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authormarha <marha@users.sourceforge.net>2012-04-10 11:54:31 +0200
committermarha <marha@users.sourceforge.net>2012-04-10 11:54:31 +0200
commit5564e91e3cf4ba5cb2fbebbc2d63d18f588016b8 (patch)
treec800a66664ea3af61eb13928db45a26275930b0b /openssl/crypto/bn/bn_nist.c
parentd79e641dea89c0d5d651b11971c4c9e14df34629 (diff)
parent67326634496ef21b4acbf4cef2f05040d34aef9b (diff)
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Merge remote-tracking branch 'origin/released'
Conflicts: openssl/Configure openssl/Makefile openssl/crypto/opensslconf.h openssl/util/mk1mf.pl openssl/util/pl/VC-32.pl
Diffstat (limited to 'openssl/crypto/bn/bn_nist.c')
-rw-r--r--openssl/crypto/bn/bn_nist.c338
1 files changed, 298 insertions, 40 deletions
diff --git a/openssl/crypto/bn/bn_nist.c b/openssl/crypto/bn/bn_nist.c
index c6de03269..43caee477 100644
--- a/openssl/crypto/bn/bn_nist.c
+++ b/openssl/crypto/bn/bn_nist.c
@@ -319,6 +319,13 @@ static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
:(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)
+# if defined(L_ENDIAN)
+# if defined(__arch64__)
+# define NIST_INT64 long
+# else
+# define NIST_INT64 long long
+# endif
+# endif
#else
#define bn_cp_64(to, n, from, m) \
{ \
@@ -330,13 +337,15 @@ static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top)
bn_32_set_0(to, (n)*2); \
bn_32_set_0(to, (n)*2+1); \
}
-#if BN_BITS2 == 32
#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;
-#endif
+# if defined(_WIN32) && !defined(__GNUC__)
+# define NIST_INT64 __int64
+# elif defined(BN_LLONG)
+# define NIST_INT64 long long
+# endif
#endif /* BN_BITS2 != 64 */
-
#define nist_set_192(to, from, a1, a2, a3) \
{ \
bn_cp_64(to, 0, from, (a3) - 3) \
@@ -350,9 +359,11 @@ int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
int top = a->top, i;
int carry;
register BN_ULONG *r_d, *a_d = a->d;
- BN_ULONG t_d[BN_NIST_192_TOP],
- buf[BN_NIST_192_TOP],
- c_d[BN_NIST_192_TOP],
+ union {
+ BN_ULONG bn[BN_NIST_192_TOP];
+ unsigned int ui[BN_NIST_192_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
+ } buf;
+ BN_ULONG c_d[BN_NIST_192_TOP],
*res;
PTR_SIZE_INT mask;
static const BIGNUM _bignum_nist_p_192_sqr = {
@@ -385,15 +396,48 @@ int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
else
r_d = a_d;
- nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
+ nist_cp_bn_0(buf.bn, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP);
+
+#if defined(NIST_INT64)
+ {
+ NIST_INT64 acc; /* accumulator */
+ unsigned int *rp=(unsigned int *)r_d;
+ const unsigned int *bp=(const unsigned int *)buf.ui;
+
+ acc = rp[0]; acc += bp[3*2-6];
+ acc += bp[5*2-6]; rp[0] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[1]; acc += bp[3*2-5];
+ acc += bp[5*2-5]; rp[1] = (unsigned int)acc; acc >>= 32;
- nist_set_192(t_d, buf, 0, 3, 3);
+ acc += rp[2]; acc += bp[3*2-6];
+ acc += bp[4*2-6];
+ acc += bp[5*2-6]; rp[2] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[3]; acc += bp[3*2-5];
+ acc += bp[4*2-5];
+ acc += bp[5*2-5]; rp[3] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[4]; acc += bp[4*2-6];
+ acc += bp[5*2-6]; rp[4] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[5]; acc += bp[4*2-5];
+ acc += bp[5*2-5]; rp[5] = (unsigned int)acc;
+
+ carry = (int)(acc>>32);
+ }
+#else
+ {
+ BN_ULONG t_d[BN_NIST_192_TOP];
+
+ nist_set_192(t_d, buf.bn, 0, 3, 3);
carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
- nist_set_192(t_d, buf, 4, 4, 0);
+ nist_set_192(t_d, buf.bn, 4, 4, 0);
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
- nist_set_192(t_d, buf, 5, 5, 5)
+ nist_set_192(t_d, buf.bn, 5, 5, 5)
carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP);
-
+ }
+#endif
if (carry > 0)
carry = (int)bn_sub_words(r_d,r_d,_nist_p_192[carry-1],BN_NIST_192_TOP);
else
@@ -435,8 +479,7 @@ int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
int top = a->top, i;
int carry;
BN_ULONG *r_d, *a_d = a->d;
- BN_ULONG t_d[BN_NIST_224_TOP],
- buf[BN_NIST_224_TOP],
+ BN_ULONG buf[BN_NIST_224_TOP],
c_d[BN_NIST_224_TOP],
*res;
PTR_SIZE_INT mask;
@@ -474,14 +517,54 @@ int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
#if BN_BITS2==64
/* copy upper 256 bits of 448 bit number ... */
- nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
+ nist_cp_bn_0(c_d, a_d + (BN_NIST_224_TOP-1), top - (BN_NIST_224_TOP-1), BN_NIST_224_TOP);
/* ... and right shift by 32 to obtain upper 224 bits */
- nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8);
+ nist_set_224(buf, c_d, 14, 13, 12, 11, 10, 9, 8);
/* truncate lower part to 224 bits too */
r_d[BN_NIST_224_TOP-1] &= BN_MASK2l;
#else
nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP);
#endif
+
+#if defined(NIST_INT64) && BN_BITS2!=64
+ {
+ NIST_INT64 acc; /* accumulator */
+ unsigned int *rp=(unsigned int *)r_d;
+ const unsigned int *bp=(const unsigned int *)buf;
+
+ acc = rp[0]; acc -= bp[7-7];
+ acc -= bp[11-7]; rp[0] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[1]; acc -= bp[8-7];
+ acc -= bp[12-7]; rp[1] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[2]; acc -= bp[9-7];
+ acc -= bp[13-7]; rp[2] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[3]; acc += bp[7-7];
+ acc += bp[11-7];
+ acc -= bp[10-7]; rp[3] = (unsigned int)acc; acc>>= 32;
+
+ acc += rp[4]; acc += bp[8-7];
+ acc += bp[12-7];
+ acc -= bp[11-7]; rp[4] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[5]; acc += bp[9-7];
+ acc += bp[13-7];
+ acc -= bp[12-7]; rp[5] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[6]; acc += bp[10-7];
+ acc -= bp[13-7]; rp[6] = (unsigned int)acc;
+
+ carry = (int)(acc>>32);
+# if BN_BITS2==64
+ rp[7] = carry;
+# endif
+ }
+#else
+ {
+ BN_ULONG t_d[BN_NIST_224_TOP];
+
nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0);
carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP);
nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0);
@@ -494,6 +577,8 @@ int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
#if BN_BITS2==64
carry = (int)(r_d[BN_NIST_224_TOP-1]>>32);
#endif
+ }
+#endif
u.f = bn_sub_words;
if (carry > 0)
{
@@ -548,9 +633,11 @@ int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
int i, top = a->top;
int carry = 0;
register BN_ULONG *a_d = a->d, *r_d;
- BN_ULONG t_d[BN_NIST_256_TOP],
- buf[BN_NIST_256_TOP],
- c_d[BN_NIST_256_TOP],
+ union {
+ BN_ULONG bn[BN_NIST_256_TOP];
+ unsigned int ui[BN_NIST_256_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
+ } buf;
+ BN_ULONG c_d[BN_NIST_256_TOP],
*res;
PTR_SIZE_INT mask;
union { bn_addsub_f f; PTR_SIZE_INT p; } u;
@@ -584,12 +671,87 @@ int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
else
r_d = a_d;
- nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
+ nist_cp_bn_0(buf.bn, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP);
+
+#if defined(NIST_INT64)
+ {
+ NIST_INT64 acc; /* accumulator */
+ unsigned int *rp=(unsigned int *)r_d;
+ const unsigned int *bp=(const unsigned int *)buf.ui;
+
+ acc = rp[0]; acc += bp[8-8];
+ acc += bp[9-8];
+ acc -= bp[11-8];
+ acc -= bp[12-8];
+ acc -= bp[13-8];
+ acc -= bp[14-8]; rp[0] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[1]; acc += bp[9-8];
+ acc += bp[10-8];
+ acc -= bp[12-8];
+ acc -= bp[13-8];
+ acc -= bp[14-8];
+ acc -= bp[15-8]; rp[1] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[2]; acc += bp[10-8];
+ acc += bp[11-8];
+ acc -= bp[13-8];
+ acc -= bp[14-8];
+ acc -= bp[15-8]; rp[2] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[3]; acc += bp[11-8];
+ acc += bp[11-8];
+ acc += bp[12-8];
+ acc += bp[12-8];
+ acc += bp[13-8];
+ acc -= bp[15-8];
+ acc -= bp[8-8];
+ acc -= bp[9-8]; rp[3] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[4]; acc += bp[12-8];
+ acc += bp[12-8];
+ acc += bp[13-8];
+ acc += bp[13-8];
+ acc += bp[14-8];
+ acc -= bp[9-8];
+ acc -= bp[10-8]; rp[4] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[5]; acc += bp[13-8];
+ acc += bp[13-8];
+ acc += bp[14-8];
+ acc += bp[14-8];
+ acc += bp[15-8];
+ acc -= bp[10-8];
+ acc -= bp[11-8]; rp[5] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[6]; acc += bp[14-8];
+ acc += bp[14-8];
+ acc += bp[15-8];
+ acc += bp[15-8];
+ acc += bp[14-8];
+ acc += bp[13-8];
+ acc -= bp[8-8];
+ acc -= bp[9-8]; rp[6] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[7]; acc += bp[15-8];
+ acc += bp[15-8];
+ acc += bp[15-8];
+ acc += bp[8 -8];
+ acc -= bp[10-8];
+ acc -= bp[11-8];
+ acc -= bp[12-8];
+ acc -= bp[13-8]; rp[7] = (unsigned int)acc;
+
+ carry = (int)(acc>>32);
+ }
+#else
+ {
+ BN_ULONG t_d[BN_NIST_256_TOP];
/*S1*/
- nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0);
+ nist_set_256(t_d, buf.bn, 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.bn, 0, 15, 14, 13, 12, 0, 0, 0);
carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP);
/* left shift */
{
@@ -607,24 +769,26 @@ int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
}
carry += (int)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);
+ nist_set_256(t_d, buf.bn, 15, 14, 0, 0, 0, 10, 9, 8);
carry += (int)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);
+ nist_set_256(t_d, buf.bn, 8, 13, 15, 14, 13, 11, 10, 9);
carry += (int)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);
+ nist_set_256(t_d, buf.bn, 10, 8, 0, 0, 0, 13, 12, 11);
carry -= (int)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);
+ nist_set_256(t_d, buf.bn, 11, 9, 0, 0, 15, 14, 13, 12);
carry -= (int)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);
+ nist_set_256(t_d, buf.bn, 12, 0, 10, 9, 8, 15, 14, 13);
carry -= (int)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);
+ nist_set_256(t_d, buf.bn, 13, 0, 11, 10, 9, 0, 15, 14);
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP);
+ }
+#endif
/* see BN_nist_mod_224 for explanation */
u.f = bn_sub_words;
if (carry > 0)
@@ -672,9 +836,11 @@ int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
int i, top = a->top;
int carry = 0;
register BN_ULONG *r_d, *a_d = a->d;
- BN_ULONG t_d[BN_NIST_384_TOP],
- buf[BN_NIST_384_TOP],
- c_d[BN_NIST_384_TOP],
+ union {
+ BN_ULONG bn[BN_NIST_384_TOP];
+ unsigned int ui[BN_NIST_384_TOP*sizeof(BN_ULONG)/sizeof(unsigned int)];
+ } buf;
+ BN_ULONG c_d[BN_NIST_384_TOP],
*res;
PTR_SIZE_INT mask;
union { bn_addsub_f f; PTR_SIZE_INT p; } u;
@@ -709,10 +875,100 @@ int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
else
r_d = a_d;
- nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
+ nist_cp_bn_0(buf.bn, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP);
+
+#if defined(NIST_INT64)
+ {
+ NIST_INT64 acc; /* accumulator */
+ unsigned int *rp=(unsigned int *)r_d;
+ const unsigned int *bp=(const unsigned int *)buf.ui;
+
+ acc = rp[0]; acc += bp[12-12];
+ acc += bp[21-12];
+ acc += bp[20-12];
+ acc -= bp[23-12]; rp[0] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[1]; acc += bp[13-12];
+ acc += bp[22-12];
+ acc += bp[23-12];
+ acc -= bp[12-12];
+ acc -= bp[20-12]; rp[1] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[2]; acc += bp[14-12];
+ acc += bp[23-12];
+ acc -= bp[13-12];
+ acc -= bp[21-12]; rp[2] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[3]; acc += bp[15-12];
+ acc += bp[12-12];
+ acc += bp[20-12];
+ acc += bp[21-12];
+ acc -= bp[14-12];
+ acc -= bp[22-12];
+ acc -= bp[23-12]; rp[3] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[4]; acc += bp[21-12];
+ acc += bp[21-12];
+ acc += bp[16-12];
+ acc += bp[13-12];
+ acc += bp[12-12];
+ acc += bp[20-12];
+ acc += bp[22-12];
+ acc -= bp[15-12];
+ acc -= bp[23-12];
+ acc -= bp[23-12]; rp[4] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[5]; acc += bp[22-12];
+ acc += bp[22-12];
+ acc += bp[17-12];
+ acc += bp[14-12];
+ acc += bp[13-12];
+ acc += bp[21-12];
+ acc += bp[23-12];
+ acc -= bp[16-12]; rp[5] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[6]; acc += bp[23-12];
+ acc += bp[23-12];
+ acc += bp[18-12];
+ acc += bp[15-12];
+ acc += bp[14-12];
+ acc += bp[22-12];
+ acc -= bp[17-12]; rp[6] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[7]; acc += bp[19-12];
+ acc += bp[16-12];
+ acc += bp[15-12];
+ acc += bp[23-12];
+ acc -= bp[18-12]; rp[7] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[8]; acc += bp[20-12];
+ acc += bp[17-12];
+ acc += bp[16-12];
+ acc -= bp[19-12]; rp[8] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[9]; acc += bp[21-12];
+ acc += bp[18-12];
+ acc += bp[17-12];
+ acc -= bp[20-12]; rp[9] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[10]; acc += bp[22-12];
+ acc += bp[19-12];
+ acc += bp[18-12];
+ acc -= bp[21-12]; rp[10] = (unsigned int)acc; acc >>= 32;
+
+ acc += rp[11]; acc += bp[23-12];
+ acc += bp[20-12];
+ acc += bp[19-12];
+ acc -= bp[22-12]; rp[11] = (unsigned int)acc;
+
+ carry = (int)(acc>>32);
+ }
+#else
+ {
+ BN_ULONG t_d[BN_NIST_384_TOP];
/*S1*/
- nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
+ nist_set_256(t_d, buf.bn, 0, 0, 0, 0, 0, 23-4, 22-4, 21-4);
/* left shift */
{
register BN_ULONG *ap,t,c;
@@ -729,29 +985,31 @@ int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field,
carry = (int)bn_add_words(r_d+(128/BN_BITS2), r_d+(128/BN_BITS2),
t_d, BN_NIST_256_TOP);
/*S2 */
- carry += (int)bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP);
+ carry += (int)bn_add_words(r_d, r_d, buf.bn, BN_NIST_384_TOP);
/*S3*/
- nist_set_384(t_d,buf,20,19,18,17,16,15,14,13,12,23,22,21);
+ nist_set_384(t_d,buf.bn,20,19,18,17,16,15,14,13,12,23,22,21);
carry += (int)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);
+ nist_set_384(t_d,buf.bn,19,18,17,16,15,14,13,12,20,0,23,0);
carry += (int)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);
+ nist_set_384(t_d, buf.bn,0,0,0,0,23,22,21,20,0,0,0,0);
carry += (int)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);
+ nist_set_384(t_d,buf.bn,0,0,0,0,0,0,23,22,21,0,0,20);
carry += (int)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);
+ nist_set_384(t_d,buf.bn,22,21,20,19,18,17,16,15,14,13,12,23);
carry -= (int)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);
+ nist_set_384(t_d,buf.bn,0,0,0,0,0,0,0,23,22,21,20,0);
carry -= (int)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);
+ nist_set_384(t_d,buf.bn,0,0,0,0,0,0,0,23,23,0,0,0);
carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP);
+ }
+#endif
/* see BN_nist_mod_224 for explanation */
u.f = bn_sub_words;
if (carry > 0)