fast reduction for NIST curves

Submitted by: Nils Larsch

1 files changed, 828 insertions, 0 deletions

diff --git a/crypto/bn/bn_nist.c b/crypto/bn/bn_nist.c
new file mode 100644
index 0000000000..4e21a05456
--- /dev/null
+++ b/crypto/bn/bn_nist.c
@@ -0,0 +1,828 @@
+/* crypto/bn/bn_nist.p */
+/* ====================================================================
+ * Copyright (c) 1998-2002 The OpenSSL Project.  All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer. 
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ *
+ * 3. All advertising materials mentioning features or use of this
+ *    software must display the following acknowledgment:
+ *    "This product includes software developed by the OpenSSL Project
+ *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
+ *
+ * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
+ *    endorse or promote products derived from this software without
+ *    prior written permission. For written permission, please contact
+ *    openssl-core@openssl.org.
+ *
+ * 5. Products derived from this software may not be called "OpenSSL"
+ *    nor may "OpenSSL" appear in their names without prior written
+ *    permission of the OpenSSL Project.
+ *
+ * 6. Redistributions of any form whatsoever must retain the following
+ *    acknowledgment:
+ *    "This product includes software developed by the OpenSSL Project
+ *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
+ * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+ * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE OpenSSL PROJECT OR
+ * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
+ * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
+ * OF THE POSSIBILITY OF SUCH DAMAGE.
+ * ====================================================================
+ *
+ * This product includes cryptographic software written by Eric Young
+ * (eay@cryptsoft.com).  This product includes software written by Tim
+ * Hudson (tjh@cryptsoft.com).
+ *
+ */
+
+#include "bn_lcl.h"
+
+#define BN_NIST_192_TOP	(192+BN_BITS2-1)/BN_BITS2
+#define BN_NIST_224_TOP	(224+BN_BITS2-1)/BN_BITS2
+#define BN_NIST_256_TOP	(256+BN_BITS2-1)/BN_BITS2
+#define	BN_NIST_384_TOP	(384+BN_BITS2-1)/BN_BITS2
+#define BN_NIST_521_TOP	(521+BN_BITS2-1)/BN_BITS2
+
+#if BN_BITS2 == 64
+const static BN_ULONG _nist_p_192[] = {0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFE,
+	0xFFFFFFFFFFFFFFFF};
+const static BN_ULONG _nist_p_224[] = {0x0000000000000001,0xFFFFFFFF00000000,
+	0xFFFFFFFFFFFFFFFF,0x00000000FFFFFFFF};
+const static BN_ULONG _nist_p_256[] = {0xFFFFFFFFFFFFFFFF,0x00000000FFFFFFFF,
+	0x0000000000000000,0xFFFFFFFF00000001};
+const static BN_ULONG _nist_p_384[] = {0x00000000FFFFFFFF,0xFFFFFFFF00000000,
+	0xFFFFFFFFFFFFFFFE,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,
+	0xFFFFFFFFFFFFFFFF};
+const static BN_ULONG _nist_p_521[] = {0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,
+	0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,
+	0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,0xFFFFFFFFFFFFFFFF,
+	0x00000000000001FF};
+#elif BN_BITS2 == 32
+const static BN_ULONG _nist_p_192[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFE,
+	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
+const static BN_ULONG _nist_p_224[] = {0x00000001,0x00000000,0x00000000,
+	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
+const static BN_ULONG _nist_p_256[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
+	0x00000000,0x00000000,0x00000000,0x00000001,0xFFFFFFFF};
+const static BN_ULONG _nist_p_384[] = {0xFFFFFFFF,0x00000000,0x00000000,
+	0xFFFFFFFF,0xFFFFFFFE,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
+	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF};
+const static BN_ULONG _nist_p_521[] = {0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
+	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
+	0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,0xFFFFFFFF,
+	0xFFFFFFFF,0x000001FF};
+#elif BN_BITS2 == 16
+const static BN_ULONG _nist_p_192[] = {0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFE,
+	0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF};
+const static BN_ULONG _nist_p_224[] = {0x0001,0x0000,0x0000,0x0000,0x0000,
+	0x0000,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF};
+const static BN_ULONG _nist_p_256[] = {0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
+	0xFFFF,0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,0x0001,0x0000,0xFFFF,
+	0xFFFF};
+const static BN_ULONG _nist_p_384[] = {0xFFFF,0xFFFF,0x0000,0x0000,0x0000,
+	0x0000,0xFFFF,0xFFFF,0xFFFE,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
+	0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF};
+const static BN_ULONG _nist_p_521[] = {0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
+	0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
+	0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,
+	0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0xFFFF,0x01FF};
+#elif BN_BITS2 == 8
+const static BN_ULONG _nist_p_192[] = {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+	0xFE,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+	0xFF,0xFF};
+const static BN_ULONG _nist_p_224[] = {0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+	0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF};
+const static BN_ULONG _nist_p_256[] = {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+	0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+	0x00,0x00,0x01,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF};
+const static BN_ULONG _nist_p_384[] = {0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,
+	0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,0xFF,
+	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF};
+const static BN_ULONG _nist_p_521[] = {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+	0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+	0xFF,0x01};
+#endif
+
+const BIGNUM *BN_get0_nist_prime_192(void)
+	{
+	static BIGNUM const_nist_192={(BN_ULONG *)_nist_p_192,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,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,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,BN_NIST_384_TOP,
+		BN_NIST_384_TOP, 0, BN_FLG_STATIC_DATA};
+	return &const_nist_384;
+	}
+
+const BIGNUM *BN_get0_nist_prime_521(void)
+	{
+	static BIGNUM const_nist_521={(BN_ULONG *)_nist_p_521,BN_NIST_521_TOP,
+		BN_NIST_521_TOP, 0, BN_FLG_STATIC_DATA};
+	return &const_nist_521;
+	}
+
+/* some misc internal functions */
+static BN_ULONG _256_data[BN_NIST_256_TOP*6];
+static int _is_set_256_data = 0;
+static void _init_256_data(void);
+
+static BN_ULONG _384_data[BN_NIST_384_TOP*8];
+static int _is_set_384_data = 0;
+static void _init_384_data(void);
+
+#define BN_NIST_ADD_ONE(a)	while (!(++(*(a)))) ++(a);
+#define __buf_0			(BN_ULONG)0
+#define __buf_0_1		(BN_ULONG)0
+#define __buf_0_2		(BN_ULONG)0
+#if BN_BITS2 == 64
+#define BN_64_BIT_BUF(n)	BN_ULONG __buf_##n = (BN_ULONG)0;
+#define BN_CP_64_TO_BUF(n)	__buf_##n = (a)[(n)];
+#define BN_CP_64_FROM_BUF(a,n)	*(a)++ = __buf_##n;
+#define BN_CASE_64_BIT(n,a)	case (n): __buf_##n = (a)[(n)];
+#if	UINT_MAX == 4294967295UL
+#define	nist32	unsigned int
+#define BN_32_BIT_BUF(n)	nist32 __buf_##n = (nist32)0;
+#define BN_CP_32_TO_BUF(n)	__buf_##n = ((nist32 *)(a))[(n)];
+#define BN_CP_32_FROM_BUF(a,n)	*((nist32)(a))++ = __buf_##n;
+#define BN_CASE_32_BIT(n,a)	case (n): __buf_##n = ((nist32)(a))[(n)];
+#elif	ULONG_MAX == 4294967295UL
+#define	nist32	unsigned long
+#define BN_32_BIT_BUF(n)	nist32 __buf_##n = (nist32)0;
+#define BN_CP_32_TO_BUF(n)	__buf_##n = ((nist32 *)(a))[(n)];
+#define BN_CP_32_FROM_BUF(a,n)	*((nist32)(a))++ = __buf_##n;
+#define BN_CASE_32_BIT(n,a)	case (n): __buf_##n = ((nist32)(a))[(n)];
+#else
+#define	NO_32_BIT_TYPE
+#endif
+#elif BN_BITS2 == 32
+#define BN_64_BIT_BUF(n)	BN_ULONG __buf_##n##_1 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_2 = (BN_ULONG)0;
+#define BN_CP_64_TO_BUF(n)	__buf_##n##_2 = (a)[2*(n)+1];\
+				__buf_##n##_1 = (a)[2*(n)];
+#define BN_CP_64_FROM_BUF(a,n)	*(a)++ = __buf_##n##_1;\
+				*(a)++ = __buf_##n##_2;
+#define BN_CASE_64_BIT(n,a)	case 2*(n)+1: __buf_##n##_2 = (a)[2*(n)+1];\
+				case 2*(n):   __buf_##n##_1 = (a)[2*(n)];
+				
+#define BN_32_BIT_BUF(n)	BN_ULONG __buf_##n = (BN_ULONG)0;
+#define BN_CP_32_TO_BUF(n)	__buf_##n = (a)[(n)];
+#define BN_CP_32_FROM_BUF(a,n)	*(a)++ = __buf_##n;
+#define BN_CASE_32_BIT(n,a)	case (n): __buf_##n = (a)[(n)];
+#elif BN_BITS2 == 16
+#define __buf_0_3		(BN_ULONG)0
+#define __buf_0_4		(BN_ULONG)0
+#define BN_64_BIT_BUF(n)	BN_ULONG __buf_##n##_1 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_2 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_3 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_4 = (BN_ULONG)0;
+#define BN_CP_64_TO_BUF(n)	__buf_##n##_4 = (a)[4*(n)+3];\
+				__buf_##n##_3 = (a)[4*(n)+2];\
+				__buf_##n##_2 = (a)[4*(n)+1];\
+				__buf_##n##_1 = (a)[4*(n)];
+#define BN_CP_64_FROM_BUF(a,n)	*(a)++ = __buf_##n##_1;\
+				*(a)++ = __buf_##n##_2;\
+				*(a)++ = __buf_##n##_3;\
+				*(a)++ = __buf_##n##_4;
+#define BN_CASE_64_BIT(n,a)	case 4*(n)+3: __buf_##n##_4 = (a)[4*(n)+3];\
+				case 4*(n)+2: __buf_##n##_3 = (a)[4*(n)+2];\
+				case 4*(n)+1: __buf_##n##_2 = (a)[4*(n)+1];\
+				case 4*(n):   __buf_##n##_1 = (a)[4*(n)];
+#define BN_32_BIT_BUF(n)	BN_ULONG __buf_##n##_1 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_2 = (BN_ULONG)0;
+#define BN_CP_32_TO_BUF(n)	__buf_##n##_1 = (a)[2*(n)];\
+				__buf_##n##_2 = (a)[2*(n)+1];
+#define BN_CP_32_FROM_BUF(a,n)	*(a)++ = __buf_##n##_1;\
+				*(a)++ = __buf_##n##_2;
+#define BN_CASE_32_BIT(n,a)	case 2*(n)+1: __buf_##n##_2 = (a)[2*(n)+1];\
+				case 2*(n):   __buf_##n##_1 = (a)[2*(n)];
+#elif BN_BITS2 == 8
+#define __buf_0_3		(BN_ULONG)0
+#define __buf_0_4		(BN_ULONG)0
+#define __buf_0_5		(BN_ULONG)0
+#define __buf_0_6		(BN_ULONG)0
+#define __buf_0_7		(BN_ULONG)0
+#define __buf_0_8		(BN_ULONG)0
+#define BN_64_BIT_BUF(n)	BN_ULONG __buf_##n##_1 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_2 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_3 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_4 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_5 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_6 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_7 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_8 = (BN_ULONG)0;
+#define BN_CP_64_TO_BUF(n)	__buf_##n##_8 = (a)[8*(n)+7];\
+				__buf_##n##_7 = (a)[8*(n)+6];\
+				__buf_##n##_6 = (a)[8*(n)+5];\
+				__buf_##n##_5 = (a)[8*(n)+4];\
+				__buf_##n##_4 = (a)[8*(n)+3];\
+				__buf_##n##_3 = (a)[8*(n)+2];\
+				__buf_##n##_2 = (a)[8*(n)+1];\
+				__buf_##n##_1 = (a)[8*(n)];
+#define BN_CP_64_FROM_BUF(a,n)	*(a)++ = __buf_##n##_1;\
+				*(a)++ = __buf_##n##_2;\
+				*(a)++ = __buf_##n##_3;\
+				*(a)++ = __buf_##n##_4;\
+				*(a)++ = __buf_##n##_5;\
+				*(a)++ = __buf_##n##_6;\
+				*(a)++ = __buf_##n##_7;\
+				*(a)++ = __buf_##n##_8;
+#define BN_CASE_64_BIT(n,a)	case 8*(n)+7: __buf_##n##_8 = (a)[8*(n)+7];\
+				case 8*(n)+6: __buf_##n##_7 = (a)[8*(n)+6];\
+				case 8*(n)+5: __buf_##n##_6 = (a)[8*(n)+5];\
+				case 8*(n)+4: __buf_##n##_5 = (a)[8*(n)+4];\
+				case 8*(n)+3: __buf_##n##_4 = (a)[8*(n)+3];\
+				case 8*(n)+2: __buf_##n##_3 = (a)[8*(n)+2];\
+				case 8*(n)+1: __buf_##n##_2 = (a)[8*(n)+1];\
+				case 8*(n):   __buf_##n##_1 = (a)[8*(n)];
+#define BN_32_BIT_BUF(n)	BN_ULONG __buf_##n##_1 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_2 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_3 = (BN_ULONG)0;\
+				BN_ULONG __buf_##n##_4 = (BN_ULONG)0;
+#define BN_CP_32_TO_BUF(n)	__buf_##n##_1 = (a)[4*(n)];\
+				__buf_##n##_2 = (a)[4*(n)+1];\
+				__buf_##n##_3 = (a)[4*(n)+2];\
+				__buf_##n##_4 = (a)[4*(n)+3];
+#define BN_CP_32_FROM_BUF(a,n)	*(a)++ = __buf_##n##_1;\
+				*(a)++ = __buf_##n##_2;\
+				*(a)++ = __buf_##n##_3;\
+				*(a)++ = __buf_##n##_4;
+#define BN_CASE_32_BIT(n,a)	case 4*(n)+3: __buf_##n##_4 = (a)[4*(n)+3];\
+				case 4*(n)+2: __buf_##n##_3 = (a)[4*(n)+2];\
+				case 4*(n)+1: __buf_##n##_2 = (a)[4*(n)+1];\
+				case 4*(n):   __buf_##n##_1 = (a)[4*(n)];
+#endif
+
+
+#define BN_192_SET(d,a1,a2,a3) \
+	{\
+	register BN_ULONG *td = (d);\
+	BN_CP_64_FROM_BUF(td,a3); BN_CP_64_FROM_BUF(td,a2);\
+	BN_CP_64_FROM_BUF(td,a1);\
+	}
+
+int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
+	BN_CTX *ctx)
+	{
+	int      top;
+	BN_ULONG carry = 0;
+	register BN_ULONG *r_d, *a_d;
+	BN_ULONG t_d[BN_NIST_192_TOP];
+	BN_64_BIT_BUF(3)  BN_64_BIT_BUF(4)
+	BN_64_BIT_BUF(5)
+
+	top = BN_ucmp(field, a);
+	if (top == 0)
+		return BN_zero(r);
+	else if (top > 0)
+		return (r == a)? 1 : !!BN_copy(r ,a);
+
+	if (r != a)
+		if (!BN_ncopy(r, a, BN_NIST_192_TOP))
+			return 0;
+
+	r_d = r->d;
+	a_d = a->d;
+	top = a->top-1;
+
+	switch (top)
+		{
+		BN_CASE_64_BIT(5, a_d)
+		BN_CASE_64_BIT(4, a_d)
+		BN_CASE_64_BIT(3, a_d)
+			break;
+		default: /* a->top == field->top */
+			return BN_usub(r, a, field);
+		}
+
+	BN_192_SET(t_d,0,3,3)
+	if (bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP))
+		++carry;
+
+	BN_192_SET(t_d,4,4,0)
+	if (bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP))
+		++carry;
+
+	BN_192_SET(t_d,5,5,5)
+	if (bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP))
+		++carry;
+
+	while (carry)
+		{
+		if (bn_sub_words(r_d, r_d, _nist_p_192, BN_NIST_192_TOP))
+			--carry; 
+		}
+	r->top = BN_NIST_192_TOP;
+
+#if 0
+	bn_clear_top2max(r);
+#endif
+	bn_fix_top(r);
+
+	if (BN_ucmp(r, field) >= 0)
+		{
+		bn_sub_words(r_d, r_d, _nist_p_192, BN_NIST_192_TOP);
+		bn_fix_top(r);
+		}
+
+	return 1;
+	}
+
+#define BN_224_SET(d,a1,a2,a3,a4,a5,a6,a7) \
+	{\
+	register BN_ULONG *td = (d);\
+	BN_CP_32_FROM_BUF(td,a7); BN_CP_32_FROM_BUF(td,a6);\
+	BN_CP_32_FROM_BUF(td,a5); BN_CP_32_FROM_BUF(td,a4);\
+	BN_CP_32_FROM_BUF(td,a3); BN_CP_32_FROM_BUF(td,a2);\
+	BN_CP_32_FROM_BUF(td,a1);\
+	}
+
+int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
+	BN_CTX *ctx)
+	{
+#ifndef NO_32_BIT_TYPE
+	int	tmp_int;
+	int	carry = 0;
+	BN_ULONG *r_d, *a_d;
+	BN_ULONG t_d[BN_NIST_224_TOP];
+	BN_32_BIT_BUF(7)  BN_32_BIT_BUF(8)
+	BN_32_BIT_BUF(9)  BN_32_BIT_BUF(10)
+	BN_32_BIT_BUF(11) BN_32_BIT_BUF(12)
+	BN_32_BIT_BUF(13)
+
+	tmp_int = BN_ucmp(field, a);
+	if (tmp_int == 0)
+		return BN_zero(r);
+	else if (tmp_int > 0)
+		return (r == a)? 1 : !!BN_copy(r ,a);
+
+	if (r != a)
+		if (!BN_ncopy(r, a, BN_NIST_224_TOP))
+			return 0;
+
+	r_d = r->d;
+	a_d = a->d;
+
+	tmp_int = a->top-1;
+
+	switch (tmp_int)
+		{
+		BN_CASE_32_BIT(13, a_d)
+		BN_CASE_32_BIT(12, a_d)
+		BN_CASE_32_BIT(11, a_d)
+		BN_CASE_32_BIT(10, a_d)
+		BN_CASE_32_BIT(9,  a_d)
+		BN_CASE_32_BIT(8,  a_d)
+		BN_CASE_32_BIT(7,  a_d)
+			break;
+		default: /* a->top == field->top */
+			return BN_usub(r, a, field);
+		}
+
+	BN_224_SET(t_d,10,9,8,7,0,0,0)
+	if (bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP))
+		++carry;
+	BN_224_SET(t_d,0,13,12,11,0,0,0)
+	if (bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP))
+		++carry;
+	BN_224_SET(t_d,13,12,11,10,9,8,7)
+	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP))
+		--carry;
+	BN_224_SET(t_d,0,0,0,0,13,12,11)
+	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP))
+		--carry;
+
+	if (carry > 0)
+		while (carry)
+			{
+			if (bn_sub_words(r_d,r_d,_nist_p_224,BN_NIST_224_TOP))
+				--carry;
+			}
+	else if (carry < 0)
+		while (carry)
+			{
+			if (bn_add_words(r_d,r_d,_nist_p_224,BN_NIST_224_TOP))
+				++carry;
+			}
+
+	r->top = BN_NIST_224_TOP;
+#if 0
+	bn_clear_top2max(r);
+#endif
+	bn_fix_top(r);
+
+	if (BN_ucmp(r, field) >= 0)
+		{
+		bn_sub_words(r_d, r_d, _nist_p_224, BN_NIST_224_TOP);
+		bn_fix_top(r);
+		}
+	return 1;
+#else
+	return 0;
+#endif
+	}
+
+static void _init_256_data(void)
+	{
+	int	i;
+	BN_ULONG *tmp1 = _256_data;
+	const BN_ULONG *tmp2 = tmp1;
+
+	memcpy(tmp1, _nist_p_256, BN_NIST_256_TOP * sizeof(BN_ULONG));
+	tmp1 += BN_NIST_256_TOP;
+
+	for (i=0; i<5; i++)
+		{
+		bn_add_words(tmp1, _nist_p_256, tmp2, BN_NIST_256_TOP);
+		tmp2  = tmp1;
+		tmp1 += BN_NIST_256_TOP;
+		}
+	_is_set_256_data = 1;
+	}
+
+#define BN_256_SET(d,a1,a2,a3,a4,a5,a6,a7,a8) \
+	{\
+	register BN_ULONG *td = (d);\
+	BN_CP_32_FROM_BUF(td,a8); BN_CP_32_FROM_BUF(td,a7);\
+	BN_CP_32_FROM_BUF(td,a6); BN_CP_32_FROM_BUF(td,a5);\
+	BN_CP_32_FROM_BUF(td,a4); BN_CP_32_FROM_BUF(td,a3);\
+	BN_CP_32_FROM_BUF(td,a2); BN_CP_32_FROM_BUF(td,a1);\
+	}
+
+int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
+	BN_CTX *ctx)
+	{
+#ifndef NO_32_BIT_TYPE
+	int	tmp_int;
+	int	carry = 0;
+	register BN_ULONG *a_d, *r_d;
+	BN_ULONG t_d[BN_NIST_256_TOP];
+	BN_ULONG t_d2[BN_NIST_256_TOP];
+	BN_32_BIT_BUF(8)  BN_32_BIT_BUF(9)
+	BN_32_BIT_BUF(10) BN_32_BIT_BUF(11)
+	BN_32_BIT_BUF(12) BN_32_BIT_BUF(13)
+	BN_32_BIT_BUF(14) BN_32_BIT_BUF(15)
+
+	if (!_is_set_256_data)
+		_init_256_data();
+
+	tmp_int = BN_ucmp(field, a);
+	if (tmp_int == 0)
+		return BN_zero(r);
+	else if (tmp_int > 0)
+		return (r == a)? 1 : !!BN_copy(r ,a);
+
+	if (r != a)
+		if (!BN_ncopy(r, a, BN_NIST_256_TOP))
+			return 0;
+
+	tmp_int = a->top-1;
+
+	a_d = a->d;
+	r_d = r->d;
+	switch (tmp_int)
+		{
+		BN_CASE_32_BIT(15, a_d)
+		BN_CASE_32_BIT(14, a_d)
+		BN_CASE_32_BIT(13, a_d)
+		BN_CASE_32_BIT(12, a_d)
+		BN_CASE_32_BIT(11, a_d)
+		BN_CASE_32_BIT(10, a_d)
+		BN_CASE_32_BIT(9,  a_d)
+		BN_CASE_32_BIT(8,  a_d)
+			break;
+		default: /* a->top == field->top */
+			return BN_usub(r, a, field);
+		}
+
+	/*S1*/
+	BN_256_SET(t_d,15,14,13,12,11,0,0,0)
+	/*S2*/
+	BN_256_SET(t_d2,0,15,14,13,12,0,0,0)
+	if (bn_add_words(t_d, t_d, t_d2, BN_NIST_256_TOP))
+		carry = 2;
+	/* left shift */
+		{
+		register BN_ULONG *ap,t,c;
+		ap = t_d;
+		c=0;
+		for (tmp_int=BN_NIST_256_TOP; tmp_int != 0; --tmp_int)
+			{
+			t= *ap;
+			*(ap++)=((t<<1)|c)&BN_MASK2;
+			c=(t & BN_TBIT)?1:0;
+			}
+		if (c)
+			++carry;
+		}
+
+	if (bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP))
+		++carry;
+	/*S3*/
+	BN_256_SET(t_d,15,14,0,0,0,10,9,8)
+	if (bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP))
+		++carry;
+	/*S4*/
+	BN_256_SET(t_d,8,13,15,14,13,11,10,9)
+	if (bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP))
+		++carry;
+	/*D1*/
+	BN_256_SET(t_d,10,8,0,0,0,13,12,11)
+	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP))
+		--carry;
+	/*D2*/
+	BN_256_SET(t_d,11,9,0,0,15,14,13,12)
+	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP))
+		--carry;
+	/*D3*/
+	BN_256_SET(t_d,12,0,10,9,8,15,14,13)
+	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP))
+		--carry;
+	/*D4*/
+	BN_256_SET(t_d,13,0,11,10,9,0,15,14)
+	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP))
+		--carry;
+	
+	if (carry)
+		{
+		if (carry > 0)
+			bn_sub_words(r_d, r_d, _256_data + BN_NIST_256_TOP *
+				--carry, BN_NIST_256_TOP);
+		else
+			{
+			carry = -carry;
+			bn_add_words(r_d, r_d, _256_data + BN_NIST_256_TOP *
+				--carry, BN_NIST_256_TOP);
+			}
+		}
+
+	r->top = BN_NIST_256_TOP;
+#if 0
+	bn_clear_top2max(r);
+#endif
+	bn_fix_top(r);
+
+	if (BN_ucmp(r, field) >= 0)
+		{
+		bn_sub_words(r_d, r_d, _nist_p_256, BN_NIST_256_TOP);
+		bn_fix_top(r);
+		}
+	return 1;
+#else
+	return 0;
+#endif
+	}
+
+static void _init_384_data(void)
+	{
+	int	i;
+	BN_ULONG *tmp1 = _384_data;
+	const BN_ULONG *tmp2 = tmp1;
+
+	memcpy(tmp1, _nist_p_384, BN_NIST_384_TOP * sizeof(BN_ULONG));
+	tmp1 += BN_NIST_384_TOP;
+
+	for (i=0; i<7; i++)
+		{
+		bn_add_words(tmp1, _nist_p_384, tmp2, BN_NIST_384_TOP);
+		tmp2  = tmp1;
+		tmp1 += BN_NIST_384_TOP;
+		}
+	_is_set_384_data = 1;
+	}
+
+#define BN_384_SET(d,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \
+	{\
+	register BN_ULONG *td = (d);\
+	BN_CP_32_FROM_BUF(td,a12); BN_CP_32_FROM_BUF(td,a11);\
+	BN_CP_32_FROM_BUF(td,a10); BN_CP_32_FROM_BUF(td,a9);\
+	BN_CP_32_FROM_BUF(td,a8);  BN_CP_32_FROM_BUF(td,a7);\
+	BN_CP_32_FROM_BUF(td,a6);  BN_CP_32_FROM_BUF(td,a5);\
+	BN_CP_32_FROM_BUF(td,a4);  BN_CP_32_FROM_BUF(td,a3);\
+	BN_CP_32_FROM_BUF(td,a2);  BN_CP_32_FROM_BUF(td,a1);\
+	}
+
+int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
+	BN_CTX *ctx)
+	{
+#ifndef NO_32_BIT_TYPE
+	int	tmp_int;
+	int	carry = 0;
+	register BN_ULONG *r_d, *a_d;
+	BN_ULONG t_d[BN_NIST_384_TOP];
+	BN_32_BIT_BUF(12) BN_32_BIT_BUF(13)
+	BN_32_BIT_BUF(14) BN_32_BIT_BUF(15)
+	BN_32_BIT_BUF(16) BN_32_BIT_BUF(17)
+	BN_32_BIT_BUF(18) BN_32_BIT_BUF(19)
+	BN_32_BIT_BUF(20) BN_32_BIT_BUF(21)
+	BN_32_BIT_BUF(22) BN_32_BIT_BUF(23)
+
+	if (!_is_set_384_data)
+		_init_384_data();
+
+	tmp_int = BN_ucmp(field, a);
+	if (tmp_int == 0)
+		return BN_zero(r);
+	else if (tmp_int > 0)
+		return (r == a)? 1 : !!BN_copy(r ,a);
+
+	if (r != a)
+		if (!BN_ncopy(r, a, BN_NIST_384_TOP))
+			return 0;
+
+	r_d = r->d;
+	a_d = a->d;
+	tmp_int = a->top-1;
+
+	switch (tmp_int)
+		{
+		BN_CASE_32_BIT(23, a_d)
+		BN_CASE_32_BIT(22, a_d)
+		BN_CASE_32_BIT(21, a_d)
+		BN_CASE_32_BIT(20, a_d)
+		BN_CASE_32_BIT(19, a_d)
+		BN_CASE_32_BIT(18, a_d)
+		BN_CASE_32_BIT(17, a_d)
+		BN_CASE_32_BIT(16, a_d)
+		BN_CASE_32_BIT(15, a_d)
+		BN_CASE_32_BIT(14, a_d)
+		BN_CASE_32_BIT(13, a_d)
+		BN_CASE_32_BIT(12, a_d)
+			break;
+		default: /* a->top == field->top */
+			return BN_usub(r, a, field);
+		}
+
+	/*S1*/
+	BN_256_SET(t_d,0,0,0,0,0,23,22,21)
+		/* left shift */
+		{
+		register BN_ULONG *ap,t,c;
+		ap = t_d;
+		c=0;
+		for (tmp_int=BN_NIST_256_TOP; tmp_int != 0; --tmp_int)
+			{
+			t= *ap;
+			*(ap++)=((t<<1)|c)&BN_MASK2;
+			c=(t & BN_TBIT)?1:0;
+			}
+		}
+	if (bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2), 
+		t_d, BN_NIST_256_TOP))
+		++carry;
+	/*S2*/
+	BN_384_SET(t_d,23,22,21,20,19,18,17,16,15,14,13,12)
+	if (bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP))
+		++carry;
+	/*S3*/
+	BN_384_SET(t_d,20,19,18,17,16,15,14,13,12,23,22,21)
+	if (bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP))
+		++carry;
+	/*S4*/
+	BN_384_SET(t_d,19,18,17,16,15,14,13,12,20,0,23,0)
+	if (bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP))
+		++carry;
+	/*S5*/
+	BN_256_SET(t_d,0,0,0,0,23,22,21,20)
+	if (bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2), 
+		t_d, BN_NIST_256_TOP))
+		++carry;
+	/*S6*/
+	BN_384_SET(t_d,0,0,0,0,0,0,23,22,21,0,0,20)
+	if (bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP))
+		++carry;
+	/*D1*/
+	BN_384_SET(t_d,22,21,20,19,18,17,16,15,14,13,12,23)
+	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP))
+		--carry;
+	/*D2*/
+	BN_384_SET(t_d,0,0,0,0,0,0,0,23,22,21,20,0)
+	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP))
+		--carry;
+	/*D3*/
+	BN_384_SET(t_d,0,0,0,0,0,0,0,23,23,0,0,0)
+	if (bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP))
+		--carry;
+	
+	if (carry)
+		{
+		if (carry > 0)
+			bn_sub_words(r_d, r_d, _384_data + BN_NIST_384_TOP *
+				--carry, BN_NIST_384_TOP);
+		else
+			{
+			carry = -carry;
+			bn_add_words(r_d, r_d, _384_data + BN_NIST_384_TOP *
+				--carry, BN_NIST_384_TOP);
+			}
+		}
+
+	r->top = BN_NIST_384_TOP;
+#if 0
+	bn_clear_top2max(r);
+#endif
+	bn_fix_top(r);
+
+	if (BN_ucmp(r, field) >= 0)
+		{
+		bn_sub_words(r_d, r_d, _nist_p_384, BN_NIST_384_TOP);
+		bn_fix_top(r);
+		}
+	return 1;
+#else
+	return 0;
+#endif
+	}
+
+int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
+	BN_CTX *ctx)
+	{
+#if BN_BITS2 == 64
+#define BN_NIST_521_TOP_MASK	(BN_ULONG)0x1FF
+#elif BN_BITS2 == 32
+#define BN_NIST_521_TOP_MASK	(BN_ULONG)0x1FF
+#elif BN_BITS2 == 16
+#define BN_NIST_521_TOP_MASK	(BN_ULONG)0x1FF
+#elif BN_BITS2 == 8
+#define BN_NIST_521_TOP_MASK	(BN_ULONG)0x1
+#endif
+	int	top, ret = 0;
+	BN_ULONG *r_d;
+	BIGNUM	*tmp;
+
+	/* check whether a reduction is necessary */
+	top = a->top;
+	if (top < BN_NIST_521_TOP  || ( top == BN_NIST_521_TOP &&
+           (!(a->d[BN_NIST_521_TOP-1] & ~(BN_NIST_521_TOP_MASK)))))
+		return (r == a)? 1 : !!BN_copy(r ,a);
+
+	BN_CTX_start(ctx);
+	tmp = BN_CTX_get(ctx);
+	if (!tmp)
+		goto err;
+
+	if (!BN_ncopy(tmp, a, BN_NIST_521_TOP))
+		return 0;
+	if (!BN_rshift(r, a, 521))
+		return 0;
+
+	if (tmp->top == BN_NIST_521_TOP)
+		tmp->d[BN_NIST_521_TOP-1]  &= BN_NIST_521_TOP_MASK;
+
+	if (!BN_uadd(r, tmp, r))
+		return 0;
+	top = r->top;
+	r_d = r->d;
+	if (top == BN_NIST_521_TOP  && 
+           (r_d[BN_NIST_521_TOP-1] & ~(BN_NIST_521_TOP_MASK)))
+		{
+		BN_NIST_ADD_ONE(r_d)
+		r_d[BN_NIST_521_TOP-1] &= BN_NIST_521_TOP_MASK; 
+		}
+	bn_fix_top(r);
+
+	ret = 1;
+err:
+	BN_CTX_end(ctx);
+	
+	return ret;
+	}