)tempx);
Py_DECREF((PyObject*)tempy);
Py_DECREF((PyObject*)q);
return NULL;
}
mpz_cdiv_q(q->z, tempx->z, tempy->z);
Py_DECREF((PyObject*)tempx);
Py_DECREF((PyObject*)tempy);
}
return (PyObject*)q;
}
void getPrivateKey(mpz_t p, mpz_t q, mpz_t modulii, mpz_t publicKey, mpz_t privateKey) {
mpz_cdiv_q(q, modulii, p);
//q is now other prime
//get keys
getKeysWithPrimes(p, q, publicKey, privateKey);
}
void
fmpz_cdiv_q(fmpz_t f, const fmpz_t g, const fmpz_t h)
{
fmpz c1 = *g;
fmpz c2 = *h;
if (fmpz_is_zero(h))
{
printf("Exception: division by zero in fmpz_cdiv_q\n");
abort();
}
if (!COEFF_IS_MPZ(c1)) /* g is small */
{
if (!COEFF_IS_MPZ(c2)) /* h is also small */
{
fmpz q = c1 / c2; /* compute C quotient */
fmpz r = c1 - c2 * q; /* compute remainder */
if (r && ((c2 ^ r) > 0L)) /* r != 0, c2 and r same sign */
++q;
fmpz_set_si(f, q);
}
else /* h is large and g is small */
{
if ((c1 < 0L && fmpz_sgn(h) < 0) || (c1 > 0L && fmpz_sgn(h) > 0)) /* signs are the same */
fmpz_set_ui(f, 1); /* quotient is positive, round up to one */
else
fmpz_zero(f); /* quotient is zero, or negative, round up to zero */
}
}
else /* g is large */
{
__mpz_struct * mpz_ptr = _fmpz_promote(f);
if (!COEFF_IS_MPZ(c2)) /* h is small */
{
if (c2 > 0) /* h > 0 */
{
mpz_cdiv_q_ui(mpz_ptr, COEFF_TO_PTR(c1), c2);
}
else
{
mpz_fdiv_q_ui(mpz_ptr, COEFF_TO_PTR(c1), -c2);
mpz_neg(mpz_ptr, mpz_ptr);
}
}
else /* both are large */
{
mpz_cdiv_q(mpz_ptr, COEFF_TO_PTR(c1), COEFF_TO_PTR(c2));
}
_fmpz_demote_val(f); /* division by h may result in small value */
}
}
/**
* Applique euclide etendu a nb1 et nb2
* @param resultat tableau de 3 entiers : u, v et r tels que r=pgcd(nb1, nb2) et a*u+b*v=r
*/
void euclide_etendu(mpz_t nb1, mpz_t nb2, mpz_t *resultat){
mpz_t r, r1, u, u1, v, v1;
mpz_inits(r, r1, NULL);
mpz_set(r, nb1);
mpz_set(r1, nb2);
mpz_init_set_si(u, 1);
mpz_init_set_si(u1, 0);
mpz_init_set_si(v, 0);
mpz_init_set_si(v1, 1);
/* printf("u=%ld, v=%ld, pgcd=%ld\n",mpz_get_si(u),mpz_get_si(v), mpz_get_si(r)); */
mpz_t q, r_temp, u_temp, v_temp, tmp;
mpz_inits(q, r_temp, u_temp, v_temp, tmp, NULL);
while (mpz_get_si(r1) != 0){
mpz_cdiv_q(q,r,r1); /* Division entiere */
mpz_set(r_temp,r);
mpz_set(u_temp,u);
mpz_set(v_temp,v);
mpz_set(r,r1);
mpz_set(u,u1);
mpz_set(v,v1);
mpz_mul(tmp, q, r1);
mpz_sub(r1, r_temp, tmp);
/* r1=r_temp-q*r1; */
mpz_mul(tmp, q, u1);
mpz_sub(u1, u_temp, tmp);
mpz_mul(tmp, q, v1);
mpz_sub(v1, v_temp, tmp);
}
if(mpz_get_si(r)<0){
mpz_neg(u,u);
mpz_neg(v,v);
mpz_neg(r,r);
}
mpz_set(resultat[0],u);
mpz_set(resultat[1],v);
mpz_set(resultat[2],r);
/* Creer une fonction */
/* Clear */
mpz_clear(r);
mpz_clear(r1);
mpz_clear(u);
mpz_clear(u1);
mpz_clear(v);
mpz_clear(v1);
}
static Variant HHVM_FUNCTION(gmp_div_q,
const Variant& dataA,
const Variant& dataB,
int64_t round = GMP_ROUND_ZERO) {
mpz_t gmpDataA, gmpDataB, gmpReturn;
if (!variantToGMPData(cs_GMP_FUNC_NAME_GMP_DIV_Q, gmpDataA, dataA)) {
return false;
}
if (!variantToGMPData(cs_GMP_FUNC_NAME_GMP_DIV_Q, gmpDataB, dataB)) {
mpz_clear(gmpDataA);
return false;
}
if (mpz_sgn(gmpDataB) == 0) {
mpz_clear(gmpDataA);
mpz_clear(gmpDataB);
raise_warning(cs_GMP_INVALID_VALUE_MUST_NOT_BE_ZERO,
cs_GMP_FUNC_NAME_GMP_DIV_Q);
return false;
}
mpz_init(gmpReturn);
switch (round)
{
case GMP_ROUND_ZERO:
mpz_tdiv_q(gmpReturn, gmpDataA, gmpDataB);
break;
case GMP_ROUND_PLUSINF:
mpz_cdiv_q(gmpReturn, gmpDataA, gmpDataB);
break;
case GMP_ROUND_MINUSINF:
mpz_fdiv_q(gmpReturn, gmpDataA, gmpDataB);
break;
default:
mpz_clear(gmpDataA);
mpz_clear(gmpDataB);
mpz_clear(gmpReturn);
return null_variant;
}
Variant ret = NEWOBJ(GMPResource)(gmpReturn);
mpz_clear(gmpDataA);
mpz_clear(gmpDataB);
mpz_clear(gmpReturn);
return ret;
}
static PyObject *
Pympq_ceil(PyObject *self, PyObject *other)
{
PympzObject *result;
if ((result = (PympzObject*)Pympz_new())) {
mpz_cdiv_q(result->z,
mpq_numref(Pympq_AS_MPQ(self)),
mpq_denref(Pympq_AS_MPQ(self)));
}
return (PyObject*)result;
}
/*
* Step 2.a of bleichenbacher's algorithm : initial search
*/
int b98_initial_search(struct bleichenbacher_98_t *b98)
{
int pad_check = 0x00;
mpz_cdiv_q (b98->s, b98->n, b98->max_range);
while(!pad_check)
{
mpz_add_ui(b98->s, b98->s, 1);
pad_check = b98_check_padding(b98);
}
return 0x00;
}
static int
transform_sections (mpz_t X1, mpz_t X2, mpz_t no_of_elements,
gfc_expr * l_start, gfc_expr * l_end, gfc_expr * l_stride,
gfc_expr * r_start, gfc_expr * r_stride)
{
if (NULL == l_start || NULL == l_end || NULL == r_start)
return 1;
/* TODO : Currently we check the dependency only when start, end and stride
are constant. We could also check for equal (variable) values, and
common subexpressions, eg. x vs. x+1. */
if (l_end->expr_type != EXPR_CONSTANT
|| l_start->expr_type != EXPR_CONSTANT
|| r_start->expr_type != EXPR_CONSTANT
|| ((NULL != l_stride) && (l_stride->expr_type != EXPR_CONSTANT))
|| ((NULL != r_stride) && (r_stride->expr_type != EXPR_CONSTANT)))
{
return 1;
}
get_no_of_elements (no_of_elements, l_end, l_start, l_stride);
mpz_sub (X1, r_start->value.integer, l_start->value.integer);
if (l_stride != NULL)
mpz_cdiv_q (X1, X1, l_stride->value.integer);
if (r_stride == NULL)
mpz_set (X2, no_of_elements);
else
mpz_mul (X2, no_of_elements, r_stride->value.integer);
if (l_stride != NULL)
mpz_cdiv_q (X2, X2, r_stride->value.integer);
mpz_add (X2, X2, X1);
return 0;
}
enum lp_result PL_polyhedron_opt(Polyhedron *P, Value *obj, Value denom,
enum lp_dir dir, Value *opt)
{
int i;
int first = 1;
Value val, d;
enum lp_result res = lp_empty;
POL_ENSURE_VERTICES(P);
if (emptyQ(P))
return res;
value_init(val);
value_init(d);
for (i = 0; i < P->NbRays; ++ i) {
Inner_Product(P->Ray[i]+1, obj, P->Dimension+1, &val);
if (value_zero_p(P->Ray[i][0]) && value_notzero_p(val)) {
res = lp_unbounded;
break;
}
if (value_zero_p(P->Ray[i][1+P->Dimension])) {
if ((dir == lp_min && value_neg_p(val)) ||
(dir == lp_max && value_pos_p(val))) {
res = lp_unbounded;
break;
}
} else {
res = lp_ok;
value_multiply(d, denom, P->Ray[i][1+P->Dimension]);
if (dir == lp_min)
mpz_cdiv_q(val, val, d);
else
mpz_fdiv_q(val, val, d);
if (first || (dir == lp_min ? value_lt(val, *opt) :
value_gt(val, *opt)))
value_assign(*opt, val);
first = 0;
}
}
value_clear(d);
value_clear(val);
return res;
}
static void find_factors(mpz_t base)
{
char *str;
int res;
mpz_t i;
mpz_t half;
mpz_t two;
mpz_init_set_str(two, "2", 10);
mpz_init_set_str(i, "2", 10);
mpz_init(half);
mpz_cdiv_q(half, base, two);
str = mpz_to_str(base);
if (!str)
return;
/*
* We simply return the prime number itself if the base is prime.
* (We use the GMP probabilistic function with 10 repetitions).
*/
res = mpz_probab_prime_p(base, 10);
if (res) {
printf("%s is a prime number\n", str);
free(str);
return;
}
printf("Trial: prime factors for %s are:", str);
free(str);
do {
if (mpz_divisible_p(base, i) && verify_is_prime(i)) {
str = mpz_to_str(i);
if (!str)
return;
printf(" %s", str);
free(str);
}
mpz_nextprime(i, i);
} while (mpz_cmp(i, half) <= 0);
printf("\n");
}
/*
* It is a function that performs binomial theorem/expansion
* (a+b)^n = {n "summation" k} [n k]*a^(n-k)b*^k
* input: mpz_t n, mpz_t k and mpz_t *bin(pointer) to retrieve the output
* output: mpz_t *bin as a pointer
*/
void binomial(mpz_t n, mpz_t k, mpz_t *bin){
mpz_t f1;
mpz_t f2;
mpz_t f3;
mpz_t temp;
mpz_t denominator;
mpz_init(f1);
mpz_init(f2);
mpz_init(f3);
mpz_init(temp);
mpz_init(denominator);
factorial(k, &f1);
mpz_sub(temp, n, k);
factorial(temp, &f2);
mpz_mul(denominator, f1, f2);
//gmp_printf("%Zd\n", denominator);
factorial(n, &f3);
//gmp_printf("%Zd\n", f3);
mpz_cdiv_q(*bin, f3, denominator);
}
static void copy_solution(struct isl_vec *vec, int maximize, isl_int *opt,
isl_int *opt_denom, PipQuast *sol)
{
int i;
PipList *list;
isl_int tmp;
if (opt) {
if (opt_denom) {
isl_seq_cpy_from_pip(opt,
&sol->list->vector->the_vector[0], 1);
isl_seq_cpy_from_pip(opt_denom,
&sol->list->vector->the_deno[0], 1);
} else if (maximize)
mpz_fdiv_q(*opt, sol->list->vector->the_vector[0],
sol->list->vector->the_deno[0]);
else
mpz_cdiv_q(*opt, sol->list->vector->the_vector[0],
sol->list->vector->the_deno[0]);
}
if (!vec)
return;
isl_int_init(tmp);
isl_int_set_si(vec->el[0], 1);
for (i = 0, list = sol->list->next; list; ++i, list = list->next) {
isl_seq_cpy_from_pip(&vec->el[1 + i],
&list->vector->the_deno[0], 1);
isl_int_lcm(vec->el[0], vec->el[0], vec->el[1 + i]);
}
for (i = 0, list = sol->list->next; list; ++i, list = list->next) {
isl_seq_cpy_from_pip(&tmp, &list->vector->the_deno[0], 1);
isl_int_divexact(tmp, vec->el[0], tmp);
isl_seq_cpy_from_pip(&vec->el[1 + i],
&list->vector->the_vector[0], 1);
isl_int_mul(vec->el[1 + i], vec->el[1 + i], tmp);
}
isl_int_clear(tmp);
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("cdiv_q....");
fflush(stdout);
for (i = 0; i < 10000 * flint_test_multiplier(); i++)
{
fmpz_t a, b, c;
mpz_t d, e, f, g;
fmpz_init(a);
fmpz_init(b);
fmpz_init(c);
mpz_init(d);
mpz_init(e);
mpz_init(f);
mpz_init(g);
fmpz_randtest(a, state, 200);
fmpz_randtest_not_zero(b, state, 200);
fmpz_get_mpz(d, a);
fmpz_get_mpz(e, b);
fmpz_cdiv_q(c, a, b);
mpz_cdiv_q(f, d, e);
fmpz_get_mpz(g, c);
result = (mpz_cmp(f, g) == 0);
if (!result)
{
flint_printf("FAIL\n");
gmp_printf("d = %Zd, e = %Zd, f = %Zd, g = %Zd\n", d, e, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(c);
mpz_clear(d);
mpz_clear(e);
mpz_clear(f);
mpz_clear(g);
}
/* Check aliasing of a and b */
for (i = 0; i < 10000 * flint_test_multiplier(); i++)
{
fmpz_t a, c;
mpz_t d, f, g;
fmpz_init(a);
fmpz_init(c);
mpz_init(d);
mpz_init(f);
mpz_init(g);
fmpz_randtest_not_zero(a, state, 200);
fmpz_get_mpz(d, a);
fmpz_cdiv_q(c, a, a);
mpz_cdiv_q(f, d, d);
fmpz_get_mpz(g, c);
result = (mpz_cmp(f, g) == 0);
if (!result)
{
flint_printf("FAIL\n");
gmp_printf("d = %Zd, f = %Zd, g = %Zd\n", d, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(c);
mpz_clear(d);
mpz_clear(f);
mpz_clear(g);
}
/* Test aliasing of a and c */
for (i = 0; i < 10000 * flint_test_multiplier(); i++)
{
fmpz_t a, b;
mpz_t d, e, f, g;
fmpz_init(a);
fmpz_init(b);
mpz_init(d);
mpz_init(e);
mpz_init(f);
mpz_init(g);
fmpz_randtest(a, state, 200);
fmpz_randtest_not_zero(b, state, 200);
fmpz_get_mpz(d, a);
fmpz_get_mpz(e, b);
fmpz_cdiv_q(a, a, b);
mpz_cdiv_q(f, d, e);
fmpz_get_mpz(g, a);
result = (mpz_cmp(f, g) == 0);
if (!result)
{
flint_printf("FAIL\n");
gmp_printf("d = %Zd, e = %Zd, f = %Zd, g = %Zd\n", d, e, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(b);
mpz_clear(d);
mpz_clear(e);
mpz_clear(f);
mpz_clear(g);
}
/* Test aliasing of b and c */
for (i = 0; i < 10000 * flint_test_multiplier(); i++)
{
fmpz_t a, b;
mpz_t d, e, f, g;
fmpz_init(a);
fmpz_init(b);
mpz_init(d);
mpz_init(e);
mpz_init(f);
mpz_init(g);
fmpz_randtest(a, state, 200);
fmpz_randtest_not_zero(b, state, 200);
fmpz_get_mpz(d, a);
fmpz_get_mpz(e, b);
fmpz_cdiv_q(b, a, b);
mpz_cdiv_q(f, d, e);
fmpz_get_mpz(g, b);
result = (mpz_cmp(f, g) == 0);
if (!result)
{
flint_printf("FAIL\n");
gmp_printf("d = %Zd, e = %Zd, f = %Zd, g = %Zd\n", d, e, f, g);
abort();
}
fmpz_clear(a);
fmpz_clear(b);
mpz_clear(d);
mpz_clear(e);
mpz_clear(f);
mpz_clear(g);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void response(int sockfd)
{
int ret;
const char public_key[] = KEY_STRING;
const char id[] = ID_STRING;
const char http1[] = HTTP_RESPONSE_STRING1;
const char http2[] = HTTP_RESPONSE_STRING2;
char timestamp[36] = TIMESTAMP;
char private_key[MAX_BUFFER];
char buf[MAX_BUFFER];
int len = MAX_BUFFER;
char* pch = buf;
char* pend = pch + MAX_BUFFER;
char* pcheck = pch + Q1_STRING_LEN - 1;
int found = 0;
time_t tnow;
struct tm* now;
mpz_t x, xy, y;
mpz_inits(x, y, xy, 0);
//read
while (!found)
{
#ifdef _DEBUG
printf("reading...\n");
#endif
ret = read(sockfd, pch, pend - pch);
if (ret < 0)
{
perror("read failed...");
close(sockfd);
return;
}
if (ret == 0)
break;
pch += ret;
while (pch > pcheck)
{
if (*pcheck == ' ')
{
found = 1;
break;
}
pcheck++;
}
if (ret == 0)
{
printf("read ret 0...");
//might be health check
close(sockfd);
return;
}
}
if (strncmp(buf, Q1_STRING, Q1_STRING_LEN) != 0)
{
#ifdef _DEBUG
printf("unknown message...");
#endif
write(sockfd, HTTP_HEALTH_STRING, HTTP_HEALTH_STRING_LEN);
close(sockfd);
return;
}
//prepare response buffer
*pcheck = '\0';
#ifdef _DEBUG
printf("request: %s\n", buf);
#endif
mpz_set_str(xy, buf + Q1_STRING_LEN, 10);
mpz_set_str(x, public_key, 10);
mpz_cdiv_q(y, xy, x);
mpz_get_str(private_key, 10, y);
time(&tnow);
now = localtime(&tnow);
strftime(buf + DATE_OFFSET, sizeof(buf)-DATE_OFFSET, "%a, %d %b %Y %H:%M:%S %z", now);
buf[DATEEND_OFFSET] = '\n';
strftime(timestamp, sizeof(timestamp), "%Y:%m:%d %H:%M:%S", now);
len = strlen(private_key) + 1 + ID_STRING_LEN + 1 + strlen(timestamp) + 1;
sprintf(buf, "%s%d%s%s\n%s\n%s\n", http1, len, http2, private_key, id, timestamp);
#ifdef _DEBUG
printf("response: %s\n", buf);
#endif
//write
pend = buf + strlen(buf);
pch = buf;
while (pch < pend)
{
ret = write(sockfd, buf, pend - pch);
if (ret < 0)
{
perror("write failed...");
close(sockfd);
return;
}
pch += ret;
}
close(sockfd);
}
int main(int argc, char **argv) {
gettimeofday(&start_global, NULL);
print_lib_version();
mpz_init(N);
mpz_t B;
mpz_init(B);
unsigned long int uBase;
int64_t nb_primes;
modular_root_t *modular_roots;
uint64_t i, j;
if (mpz_init_set_str(N, argv[1], 10) == -1) {
printf("Cannot load N %s\n", argv[1]);
exit(2);
}
mpz_t sqrtN, rem;
mpz_init(sqrtN);
mpz_init(rem);
mpz_sqrtrem(sqrtN, rem, N);
if (mpz_cmp_ui(rem, 0) != 0) /* if not perfect square, calculate the ceiling */
mpz_add_ui(sqrtN, sqrtN, 1);
else /* N is a perfect square, factored! */
{
printf("\n<<<[FACTOR]>>> %s\n", mpz_get_str(NULL, 10, sqrtN));
return 0;
}
if (mpz_probab_prime_p(N, 10) > 0) /* don't bother factoring */
{
printf("N:%s is prime\n", mpz_get_str(NULL, 10, N));
exit(0);
}
OPEN_LOG_FILE("freq");
//--------------------------------------------------------
// calculate the smoothness base for the given N
//--------------------------------------------------------
get_smoothness_base(B, N); /* if N is too small, the program will surely fail, please consider a pen and paper instead */
uBase = mpz_get_ui(B);
printf("n: %s\tBase: %s\n", mpz_get_str(NULL, 10, N),
mpz_get_str(NULL, 10, B));
//--------------------------------------------------------
// sieve primes that are less than the smoothness base using Eratosthenes sieve
//--------------------------------------------------------
START_TIMER();
nb_primes = sieve_primes_up_to((int64_t) (uBase));
printf("\nPrimes found %" PRId64 " [Smoothness Base %lu]\n", nb_primes,
uBase);
STOP_TIMER_PRINT_TIME("\tEratosthenes Sieving done");
//--------------------------------------------------------
// fill the primes array with primes to which n is a quadratic residue
//--------------------------------------------------------
START_TIMER();
primes = calloc(nb_primes, sizeof(int64_t));
nb_qr_primes = fill_primes_with_quadratic_residue(primes, N);
/*for(i=0; i<nb_qr_primes; i++)
printf("%" PRId64 "\n", primes[i]);*/
printf("\nN-Quadratic primes found %" PRId64 "\n", nb_qr_primes);
STOP_TIMER_PRINT_TIME("\tQuadratic prime filtering done");
//--------------------------------------------------------
// calculate modular roots
//--------------------------------------------------------
START_TIMER();
modular_roots = calloc(nb_qr_primes, sizeof(modular_root_t));
mpz_t tmp, r1, r2;
mpz_init(tmp);
mpz_init(r1);
mpz_init(r2);
for (i = 0; i < nb_qr_primes; i++) {
mpz_set_ui(tmp, (unsigned long) primes[i]);
mpz_sqrtm(r1, N, tmp); /* calculate the modular root */
mpz_neg(r2, r1); /* -q mod n */
mpz_mod(r2, r2, tmp);
modular_roots[i].root1 = mpz_get_ui(r1);
modular_roots[i].root2 = mpz_get_ui(r2);
}
mpz_clear(tmp);
mpz_clear(r1);
mpz_clear(r2);
STOP_TIMER_PRINT_TIME("\nModular roots calculation done");
/*for(i=0; i<nb_qr_primes; i++)
{
printf("[%10" PRId64 "-> roots: %10u - %10u]\n", primes[i], modular_roots[i].root1, modular_roots[i].root2);
}*/
//--------------------------------------------------------
// ***** initialize the matrix *****
//--------------------------------------------------------
START_TIMER();
init_matrix(&matrix, nb_qr_primes + NB_VECTORS_OFFSET, nb_qr_primes);
mpz_init2(tmp_matrix_row, nb_qr_primes);
STOP_TIMER_PRINT_TIME("\nMatrix initialized");
//--------------------------------------------------------
// [Sieving]
//--------------------------------------------------------
START_TIMER();
mpz_t x, sieving_index, next_sieving_index;
unsigned long ui_index, SIEVING_STEP = 50000; /* we sieve for 50000 elements at each loop */
uint64_t p_pow;
smooth_number_t *x_squared;
x_squared = calloc(SIEVING_STEP, sizeof(smooth_number_t));
smooth_numbers = calloc(nb_qr_primes + NB_VECTORS_OFFSET,
sizeof(smooth_number_t));
mpz_init_set(x, sqrtN);
mpz_init_set(sieving_index, x);
mpz_init_set(next_sieving_index, x);
mpz_t p;
mpz_init(p);
mpz_t str;
mpz_init_set(str, sieving_index);
printf("\nSieving ...\n");
//--------------------------------------------------------
// Init before sieving
//--------------------------------------------------------
for (i = 0; i < SIEVING_STEP; i++) {
mpz_init(x_squared[i].value_x);
mpz_init(x_squared[i].value_x_squared);
/* the factors_exp array is used to keep track of exponents */
//x_squared[i].factors_exp = calloc(nb_qr_primes, sizeof(uint64_t));
/* we use directly the exponents vector modulo 2 to preserve space */mpz_init2(
x_squared[i].factors_vect, nb_qr_primes);
mpz_add_ui(x, x, 1);
}
int nb_smooth_per_round = 0;
char s[512];
//--------------------------------------------------------
// WHILE smooth numbers found less than the primes in the smooth base + NB_VECTORS_OFFSET
//--------------------------------------------------------
while (nb_smooth_numbers_found < nb_qr_primes + NB_VECTORS_OFFSET) {
nb_smooth_per_round = 0;
mpz_set(x, next_sieving_index); /* sieve numbers from sieving_index to sieving_index + sieving_step */
mpz_set(sieving_index, next_sieving_index);
printf("\r");
printf(
"\t\tSieving at: %s30 <--> Smooth numbers found: %" PRId64 "/%" PRId64 "",
mpz_get_str(NULL, 10, sieving_index), nb_smooth_numbers_found,
nb_qr_primes);
fflush(stdout);
for (i = 0; i < SIEVING_STEP; i++) {
mpz_set(x_squared[i].value_x, x);
mpz_pow_ui(x_squared[i].value_x_squared, x, 2); /* calculate value_x_squared <- x²-n */
mpz_sub(x_squared[i].value_x_squared, x_squared[i].value_x_squared,
N);
mpz_clear(x_squared[i].factors_vect);
mpz_init2(x_squared[i].factors_vect, nb_qr_primes); /* reconstruct a new fresh 0ed vector of size nb_qr_primes bits */
mpz_add_ui(x, x, 1);
}
mpz_set(next_sieving_index, x);
//--------------------------------------------------------
// eliminate factors in the x_squared array, those who are 'destructed' to 1 are smooth
//--------------------------------------------------------
for (i = 0; i < nb_qr_primes; i++) {
mpz_set_ui(p, (unsigned long) primes[i]);
mpz_set(x, sieving_index);
/* get the first multiple of p that is directly larger that sieving_index
* Quadratic SIEVING: all elements from this number and in positions multiples of root1 and root2
* are also multiples of p */
get_sieving_start_index(x, x, p, modular_roots[i].root1);
mpz_set(str, x);
mpz_sub(x, x, sieving_index); /* x contains index of first number that is divisible by p */
for (j = mpz_get_ui(x); j < SIEVING_STEP; j += primes[i]) {
p_pow = mpz_remove(x_squared[j].value_x_squared,
x_squared[j].value_x_squared, p); /* eliminate all factors of p */
if (p_pow & 1) /* mark bit if odd power of p exists in this x_squared[j] */
{
mpz_setbit(x_squared[j].factors_vect, i);
}
if (mpz_cmp_ui(x_squared[j].value_x_squared, 1) == 0) {
save_smooth_number(x_squared[j]);
nb_smooth_per_round++;
}
/* sieve next element located p steps from here */
}
/* same goes for root2 */
if (modular_roots[i].root2 == modular_roots[i].root1)
continue;
mpz_set(x, sieving_index);
get_sieving_start_index(x, x, p, modular_roots[i].root2);
mpz_set(str, x);
mpz_sub(x, x, sieving_index);
for (j = mpz_get_ui(x); j < SIEVING_STEP; j += primes[i]) {
p_pow = mpz_remove(x_squared[j].value_x_squared,
x_squared[j].value_x_squared, p);
if (p_pow & 1) {
mpz_setbit(x_squared[j].factors_vect, i);
}
if (mpz_cmp_ui(x_squared[j].value_x_squared, 1) == 0) {
save_smooth_number(x_squared[j]);
nb_smooth_per_round++;
}
}
}
//printf("\tSmooth numbers found %" PRId64 "\n", nb_smooth_numbers_found);
/*sprintf(s, "[start: %s - end: %s - step: %" PRId64 "] nb_smooth_per_round: %d",
mpz_get_str(NULL, 10, sieving_index),
mpz_get_str(NULL, 10, next_sieving_index),
SIEVING_STEP,
nb_smooth_per_round);
APPEND_TO_LOG_FILE(s);*/
}
STOP_TIMER_PRINT_TIME("\nSieving DONE");
uint64_t t = 0;
//--------------------------------------------------------
//the matrix ready, start Gauss elimination. The Matrix is filled on the call of save_smooth_number()
//--------------------------------------------------------
START_TIMER();
gauss_elimination(&matrix);
STOP_TIMER_PRINT_TIME("\nGauss elimination done");
//print_matrix_matrix(&matrix);
//print_matrix_identity(&matrix);
uint64_t row_index = nb_qr_primes + NB_VECTORS_OFFSET - 1; /* last row in the matrix */
int nb_linear_relations = 0;
mpz_t linear_relation_z, solution_z;
mpz_init(linear_relation_z);
mpz_init(solution_z);
get_matrix_row(linear_relation_z, &matrix, row_index--); /* get the last few rows in the Gauss eliminated matrix*/
while (mpz_cmp_ui(linear_relation_z, 0) == 0) {
nb_linear_relations++;
get_matrix_row(linear_relation_z, &matrix, row_index--);
}
printf("\tLinear dependent relations found : %d\n", nb_linear_relations);
//--------------------------------------------------------
// Factor
//--------------------------------------------------------
//We use the last linear relation to reconstruct our solution
START_TIMER();
printf("\nFactorizing..\n");
mpz_t solution_X, solution_Y;
mpz_init(solution_X);
mpz_init(solution_Y);
/* we start testing from the first linear relation encountered in the matrix */
for (j = nb_linear_relations; j > 0; j--) {
printf("Trying %d..\n", nb_linear_relations - j + 1);
mpz_set_ui(solution_X, 1);
mpz_set_ui(solution_Y, 1);
get_identity_row(solution_z, &matrix,
nb_qr_primes + NB_VECTORS_OFFSET - j + 1);
for (i = 0; i < nb_qr_primes; i++) {
if (mpz_tstbit(solution_z, i)) {
mpz_mul(solution_X, solution_X, smooth_numbers[i].value_x);
mpz_mod(solution_X, solution_X, N); /* reduce x to modulo N */
mpz_mul(solution_Y, solution_Y,
smooth_numbers[i].value_x_squared);
/*TODO: handling huge stuff here, there is no modulo N like in the solution_X case!
* eliminate squares as long as you go*/
}
}
mpz_sqrt(solution_Y, solution_Y);
mpz_mod(solution_Y, solution_Y, N); /* y = sqrt(MUL(xi²-n)) mod N */
mpz_sub(solution_X, solution_X, solution_Y);
mpz_gcd(solution_X, solution_X, N);
if (mpz_cmp(solution_X, N) != 0 && mpz_cmp_ui(solution_X, 1) != 0) /* factor can be 1 or N, try another relation */
break;
}
mpz_cdiv_q(solution_Y, N, solution_X);
printf("\n>>>>>>>>>>> FACTORED %s =\n", mpz_get_str(NULL, 10, N));
printf("\tFactor 1: %s \n\tFactor 2: %s", mpz_get_str(NULL, 10, solution_X),
mpz_get_str(NULL, 10, solution_Y));
/*sprintf(s, "\n>>>>>>>>>>> FACTORED %s =\n", mpz_get_str(NULL, 10, N));
APPEND_TO_LOG_FILE(s);
sprintf(s, "\tFactor 1: %s \n\tFactor 2: %s", mpz_get_str(NULL, 10, solution_X), mpz_get_str(NULL, 10, solution_Y));
APPEND_TO_LOG_FILE(s);
gettimeofday(&end_global, NULL);
timersub(&end_global, &start_global, &elapsed);
sprintf(s, "****** TOTAL TIME: %.3f ms\n", elapsed.tv_sec * 1000 + elapsed.tv_usec / (double) 1000);
APPEND_TO_LOG_FILE(s);*/
STOP_TIMER_PRINT_TIME("\nFactorizing done");
printf("Cleaning memory..\n");
/********************** clear the x_squared array **********************/
for (i = 0; i < SIEVING_STEP; i++) {
mpz_clear(x_squared[i].value_x);
mpz_clear(x_squared[i].value_x_squared);
//free(x_squared[i].factors_exp);
mpz_clear(x_squared[i].factors_vect);
}
free(x_squared);
/********************** clear the x_squared array **********************/
free(modular_roots);
/********************** clear the smooth_numbers array **********************/
for (i = 0; i < nb_qr_primes + NB_VECTORS_OFFSET; i++) {
mpz_clear(smooth_numbers[i].value_x);
mpz_clear(smooth_numbers[i].value_x_squared);
//free(smooth_numbers[i].factors_exp);
}
free(smooth_numbers);
/********************** clear the smooth_numbers array **********************/
free(primes);
/********************** clear mpz _t **********************/mpz_clear(B);
mpz_clear(N);
sqrtN, rem;
mpz_clear(x);
mpz_clear(sieving_index);
mpz_clear(next_sieving_index);
mpz_clear(p);
mpz_clear(str);
/********************** clear mpz _t **********************/
free_matrix(&matrix);
gettimeofday(&end_global, NULL);
timersub(&end_global, &start_global, &elapsed);
printf("****** TOTAL TIME: %.3f ms\n",
elapsed.tv_sec * 1000 + elapsed.tv_usec / (double) 1000);
show_mem_usage();
return 0;
}
/*
* It is a function that performs Miller Rabin Primality test
* input: number(mpz_t) to be tested and number of iterations(int) to run the test
* output: int 1 and 0 which represents pass and fail the test respectively
*/
int Miller(mpz_t p, int iterations){
mpz_t a;
mpz_init(a);
mpz_t p4;
mpz_init(p4);
mpz_sub_ui(p4, p, 4);
mpz_t p1;
mpz_init(p1);
mpz_sub_ui(p1, p, 1);
mpz_t x;
mpz_init(x);
mpz_t m;
mpz_init_set_str(m, "1", 10);
mpz_t val;
mpz_init(val);
gmp_randstate_t state;
srand(time(NULL));
int seed = rand();
gmp_randinit_default (state);
gmp_randseed_ui(state, seed);
//find t and m
int check = 0;
int t = 1;
while(check != 1){
mpz_ui_pow_ui(val, 2, t);
mpz_cdiv_r(m,p1,val);
if(mpz_cmp_ui(m,0) == 0){
mpz_cdiv_q(m,p1,val);
check = 1;
}
else{
t++;
}
}
//step 1
mpz_urandomb(a,state,64);
mpz_mod(a, a, p4);
mpz_add_ui(a, a, 2); //base must not be bigger than p - 2
//gmp_printf("a = %Zd\n", a);
//step 2
mpz_powm(x, a, m, p);
//gmp_printf("x = %Zd\n", x);
if(mpz_cmp_ui(x, 1) == 0 || mpz_cmp(x, p1) == 0) return 1;
else if(t == 1) return 0;
int j = 1;
//step 3 & 4
int capture;
do
{
printf("what is t, %d\n", t);
capture = step3(j,m,x,a,p,p1);
printf("capture = %d\n", capture);
if(capture == 0) return 0;
else if(capture == 1) return 1;
else{
j = capture;
printf("here when j = %d\n", j);
}
}while(j < (t-1));
//step 5
capture = step3(j+1, m, x, a, p, p1);
if(capture == 1) return 1;
else return 0;
}
/*-----------------------------------------------------------------------------*/
void build_tree(tree_t tree)
{
mpz_t M_tmp;
mpz_init(M_tmp);
/* si on est appelé et que l'on a le droit à aucune addition, */
/* cela signifie que l'on a déjà trouvé une solution directe */
/* par ailleurs: on rend la main et disant qu'on n'a pas trouvé. */
if(mpz_cmp_ui(tree->max_add, 0) <= 0)
{
mpz_set_si(tree->max_add,-1);
return;
}
if(!mpz_cmp_ui(tree->M_red, 1))
{
mpz_set_ui(tree->max_add,0);
}
else
{
char *bin;
int len;
int k;
tree_t node;
/* M = M'+1 */
mpz_sub_ui(M_tmp, tree->M_red, 1);
tree->node[0] = create_node(M_tmp);
mpz_sub_ui(tree->node[0]->max_add, tree->max_add, 1);
mpz_set_si(tree->max_add, -1);
build_tree(tree->node[0]);
if(mpz_cmp_si(tree->node[0]->max_add, -1) != 0)
{
mpz_set(tree->max_add, tree->node[0]->max_add);
mpz_add_ui(tree->max_add, tree->max_add, 1);
}
/* M = M'-1 */
mpz_add_ui(M_tmp, tree->M_red, 1);
tree->node[1] = create_node(M_tmp);
mpz_sub_ui(tree->node[1]->max_add, tree->max_add, 1);
build_tree(tree->node[1]);
if(mpz_cmp_si(tree->node[1]->max_add, -1) != 0)
{
mpz_set(tree->max_add, tree->node[1]->max_add);
mpz_add_ui(tree->max_add, tree->max_add, 1);
}
bin = mpz_get_str(NULL, 2, tree->M_red);
len = strlen(bin);
free(bin);
/* M = (2^k+1)M' */
tree->node[2] = NULL;
for(k=len-1;k>0;k--)
{
mpz_set_ui(M_tmp, 1);
mpz_mul_2exp(M_tmp, M_tmp, k);
mpz_add_ui(M_tmp, M_tmp, 1);
if(mpz_divisible_p(tree->M_red, M_tmp))
{
mpz_cdiv_q(M_tmp, tree->M_red, M_tmp);
node = create_node(M_tmp);
mpz_sub_ui(node->max_add, tree->max_add, 1);
build_tree(node);
if(mpz_cmp_si(node->max_add, -1) != 0)
{
destroy_node(tree->node[2]);
tree->node[2] = node;
tree->k = k;
mpz_set(tree->max_add, tree->node[2]->max_add);
mpz_add_ui(tree->max_add, tree->max_add, 1);
}
else
destroy_node(node);
}
}
/* M = (2^k-1)M' */
tree->node[3] = NULL;
for(k=len-1;k>0;k--)
{
mpz_set_ui(M_tmp, 1);
mpz_mul_2exp(M_tmp, M_tmp, k);
mpz_sub_ui(M_tmp, M_tmp, 1);
if(mpz_divisible_p(tree->M_red, M_tmp))
{
mpz_cdiv_q(M_tmp, tree->M_red, M_tmp);
node = create_node(M_tmp);
mpz_sub_ui(node->max_add, tree->max_add, 1);
build_tree(node);
if(mpz_cmp_si(node->max_add, -1) != 0)
{
destroy_node(tree->node[3]);
tree->node[3] = node;
tree->k = k;
mpz_set(tree->max_add, tree->node[3]->max_add);
mpz_add_ui(tree->max_add, tree->max_add, 1);
}
else
destroy_node(node);
}
}
}
mpz_clear(M_tmp);
}
int scanhash_m7m_hash(int thr_id, uint32_t *pdata, const uint32_t *ptarget,
uint64_t max_nonce, unsigned long *hashes_done)
{
uint32_t data[32] __attribute__((aligned(128)));
uint32_t *data_p64 = data + (M7_MIDSTATE_LEN / sizeof(data[0]));
uint32_t hash[8] __attribute__((aligned(32)));
uint8_t bhash[7][64] __attribute__((aligned(32)));
uint32_t n = pdata[19] - 1;
const uint32_t first_nonce = pdata[19];
char data_str[161], hash_str[65], target_str[65];
uint8_t *bdata = 0;
mpz_t bns[8];
int rc = 0;
int bytes, nnNonce2;
mpz_t product;
mpz_init(product);
for(int i=0; i < 8; i++){
mpz_init(bns[i]);
}
memcpy(data, pdata, 80);
sph_sha256_context ctx_final_sha256;
sph_sha256_context ctx_sha256;
sph_sha512_context ctx_sha512;
sph_keccak512_context ctx_keccak;
sph_whirlpool_context ctx_whirlpool;
sph_haval256_5_context ctx_haval;
sph_tiger_context ctx_tiger;
sph_ripemd160_context ctx_ripemd;
sph_sha256_init(&ctx_sha256);
sph_sha256 (&ctx_sha256, data, M7_MIDSTATE_LEN);
sph_sha512_init(&ctx_sha512);
sph_sha512 (&ctx_sha512, data, M7_MIDSTATE_LEN);
sph_keccak512_init(&ctx_keccak);
sph_keccak512 (&ctx_keccak, data, M7_MIDSTATE_LEN);
sph_whirlpool_init(&ctx_whirlpool);
sph_whirlpool (&ctx_whirlpool, data, M7_MIDSTATE_LEN);
sph_haval256_5_init(&ctx_haval);
sph_haval256_5 (&ctx_haval, data, M7_MIDSTATE_LEN);
sph_tiger_init(&ctx_tiger);
sph_tiger (&ctx_tiger, data, M7_MIDSTATE_LEN);
sph_ripemd160_init(&ctx_ripemd);
sph_ripemd160 (&ctx_ripemd, data, M7_MIDSTATE_LEN);
sph_sha256_context ctx2_sha256;
sph_sha512_context ctx2_sha512;
sph_keccak512_context ctx2_keccak;
sph_whirlpool_context ctx2_whirlpool;
sph_haval256_5_context ctx2_haval;
sph_tiger_context ctx2_tiger;
sph_ripemd160_context ctx2_ripemd;
do {
data[19] = ++n;
nnNonce2 = (int)(data[19]/2);
memset(bhash, 0, 7 * 64);
ctx2_sha256 = ctx_sha256;
sph_sha256 (&ctx2_sha256, data_p64, 80 - M7_MIDSTATE_LEN);
sph_sha256_close(&ctx2_sha256, (void*)(bhash[0]));
ctx2_sha512 = ctx_sha512;
sph_sha512 (&ctx2_sha512, data_p64, 80 - M7_MIDSTATE_LEN);
sph_sha512_close(&ctx2_sha512, (void*)(bhash[1]));
ctx2_keccak = ctx_keccak;
sph_keccak512 (&ctx2_keccak, data_p64, 80 - M7_MIDSTATE_LEN);
sph_keccak512_close(&ctx2_keccak, (void*)(bhash[2]));
ctx2_whirlpool = ctx_whirlpool;
sph_whirlpool (&ctx2_whirlpool, data_p64, 80 - M7_MIDSTATE_LEN);
sph_whirlpool_close(&ctx2_whirlpool, (void*)(bhash[3]));
ctx2_haval = ctx_haval;
sph_haval256_5 (&ctx2_haval, data_p64, 80 - M7_MIDSTATE_LEN);
sph_haval256_5_close(&ctx2_haval, (void*)(bhash[4]));
ctx2_tiger = ctx_tiger;
sph_tiger (&ctx2_tiger, data_p64, 80 - M7_MIDSTATE_LEN);
sph_tiger_close(&ctx2_tiger, (void*)(bhash[5]));
ctx2_ripemd = ctx_ripemd;
sph_ripemd160 (&ctx2_ripemd, data_p64, 80 - M7_MIDSTATE_LEN);
sph_ripemd160_close(&ctx2_ripemd, (void*)(bhash[6]));
for(int i=0; i < 7; i++){
set_one_if_zero(bhash[i]);
mpz_set_uint512(bns[i],bhash[i]);
}
mpz_set_ui(bns[7],0);
for(int i=0; i < 7; i++){
mpz_add(bns[7], bns[7], bns[i]);
}
mpz_set_ui(product,1);
for(int i=0; i < 8; i++){
mpz_mul(product,product,bns[i]);
}
mpz_pow_ui(product, product, 2);
bytes = mpz_sizeinbase(product, 256);
bdata = (uint8_t *)realloc(bdata, bytes);
mpz_export((void *)bdata, NULL, -1, 1, 0, 0, product);
sph_sha256_init(&ctx_final_sha256);
sph_sha256 (&ctx_final_sha256, bdata, bytes);
sph_sha256_close(&ctx_final_sha256, (void*)(hash));
int digits=(int)((sqrt((double)(nnNonce2))*(1.+EPS))/9000+75);
int iterations=20;
mpf_set_default_prec((long int)(digits*BITS_PER_DIGIT+16));
mpz_t magipi;
mpz_t magisw;
mpf_t magifpi;
mpf_t mpa1, mpb1, mpt1, mpp1;
mpf_t mpa2, mpb2, mpt2, mpp2;
mpf_t mpsft;
mpz_init(magipi);
mpz_init(magisw);
mpf_init(magifpi);
mpf_init(mpsft);
mpf_init(mpa1);
mpf_init(mpb1);
mpf_init(mpt1);
mpf_init(mpp1);
mpf_init(mpa2);
mpf_init(mpb2);
mpf_init(mpt2);
mpf_init(mpp2);
uint32_t usw_;
usw_ = sw_(nnNonce2, SW_DIVS);
if (usw_ < 1) usw_ = 1;
mpz_set_ui(magisw, usw_);
uint32_t mpzscale=mpz_size(magisw);
for(int i=0; i < NM7M; i++){
if (mpzscale > 1000) {
mpzscale = 1000;
}
else if (mpzscale < 1) {
mpzscale = 1;
}
mpf_set_ui(mpa1, 1);
mpf_set_ui(mpb1, 2);
mpf_set_d(mpt1, 0.25*mpzscale);
mpf_set_ui(mpp1, 1);
mpf_sqrt(mpb1, mpb1);
mpf_ui_div(mpb1, 1, mpb1);
mpf_set_ui(mpsft, 10);
for(int j=0; j <= iterations; j++){
mpf_add(mpa2, mpa1, mpb1);
mpf_div_ui(mpa2, mpa2, 2);
mpf_mul(mpb2, mpa1, mpb1);
mpf_abs(mpb2, mpb2);
mpf_sqrt(mpb2, mpb2);
mpf_sub(mpt2, mpa1, mpa2);
mpf_abs(mpt2, mpt2);
mpf_sqrt(mpt2, mpt2);
mpf_mul(mpt2, mpt2, mpp1);
mpf_sub(mpt2, mpt1, mpt2);
mpf_mul_ui(mpp2, mpp1, 2);
mpf_swap(mpa1, mpa2);
mpf_swap(mpb1, mpb2);
mpf_swap(mpt1, mpt2);
mpf_swap(mpp1, mpp2);
}
mpf_add(magifpi, mpa1, mpb1);
mpf_pow_ui(magifpi, magifpi, 2);
mpf_div_ui(magifpi, magifpi, 4);
mpf_abs(mpt1, mpt1);
mpf_div(magifpi, magifpi, mpt1);
mpf_pow_ui(mpsft, mpsft, digits/2);
mpf_mul(magifpi, magifpi, mpsft);
mpz_set_f(magipi, magifpi);
mpz_add(product,product,magipi);
mpz_add(product,product,magisw);
mpz_set_uint256(bns[0], (void*)(hash));
mpz_add(bns[7], bns[7], bns[0]);
mpz_mul(product,product,bns[7]);
mpz_cdiv_q (product, product, bns[0]);
if (mpz_sgn(product) <= 0) mpz_set_ui(product,1);
bytes = mpz_sizeinbase(product, 256);
mpzscale=bytes;
bdata = (uint8_t *)realloc(bdata, bytes);
mpz_export(bdata, NULL, -1, 1, 0, 0, product);
sph_sha256_init(&ctx_final_sha256);
sph_sha256 (&ctx_final_sha256, bdata, bytes);
sph_sha256_close(&ctx_final_sha256, (void*)(hash));
}
mpz_clear(magipi);
mpz_clear(magisw);
mpf_clear(magifpi);
mpf_clear(mpsft);
mpf_clear(mpa1);
mpf_clear(mpb1);
mpf_clear(mpt1);
mpf_clear(mpp1);
mpf_clear(mpa2);
mpf_clear(mpb2);
mpf_clear(mpt2);
mpf_clear(mpp2);
rc = fulltest_m7hash(hash, ptarget);
if (rc) {
if (opt_debug) {
bin2hex(hash_str, (unsigned char *)hash, 32);
bin2hex(target_str, (unsigned char *)ptarget, 32);
bin2hex(data_str, (unsigned char *)data, 80);
applog(LOG_DEBUG, "DEBUG: [%d thread] Found share!\ndata %s\nhash %s\ntarget %s", thr_id,
data_str,
hash_str,
target_str);
}
pdata[19] = data[19];
goto out;
}
} while (n < max_nonce && !work_restart[thr_id].restart);
pdata[19] = n;
out:
for(int i=0; i < 8; i++){
mpz_clear(bns[i]);
}
mpz_clear(product);
free(bdata);
*hashes_done = n - first_nonce + 1;
return rc;
}
//#define SW_MAX 1000
void m7magi_hash(const char* input, char* output)
{
unsigned int nnNonce;
uint32_t pdata[32];
memcpy(pdata, input, 80);
// memcpy(&nnNonce, input+76, 4);
int i, j, bytes, nnNonce2;
nnNonce2 = (int)(pdata[19]/2);
size_t sz = 80;
uint8_t bhash[7][64];
uint32_t hash[8];
memset(bhash, 0, 7 * 64);
sph_sha256_context ctx_final_sha256;
sph_sha256_context ctx_sha256;
sph_sha512_context ctx_sha512;
sph_keccak512_context ctx_keccak;
sph_whirlpool_context ctx_whirlpool;
sph_haval256_5_context ctx_haval;
sph_tiger_context ctx_tiger;
sph_ripemd160_context ctx_ripemd;
sph_sha256_init(&ctx_sha256);
// ZSHA256;
sph_sha256 (&ctx_sha256, input, sz);
sph_sha256_close(&ctx_sha256, (void*)(bhash[0]));
sph_sha512_init(&ctx_sha512);
// ZSHA512;
sph_sha512 (&ctx_sha512, input, sz);
sph_sha512_close(&ctx_sha512, (void*)(bhash[1]));
sph_keccak512_init(&ctx_keccak);
// ZKECCAK;
sph_keccak512 (&ctx_keccak, input, sz);
sph_keccak512_close(&ctx_keccak, (void*)(bhash[2]));
sph_whirlpool_init(&ctx_whirlpool);
// ZWHIRLPOOL;
sph_whirlpool (&ctx_whirlpool, input, sz);
sph_whirlpool_close(&ctx_whirlpool, (void*)(bhash[3]));
sph_haval256_5_init(&ctx_haval);
// ZHAVAL;
sph_haval256_5 (&ctx_haval, input, sz);
sph_haval256_5_close(&ctx_haval, (void*)(bhash[4]));
sph_tiger_init(&ctx_tiger);
// ZTIGER;
sph_tiger (&ctx_tiger, input, sz);
sph_tiger_close(&ctx_tiger, (void*)(bhash[5]));
sph_ripemd160_init(&ctx_ripemd);
// ZRIPEMD;
sph_ripemd160 (&ctx_ripemd, input, sz);
sph_ripemd160_close(&ctx_ripemd, (void*)(bhash[6]));
// printf("%s\n", hash[6].GetHex().c_str());
mpz_t bns[8];
for(i=0; i < 8; i++){
mpz_init(bns[i]);
}
//Take care of zeros and load gmp
for(i=0; i < 7; i++){
set_one_if_zero(bhash[i]);
mpz_set_uint512(bns[i],bhash[i]);
}
mpz_set_ui(bns[7],0);
for(i=0; i < 7; i++)
mpz_add(bns[7], bns[7], bns[i]);
mpz_t product;
mpz_init(product);
mpz_set_ui(product,1);
// mpz_pow_ui(bns[7], bns[7], 2);
for(i=0; i < 8; i++){
mpz_mul(product,product,bns[i]);
}
mpz_pow_ui(product, product, 2);
bytes = mpz_sizeinbase(product, 256);
// printf("M7M data space: %iB\n", bytes);
char *data = (char*)malloc(bytes);
mpz_export(data, NULL, -1, 1, 0, 0, product);
sph_sha256_init(&ctx_final_sha256);
// ZSHA256;
sph_sha256 (&ctx_final_sha256, data, bytes);
sph_sha256_close(&ctx_final_sha256, (void*)(hash));
free(data);
int digits=(int)((sqrt((double)(nnNonce2))*(1.+EPS))/9000+75);
// int iterations=(int)((sqrt((double)(nnNonce2))+EPS)/500+350); // <= 500
// int digits=100;
int iterations=20; // <= 500
mpf_set_default_prec((long int)(digits*BITS_PER_DIGIT+16));
mpz_t magipi;
mpz_t magisw;
mpf_t magifpi;
mpf_t mpa1, mpb1, mpt1, mpp1;
mpf_t mpa2, mpb2, mpt2, mpp2;
mpf_t mpsft;
mpz_init(magipi);
mpz_init(magisw);
mpf_init(magifpi);
mpf_init(mpsft);
mpf_init(mpa1);
mpf_init(mpb1);
mpf_init(mpt1);
mpf_init(mpp1);
mpf_init(mpa2);
mpf_init(mpb2);
mpf_init(mpt2);
mpf_init(mpp2);
uint32_t usw_;
usw_ = sw_(nnNonce2, SW_DIVS);
if (usw_ < 1) usw_ = 1;
// if(fDebugMagi) printf("usw_: %d\n", usw_);
mpz_set_ui(magisw, usw_);
uint32_t mpzscale=mpz_size(magisw);
for(i=0; i < NM7M; i++)
{
if (mpzscale > 1000) {
mpzscale = 1000;
}
else if (mpzscale < 1) {
mpzscale = 1;
}
// if(fDebugMagi) printf("mpzscale: %d\n", mpzscale);
mpf_set_ui(mpa1, 1);
mpf_set_ui(mpb1, 2);
mpf_set_d(mpt1, 0.25*mpzscale);
mpf_set_ui(mpp1, 1);
mpf_sqrt(mpb1, mpb1);
mpf_ui_div(mpb1, 1, mpb1);
mpf_set_ui(mpsft, 10);
for(j=0; j <= iterations; j++)
{
mpf_add(mpa2, mpa1, mpb1);
mpf_div_ui(mpa2, mpa2, 2);
mpf_mul(mpb2, mpa1, mpb1);
mpf_abs(mpb2, mpb2);
mpf_sqrt(mpb2, mpb2);
mpf_sub(mpt2, mpa1, mpa2);
mpf_abs(mpt2, mpt2);
mpf_sqrt(mpt2, mpt2);
mpf_mul(mpt2, mpt2, mpp1);
mpf_sub(mpt2, mpt1, mpt2);
mpf_mul_ui(mpp2, mpp1, 2);
mpf_swap(mpa1, mpa2);
mpf_swap(mpb1, mpb2);
mpf_swap(mpt1, mpt2);
mpf_swap(mpp1, mpp2);
}
mpf_add(magifpi, mpa1, mpb1);
mpf_pow_ui(magifpi, magifpi, 2);
mpf_div_ui(magifpi, magifpi, 4);
mpf_abs(mpt1, mpt1);
mpf_div(magifpi, magifpi, mpt1);
// mpf_out_str(stdout, 10, digits+2, magifpi);
mpf_pow_ui(mpsft, mpsft, digits/2);
mpf_mul(magifpi, magifpi, mpsft);
mpz_set_f(magipi, magifpi);
//mpz_set_ui(magipi,1);
mpz_add(product,product,magipi);
mpz_add(product,product,magisw);
mpz_set_uint256(bns[0], (void*)(hash));
mpz_add(bns[7], bns[7], bns[0]);
mpz_mul(product,product,bns[7]);
mpz_cdiv_q (product, product, bns[0]);
if (mpz_sgn(product) <= 0) mpz_set_ui(product,1);
bytes = mpz_sizeinbase(product, 256);
mpzscale=bytes;
// printf("M7M data space: %iB\n", bytes);
char *bdata = (char*)malloc(bytes);
mpz_export(bdata, NULL, -1, 1, 0, 0, product);
sph_sha256_init(&ctx_final_sha256);
// ZSHA256;
sph_sha256 (&ctx_final_sha256, bdata, bytes);
sph_sha256_close(&ctx_final_sha256, (void*)(hash));
free(bdata);
}
//Free the memory
for(i=0; i < 8; i++){
mpz_clear(bns[i]);
}
// mpz_clear(dSpectralWeight);
mpz_clear(product);
mpz_clear(magipi);
mpz_clear(magisw);
mpf_clear(magifpi);
mpf_clear(mpsft);
mpf_clear(mpa1);
mpf_clear(mpb1);
mpf_clear(mpt1);
mpf_clear(mpp1);
mpf_clear(mpa2);
mpf_clear(mpb2);
mpf_clear(mpt2);
mpf_clear(mpp2);
memcpy(output, hash, 32);
}
static int
rsa_provable_prime (mpz_t p,
unsigned *prime_seed_length, void *prime_seed,
unsigned bits,
unsigned seed_length, const void *seed,
mpz_t e,
void *progress_ctx, nettle_progress_func * progress)
{
mpz_t x, t, s, r1, r2, p0, sq;
int ret;
unsigned pcounter = 0;
unsigned iterations;
unsigned storage_length = 0, i;
uint8_t *storage = NULL;
uint8_t pseed[MAX_PVP_SEED_SIZE+1];
unsigned pseed_length = sizeof(pseed), tseed_length;
unsigned max = bits*5;
mpz_init(p0);
mpz_init(sq);
mpz_init(x);
mpz_init(t);
mpz_init(s);
mpz_init(r1);
mpz_init(r2);
/* p1 = p2 = 1 */
ret = st_provable_prime(p0, &pseed_length, pseed,
NULL, 1+div_ceil(bits,2), seed_length,
seed, progress_ctx, progress);
if (ret == 0) {
goto cleanup;
}
iterations = div_ceil(bits, DIGEST_SIZE*8);
mpz_set_ui(x, 0);
if (iterations > 0) {
storage_length = iterations * DIGEST_SIZE;
storage = malloc(storage_length);
if (storage == NULL) {
goto fail;
}
nettle_mpz_set_str_256_u(s, pseed_length, pseed);
for (i = 0; i < iterations; i++) {
tseed_length = mpz_seed_sizeinbase_256_u(s, pseed_length);
if (tseed_length > sizeof(pseed))
goto fail;
nettle_mpz_get_str_256(tseed_length, pseed, s);
hash(&storage[(iterations - i - 1) * DIGEST_SIZE],
tseed_length, pseed);
mpz_add_ui(s, s, 1);
}
nettle_mpz_set_str_256_u(x, storage_length, storage);
}
/* x = sqrt(2)*2^(bits-1) + (x mod 2^(bits) - sqrt(2)*2(bits-1)) */
/* sq = sqrt(2)*2^(bits-1) */
mpz_set_ui(r1, 1);
mpz_mul_2exp(r1, r1, 2*bits-1);
mpz_sqrt(sq, r1);
/* r2 = 2^bits - sq */
mpz_set_ui(r2, 1);
mpz_mul_2exp(r2, r2, bits);
mpz_sub(r2, r2, sq);
/* x = sqrt(2)*2^(bits-1) + (x mod (2^L - sqrt(2)*2^(bits-1)) */
mpz_mod(x, x, r2);
mpz_add(x, x, sq);
/* y = p2 = p1 = 1 */
/* r1 = (2 y p0 p1) */
mpz_mul_2exp(r1, p0, 1);
/* r2 = 2 p0 p1 p2 (p2=y=1) */
mpz_set(r2, r1);
/* r1 = (2 y p0 p1) + x */
mpz_add(r1, r1, x);
/* t = ((2 y p0 p1) + x) / (2 p0 p1 p2) */
mpz_cdiv_q(t, r1, r2);
retry:
/* p = t p2 - y = t - 1 */
mpz_sub_ui(p, t, 1);
/* p = 2(tp2-y)p0p1 */
mpz_mul(p, p, p0);
mpz_mul_2exp(p, p, 1);
/* p = 2(tp2-y)p0p1 + 1*/
mpz_add_ui(p, p, 1);
mpz_set_ui(r2, 1);
mpz_mul_2exp(r2, r2, bits);
if (mpz_cmp(p, r2) > 0) {
/* t = (2 y p0 p1) + sqrt(2)*2^(bits-1) / (2p0p1p2) */
mpz_set(r1, p0);
/* r1 = (2 y p0 p1) */
mpz_mul_2exp(r1, r1, 1);
/* sq = sqrt(2)*2^(bits-1) */
/* r1 = (2 y p0 p1) + sq */
mpz_add(r1, r1, sq);
/* r2 = 2 p0 p1 p2 */
mpz_mul_2exp(r2, p0, 1);
/* t = ((2 y p0 p1) + sq) / (2 p0 p1 p2) */
mpz_cdiv_q(t, r1, r2);
}
pcounter++;
/* r2 = p - 1 */
mpz_sub_ui(r2, p, 1);
/* r1 = GCD(p1, e) */
mpz_gcd(r1, e, r2);
if (mpz_cmp_ui(r1, 1) == 0) {
mpz_set_ui(x, 0); /* a = 0 */
if (iterations > 0) {
for (i = 0; i < iterations; i++) {
tseed_length = mpz_seed_sizeinbase_256_u(s, pseed_length);
if (tseed_length > sizeof(pseed))
goto fail;
nettle_mpz_get_str_256(tseed_length, pseed, s);
hash(&storage[(iterations - i - 1) * DIGEST_SIZE],
tseed_length, pseed);
mpz_add_ui(s, s, 1);
}
nettle_mpz_set_str_256_u(x, storage_length, storage);
}
/* a = 2 + a mod p-3 */
mpz_sub_ui(r1, p, 3); /* p is too large to worry about negatives */
mpz_mod(x, x, r1);
mpz_add_ui(x, x, 2);
/* z = a^(2(tp2-y)p1) mod p */
/* r1 = (tp2-y) */
mpz_sub_ui(r1, t, 1);
/* r1 = 2(tp2-y)p1 */
mpz_mul_2exp(r1, r1, 1);
/* z = r2 = a^r1 mod p */
mpz_powm(r2, x, r1, p);
mpz_sub_ui(r1, r2, 1);
mpz_gcd(x, r1, p);
if (mpz_cmp_ui(x, 1) == 0) {
mpz_powm(r1, r2, p0, p);
if (mpz_cmp_ui(r1, 1) == 0) {
if (prime_seed_length != NULL) {
tseed_length = mpz_seed_sizeinbase_256_u(s, pseed_length);
if (tseed_length > sizeof(pseed))
goto fail;
nettle_mpz_get_str_256(tseed_length, pseed, s);
if (*prime_seed_length < tseed_length) {
*prime_seed_length = tseed_length;
goto fail;
}
*prime_seed_length = tseed_length;
if (prime_seed != NULL)
memcpy(prime_seed, pseed, tseed_length);
}
ret = 1;
goto cleanup;
}
}
}
if (pcounter >= max) {
goto fail;
}
mpz_add_ui(t, t, 1);
goto retry;
fail:
ret = 0;
cleanup:
free(storage);
mpz_clear(p0);
mpz_clear(sq);
mpz_clear(r1);
mpz_clear(r2);
mpz_clear(x);
mpz_clear(t);
mpz_clear(s);
return ret;
}
/* assuming slaves (workers)) are all homogenous, let them all do the calculations
regarding primes sieving, calculating the smoothness base and the modular roots */
int main(int argc, char **argv) {
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
MPI_Comm_size(MPI_COMM_WORLD, &mpi_group_size);
int len;
MPI_Get_processor_name(processor_name, &len);
gettimeofday(&start_global, NULL);
print_lib_version();
mpz_init(N);
mpz_t B;
mpz_init(B);
unsigned long int uBase;
int64_t nb_primes;
modular_root_t *modular_roots;
uint64_t i, j;
if (argc < 2) {
PRINT(my_rank, "usage: %s Number_to_factorize\n", argv[0]);
exit(2);
}
if (mpz_init_set_str(N, argv[1], 10) == -1) {
PRINT(my_rank, "Cannot load N %s\n", argv[1]);
exit(2);
}
mpz_t sqrtN, rem;
mpz_init(sqrtN);
mpz_init(rem);
mpz_sqrtrem(sqrtN, rem, N);
if (mpz_cmp_ui(rem, 0) != 0) /* if not perfect square, calculate the ceiling */
mpz_add_ui(sqrtN, sqrtN, 1);
else /* N is a perfect square, factored! */
{
PRINT(my_rank, "\n<<<[FACTOR]>>> %s\n", mpz_get_str(NULL, 10, sqrtN));
return 0;
}
if (mpz_probab_prime_p(N, 10) > 0) /* don't bother factoring */
{
PRINT(my_rank, "N:%s is prime\n", mpz_get_str(NULL, 10, N));
exit(0);
}
OPEN_LOG_FILE("freq");
//--------------------------------------------------------
// calculate the smoothness base for the given N
//--------------------------------------------------------
get_smoothness_base(B, N); /* if N is too small, the program will surely fail, please consider a pen and paper instead */
uBase = mpz_get_ui(B);
PRINT(my_rank, "n: %s\tBase: %s\n",
mpz_get_str(NULL, 10, N), mpz_get_str(NULL, 10, B));
//--------------------------------------------------------
// sieve primes that are less than the smoothness base using Eratosthenes sieve
//--------------------------------------------------------
START_TIMER();
nb_primes = sieve_primes_up_to((int64_t) (uBase));
PRINT(my_rank, "\tPrimes found %" PRId64 " [Smoothness Base %lu]\n",
nb_primes, uBase);
STOP_TIMER_PRINT_TIME("\tEratosthenes Sieving done");
//--------------------------------------------------------
// fill the primes array with primes to which n is a quadratic residue
//--------------------------------------------------------
START_TIMER();
primes = calloc(nb_primes, sizeof(int64_t));
nb_qr_primes = fill_primes_with_quadratic_residue(primes, N);
/*for(i=0; i<nb_qr_primes; i++)
PRINT(my_rank, "%" PRId64 "\n", primes[i]);*/
PRINT(my_rank, "\tN-Quadratic primes found %" PRId64 "\n", nb_qr_primes);
STOP_TIMER_PRINT_TIME("\tQuadratic prime filtering done");
//--------------------------------------------------------
// calculate modular roots
//--------------------------------------------------------
START_TIMER();
modular_roots = calloc(nb_qr_primes, sizeof(modular_root_t));
mpz_t tmp, r1, r2;
mpz_init(tmp);
mpz_init(r1);
mpz_init(r2);
for (i = 0; i < nb_qr_primes; i++) {
mpz_set_ui(tmp, (unsigned long) primes[i]);
mpz_sqrtm(r1, N, tmp); /* calculate the modular root */
mpz_neg(r2, r1); /* -q mod n */
mpz_mod(r2, r2, tmp);
modular_roots[i].root1 = mpz_get_ui(r1);
modular_roots[i].root2 = mpz_get_ui(r2);
}
mpz_clear(tmp);
mpz_clear(r1);
mpz_clear(r2);
STOP_TIMER_PRINT_TIME("Modular roots calculation done");
//--------------------------------------------------------
// ***** initialize the matrix *****
//--------------------------------------------------------
if (my_rank == 0) /* only the master have the matrix */
{
START_TIMER();
init_matrix(&matrix, nb_qr_primes + NB_VECTORS_OFFSET, nb_qr_primes);
mpz_init2(tmp_matrix_row, nb_qr_primes);
STOP_TIMER_PRINT_TIME("Matrix initialized");
}
//--------------------------------------------------------
// [Sieving] - everyones sieves including the master
//--------------------------------------------------------
START_TIMER();
mpz_t x, sieving_index, next_sieving_index, relative_start, global_step;
unsigned long ui_index, SIEVING_STEP = 50000; /* we sieve for 50000 elements at each loop */
int LOCAL_SIEVING_ROUNDS = 10; /* number of iterations a worker sieves before communicating results to the master */
unsigned long sieving_round = 0;
unsigned long nb_big_rounds = 0;
uint64_t p_pow;
smooth_number_t *x_squared;
x_squared = calloc(SIEVING_STEP, sizeof(smooth_number_t));
if (my_rank == 0)
smooth_numbers = calloc(nb_qr_primes + NB_VECTORS_OFFSET,
sizeof(smooth_number_t));
else
temp_slaves_smooth_numbers = calloc(500, sizeof(smooth_number_t));
/* TODO: this is not properly correct, using a linkedlist is better to keep track of temporary
* smooth numbers at the slaves nodes however it's pretty rare to find 500 smooth numbers in
* 50000 * 10 interval. */
mpz_init_set(x, sqrtN);
mpz_init(global_step);
mpz_init(relative_start);
mpz_init(sieving_index);
mpz_init(next_sieving_index);
mpz_t p;
mpz_init(p);
mpz_t str;
mpz_init_set(str, sieving_index);
PRINT(my_rank, "\n[%s] Sieving ...\n", processor_name);
//--------------------------------------------------------
// Init before sieving
//--------------------------------------------------------
for (i = 0; i < SIEVING_STEP; i++) {
mpz_init(x_squared[i].value_x);
mpz_init(x_squared[i].value_x_squared);
mpz_init2(x_squared[i].factors_vect, nb_qr_primes);
mpz_add_ui(x, x, 1);
}
int nb_smooth_per_round = 0;
char s[512];
//--------------------------------------------------------
// WHILE smooth numbers found less than the primes in the smooth base + NB_VECTORS_OFFSET for master
// Or master asked for more smooth numbers from slaves
//--------------------------------------------------------
while (1) {
mpz_set_ui(global_step, nb_big_rounds); /* calculates the coordinate where the workers start sieving from */
mpz_mul_ui(global_step, global_step, (unsigned long) mpi_group_size);
mpz_mul_ui(global_step, global_step, SIEVING_STEP);
mpz_mul_ui(global_step, global_step, LOCAL_SIEVING_ROUNDS);
mpz_add(global_step, global_step, sqrtN);
mpz_set_ui(relative_start, SIEVING_STEP);
mpz_mul_ui(relative_start, relative_start, LOCAL_SIEVING_ROUNDS);
mpz_mul_ui(relative_start, relative_start, (unsigned long) my_rank);
mpz_add(relative_start, relative_start, global_step);
mpz_set(sieving_index, relative_start);
mpz_set(next_sieving_index, relative_start);
for (sieving_round = 0; sieving_round < LOCAL_SIEVING_ROUNDS; /* each slave sieves for LOCAL_SIEVING_ROUNDS rounds */
sieving_round++) {
nb_smooth_per_round = 0;
mpz_set(x, next_sieving_index); /* sieve numbers from sieving_index to sieving_index + sieving_step */
mpz_set(sieving_index, next_sieving_index);
if (my_rank == 0) {
printf("\r");
printf(
"\t\tSieving at: %s30 <--> Smooth numbers found: %" PRId64 "/%" PRId64 "",
mpz_get_str(NULL, 10, sieving_index),
nb_global_smooth_numbers_found, nb_qr_primes);
fflush(stdout);
}
for (i = 0; i < SIEVING_STEP; i++) {
mpz_set(x_squared[i].value_x, x);
mpz_pow_ui(x_squared[i].value_x_squared, x, 2); /* calculate value_x_squared <- x²-n */
mpz_sub(x_squared[i].value_x_squared,
x_squared[i].value_x_squared, N);
mpz_clear(x_squared[i].factors_vect);
mpz_init2(x_squared[i].factors_vect, nb_qr_primes); /* reconstruct a new fresh 0ed vector of size nb_qr_primes bits */
mpz_add_ui(x, x, 1);
}
mpz_set(next_sieving_index, x);
//--------------------------------------------------------
// eliminate factors in the x_squared array, those who are 'destructed' to 1 are smooth
//--------------------------------------------------------
for (i = 0; i < nb_qr_primes; i++) {
mpz_set_ui(p, (unsigned long) primes[i]);
mpz_set(x, sieving_index);
/* get the first multiple of p that is directly larger that sieving_index
* Quadratic SIEVING: all elements from this number and in positions multiples of root1 and root2
* are also multiples of p */
get_sieving_start_index(x, x, p, modular_roots[i].root1);
mpz_set(str, x);
mpz_sub(x, x, sieving_index); /* x contains index of first number that is divisible by p */
for (j = mpz_get_ui(x); j < SIEVING_STEP; j += primes[i]) {
p_pow = mpz_remove(x_squared[j].value_x_squared,
x_squared[j].value_x_squared, p); /* eliminate all factors of p */
if (p_pow & 1) /* mark bit if odd power of p exists in this x_squared[j] */
{
mpz_setbit(x_squared[j].factors_vect, i);
}
if (mpz_cmp_ui(x_squared[j].value_x_squared, 1) == 0) {
save_smooth_number(x_squared[j]);
nb_smooth_per_round++;
}
/* sieve next element located p steps from here */
}
/* same goes for root2 */
if (modular_roots[i].root2 == modular_roots[i].root1)
continue;
mpz_set(x, sieving_index);
get_sieving_start_index(x, x, p, modular_roots[i].root2);
mpz_set(str, x);
mpz_sub(x, x, sieving_index);
for (j = mpz_get_ui(x); j < SIEVING_STEP; j += primes[i]) {
p_pow = mpz_remove(x_squared[j].value_x_squared,
x_squared[j].value_x_squared, p);
if (p_pow & 1) {
mpz_setbit(x_squared[j].factors_vect, i);
}
if (mpz_cmp_ui(x_squared[j].value_x_squared, 1) == 0) {
save_smooth_number(x_squared[j]);
nb_smooth_per_round++;
}
}
}
}
if (my_rank == 0) /* master gathers smooth numbers from slaves */
{
gather_smooth_numbers();
notify_slaves();
} else /* slaves send their smooth numbers to master */
{
send_smooth_numbers_to_master();
nb_global_smooth_numbers_found = get_server_notification();
}
if (nb_global_smooth_numbers_found >= nb_qr_primes + NB_VECTORS_OFFSET)
break;
nb_big_rounds++;
}
STOP_TIMER_PRINT_TIME("\nSieving DONE");
if (my_rank == 0) {
uint64_t t = 0;
//--------------------------------------------------------
//the matrix ready, start Gauss elimination. The Matrix is filled on the call of save_smooth_number()
//--------------------------------------------------------
START_TIMER();
gauss_elimination(&matrix);
STOP_TIMER_PRINT_TIME("\nGauss elimination done");
uint64_t row_index = nb_qr_primes + NB_VECTORS_OFFSET - 1; /* last row in the matrix */
int nb_linear_relations = 0;
mpz_t linear_relation_z, solution_z;
mpz_init(linear_relation_z);
mpz_init(solution_z);
get_matrix_row(linear_relation_z, &matrix, row_index--); /* get the last few rows in the Gauss eliminated matrix*/
while (mpz_cmp_ui(linear_relation_z, 0) == 0) {
nb_linear_relations++;
get_matrix_row(linear_relation_z, &matrix, row_index--);
}
PRINT(my_rank, "\tLinear dependent relations found : %d\n",
nb_linear_relations);
//--------------------------------------------------------
// Factor
//--------------------------------------------------------
//We use the last linear relation to reconstruct our solution
START_TIMER();
PRINT(my_rank, "%s", "\nFactorizing..\n");
mpz_t solution_X, solution_Y;
mpz_init(solution_X);
mpz_init(solution_Y);
/* we start testing from the first linear relation encountered in the matrix */
for (j = nb_linear_relations; j > 0; j--) {
PRINT(my_rank, "Trying %d..\n", nb_linear_relations - j + 1);
mpz_set_ui(solution_X, 1);
mpz_set_ui(solution_Y, 1);
get_identity_row(solution_z, &matrix,
nb_qr_primes + NB_VECTORS_OFFSET - j + 1);
for (i = 0; i < nb_qr_primes; i++) {
if (mpz_tstbit(solution_z, i)) {
mpz_mul(solution_X, solution_X, smooth_numbers[i].value_x);
mpz_mod(solution_X, solution_X, N); /* reduce x to modulo N */
mpz_mul(solution_Y, solution_Y,
smooth_numbers[i].value_x_squared);
/*TODO: handling huge stuff here, there is no modulo N like in the solution_X case!
* eliminate squares as long as you go*/
}
}
mpz_sqrt(solution_Y, solution_Y);
mpz_mod(solution_Y, solution_Y, N); /* y = sqrt(MUL(xi²-n)) mod N */
mpz_sub(solution_X, solution_X, solution_Y);
mpz_gcd(solution_X, solution_X, N);
if (mpz_cmp(solution_X, N) != 0 && mpz_cmp_ui(solution_X, 1) != 0) /* factor can be 1 or N, try another relation */
break;
}
mpz_cdiv_q(solution_Y, N, solution_X);
PRINT(my_rank, "\n>>>>>>>>>>> FACTORED %s =\n",
mpz_get_str(NULL, 10, N));
PRINT(
my_rank,
"\tFactor 1: %s \n\tFactor 2: %s",
mpz_get_str(NULL, 10, solution_X), mpz_get_str(NULL, 10, solution_Y));
sprintf(s, "\n>>>>>>>>>>> FACTORED %s =\n", mpz_get_str(NULL, 10, N));
APPEND_TO_LOG_FILE(s);
sprintf(s, "\tFactor 1: %s \n\tFactor 2: %s",
mpz_get_str(NULL, 10, solution_X),
mpz_get_str(NULL, 10, solution_Y));
APPEND_TO_LOG_FILE(s);
gettimeofday(&end_global, NULL);
timersub(&end_global, &start_global, &elapsed);
sprintf(s, "****** TOTAL TIME: %.3f ms\n",
elapsed.tv_sec * 1000 + elapsed.tv_usec / (double) 1000);
APPEND_TO_LOG_FILE(s);
STOP_TIMER_PRINT_TIME("\nFactorizing done");
}
PRINT(my_rank, "%s", "\nCleaning memory..\n");
/********************** clear the x_squared array **********************/
for (i = 0; i < SIEVING_STEP; i++) {
mpz_clear(x_squared[i].value_x);
mpz_clear(x_squared[i].value_x_squared);
//free(x_squared[i].factors_exp);
mpz_clear(x_squared[i].factors_vect);
}
free(x_squared);
/********************** clear the x_squared array **********************/
free(modular_roots);
/********************** clear the smooth_numbers array **********************/
if (my_rank == 0) {
for (i = 0; i < nb_qr_primes + NB_VECTORS_OFFSET; i++) {
mpz_clear(smooth_numbers[i].value_x);
mpz_clear(smooth_numbers[i].value_x_squared);
mpz_clear(smooth_numbers[i].factors_vect);
//free(smooth_numbers[i].factors_exp);
}
free(smooth_numbers);
} else {
for (i = 0; i < 500; i++) {
mpz_clear(temp_slaves_smooth_numbers[i].value_x);
mpz_clear(temp_slaves_smooth_numbers[i].value_x_squared);
mpz_clear(temp_slaves_smooth_numbers[i].factors_vect);
}
free(temp_slaves_smooth_numbers);
}
/********************** clear the smooth_numbers array **********************/
free(primes);
/********************** clear mpz _t **********************/mpz_clear(B);
mpz_clear(N);
sqrtN, rem;
mpz_clear(x);
mpz_clear(sieving_index);
mpz_clear(next_sieving_index);
mpz_clear(p);
mpz_clear(str);
/********************** clear mpz _t **********************/
free_matrix(&matrix);
gettimeofday(&end_global, NULL);
timersub(&end_global, &start_global, &elapsed);
PRINT(my_rank, "****** TOTAL TIME: %.3f ms\n",
elapsed.tv_sec * 1000 + elapsed.tv_usec / (double) 1000);
show_mem_usage();
MPI_Finalize();
return 0;
}
void BigNumberBase::setPrec(int32_t prec, PrecFlag flag)
{
if (prec == -1)
{
prec = Calc::PRECISE;
}
if (m_prec == prec)
{
return;
}
if (m_prec < prec)
{
GmpInt::TenExp(m_gmp->m_integer, (prec - m_prec));
m_prec = prec;
return;
}
if (flag == BigNumberBase::HALF_ADJUST)
{
std::string result = toString();
if (result[result.size() - (m_prec - prec)] < '5')
{
setPrec(prec, BigNumberBase::ROUND_OFF);
return;
}
if (BigNumberBase::Compare(*this, "0") == BigNumberCompare::BIG)
{
setPrec(prec, BigNumberBase::ROUND_UP);
return;
}
setPrec(prec, BigNumberBase::ROUND_DOWN);
return;
}
int32_t exp = m_prec - prec;
char* szExp = (char*)malloc(exp + 2);
memset(szExp, 48, exp + 1);
szExp[exp + 1] = 0;
szExp[0] = 49;
mpz_t mpzExp;
mpz_init_set_str(mpzExp, szExp, 10);
switch (flag)
{
case BigNumberBase::ROUND_OFF:
{
mpz_tdiv_q(m_gmp->m_integer, m_gmp->m_integer, mpzExp);
break;
}
case BigNumberBase::ROUND_UP:
{
mpz_cdiv_q(m_gmp->m_integer, m_gmp->m_integer, mpzExp);
break;
}
case BigNumberBase::ROUND_DOWN:
{
mpz_fdiv_q(m_gmp->m_integer, m_gmp->m_integer, mpzExp);
break;
}
default:
break;
}
mpz_clear(mpzExp);
::free(szExp);
m_prec = prec;
}
