Commit 830b8877 authored by Andy Polyakov's avatar Andy Polyakov
Browse files

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
parent 9912ab67

crypto/bn/bn_nist.c

+219 −231
Original line number Diff line number Diff line
@@ -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);

	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;

	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));

		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)
@@ -393,109 +451,82 @@ int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field, 
	/*S2*/

	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);

	carry -= bn_sub_words(r_d, r_d, t_d, BN_NIST_256_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_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;

	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));	

		u.p = ((size_t)bn_sub_words&mask) | ((size_t)bn_add_words&~mask);

		}

	else

		carry = 1;



	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

	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);

	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;

	res = (BN_ULONG *)(((size_t)c_d&mask) | ((size_t)r_d&~mask));

		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,