Takanori Yanagisawa has shown how to correctly use pre-computed values.
[openssl.git] / crypto / bn / bn_nist.c
index e14232f..d8b443c 100644 (file)
 #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,