#include <time.h>
#include "cryptlib.h"
#include "bn_lcl.h"
-#include "rand.h"
+#include <openssl/rand.h>
-/* The quick seive algorithm approach to weeding out primes is
+/* The quick sieve algorithm approach to weeding out primes is
* Philip Zimmermann's, as implemented in PGP. I have had a read of
* his comments and implemented my own version.
*/
#include "bn_prime.h"
-#ifndef NOPROTO
-static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,BN_CTX *ctx2,
- BN_MONT_CTX *mont);
+static int witness(BIGNUM *w, BIGNUM *a, BIGNUM *a1, BIGNUM *a1_odd, int k,
+ BN_CTX *ctx, BN_MONT_CTX *mont);
static int probable_prime(BIGNUM *rnd, int bits);
static int probable_prime_dh(BIGNUM *rnd, int bits,
BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
-static int probable_prime_dh_strong(BIGNUM *rnd, int bits,
+static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
BIGNUM *add, BIGNUM *rem, BN_CTX *ctx);
-#else
-static int witness();
-static int probable_prime();
-static int probable_prime_dh();
-static int probable_prime_dh_strong();
-#endif
-
-BIGNUM *BN_generate_prime(bits,strong,add,rem,callback,cb_arg)
-int bits;
-int strong;
-BIGNUM *add;
-BIGNUM *rem;
-void (*callback)(P_I_I_P);
-char *cb_arg;
+
+BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int safe, BIGNUM *add,
+ BIGNUM *rem, void (*callback)(int,int,void *), void *cb_arg)
{
BIGNUM *rnd=NULL;
- BIGNUM *ret=NULL;
- BIGNUM *t=NULL;
+ BIGNUM t;
+ int found=0;
int i,j,c1=0;
BN_CTX *ctx;
+ int checks = BN_prime_checks_for_size(bits);
ctx=BN_CTX_new();
if (ctx == NULL) goto err;
- if ((rnd=BN_new()) == NULL) goto err;
- if (strong)
- if ((t=BN_new()) == NULL) goto err;
+ if (ret == NULL)
+ {
+ if ((rnd=BN_new()) == NULL) goto err;
+ }
+ else
+ rnd=ret;
+ BN_init(&t);
loop:
/* make a random number and set the top and bottom bits */
if (add == NULL)
}
else
{
- if (strong)
+ if (safe)
{
- if (!probable_prime_dh_strong(rnd,bits,add,rem,ctx))
+ if (!probable_prime_dh_safe(rnd,bits,add,rem,ctx))
goto err;
}
else
/* if (BN_mod_word(rnd,(BN_ULONG)3) == 1) goto loop; */
if (callback != NULL) callback(0,c1++,cb_arg);
- if (!strong)
+ if (!safe)
{
- i=BN_is_prime(rnd,BN_prime_checks,callback,ctx,cb_arg);
+ i=BN_is_prime_fasttest(rnd,checks,callback,ctx,cb_arg,0);
if (i == -1) goto err;
if (i == 0) goto loop;
}
else
{
- /* for a strong prime generation,
+ /* for "safe prime" generation,
* check that (p-1)/2 is prime.
* Since a prime is odd, We just
* need to divide by 2 */
- if (!BN_rshift1(t,rnd)) goto err;
+ if (!BN_rshift1(&t,rnd)) goto err;
- for (i=0; i<BN_prime_checks; i++)
+ for (i=0; i<checks; i++)
{
- j=BN_is_prime(rnd,1,callback,ctx,cb_arg);
+ j=BN_is_prime_fasttest(rnd,1,callback,ctx,cb_arg,0);
if (j == -1) goto err;
if (j == 0) goto loop;
- j=BN_is_prime(t,1,callback,ctx,cb_arg);
+ j=BN_is_prime_fasttest(&t,1,callback,ctx,cb_arg,0);
if (j == -1) goto err;
if (j == 0) goto loop;
if (callback != NULL) callback(2,c1-1,cb_arg);
- /* We have a strong prime test pass */
+ /* We have a safe prime test pass */
}
}
/* we have a prime :-) */
- ret=rnd;
+ found = 1;
err:
- if ((ret == NULL) && (rnd != NULL)) BN_free(rnd);
- if (t != NULL) BN_free(t);
+ if (!found && (ret == NULL) && (rnd != NULL)) BN_free(rnd);
+ BN_free(&t);
if (ctx != NULL) BN_CTX_free(ctx);
- return(ret);
+ return(found ? rnd : NULL);
+ }
+
+int BN_is_prime(BIGNUM *a, int checks, void (*callback)(int,int,void *),
+ BN_CTX *ctx_passed, void *cb_arg)
+ {
+ return BN_is_prime_fasttest(a, checks, callback, ctx_passed, cb_arg, 0);
}
-int BN_is_prime(a,checks,callback,ctx_passed,cb_arg)
-BIGNUM *a;
-int checks;
-void (*callback)(P_I_I_P);
-BN_CTX *ctx_passed;
-char *cb_arg;
+int BN_is_prime_fasttest(BIGNUM *a, int checks,
+ void (*callback)(int,int,void *),
+ BN_CTX *ctx_passed, void *cb_arg,
+ int do_trial_division)
{
- int i,j,c2=0,ret= -1;
- BIGNUM *check;
- BN_CTX *ctx=NULL,*ctx2=NULL;
- BN_MONT_CTX *mont=NULL;
+ int i, j, ret = -1;
+ int k;
+ BN_CTX *ctx = NULL;
+ BIGNUM *a1, *a1_odd, *check; /* taken from ctx */
+ BN_MONT_CTX *mont = NULL;
+ if (checks == BN_prime_checks)
+ checks = BN_prime_checks_for_size(BN_num_bits(a));
+
+ if (a->neg) /* for now, refuse to handle negative numbers */
+ return -1;
+
+ /* first look for small factors */
if (!BN_is_odd(a))
return(0);
+ if (do_trial_division)
+ {
+ for (i = 1; i < NUMPRIMES; i++)
+ if (BN_mod_word(a, primes[i]) == 0)
+ return 0;
+ if (callback != NULL) callback(1, -1, cb_arg);
+ }
+
if (ctx_passed != NULL)
- ctx=ctx_passed;
+ ctx = ctx_passed;
else
- if ((ctx=BN_CTX_new()) == NULL) goto err;
-
- if ((ctx2=BN_CTX_new()) == NULL) goto err;
- if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
-
- check=ctx->bn[ctx->tos++];
-
- /* Setup the montgomery structure */
- if (!BN_MONT_CTX_set(mont,a,ctx2)) goto err;
+ if ((ctx=BN_CTX_new()) == NULL)
+ goto err;
+ a1 = &(ctx->bn[ctx->tos++]);
+ a1_odd = &(ctx->bn[ctx->tos++]);
+ check = &(ctx->bn[ctx->tos++]);;
+
+ /* compute a1 := a - 1 */
+ if (!BN_copy(a1, a))
+ goto err;
+ if (!BN_sub_word(a1, 1))
+ goto err;
+ if (BN_is_zero(a1))
+ {
+ ret = 0;
+ goto err;
+ }
- for (i=0; i<checks; i++)
+ /* write a1 as a1_odd * 2^k */
+ k = 1;
+ while (!BN_is_bit_set(a1, k))
+ k++;
+ if (!BN_rshift(a1_odd, a1, k))
+ goto err;
+
+ /* Montgomery setup for computations mod a */
+ mont = BN_MONT_CTX_new();
+ if (mont == NULL)
+ goto err;
+ if (!BN_MONT_CTX_set(mont, a, ctx))
+ goto err;
+
+ for (i = 0; i < checks; i++)
{
- if (!BN_rand(check,BN_num_bits(a)-1,0,0)) goto err;
- j=witness(check,a,ctx,ctx2,mont);
+ if (!BN_pseudo_rand(check, BN_num_bits(a1), 0, 0))
+ goto err;
+ if (BN_cmp(check, a1) >= 0)
+ if (!BN_sub(check, check, a1))
+ goto err;
+ if (!BN_add_word(check, 1))
+ goto err;
+ /* now 1 <= check < a */
+
+ j = witness(check, a, a1, a1_odd, k, ctx, mont);
if (j == -1) goto err;
if (j)
{
ret=0;
goto err;
}
- if (callback != NULL) callback(1,c2++,cb_arg);
+ if (callback != NULL) callback(1,i,cb_arg);
}
ret=1;
err:
- ctx->tos--;
- if ((ctx_passed == NULL) && (ctx != NULL))
+ if (ctx_passed != NULL)
+ ctx_passed->tos -= 3; /* a1, a1_odd, check */
+ else if (ctx != NULL)
BN_CTX_free(ctx);
- if (ctx2 != NULL)
- BN_CTX_free(ctx2);
- if (mont != NULL) BN_MONT_CTX_free(mont);
-
+ if (mont != NULL)
+ BN_MONT_CTX_free(mont);
+
return(ret);
}
-#define RECP_MUL_MOD
-
-static int witness(a,n,ctx,ctx2,mont)
-BIGNUM *a;
-BIGNUM *n;
-BN_CTX *ctx,*ctx2;
-BN_MONT_CTX *mont;
+static int witness(BIGNUM *w, BIGNUM *a, BIGNUM *a1, BIGNUM *a1_odd, int k,
+ BN_CTX *ctx, BN_MONT_CTX *mont)
{
- int k,i,ret= -1,good;
- BIGNUM *d,*dd,*tmp,*d1,*d2,*n1;
- BIGNUM *mont_one,*mont_n1,*mont_a;
-
- d1=ctx->bn[ctx->tos];
- d2=ctx->bn[ctx->tos+1];
- n1=ctx->bn[ctx->tos+2];
- ctx->tos+=3;
-
- mont_one=ctx2->bn[ctx2->tos];
- mont_n1=ctx2->bn[ctx2->tos+1];
- mont_a=ctx2->bn[ctx2->tos+2];
- ctx2->tos+=3;
-
- d=d1;
- dd=d2;
- if (!BN_one(d)) goto err;
- if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
- k=BN_num_bits(n1);
-
- if (!BN_to_montgomery(mont_one,BN_value_one(),mont,ctx2)) goto err;
- if (!BN_to_montgomery(mont_n1,n1,mont,ctx2)) goto err;
- if (!BN_to_montgomery(mont_a,a,mont,ctx2)) goto err;
-
- BN_copy(d,mont_one);
- for (i=k-1; i>=0; i--)
+ if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
+ return -1;
+ if (BN_is_one(w))
+ return 0; /* probably prime */
+ if (BN_cmp(w, a1) == 0)
+ return 0; /* w == -1 (mod a), 'a' is probably prime */
+ while (--k)
{
- if ( (BN_cmp(d,mont_one) != 0) &&
- (BN_cmp(d,mont_n1) != 0))
- good=1;
- else
- good=0;
-
- BN_mod_mul_montgomery(dd,d,d,mont,ctx2);
-
- if (good && (BN_cmp(dd,mont_one) == 0))
- {
- ret=1;
- goto err;
- }
- if (BN_is_bit_set(n1,i))
- {
- BN_mod_mul_montgomery(d,dd,mont_a,mont,ctx2);
- }
- else
- {
- tmp=d;
- d=dd;
- dd=tmp;
- }
+ if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
+ return -1;
+ if (BN_is_one(w))
+ return 1; /* 'a' is composite, otherwise a previous 'w' would
+ * have been == -1 (mod 'a') */
+ if (BN_cmp(w, a1) == 0)
+ return 0; /* w == -1 (mod a), 'a' is probably prime */
}
- if (BN_cmp(d,mont_one) == 0)
- i=0;
- else i=1;
- ret=i;
-err:
- ctx->tos-=3;
- ctx2->tos-=3;
- return(ret);
+ /* If we get here, 'w' is the (a-1)/2-th power of the original 'w',
+ * and it is neither -1 nor +1 -- so 'a' cannot be prime */
+ return 1;
}
-static int probable_prime(rnd, bits)
-BIGNUM *rnd;
-int bits;
+static int probable_prime(BIGNUM *rnd, int bits)
{
int i;
- MS_STATIC BN_ULONG mods[NUMPRIMES];
- BN_ULONG delta;
+ BN_ULONG mods[NUMPRIMES];
+ BN_ULONG delta,d;
+again:
if (!BN_rand(rnd,bits,1,1)) return(0);
/* we now have a random number 'rand' to test. */
for (i=1; i<NUMPRIMES; i++)
* that gcd(rnd-1,primes) == 1 (except for 2) */
if (((mods[i]+delta)%primes[i]) <= 1)
{
+ d=delta;
delta+=2;
/* perhaps need to check for overflow of
- * delta (but delta can be upto 2^32) */
+ * delta (but delta can be upto 2^32)
+ * 21-May-98 eay - added overflow check */
+ if (delta < d) goto again;
goto loop;
}
}
return(1);
}
-static int probable_prime_dh(rnd, bits, add, rem,ctx)
-BIGNUM *rnd;
-int bits;
-BIGNUM *add;
-BIGNUM *rem;
-BN_CTX *ctx;
+static int probable_prime_dh(BIGNUM *rnd, int bits, BIGNUM *add, BIGNUM *rem,
+ BN_CTX *ctx)
{
int i,ret=0;
BIGNUM *t1;
- t1=ctx->bn[ctx->tos++];
+ t1= &(ctx->bn[ctx->tos++]);
if (!BN_rand(rnd,bits,0,1)) goto err;
loop: for (i=1; i<NUMPRIMES; i++)
{
/* check that rnd is a prime */
- if (BN_mod_word(rnd,(BN_LONG)primes[i]) <= 1)
+ if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1)
{
if (!BN_add(rnd,rnd,add)) goto err;
goto loop;
return(ret);
}
-static int probable_prime_dh_strong(p, bits, padd, rem,ctx)
-BIGNUM *p;
-int bits;
-BIGNUM *padd;
-BIGNUM *rem;
-BN_CTX *ctx;
+static int probable_prime_dh_safe(BIGNUM *p, int bits, BIGNUM *padd,
+ BIGNUM *rem, BN_CTX *ctx)
{
int i,ret=0;
BIGNUM *t1,*qadd=NULL,*q=NULL;
bits--;
- t1=ctx->bn[ctx->tos++];
- q=ctx->bn[ctx->tos++];
- qadd=ctx->bn[ctx->tos++];
+ t1= &(ctx->bn[ctx->tos++]);
+ q= &(ctx->bn[ctx->tos++]);
+ qadd= &(ctx->bn[ctx->tos++]);
if (!BN_rshift1(qadd,padd)) goto err;
/* check that p and q are prime */
/* check that for p and q
* gcd(p-1,primes) == 1 (except for 2) */
- if ( (BN_mod_word(p,(BN_LONG)primes[i]) == 0) ||
- (BN_mod_word(q,(BN_LONG)primes[i]) == 0))
+ if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) ||
+ (BN_mod_word(q,(BN_ULONG)primes[i]) == 0))
{
if (!BN_add(p,p,padd)) goto err;
if (!BN_add(q,q,qadd)) goto err;
ctx->tos-=3;
return(ret);
}
-
-#if 0
-static int witness(a, n,ctx)
-BIGNUM *a;
-BIGNUM *n;
-BN_CTX *ctx;
- {
- int k,i,nb,ret= -1;
- BIGNUM *d,*dd,*tmp;
- BIGNUM *d1,*d2,*x,*n1,*inv;
-
- d1=ctx->bn[ctx->tos];
- d2=ctx->bn[ctx->tos+1];
- x=ctx->bn[ctx->tos+2];
- n1=ctx->bn[ctx->tos+3];
- inv=ctx->bn[ctx->tos+4];
- ctx->tos+=5;
-
- d=d1;
- dd=d2;
- if (!BN_one(d)) goto err;
- if (!BN_sub(n1,n,d)) goto err; /* n1=n-1; */
- k=BN_num_bits(n1);
-
- /* i=BN_num_bits(n); */
-#ifdef RECP_MUL_MOD
- nb=BN_reciprocal(inv,n,ctx); /**/
- if (nb == -1) goto err;
-#endif
-
- for (i=k-1; i>=0; i--)
- {
- if (BN_copy(x,d) == NULL) goto err;
-#ifndef RECP_MUL_MOD
- if (!BN_mod_mul(dd,d,d,n,ctx)) goto err;
-#else
- if (!BN_mod_mul_reciprocal(dd,d,d,n,inv,nb,ctx)) goto err;
-#endif
- if ( BN_is_one(dd) &&
- !BN_is_one(x) &&
- (BN_cmp(x,n1) != 0))
- {
- ret=1;
- goto err;
- }
- if (BN_is_bit_set(n1,i))
- {
-#ifndef RECP_MUL_MOD
- if (!BN_mod_mul(d,dd,a,n,ctx)) goto err;
-#else
- if (!BN_mod_mul_reciprocal(d,dd,a,n,inv,nb,ctx)) goto err;
-#endif
- }
- else
- {
- tmp=d;
- d=dd;
- dd=tmp;
- }
- }
- if (BN_is_one(d))
- i=0;
- else i=1;
- ret=i;
-err:
- ctx->tos-=5;
- return(ret);
- }
-#endif
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