diff --git a/CHANGES b/CHANGES
index aa62657c18e757df6515cccc9a2d52816a2171d7..8ec710732e81b219de43779718dbd6fe7a8f0158 100644
--- a/CHANGES
+++ b/CHANGES
@@ -4,6 +4,14 @@
 
  Changes between 0.9.4 and 0.9.5  [xx XXX 1999]
 
+  *) Do more iterations of Rabin-Miller probable prime test (specifically,
+     3 for 1024-bit primes, 6 for 512-bit primes, 12 for 256-bit primes
+     instead of only 2 for all lengths; see BN_prime_checks definition
+     in crypto/bn/bn.h for the complete table).  This guarantees a
+     false-positive rate of at most 2^-80 (actually less because we are
+     additionally doing trial division) for random input.
+     [Bodo Moeller]
+
   *) Rewrite ssl3_read_n (ssl/s3_pkt.c) avoiding a couple of bugs.
      [Bodo Moeller]
 
diff --git a/crypto/bn/bn.h b/crypto/bn/bn.h
index f935e1ca79d7f1699d56cfbbdd5fadb09b26df84..dd1d263098dec754759bc6b42be2af3af53c2d59 100644
--- a/crypto/bn/bn.h
+++ b/crypto/bn/bn.h
@@ -283,7 +283,23 @@ typedef struct bn_recp_ctx_st
 #define BN_to_montgomery(r,a,mont,ctx)	BN_mod_mul_montgomery(\
 	r,a,&((mont)->RR),(mont),ctx)
 
-#define BN_prime_checks		(5)
+/* number of Miller-Rabin iterations for an error rate  of less than 2^-80
+ * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook
+ * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996];
+ * original paper: Damgaard, Landrock, Pomerance: Average case error estimates
+ * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */
+#define BN_prime_checks(b) ((b) >= 1300 ?  2 : \
+                            (b) >=  850 ?  3 : \
+                            (b) >=  650 ?  4 : \
+                            (b) >=  550 ?  5 : \
+                            (b) >=  450 ?  6 : \
+                            (b) >=  400 ?  7 : \
+                            (b) >=  350 ?  8 : \
+                            (b) >=  300 ?  9 : \
+                            (b) >=  250 ? 12 : \
+                            (b) >=  200 ? 15 : \
+                            (b) >=  150 ? 18 : \
+                            /* b >= 100 */ 27)
 
 #define BN_num_bytes(a)	((BN_num_bits(a)+7)/8)
 #define BN_is_word(a,w)	(((a)->top == 1) && ((a)->d[0] == (BN_ULONG)(w)))
@@ -381,7 +397,7 @@ int 	BN_hex2bn(BIGNUM **a, const char *str);
 int 	BN_dec2bn(BIGNUM **a, const char *str);
 int	BN_gcd(BIGNUM *r,BIGNUM *in_a,BIGNUM *in_b,BN_CTX *ctx);
 BIGNUM *BN_mod_inverse(BIGNUM *ret,BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
-BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int strong,BIGNUM *add,
+BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,BIGNUM *add,
 		BIGNUM *rem,void (*callback)(int,int,void *),void *cb_arg);
 int	BN_is_prime(BIGNUM *p,int nchecks,void (*callback)(int,int,void *),
 		BN_CTX *ctx,void *cb_arg);
diff --git a/crypto/bn/bn_prime.c b/crypto/bn/bn_prime.c
index 6fa0f9be1ee32b4767e8ed154832b88923601119..57305c7273b5b271665a0d9d29e0453b2849d1d8 100644
--- a/crypto/bn/bn_prime.c
+++ b/crypto/bn/bn_prime.c
@@ -73,15 +73,16 @@ static int witness(BIGNUM *a, BIGNUM *n, BN_CTX *ctx,BN_CTX *ctx2,
 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);
-BIGNUM *BN_generate_prime(BIGNUM *ret, int bits, int strong, BIGNUM *add,
+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 t;
 	int i,j,c1=0;
 	BN_CTX *ctx;
+	int checks = BN_prime_checks(bits);
 
 	ctx=BN_CTX_new();
 	if (ctx == NULL) goto err;
@@ -100,9 +101,9 @@ loop:
 		}
 	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
@@ -114,21 +115,21 @@ loop:
 	/* 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(rnd,checks,callback,ctx,cb_arg);
 		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;
 
-		for (i=0; i<BN_prime_checks; i++)
+		for (i=0; i<checks; i++)
 			{
 			j=BN_is_prime(rnd,1,callback,ctx,cb_arg);
 			if (j == -1) goto err;
@@ -139,7 +140,7 @@ loop:
 			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 :-) */
@@ -331,7 +332,7 @@ err:
 	return(ret);
 	}
 
-static int probable_prime_dh_strong(BIGNUM *p, int bits, BIGNUM *padd,
+static int probable_prime_dh_safe(BIGNUM *p, int bits, BIGNUM *padd,
 	     BIGNUM *rem, BN_CTX *ctx)
 	{
 	int i,ret=0;
diff --git a/crypto/bn/bn_prime.h b/crypto/bn/bn_prime.h
index c10217dfea830cd67e4c14f727ae61b819c1f1ba..8bb168517da3af06d34e2a4702490360bdecbdd1 100644
--- a/crypto/bn/bn_prime.h
+++ b/crypto/bn/bn_prime.h
@@ -55,6 +55,7 @@
  * copied and put under another distribution licence
  * [including the GNU Public Licence.]
  */
+
 #ifndef EIGHT_BIT
 #define NUMPRIMES 2048
 #else
diff --git a/crypto/dh/dh_check.c b/crypto/dh/dh_check.c
index 95ce9cfad012f9e531d298496b8244c6e3f7c705..a2e7433b9c8dab373b74978477192674b0808fe7 100644
--- a/crypto/dh/dh_check.c
+++ b/crypto/dh/dh_check.c
@@ -102,12 +102,12 @@ int DH_check(DH *dh, int *ret)
 	else
 		*ret|=DH_UNABLE_TO_CHECK_GENERATOR;
 
-	if (!BN_is_prime(dh->p,BN_prime_checks,NULL,ctx,NULL))
+	if (!BN_is_prime(dh->p,BN_prime_checks(BN_num_bits(dh->p)),NULL,ctx,NULL))
 		*ret|=DH_CHECK_P_NOT_PRIME;
 	else
 		{
 		if (!BN_rshift1(q,dh->p)) goto err;
-		if (!BN_is_prime(q,BN_prime_checks,NULL,ctx,NULL))
+		if (!BN_is_prime(q,BN_prime_checks(BN_num_bits(q)),NULL,ctx,NULL))
 			*ret|=DH_CHECK_P_NOT_STRONG_PRIME;
 		}
 	ok=1;
diff --git a/crypto/rsa/rsa_chk.c b/crypto/rsa/rsa_chk.c
index 91b91157983fe9e09025f7896314bec53c8dc82d..03497f846387fbeb555f129124c3d7caf14e9a5e 100644
--- a/crypto/rsa/rsa_chk.c
+++ b/crypto/rsa/rsa_chk.c
@@ -75,7 +75,7 @@ int RSA_check_key(RSA *key)
 		}
 	
 	/* p prime? */
-	r = BN_is_prime(key->p, BN_prime_checks, NULL, NULL, NULL);
+	r = BN_is_prime(key->p, BN_prime_checks(BN_num_bits(key->p)), NULL, NULL, NULL);
 	if (r != 1)
 		{
 		ret = r;
@@ -85,7 +85,7 @@ int RSA_check_key(RSA *key)
 		}
 	
 	/* q prime? */
-	r = BN_is_prime(key->q, BN_prime_checks, NULL, NULL, NULL);
+	r = BN_is_prime(key->q, BN_prime_checks(BN_num_bits(key->q)), NULL, NULL, NULL);
 	if (r != 1)
 		{
 		ret = r;