Takanori Yanagisawa has shown how to correctly use pre-computed values.

So in a sense this commit reverts few latest ones fixing bugs in original
code and improving it, most notably adding 64-bit support [though not in
BN_nist_mod_224 yet].
PR: 1593

1 files changed, 219 insertions, 231 deletions

diff --git a/crypto/bn/bn_nist.c b/crypto/bn/bn_nist.c
index e14232fdbb..d8b443c562 100644
--- a/crypto/bn/bn_nist.c
+++ b/crypto/bn/bn_nist.c
@@ -65,20 +65,43 @@
 #define BN_NIST_384_TOP	(384+BN_BITS2-1)/BN_BITS2
 #define BN_NIST_521_TOP	(521+BN_BITS2-1)/BN_BITS2
 
+/* pre-computed tables are "carry-less" values of modulus*(i+1) */
 #if BN_BITS2 == 64
-static const BN_ULONG _nist_p_192[] =
-	{0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFEULL,
-	0xFFFFFFFFFFFFFFFFULL};
-static const BN_ULONG _nist_p_224[] =
+static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
+	{0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFFULL},
+	{0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFFULL},
+	{0xFFFFFFFFFFFFFFFDULL,0xFFFFFFFFFFFFFFFCULL,0xFFFFFFFFFFFFFFFFULL}
+	};
+static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
 	{0x0000000000000001ULL,0xFFFFFFFF00000000ULL,
-	0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL};
-static const BN_ULONG _nist_p_256[] =
+	 0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL},
+	{0x0000000000000002ULL,0xFFFFFFFE00000000ULL,
+	 0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL}
+	};
+static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
 	{0xFFFFFFFFFFFFFFFFULL,0x00000000FFFFFFFFULL,
-	0x0000000000000000ULL,0xFFFFFFFF00000001ULL};
-static const BN_ULONG _nist_p_384[] =
-	{0x00000000FFFFFFFFULL,0xFFFFFFFF00000000ULL,
-	0xFFFFFFFFFFFFFFFEULL,0xFFFFFFFFFFFFFFFFULL,
-	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL};
+	 0x0000000000000000ULL,0xFFFFFFFF00000001ULL},
+	{0xFFFFFFFFFFFFFFFEULL,0x00000001FFFFFFFFULL,
+	 0x0000000000000000ULL,0xFFFFFFFE00000002ULL},
+	{0xFFFFFFFFFFFFFFFDULL,0x00000002FFFFFFFFULL,
+	 0x0000000000000000ULL,0xFFFFFFFD00000003ULL},
+	{0xFFFFFFFFFFFFFFFCULL,0x00000003FFFFFFFFULL,
+	 0x0000000000000000ULL,0xFFFFFFFC00000004ULL},
+	{0xFFFFFFFFFFFFFFFBULL,0x00000004FFFFFFFFULL,
+	 0x0000000000000000ULL,0xFFFFFFFB00000005ULL},
+	};
+static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
+	{0x00000000FFFFFFFFULL,0xFFFFFFFF00000000ULL,0xFFFFFFFFFFFFFFFEULL,
+	 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
+	{0x00000001FFFFFFFEULL,0xFFFFFFFE00000000ULL,0xFFFFFFFFFFFFFFFDULL,
+	 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
+	{0x00000002FFFFFFFDULL,0xFFFFFFFD00000000ULL,0xFFFFFFFFFFFFFFFCULL,
+	 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
+	{0x00000003FFFFFFFCULL,0xFFFFFFFC00000000ULL,0xFFFFFFFFFFFFFFFBULL,
+	 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
+	{0x00000004FFFFFFFBULL,0xFFFFFFFB00000000ULL,0xFFFFFFFFFFFFFFFAULL,
+	 0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL},
+	};
 static const BN_ULONG _nist_p_521[] =
 	{0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
@@ -86,15 +109,41 @@ static const BN_ULONG _nist_p_521[] =
 	0xFFFFFFFFFFFFFFFFULL,0xFFFFFFFFFFFFFFFFULL,
 	0x00000000000001FFULL};
 #elif BN_BITS2 == 32
-static const BN_ULONG _nist_p_192[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,
-	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
-static const BN_ULONG _nist_p_224[] = {0x00000001,0x00000000,0x00000000,
-	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
-static const BN_ULONG _nist_p_256[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
-	0x00000000,0x00000000,0x00000000,0x00000001,0xFFFFFFFF};
-static const BN_ULONG _nist_p_384[] = {0xFFFFFFFF,0x00000000,0x00000000,
-	0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
-	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
+static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = {
+	{0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
+	{0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
+	{0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
+	};
+static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = {
+	{0x00000001,0x00000000,0x00000000,0xFFFFFFFF,
+	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
+	{0x00000002,0x00000000,0x00000000,0xFFFFFFFE,
+	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF}
+	};
+static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = {
+	{0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0x00000000,
+	 0x00000000,0x00000000,0x00000001,0xFFFFFFFF},
+	{0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0x00000001,
+	 0x00000000,0x00000000,0x00000002,0xFFFFFFFE},
+	{0xFFFFFFFD,0xFFFFFFFF,0xFFFFFFFF,0x00000002,
+	 0x00000000,0x00000000,0x00000003,0xFFFFFFFD},
+	{0xFFFFFFFC,0xFFFFFFFF,0xFFFFFFFF,0x00000003,
+	 0x00000000,0x00000000,0x00000004,0xFFFFFFFC},
+	{0xFFFFFFFB,0xFFFFFFFF,0xFFFFFFFF,0x00000004,
+	 0x00000000,0x00000000,0x00000005,0xFFFFFFFB},
+	};
+static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = {
+	{0xFFFFFFFF,0x00000000,0x00000000,0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,
+	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
+	{0xFFFFFFFE,0x00000001,0x00000000,0xFFFFFFFE,0xFFFFFFFD,0xFFFFFFFF,
+	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
+	{0xFFFFFFFD,0x00000002,0x00000000,0xFFFFFFFD,0xFFFFFFFC,0xFFFFFFFF,
+	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
+	{0xFFFFFFFC,0x00000003,0x00000000,0xFFFFFFFC,0xFFFFFFFB,0xFFFFFFFF,
+	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
+	{0xFFFFFFFB,0x00000004,0x00000000,0xFFFFFFFB,0xFFFFFFFA,0xFFFFFFFF,
+	 0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF},
+	};
 static const BN_ULONG _nist_p_521[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
@@ -103,28 +152,28 @@ static const BN_ULONG _nist_p_521[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
 
 const BIGNUM *BN_get0_nist_prime_192(void)
 	{
-	static BIGNUM const_nist_192 = { (BN_ULONG *)_nist_p_192,
+	static BIGNUM const_nist_192 = { (BN_ULONG *)_nist_p_192[0],
 		BN_NIST_192_TOP, BN_NIST_192_TOP, 0, BN_FLG_STATIC_DATA };
 	return &const_nist_192;
 	}
 
 const BIGNUM *BN_get0_nist_prime_224(void)
 	{
-	static BIGNUM const_nist_224 = { (BN_ULONG *)_nist_p_224,
+	static BIGNUM const_nist_224 = { (BN_ULONG *)_nist_p_224[0],
 		BN_NIST_224_TOP, BN_NIST_224_TOP, 0, BN_FLG_STATIC_DATA };
 	return &const_nist_224;
 	}
 
 const BIGNUM *BN_get0_nist_prime_256(void)
 	{
-	static BIGNUM const_nist_256 = { (BN_ULONG *)_nist_p_256,
+	static BIGNUM const_nist_256 = { (BN_ULONG *)_nist_p_256[0],
 		BN_NIST_256_TOP, BN_NIST_256_TOP, 0, BN_FLG_STATIC_DATA };
 	return &const_nist_256;
 	}
 
 const BIGNUM *BN_get0_nist_prime_384(void)
 	{
-	static BIGNUM const_nist_384 = { (BN_ULONG *)_nist_p_384,
+	static BIGNUM const_nist_384 = { (BN_ULONG *)_nist_p_384[0],
 		BN_NIST_384_TOP, BN_NIST_384_TOP, 0, BN_FLG_STATIC_DATA };
 	return &const_nist_384;
 	}
@@ -159,9 +208,14 @@ static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
 #if BN_BITS2 == 64
 #define bn_cp_64(to, n, from, m)	(to)[n] = (m>=0)?((from)[m]):0;
 #define bn_64_set_0(to, n)		(to)[n] = (BN_ULONG)0;
-/* TBD */
-#define bn_cp_32(to, n, from, m)	(to)[n] = (m>=0)?((from)[m]):0;
-#define bn_32_set_0(to, n)		(to)[n] = (BN_ULONG)0;
+/*
+ * two following macros are implemented under assumption that they
+ * are called in a sequence with *ascending* n, i.e. as they are...
+ */
+#define bn_cp_32_naked(to, n, from, m)	(((n)&1)?(to[(n)/2]|=((m)&1)?(from[(m)/2]&BN_MASK2h):(from[(m)/2]<<32))\
+						:(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l)))
+#define bn_32_set_0(to, n)		(((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0));
+#define bn_cp_32(to,n,from,m)		((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n)
 #else
 #define bn_cp_64(to, n, from, m) \
 	{ \
@@ -182,9 +236,9 @@ static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
 
 #define nist_set_192(to, from, a1, a2, a3) \
 	{ \
-	if (a3 != 0) bn_cp_64(to, 0, from, (a3) - 3) else bn_64_set_0(to, 0)\
+	bn_cp_64(to, 0, from, (a3) - 3) \
 	bn_cp_64(to, 1, from, (a2) - 3) \
-	if (a1 != 0) bn_cp_64(to, 2, from, (a1) - 3) else bn_64_set_0(to, 2)\
+	bn_cp_64(to, 2, from, (a1) - 3) \
 	}
 
 int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
@@ -225,22 +279,25 @@ int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 
 	nist_set_192(t_d, buf, 0, 3, 3);
 	carry = bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_192,BN_NIST_192_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-	
 	nist_set_192(t_d, buf, 4, 4, 0);
-	carry = bn_add_words(r_d, res, t_d, BN_NIST_192_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_192,BN_NIST_192_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-
+	carry += bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 	nist_set_192(t_d, buf, 5, 5, 5)
-	carry = bn_add_words(r_d, res, t_d, BN_NIST_192_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_192,BN_NIST_192_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
+	carry += bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
 
+	if (carry > 0)
+		carry = bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
+	else
+		carry = 1;
+
+	/*
+	 * we need 'if (carry==0 || result>=modulus) result-=modulus;'
+	 * as comparison implies subtraction, we can write
+	 * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;'
+	 * this is what happens below, but without explicit if:-) a.
+	 */
+	mask  = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_192[0],BN_NIST_192_TOP);
+	mask &= 0-(size_t)carry;
+	res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 	nist_cp_bn(r_d, res, BN_NIST_192_TOP);
 	r->top = BN_NIST_192_TOP;
 	bn_correct_top(r);
@@ -248,15 +305,17 @@ int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 	return 1;
 	}
 
+typedef BN_ULONG (*bn_addsub_f)(BN_ULONG *,const BN_ULONG *,const BN_ULONG *,int);
+
 #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \
 	{ \
-	if (a7 != 0) bn_cp_32(to, 0, from, (a7) - 7) else bn_32_set_0(to, 0)\
-	if (a6 != 0) bn_cp_32(to, 1, from, (a6) - 7) else bn_32_set_0(to, 1)\
-	if (a5 != 0) bn_cp_32(to, 2, from, (a5) - 7) else bn_32_set_0(to, 2)\
-	if (a4 != 0) bn_cp_32(to, 3, from, (a4) - 7) else bn_32_set_0(to, 3)\
-	if (a3 != 0) bn_cp_32(to, 4, from, (a3) - 7) else bn_32_set_0(to, 4)\
-	if (a2 != 0) bn_cp_32(to, 5, from, (a2) - 7) else bn_32_set_0(to, 5)\
-	if (a1 != 0) bn_cp_32(to, 6, from, (a1) - 7) else bn_32_set_0(to, 6)\
+	bn_cp_32(to, 0, from, (a7) - 7) \
+	bn_cp_32(to, 1, from, (a6) - 7) \
+	bn_cp_32(to, 2, from, (a5) - 7) \
+	bn_cp_32(to, 3, from, (a4) - 7) \
+	bn_cp_32(to, 4, from, (a3) - 7) \
+	bn_cp_32(to, 5, from, (a2) - 7) \
+	bn_cp_32(to, 6, from, (a1) - 7) \
 	}
 
 int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
@@ -271,6 +330,7 @@ int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 		 c_d[BN_NIST_224_TOP],
 		*res;
 	size_t   mask;
+	union { bn_addsub_f f; size_t p; } u;
 
 	i = BN_ucmp(field, a);
 	if (i == 0)
@@ -298,38 +358,36 @@ int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 
 	nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
 	carry = bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_224,BN_NIST_224_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-	
 	nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
-	carry = bn_add_words(r_d, res, t_d, BN_NIST_224_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_224,BN_NIST_224_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-
+	carry += bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 	nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7);
-#if BRANCH_FREE
-	carry = bn_sub_words(r_d, res, t_d, BN_NIST_224_TOP);
-	bn_add_words(c_d,r_d,_nist_p_224,BN_NIST_224_TOP);
-	mask = 0-(size_t)carry;
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-#else
-	if (bn_sub_words(r_d, res, t_d, BN_NIST_224_TOP))
-		bn_add_words(r_d,r_d,_nist_p_224,BN_NIST_224_TOP);
-#endif
+	carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 	nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11);
-#if BRANCH_FREE
-	carry = bn_sub_words(r_d, res, t_d, BN_NIST_224_TOP);
-	bn_add_words(c_d,r_d,_nist_p_224,BN_NIST_224_TOP);
-	mask = 0-(size_t)carry;
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
+	carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP);
 
+	u.f = bn_sub_words;
+	if (carry > 0)
+		carry = bn_sub_words(r_d,r_d,_nist_p_224[carry-1],BN_NIST_224_TOP);
+	else if (carry < 0)
+		{
+		/* it's a bit more comlicated logic in this case.
+		 * if bn_add_words yields no carry, then result
+		 * has to be adjusted by unconditionally *adding*
+		 * the modulus. but if it does, then result has
+		 * to be compared to the modulus and conditionally
+		 * adjusted by *subtracting* the latter. */
+		carry = bn_add_words(r_d,r_d,_nist_p_224[-carry-1],BN_NIST_224_TOP);
+		mask = 0-(size_t)carry;
+		u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
+		}
+	else
+		carry = 1;
+
+	/* otherwise it's effectively same as in BN_nist_mod_192... */
+	mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_224[0],BN_NIST_224_TOP);
+	mask &= 0-(size_t)carry;
+	res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 	nist_cp_bn(r_d, res, BN_NIST_224_TOP);
-#else
-	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP))
-		bn_add_words(r_d,r_d,_nist_p_224,BN_NIST_224_TOP);
-#endif
 	r->top = BN_NIST_224_TOP;
 	bn_correct_top(r);
 
@@ -341,20 +399,19 @@ int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 
 #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \
 	{ \
-	if (a8 != 0) bn_cp_32(to, 0, from, (a8) - 8) else bn_32_set_0(to, 0)\
-	if (a7 != 0) bn_cp_32(to, 1, from, (a7) - 8) else bn_32_set_0(to, 1)\
-	if (a6 != 0) bn_cp_32(to, 2, from, (a6) - 8) else bn_32_set_0(to, 2)\
-	if (a5 != 0) bn_cp_32(to, 3, from, (a5) - 8) else bn_32_set_0(to, 3)\
-	if (a4 != 0) bn_cp_32(to, 4, from, (a4) - 8) else bn_32_set_0(to, 4)\
-	if (a3 != 0) bn_cp_32(to, 5, from, (a3) - 8) else bn_32_set_0(to, 5)\
-	if (a2 != 0) bn_cp_32(to, 6, from, (a2) - 8) else bn_32_set_0(to, 6)\
-	if (a1 != 0) bn_cp_32(to, 7, from, (a1) - 8) else bn_32_set_0(to, 7)\
+	bn_cp_32(to, 0, from, (a8) - 8) \
+	bn_cp_32(to, 1, from, (a7) - 8) \
+	bn_cp_32(to, 2, from, (a6) - 8) \
+	bn_cp_32(to, 3, from, (a5) - 8) \
+	bn_cp_32(to, 4, from, (a4) - 8) \
+	bn_cp_32(to, 5, from, (a3) - 8) \
+	bn_cp_32(to, 6, from, (a2) - 8) \
+	bn_cp_32(to, 7, from, (a1) - 8) \
 	}
 
 int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 	BN_CTX *ctx)
 	{
-#if BN_BITS2 == 32
 	int	i, top = a->top;
 	int	carry = 0;
 	register BN_ULONG *a_d = a->d, *r_d;
@@ -363,6 +420,7 @@ int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 		 c_d[BN_NIST_256_TOP],
 		*res;
 	size_t   mask;
+	union { bn_addsub_f f; size_t p; } u;
 
 	i = BN_ucmp(field, a);
 	if (i == 0)
@@ -391,111 +449,84 @@ int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 	/*S1*/
 	nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
 	/*S2*/
-	nist_set_256(c_d,buf, 0, 15, 14, 13, 12, 0, 0, 0);
+	nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0);
 	carry = bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,t_d,_nist_p_256,BN_NIST_256_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)t_d&~mask));
-
-	carry = bn_add_words(t_d, res, res, BN_NIST_256_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,t_d,_nist_p_256,BN_NIST_256_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)t_d&~mask));
-
-	carry = bn_add_words(r_d, r_d, res, BN_NIST_256_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_256,BN_NIST_256_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-
+	/* left shift */
+		{
+		register BN_ULONG *ap,t,c;
+		ap = t_d;
+		c=0;
+		for (i = BN_NIST_256_TOP; i != 0; --i)
+			{
+			t= *ap;
+			*(ap++)=((t<<1)|c)&BN_MASK2;
+			c=(t & BN_TBIT)?1:0;
+			}
+		carry <<= 1;
+		carry  |= c;
+		}
+	carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 	/*S3*/
 	nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8);
-	carry = bn_add_words(r_d, res, t_d, BN_NIST_256_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_256,BN_NIST_256_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-
+	carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 	/*S4*/
 	nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9);
-	carry = bn_add_words(r_d, res, t_d, BN_NIST_256_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_256,BN_NIST_256_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-
+	carry += bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 	/*D1*/
 	nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11);
-#if BRANCH_FREE
-	carry = bn_sub_words(r_d, res, t_d, BN_NIST_256_TOP);
-	bn_add_words(c_d,r_d,_nist_p_256,BN_NIST_256_TOP);
-	mask = 0-(size_t)carry;
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));	
-#else
-	if (bn_sub_words(r_d, res, t_d, BN_NIST_256_TOP))
-		bn_add_words(r_d,r_d,_nist_p_256,BN_NIST_256_TOP);
-#endif
+	carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 	/*D2*/
 	nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12);
-#if BRANCH_FREE
-	carry = bn_sub_words(r_d, res, t_d, BN_NIST_256_TOP);
-	bn_add_words(c_d,r_d,_nist_p_256,BN_NIST_256_TOP);
-	mask = 0-(size_t)carry;
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));	
-#else
-	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP))
-		bn_add_words(r_d,r_d,_nist_p_256,BN_NIST_256_TOP);
-#endif
+	carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 	/*D3*/
 	nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13);
-#if BRANCH_FREE
-	carry = bn_sub_words(r_d, res, t_d, BN_NIST_256_TOP);
-	bn_add_words(c_d,r_d,_nist_p_256,BN_NIST_256_TOP);
-	mask = 0-(size_t)carry;
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));	
-#else
-	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP))
-		bn_add_words(r_d,r_d,_nist_p_256,BN_NIST_256_TOP);
-#endif
+	carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 	/*D4*/
 	nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14);
-#if BRANCH_FREE
-	carry = bn_sub_words(r_d, res, t_d, BN_NIST_256_TOP);
-	bn_add_words(c_d,r_d,_nist_p_256,BN_NIST_256_TOP);
-	mask = 0-(size_t)carry;
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));	
+	carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
 
-	nist_cp_bn(r_d, res, BN_NIST_384_TOP);
-#else
-	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP))
-		bn_add_words(r_d,r_d,_nist_p_256,BN_NIST_256_TOP);
-#endif
+	/* see BN_nist_mod_224 for explanation */
+	u.f = bn_sub_words;
+	if (carry > 0)
+		carry = bn_sub_words(r_d,r_d,_nist_p_256[carry-1],BN_NIST_256_TOP);
+	else if (carry < 0)
+		{
+		carry = bn_add_words(r_d,r_d,_nist_p_256[-carry-1],BN_NIST_256_TOP);
+		mask = 0-(size_t)carry;
+		u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
+		}
+	else
+		carry = 1;
+
+	mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_256[0],BN_NIST_256_TOP);
+	mask &= 0-(size_t)carry;
+	res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
+	nist_cp_bn(r_d, res, BN_NIST_256_TOP);
 	r->top = BN_NIST_256_TOP;
 	bn_correct_top(r);
 
 	return 1;
-#else	/* BN_BITS!=32 */
-	return 0;
-#endif
 	}
 
 #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
 	{ \
-	if (a12 != 0) bn_cp_32(to, 0, from,  (a12) - 12) else bn_32_set_0(to, 0)\
-	if (a11 != 0) bn_cp_32(to, 1, from,  (a11) - 12) else bn_32_set_0(to, 1)\
-	if (a10 != 0) bn_cp_32(to, 2, from,  (a10) - 12) else bn_32_set_0(to, 2)\
-	if (a9 != 0)  bn_cp_32(to, 3, from,  (a9) - 12)  else bn_32_set_0(to, 3)\
-	if (a8 != 0)  bn_cp_32(to, 4, from,  (a8) - 12)  else bn_32_set_0(to, 4)\
-	if (a7 != 0)  bn_cp_32(to, 5, from,  (a7) - 12)  else bn_32_set_0(to, 5)\
-	if (a6 != 0)  bn_cp_32(to, 6, from,  (a6) - 12)  else bn_32_set_0(to, 6)\
-	if (a5 != 0)  bn_cp_32(to, 7, from,  (a5) - 12)  else bn_32_set_0(to, 7)\
-	if (a4 != 0)  bn_cp_32(to, 8, from,  (a4) - 12)  else bn_32_set_0(to, 8)\
-	if (a3 != 0)  bn_cp_32(to, 9, from,  (a3) - 12)  else bn_32_set_0(to, 9)\
-	if (a2 != 0)  bn_cp_32(to, 10, from, (a2) - 12)  else bn_32_set_0(to, 10)\
-	if (a1 != 0)  bn_cp_32(to, 11, from, (a1) - 12)  else bn_32_set_0(to, 11)\
+	bn_cp_32(to, 0, from,  (a12) - 12) \
+	bn_cp_32(to, 1, from,  (a11) - 12) \
+	bn_cp_32(to, 2, from,  (a10) - 12) \
+	bn_cp_32(to, 3, from,  (a9) - 12)  \
+	bn_cp_32(to, 4, from,  (a8) - 12)  \
+	bn_cp_32(to, 5, from,  (a7) - 12)  \
+	bn_cp_32(to, 6, from,  (a6) - 12)  \
+	bn_cp_32(to, 7, from,  (a5) - 12)  \
+	bn_cp_32(to, 8, from,  (a4) - 12)  \
+	bn_cp_32(to, 9, from,  (a3) - 12)  \
+	bn_cp_32(to, 10, from, (a2) - 12)  \
+	bn_cp_32(to, 11, from, (a1) - 12)  \
 	}
 
 int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 	BN_CTX *ctx)
 	{
-#if BN_BITS2 == 32
 	int	i, top = a->top;
 	int	carry = 0;
 	register BN_ULONG *r_d, *a_d = a->d;
@@ -504,6 +535,7 @@ int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 		 c_d[BN_NIST_384_TOP],
 		*res;
 	size_t	 mask;
+	union { bn_addsub_f f; size_t p; } u;
 
 	i = BN_ucmp(field, a);
 	if (i == 0)
@@ -546,95 +578,51 @@ int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
 		}
 	carry = bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2), 
 		t_d, BN_NIST_256_TOP);
-	/*
-	 * we need if (result>=modulus) subtract(result,modulus);
-	 * in n-bit space this can be expressed as
-	 * if (carry || result>=modulus) subtract(result,modulus);
-	 * the catch is that comparison implies subtraction and
-	 * therefore one can write tmp=subtract(result,modulus);
-	 * and then if(carry || !borrow) result=tmp; this's what
-	 * happens below, but without explicit if:-) a.
-	 */
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_384,BN_NIST_384_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-
 	/*S2 */
-	carry = bn_add_words(r_d, res, buf, BN_NIST_384_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_384,BN_NIST_384_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-
+	carry += bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
 	/*S3*/
 	nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
-	carry = bn_add_words(r_d, res, t_d, BN_NIST_384_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_384,BN_NIST_384_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-
+	carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 	/*S4*/
 	nist_set_384(t_d,buf,19,18,17,16,15,14,13,12,20,0,23,0);
-	carry = bn_add_words(r_d, res, t_d, BN_NIST_384_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_384,BN_NIST_384_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-
+	carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 	/*S5*/
 	nist_set_384(t_d, buf,0,0,0,0,23,22,21,20,0,0,0,0);
-	carry = bn_add_words(r_d, res, t_d, BN_NIST_384_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_384,BN_NIST_384_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-
+	carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 	/*S6*/
 	nist_set_384(t_d,buf,0,0,0,0,0,0,23,22,21,0,0,20);
-	carry = bn_add_words(r_d, res, t_d, BN_NIST_384_TOP);
-	mask = 0-(size_t)bn_sub_words(c_d,r_d,_nist_p_384,BN_NIST_384_TOP);
-	mask = ~mask | (0-(size_t)carry);
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-
+	carry += bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 	/*D1*/
 	nist_set_384(t_d,buf,22,21,20,19,18,17,16,15,14,13,12,23);
-#if BRANCH_FREE
-	carry = bn_sub_words(r_d, res, t_d, BN_NIST_384_TOP);
-	bn_add_words(c_d,r_d,_nist_p_384,BN_NIST_384_TOP);
-	mask = 0-(size_t)carry;
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-#else
-	if (bn_sub_words(r_d, res, t_d, BN_NIST_384_TOP))
-		bn_add_words(r_d,r_d,_nist_p_384,BN_NIST_384_TOP);
-#endif
+	carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 	/*D2*/
 	nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,22,21,20,0);
-#if BRANCH_FREE
-	carry = bn_sub_words(r_d, res, t_d, BN_NIST_384_TOP);
-	bn_add_words(c_d,r_d,_nist_p_384,BN_NIST_384_TOP);
-	mask = 0-(size_t)carry;
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
-#else
-	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP))
-		bn_add_words(r_d,r_d,_nist_p_384,BN_NIST_384_TOP);
-#endif
+	carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 	/*D3*/
 	nist_set_384(t_d,buf,0,0,0,0,0,0,0,23,23,0,0,0);
-#if BRANCH_FREE
-	carry = bn_sub_words(r_d, res, t_d, BN_NIST_384_TOP);
-	bn_add_words(c_d,r_d,_nist_p_384,BN_NIST_384_TOP);
-	mask = 0-(size_t)carry;
-	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));
+	carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
 
+	/* see BN_nist_mod_224 for explanation */
+	u.f = bn_sub_words;
+	if (carry > 0)
+		carry = bn_sub_words(r_d,r_d,_nist_p_384[carry-1],BN_NIST_384_TOP);
+	else if (carry < 0)
+		{
+		carry = bn_add_words(r_d,r_d,_nist_p_384[-carry-1],BN_NIST_384_TOP);
+		mask = 0-(size_t)carry;
+		u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);
+		}
+	else
+		carry = 1;
+
+	mask  = 0-(size_t)(*u.f)(c_d,r_d,_nist_p_384[0],BN_NIST_384_TOP);
+	mask &= 0-(size_t)carry;
+	res   = (BN_ULONG *)(((size_t)c_d&~mask) | ((size_t)r_d&mask));
 	nist_cp_bn(r_d, res, BN_NIST_384_TOP);
-#else
-	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP))
-		bn_add_words(r_d,r_d,_nist_p_384,BN_NIST_384_TOP);
-#endif
 	r->top = BN_NIST_384_TOP;
 	bn_correct_top(r);
 
 	return 1;
-#else	/* BN_BITS!=32 */
-	return 0;
-#endif
 	}
 
 int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,