Improve BN_mod_inverse performance.

Get the BN_mod_exp_mont bugfix (for handling negative inputs) correct
this time.

CHANGES

@@ -3,6 +3,12 @@
 
  Changes between 0.9.6 and 0.9.7  [xx XXX 2000]
 
+  *) Make BN_mod_inverse faster by explicitly handling small quotients
+     in the Euclid loop instead of always using BN_div.
+     (Speed gain about 20% for small moduli [256 or 512 bits], about
+     30% for larger ones [1024 or 2048 bits].)
+     [Bodo Moeller]
+
   *) Disable ssl2_peek and ssl3_peek (i.e., both implementations
      of SSL_peek) because they both are completely broken.
      They will be fixed RSN by adding an additional 'peek' parameter

crypto/bn/bn_exp.c

@@ -376,7 +376,7 @@ int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 
 	BN_init(&val[0]);
 	ts=1;
-	if (!a->neg && BN_ucmp(a,m) >= 0)
+	if (a->neg || BN_ucmp(a,m) >= 0)
 		{
 		if (!BN_nnmod(&(val[0]),a,m,ctx))
 			goto err;

crypto/bn/bn_gcd.c

@@ -204,7 +204,7 @@ err:
 BIGNUM *BN_mod_inverse(BIGNUM *in,
 	const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
 	{
-	BIGNUM *A,*B,*X,*Y,*M,*D,*R=NULL;
+	BIGNUM *A,*B,*X,*Y,*M,*D,*T,*R=NULL;
 	BIGNUM *ret=NULL;
 	int sign;
 
@@ -218,7 +218,8 @@ BIGNUM *BN_mod_inverse(BIGNUM *in,
 	D = BN_CTX_get(ctx);
 	M = BN_CTX_get(ctx);
 	Y = BN_CTX_get(ctx);
-	if (Y == NULL) goto err;
+	T = BN_CTX_get(ctx);
+	if (T == NULL) goto err;
 
 	if (in == NULL)
 		R=BN_new();
@@ -253,7 +254,47 @@ BIGNUM *BN_mod_inverse(BIGNUM *in,
 		 *     -sign*Y*a  ==  A   (mod |n|)
 		 */
 
-		if (!BN_div(D,M,A,B,ctx)) goto err;
+		/* (D, M) := (A/B, A%B) ... */
+		if (BN_num_bits(A) == BN_num_bits(B))
+			{
+			if (!BN_one(D)) goto err;
+			if (!BN_sub(M,A,B)) goto err;
+			}
+		else if (BN_num_bits(A) == BN_num_bits(B) + 1)
+			{
+			/* A/B is 1, 2, or 3 */
+			if (!BN_lshift1(T,B)) goto err;
+			if (BN_ucmp(A,T) < 0)
+				{
+				/* A < 2*B, so D=1 */
+				if (!BN_one(D)) goto err;
+				if (!BN_sub(M,A,B)) goto err;
+				}
+			else
+				{
+				/* A >= 2*B, so D=2 or D=3 */
+				if (!BN_sub(M,A,T)) goto err;
+				if (!BN_add(D,T,B)) goto err; /* use D (:= 3*B) as temp */
+				if (BN_ucmp(A,D) < 0)
+					{
+					/* A < 3*B, so D=2 */
+					if (!BN_set_word(D,2)) goto err;
+					/* M (= A - 2*B) already has the correct value */
+					}
+				else
+					{
+					/* only D=3 remains */
+					if (!BN_set_word(D,3)) goto err;
+					/* currently  M = A - 2*B,  but we need  M = A - 3*B */
+					if (!BN_sub(M,M,B)) goto err;
+					}
+				}
+			}
+		else
+			{
+			if (!BN_div(D,M,A,B,ctx)) goto err;
+			}
+		
 		/* Now
 		 *      A = D*B + M;
 		 * thus we have
@@ -286,8 +327,33 @@ BIGNUM *BN_mod_inverse(BIGNUM *in,
 		 * Note that  X  and  Y  stay non-negative all the time.
 		 */
 
-		if (!BN_mul(tmp,D,X,ctx)) goto err;
-		if (!BN_add(tmp,tmp,Y)) goto err;
+		/* most of the time D is very small, so we can optimize tmp := D*X+Y */
+		if (BN_is_one(D))
+			{
+			if (!BN_add(tmp,X,Y)) goto err;
+			}
+		else
+			{
+			if (BN_is_word(D,2))
+				{
+				if (!BN_lshift1(tmp,X)) goto err;
+				}
+			else if (BN_is_word(D,3))
+				{
+				if (!BN_lshift1(tmp,X)) goto err;
+				if (!BN_add(tmp,tmp,X)) goto err;
+				}
+			else if (BN_is_word(D,4))
+				{
+				if (!BN_lshift(tmp,X,2)) goto err;
+				}
+			else
+				{
+				if (!BN_mul(tmp,D,X,ctx)) goto err;
+				}
+			if (!BN_add(tmp,tmp,Y)) goto err;
+			}
+		
 		M=Y; /* keep the BIGNUM object, the value does not matter */
 		Y=X;
 		X=tmp;
@@ -312,7 +378,10 @@ BIGNUM *BN_mod_inverse(BIGNUM *in,
 	if (BN_is_one(A))
 		{
 		/* Y*a == 1  (mod |n|) */
-		if (!BN_mod(R,Y,n,ctx)) goto err;
+		if (BN_ucmp(Y,n) < 0)
+			if (!BN_copy(R,Y)) goto err;
+		else
+			if (!BN_nnmod(R,Y,n,ctx)) goto err;
 		}
 	else
 		{

crypto/bn/expspeed.c

@@ -60,7 +60,16 @@
 
 /* most of this code has been pilfered from my libdes speed.c program */
 
-#define BASENUM	5000
+#define BASENUM	10000
+#define NUM_START 0
+
+
+/* determine timings for modexp, gcd, or modular inverse */
+#define TEST_EXP
+#undef TEST_GCD
+#undef TEST_INV
+
+
 #undef PROG
 #define PROG bnspeed_main
 
@@ -161,11 +170,30 @@ static double Time_F(int s)
 #endif
 	}
 
-#define NUM_SIZES	6
-static int sizes[NUM_SIZES]={256,512,1024,2048,4096,8192};
-static int mul_c[NUM_SIZES]={8*8*8*8*8,8*8*8*8,8*8*8,8*8,8,1};
+#define NUM_SIZES	7
+#if NUM_START > NUM_SIZES
+#   error "NUM_START > NUM_SIZES"
+#endif
+static int sizes[NUM_SIZES]={128,256,512,1024,2048,4096,8192};
+static int mul_c[NUM_SIZES]={8*8*8*8*8*8,8*8*8*8*8,8*8*8*8,8*8*8,8*8,8,1};
 /*static int sizes[NUM_SIZES]={59,179,299,419,539}; */
 
+#define RAND_SEED(string) { const char str[] = string; RAND_seed(string, sizeof string); }
+
+static void genprime_cb(int p, int n, void *arg)
+	{
+	char c='*';
+
+	if (p == 0) c='.';
+	if (p == 1) c='+';
+	if (p == 2) c='*';
+	if (p == 3) c='\n';
+	putc(c, stderr);
+	fflush(stderr);
+	(void)n;
+	(void)arg;
+	}
+
 void do_mul_exp(BIGNUM *r,BIGNUM *a,BIGNUM *b,BIGNUM *c,BN_CTX *ctx); 
 
 int main(int argc, char **argv)
@@ -179,6 +207,10 @@ int main(int argc, char **argv)
 	c=BN_new();
 	r=BN_new();
 
+	while (!RAND_status())
+		/* not enough bits */
+		RAND_SEED("I demand a manual recount!");
+
 	do_mul_exp(r,a,b,c,ctx);
 	}
 
@@ -188,23 +220,61 @@ void do_mul_exp(BIGNUM *r, BIGNUM *a, BIGNUM *b, BIGNUM *c, BN_CTX *ctx)
 	double tm;
 	long num;
 
+#if defined(TEST_EXP) + defined(TEST_GCD) + defined(TEST_INV) != 1
+#  error "choose one test"
+#endif
+
+#ifdef TEST_INV
+#  define C_PRIME
+#endif
+
 	num=BASENUM;
-	for (i=0; i<NUM_SIZES; i++)
+	for (i=NUM_START; i<NUM_SIZES; i++)
 		{
-		BN_pseudo_rand(a,sizes[i],1,0);
-		BN_pseudo_rand(b,sizes[i],1,0);
-		BN_pseudo_rand(c,sizes[i],1,1);
-		BN_mod(a,a,c,ctx);
-		BN_mod(b,b,c,ctx);
+#ifdef C_PRIME
+		if (!BN_generate_prime(c,sizes[i],0,NULL,NULL,genprime_cb,NULL)) goto err;
+		putc('\n', stderr);
+		fflush(stderr);
+#endif
 
 		Time_F(START);
 		for (k=0; k<num; k++)
-			BN_mod_exp(r,a,b,c,ctx);
+			{
+			if (k%50 == 0) /* Average over num/50 different choices of random numbers. */
+				{
+				if (!BN_pseudo_rand(a,sizes[i],1,0)) goto err;
+				if (!BN_pseudo_rand(b,sizes[i],1,0)) goto err;
+#ifndef C_PRIME
+				if (!BN_pseudo_rand(c,sizes[i],1,1)) goto err;
+#endif
+				}
+#if defined(TEST_EXP)
+			if (!BN_mod_exp(r,a,b,c,ctx)) goto err;
+#elif defined(TEST_GCD)
+			if (!BN_gcd(r,a,b,ctx)) goto err;
+			if (!BN_gcd(r,b,c,ctx)) goto err;
+			if (!BN_gcd(r,b,c,ctx)) goto err;
+#else /* TEST_INV */
+			if (!BN_mod_inverse(r,a,c,ctx)) goto err;
+			if (!BN_mod_inverse(r,b,c,ctx)) goto err;
+#endif
+			}
 		tm=Time_F(STOP);
-		printf("mul %4d ^ %4d %% %d -> %8.3fms %5.1f\n",sizes[i],sizes[i],sizes[i],tm*1000.0/num,tm*mul_c[i]/num);
+		printf(
+#if defined(TEST_EXP)
+			"modexp %4d ^ %4d %% %4d"
+#elif defined(TEST_GCD)
+			"3*gcd %4d %4d %4d"
+#else /* TEST_INV */
+			"2*inv %4d %4d mod %4d"
+#endif
+			" -> %8.3fms %5.1f (%d)\n",sizes[i],sizes[i],sizes[i],tm*1000.0/num,tm*mul_c[i]/num, num);
 		num/=7;
 		if (num <= 0) num=1;
 		}
+	return;
 
+ err:
+	ERR_print_errors_fp(stderr);
 	}