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#include <stdio.h>
#include <stdlib.h>
#include "csprng.h"
#include "primality.h"
#include "util.h"
#include "prime_nth_count.h"
#include "lmo.h"
#include "mulmod.h"
#include "constants.h"
#include "random_prime.h"
UV random_nbit_prime(void* ctx, UV b)
{
uint32_t start = 0, range;
UV n, p;
switch (b) {
case 0:
case 1: return 0;
case 2: return urandomb(ctx,1) ? 2 : 3;
case 3: return urandomb(ctx,1) ? 5 : 7;
case 4: return urandomb(ctx,1) ? 11 : 13;
case 5: start = 7; range = 5; break;
case 6: start = 12; range = 7; break;
case 7: start = 19; range = 13; break;
case 8: start = 32; range = 23; break;
case 9: start = 55; range = 43; break;
default: break;
}
if (start)
return nth_prime(start + urandomm32(ctx,range));
if (b > BITS_PER_WORD)
return 0;
/* Trivial method */
p = (UVCONST(1) << (b-1)) + 1;
while (1) {
n = p + (urandomb(ctx,b-2) << 1);
if (is_prob_prime(n))
return n;
}
}
UV random_ndigit_prime(void* ctx, UV d)
{
UV lo, hi;
if ( (d == 0) || (BITS_PER_WORD == 32 && d >= 10) || (BITS_PER_WORD == 64 && d >= 20) ) return 0;
if (d == 1) return nth_prime(1 + urandomm32(ctx,4));
if (d == 2) return nth_prime(5 + urandomm32(ctx,21));
lo = powmod(10,d-1,UV_MAX)+1;
hi = 10*lo-11;
while (1) {
UV n = (lo + urandomm64(ctx,hi-lo+1)) | 1;
if (is_prob_prime(n))
return n;
}
}
UV random_prime(void* ctx, UV lo, UV hi)
{
UV n, oddrange;
if (lo > hi) return 0;
/* Pull edges in to nearest primes */
lo = (lo <= 2) ? 2 : next_prime(lo-1);
hi = (hi >= MPU_MAX_PRIME) ? MPU_MAX_PRIME : prev_prime(hi+1);
if (lo > hi) return 0;
/* There must be at least one prime in the range */
if (!(lo&1)) lo--; /* treat 2 as 1 */
oddrange = ((hi-lo)>>1) + 1; /* look for odds */
while (1) {
n = lo + 2 * urandomm64(ctx, oddrange);
if (n == 1 || is_prob_prime(n))
return (n == 1) ? 2 : n;
}
}
/* Note that 7 chosen bases or the first 12 prime bases are enough
* to guarantee sucess. We could choose to limit to those. */
int is_mr_random(void* ctx, UV n, UV k) {
if (k >= 3*(n/4))
return is_prob_prime(n);
/* TODO: do 16 at a time */
while (k--) {
UV base = 2 + urandomm64(ctx, n-2);
if (!miller_rabin(n, &base, 1))
return 0;
}
return 1;
}
UV random_semiprime(void* ctx, UV b) { /* Even split of bits */
static const uint16_t small_semi[] = {35,35,49,65,77,91,143,143,169,299,319,341,377,403};
UV min, max, n, L, N;
if (b < 4 || b > BITS_PER_WORD)
return 0;
switch (b) {
case 4: return 9;
case 5: return 21;
case 6: return small_semi[ 0 + urandomm32(ctx,3) ];
case 7: return small_semi[ 3 + urandomm32(ctx,3) ];
case 8: return small_semi[ 6 + urandomm32(ctx,3) ];
case 9: return small_semi[ 9 + urandomm32(ctx,5) ];
default: break;
}
min = UVCONST(1) << (b-1);
max = min + (min-1);
L = b / 2;
N = b - L;
do {
n = random_nbit_prime(ctx,L) * random_nbit_prime(ctx,N);
} while (n < min || n > max);
return n;
}
UV random_unrestricted_semiprime(void* ctx, UV b) { /* generic semiprime */
static const unsigned char small_semi[] = {4,6,9,10,14,15,21,22,25,26,33,34,35,38,39,46,49,51,55,57,58,62,65,69,74,77,82,85,86,87,91,93,94,95,106,111,115,118,119,121,122,123};
UV min, n;
if (b < 3 || b > BITS_PER_WORD)
return 0;
switch (b) {
case 3: return small_semi[ 0 + urandomm32(ctx, 2) ];
case 4: return small_semi[ 2 + urandomm32(ctx, 4) ];
case 5: return small_semi[ 6 + urandomm32(ctx, 4) ];
case 6: return small_semi[ 10 + urandomm32(ctx,12) ];
case 7: return small_semi[ 22 + urandomm32(ctx,20) ];
default: break;
}
/* There are faster ways to generate if we could be lax on distribution.
* Picking a random prime followed by a second that makes a semiprime in
* the range seems obvious and is fast, but the distribution is wrong.
* With that method, some semiprimes are much more likely than others. */
min = UVCONST(1) << (b-1);
do {
n = min + urandomb(ctx,b-1);
} while (!is_semiprime(n));
return n;
}
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