Crypto++  8.8
Free C++ class library of cryptographic schemes
donna_sse.cpp
1 // donna_sse.cpp - written and placed in public domain by Jeffrey Walton
2 // This is a integration of Andrew Moon's public domain code.
3 // Also see https://github.com/floodyberry/curve25519-donna.
4 
5 // This is a integration of Andrew Moon's public domain code. The port was
6 // clean, but it has one potential problem. The original code is C and relies
7 // upon unions. Accessing the inactive union member is undefined behavior in
8 // C++. That means copying the array into packedelem8.u is OK; but then using
9 // packedelem8.v in a calculation is UB. Fortunately most (all?) compilers
10 // take pity on C++ developers and compile the code. We will have to keep an
11 // eye on things or rewrite significant portions of this code.
12 
13 // If needed, see Moon's commit "Go back to ignoring 256th bit [sic]",
14 // https://github.com/floodyberry/curve25519-donna/commit/57a683d18721a658
15 
16 #include "pch.h"
17 
18 #include "config.h"
19 #include "donna.h"
20 #include "secblock.h"
21 #include "misc.h"
22 
23 // The data is aligned, but Clang issues warning based on type
24 // and not the actual alignment of the variable and data.
25 #if CRYPTOPP_GCC_DIAGNOSTIC_AVAILABLE
26 # pragma GCC diagnostic ignored "-Wcast-align"
27 # pragma GCC diagnostic ignored "-Wunused-function"
28 #endif
29 
30 #if CRYPTOPP_MSC_VERSION
31 # pragma warning(disable: 4244)
32 #endif
33 
34 // Squash MS LNK4221 and libtool warnings
35 extern const char DONNA_SSE_FNAME[] = __FILE__;
36 
37 #if (CRYPTOPP_CURVE25519_SSE2)
38 
39 #include "donna_sse.h"
40 
41 ANONYMOUS_NAMESPACE_BEGIN
42 
43 using CryptoPP::byte;
44 using CryptoPP::word32;
45 using CryptoPP::sword32;
46 using CryptoPP::word64;
47 using CryptoPP::sword64;
48 using CryptoPP::GetBlock;
49 using CryptoPP::LittleEndian;
50 
51 // Bring in all the symbols from the SSE header
52 using namespace CryptoPP::Donna::ArchSSE;
53 
54 /* Copy a bignum to another: out = in */
55 inline void
56 curve25519_copy(bignum25519 out, const bignum25519 in) {
57  xmmi x0,x1,x2;
58  x0 = _mm_load_si128((xmmi*)in + 0);
59  x1 = _mm_load_si128((xmmi*)in + 1);
60  x2 = _mm_load_si128((xmmi*)in + 2);
61  _mm_store_si128((xmmi*)out + 0, x0);
62  _mm_store_si128((xmmi*)out + 1, x1);
63  _mm_store_si128((xmmi*)out + 2, x2);
64 }
65 
66 /* Take a little-endian, 32-byte number and expand it into polynomial form */
67 inline void
68 curve25519_expand(bignum25519 out, const byte in[32]) {
69  word32 x0,x1,x2,x3,x4,x5,x6,x7;
70 
71  x0 = *(word32 *)(in + 0);
72  x1 = *(word32 *)(in + 4);
73  x2 = *(word32 *)(in + 8);
74  x3 = *(word32 *)(in + 12);
75  x4 = *(word32 *)(in + 16);
76  x5 = *(word32 *)(in + 20);
77  x6 = *(word32 *)(in + 24);
78  x7 = *(word32 *)(in + 28);
79 
80  out[0] = ( x0 ) & reduce_mask_26;
81  out[1] = ((((word64)x1 << 32) | x0) >> 26) & reduce_mask_25;
82  out[2] = ((((word64)x2 << 32) | x1) >> 19) & reduce_mask_26;
83  out[3] = ((((word64)x3 << 32) | x2) >> 13) & reduce_mask_25;
84  out[4] = (( x3) >> 6) & reduce_mask_26;
85  out[5] = ( x4 ) & reduce_mask_25;
86  out[6] = ((((word64)x5 << 32) | x4) >> 25) & reduce_mask_26;
87  out[7] = ((((word64)x6 << 32) | x5) >> 19) & reduce_mask_25;
88  out[8] = ((((word64)x7 << 32) | x6) >> 12) & reduce_mask_26;
89  out[9] = (( x7) >> 6) & reduce_mask_25; /* ignore the top bit */
90 
91  out[10] = 0;
92  out[11] = 0;
93 }
94 
95 /* Take a fully reduced polynomial form number and contract it into a
96  * little-endian, 32-byte array
97  */
98 inline void
99 curve25519_contract(byte out[32], const bignum25519 in) {
100  ALIGN(16) bignum25519 f;
101 
102  curve25519_copy(f, in);
103 
104  #define carry_pass() \
105  f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
106  f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
107  f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
108  f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
109  f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
110  f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
111  f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
112  f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
113  f[9] += f[8] >> 26; f[8] &= reduce_mask_26;
114 
115  #define carry_pass_full() \
116  carry_pass() \
117  f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;
118 
119  #define carry_pass_final() \
120  carry_pass() \
121  f[9] &= reduce_mask_25;
122 
123  carry_pass_full()
124  carry_pass_full()
125 
126  /* now t is between 0 and 2^255-1, properly carried. */
127  /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
128  f[0] += 19;
129  carry_pass_full()
130 
131  /* now between 19 and 2^255-1 in both cases, and offset by 19. */
132  f[0] += (1 << 26) - 19;
133  f[1] += (1 << 25) - 1;
134  f[2] += (1 << 26) - 1;
135  f[3] += (1 << 25) - 1;
136  f[4] += (1 << 26) - 1;
137  f[5] += (1 << 25) - 1;
138  f[6] += (1 << 26) - 1;
139  f[7] += (1 << 25) - 1;
140  f[8] += (1 << 26) - 1;
141  f[9] += (1 << 25) - 1;
142 
143  /* now between 2^255 and 2^256-20, and offset by 2^255. */
144  carry_pass_final()
145 
146  #undef carry_pass
147  #undef carry_full
148  #undef carry_final
149 
150  *(word32 *)(out + 0) = ((f[0] ) | (f[1] << 26));
151  *(word32 *)(out + 4) = ((f[1] >> 6) | (f[2] << 19));
152  *(word32 *)(out + 8) = ((f[2] >> 13) | (f[3] << 13));
153  *(word32 *)(out + 12) = ((f[3] >> 19) | (f[4] << 6));
154  *(word32 *)(out + 16) = ((f[5] ) | (f[6] << 25));
155  *(word32 *)(out + 20) = ((f[6] >> 7) | (f[7] << 19));
156  *(word32 *)(out + 24) = ((f[7] >> 13) | (f[8] << 12));
157  *(word32 *)(out + 28) = ((f[8] >> 20) | (f[9] << 6));
158 }
159 
160 /*
161  * Maybe swap the contents of two felem arrays (@a and @b), each 5 elements
162  * long. Perform the swap iff @swap is non-zero.
163  */
164 inline void
165 curve25519_swap_conditional(bignum25519 a, bignum25519 b, word32 iswap) {
166  const word32 swap = (word32)(-(sword32)iswap);
167  xmmi a0,a1,a2,b0,b1,b2,x0,x1,x2;
168  xmmi mask = _mm_cvtsi32_si128(swap);
169  mask = _mm_shuffle_epi32(mask, 0);
170  a0 = _mm_load_si128((xmmi *)a + 0);
171  a1 = _mm_load_si128((xmmi *)a + 1);
172  a2 = _mm_load_si128((xmmi *)a + 2);
173  b0 = _mm_load_si128((xmmi *)b + 0);
174  b1 = _mm_load_si128((xmmi *)b + 1);
175  b2 = _mm_load_si128((xmmi *)b + 2);
176  b0 = _mm_xor_si128(a0, b0);
177  b1 = _mm_xor_si128(a1, b1);
178  b2 = _mm_xor_si128(a2, b2);
179  x0 = _mm_and_si128(b0, mask);
180  x1 = _mm_and_si128(b1, mask);
181  x2 = _mm_and_si128(b2, mask);
182  x0 = _mm_xor_si128(x0, a0);
183  x1 = _mm_xor_si128(x1, a1);
184  x2 = _mm_xor_si128(x2, a2);
185  a0 = _mm_xor_si128(x0, b0);
186  a1 = _mm_xor_si128(x1, b1);
187  a2 = _mm_xor_si128(x2, b2);
188  _mm_store_si128((xmmi *)a + 0, x0);
189  _mm_store_si128((xmmi *)a + 1, x1);
190  _mm_store_si128((xmmi *)a + 2, x2);
191  _mm_store_si128((xmmi *)b + 0, a0);
192  _mm_store_si128((xmmi *)b + 1, a1);
193  _mm_store_si128((xmmi *)b + 2, a2);
194 }
195 
196 /* interleave two bignums */
197 inline void
198 curve25519_tangle32(packedelem32 *out, const bignum25519 x, const bignum25519 z) {
199  xmmi x0,x1,x2,z0,z1,z2;
200 
201  x0 = _mm_load_si128((xmmi *)(x + 0));
202  x1 = _mm_load_si128((xmmi *)(x + 4));
203  x2 = _mm_load_si128((xmmi *)(x + 8));
204  z0 = _mm_load_si128((xmmi *)(z + 0));
205  z1 = _mm_load_si128((xmmi *)(z + 4));
206  z2 = _mm_load_si128((xmmi *)(z + 8));
207 
208  out[0].v = _mm_unpacklo_epi32(x0, z0);
209  out[1].v = _mm_unpackhi_epi32(x0, z0);
210  out[2].v = _mm_unpacklo_epi32(x1, z1);
211  out[3].v = _mm_unpackhi_epi32(x1, z1);
212  out[4].v = _mm_unpacklo_epi32(x2, z2);
213 }
214 
215 /* split a packed bignum in to it's two parts */
216 inline void
217 curve25519_untangle64(bignum25519 x, bignum25519 z, const packedelem64 *in) {
218  _mm_store_si128((xmmi *)(x + 0), _mm_unpacklo_epi64(_mm_unpacklo_epi32(in[0].v, in[1].v), _mm_unpacklo_epi32(in[2].v, in[3].v)));
219  _mm_store_si128((xmmi *)(x + 4), _mm_unpacklo_epi64(_mm_unpacklo_epi32(in[4].v, in[5].v), _mm_unpacklo_epi32(in[6].v, in[7].v)));
220  _mm_store_si128((xmmi *)(x + 8), _mm_unpacklo_epi32(in[8].v, in[9].v) );
221  _mm_store_si128((xmmi *)(z + 0), _mm_unpacklo_epi64(_mm_unpackhi_epi32(in[0].v, in[1].v), _mm_unpackhi_epi32(in[2].v, in[3].v)));
222  _mm_store_si128((xmmi *)(z + 4), _mm_unpacklo_epi64(_mm_unpackhi_epi32(in[4].v, in[5].v), _mm_unpackhi_epi32(in[6].v, in[7].v)));
223  _mm_store_si128((xmmi *)(z + 8), _mm_unpackhi_epi32(in[8].v, in[9].v) );
224 }
225 
226 /* add two packed bignums */
227 inline void
228 curve25519_add_packed32(packedelem32 *out, const packedelem32 *r, const packedelem32 *s) {
229  out[0].v = _mm_add_epi32(r[0].v, s[0].v);
230  out[1].v = _mm_add_epi32(r[1].v, s[1].v);
231  out[2].v = _mm_add_epi32(r[2].v, s[2].v);
232  out[3].v = _mm_add_epi32(r[3].v, s[3].v);
233  out[4].v = _mm_add_epi32(r[4].v, s[4].v);
234 }
235 
236 /* subtract two packed bignums */
237 inline void
238 curve25519_sub_packed32(packedelem32 *out, const packedelem32 *r, const packedelem32 *s) {
239  xmmi r0,r1,r2,r3,r4;
240  xmmi s0,s1,s2,s3;
241  xmmi c1,c2;
242 
243  r0 = _mm_add_epi32(r[0].v, packed32zeromodp0.v);
244  r1 = _mm_add_epi32(r[1].v, packed32zeromodp1.v);
245  r2 = _mm_add_epi32(r[2].v, packed32zeromodp1.v);
246  r3 = _mm_add_epi32(r[3].v, packed32zeromodp1.v);
247  r4 = _mm_add_epi32(r[4].v, packed32zeromodp1.v);
248  r0 = _mm_sub_epi32(r0, s[0].v); /* 00 11 */
249  r1 = _mm_sub_epi32(r1, s[1].v); /* 22 33 */
250  r2 = _mm_sub_epi32(r2, s[2].v); /* 44 55 */
251  r3 = _mm_sub_epi32(r3, s[3].v); /* 66 77 */
252  r4 = _mm_sub_epi32(r4, s[4].v); /* 88 99 */
253 
254  s0 = _mm_unpacklo_epi64(r0, r2); /* 00 44 */
255  s1 = _mm_unpackhi_epi64(r0, r2); /* 11 55 */
256  s2 = _mm_unpacklo_epi64(r1, r3); /* 22 66 */
257  s3 = _mm_unpackhi_epi64(r1, r3); /* 33 77 */
258 
259  c1 = _mm_srli_epi32(s0, 26); c2 = _mm_srli_epi32(s2, 26); s0 = _mm_and_si128(s0, packedmask26262626.v); s2 = _mm_and_si128(s2, packedmask26262626.v); s1 = _mm_add_epi32(s1, c1); s3 = _mm_add_epi32(s3, c2);
260  c1 = _mm_srli_epi32(s1, 25); c2 = _mm_srli_epi32(s3, 25); s1 = _mm_and_si128(s1, packedmask25252525.v); s3 = _mm_and_si128(s3, packedmask25252525.v); s2 = _mm_add_epi32(s2, c1); r4 = _mm_add_epi32(r4, _mm_srli_si128(c2, 8)); s0 = _mm_add_epi32(s0, _mm_slli_si128(c2, 8));
261 
262  out[0].v = _mm_unpacklo_epi64(s0, s1); /* 00 11 */
263  out[1].v = _mm_unpacklo_epi64(s2, s3); /* 22 33 */
264  out[2].v = _mm_unpackhi_epi64(s0, s1); /* 44 55 */
265  out[3].v = _mm_unpackhi_epi64(s2, s3); /* 66 77 */
266  out[4].v = r4; /* 88 99 */
267 }
268 
269 /* multiply two packed bignums */
270 inline void
271 curve25519_mul_packed64(packedelem64 *out, const packedelem64 *r, const packedelem64 *s) {
272  xmmi r1,r2,r3,r4,r5,r6,r7,r8,r9;
273  xmmi r1_2,r3_2,r5_2,r7_2,r9_2;
274  xmmi c1,c2;
275 
276  out[0].v = _mm_mul_epu32(r[0].v, s[0].v);
277  out[1].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[1].v), _mm_mul_epu32(r[1].v, s[0].v));
278  r1_2 = _mm_slli_epi32(r[1].v, 1);
279  out[2].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r1_2 , s[1].v), _mm_mul_epu32(r[2].v, s[0].v)));
280  out[3].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[1].v), _mm_mul_epu32(r[3].v, s[0].v))));
281  r3_2 = _mm_slli_epi32(r[3].v, 1);
282  out[4].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r1_2 , s[3].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r3_2 , s[1].v), _mm_mul_epu32(r[4].v, s[0].v)))));
283  out[5].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[5].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[3].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[1].v), _mm_mul_epu32(r[5].v, s[0].v))))));
284  r5_2 = _mm_slli_epi32(r[5].v, 1);
285  out[6].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r1_2 , s[5].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r3_2 , s[3].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r5_2 , s[1].v), _mm_mul_epu32(r[6].v, s[0].v)))))));
286  out[7].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[7].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[5].v), _mm_add_epi64(_mm_mul_epu32(r[3].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[5].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[6].v, s[1].v), _mm_mul_epu32(r[7].v , s[0].v))))))));
287  r7_2 = _mm_slli_epi32(r[7].v, 1);
288  out[8].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[8].v), _mm_add_epi64(_mm_mul_epu32(r1_2 , s[7].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r3_2 , s[5].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r5_2 , s[3].v), _mm_add_epi64(_mm_mul_epu32(r[6].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r7_2 , s[1].v), _mm_mul_epu32(r[8].v, s[0].v)))))))));
289  out[9].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[9].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[8].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[7].v), _mm_add_epi64(_mm_mul_epu32(r[3].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[5].v), _mm_add_epi64(_mm_mul_epu32(r[5].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r[6].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[7].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[8].v, s[1].v), _mm_mul_epu32(r[9].v, s[0].v))))))))));
290 
291  r1 = _mm_mul_epu32(r[1].v, packednineteen.v);
292  r2 = _mm_mul_epu32(r[2].v, packednineteen.v);
293  r1_2 = _mm_slli_epi32(r1, 1);
294  r3 = _mm_mul_epu32(r[3].v, packednineteen.v);
295  r4 = _mm_mul_epu32(r[4].v, packednineteen.v);
296  r3_2 = _mm_slli_epi32(r3, 1);
297  r5 = _mm_mul_epu32(r[5].v, packednineteen.v);
298  r6 = _mm_mul_epu32(r[6].v, packednineteen.v);
299  r5_2 = _mm_slli_epi32(r5, 1);
300  r7 = _mm_mul_epu32(r[7].v, packednineteen.v);
301  r8 = _mm_mul_epu32(r[8].v, packednineteen.v);
302  r7_2 = _mm_slli_epi32(r7, 1);
303  r9 = _mm_mul_epu32(r[9].v, packednineteen.v);
304  r9_2 = _mm_slli_epi32(r9, 1);
305 
306  out[0].v = _mm_add_epi64(out[0].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[1].v), _mm_add_epi64(_mm_mul_epu32(r8, s[2].v), _mm_add_epi64(_mm_mul_epu32(r7_2, s[3].v), _mm_add_epi64(_mm_mul_epu32(r6, s[4].v), _mm_add_epi64(_mm_mul_epu32(r5_2, s[5].v), _mm_add_epi64(_mm_mul_epu32(r4, s[6].v), _mm_add_epi64(_mm_mul_epu32(r3_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r2, s[8].v), _mm_mul_epu32(r1_2, s[9].v))))))))));
307  out[1].v = _mm_add_epi64(out[1].v, _mm_add_epi64(_mm_mul_epu32(r9 , s[2].v), _mm_add_epi64(_mm_mul_epu32(r8, s[3].v), _mm_add_epi64(_mm_mul_epu32(r7 , s[4].v), _mm_add_epi64(_mm_mul_epu32(r6, s[5].v), _mm_add_epi64(_mm_mul_epu32(r5 , s[6].v), _mm_add_epi64(_mm_mul_epu32(r4, s[7].v), _mm_add_epi64(_mm_mul_epu32(r3 , s[8].v), _mm_mul_epu32(r2, s[9].v)))))))));
308  out[2].v = _mm_add_epi64(out[2].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[3].v), _mm_add_epi64(_mm_mul_epu32(r8, s[4].v), _mm_add_epi64(_mm_mul_epu32(r7_2, s[5].v), _mm_add_epi64(_mm_mul_epu32(r6, s[6].v), _mm_add_epi64(_mm_mul_epu32(r5_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r4, s[8].v), _mm_mul_epu32(r3_2, s[9].v))))))));
309  out[3].v = _mm_add_epi64(out[3].v, _mm_add_epi64(_mm_mul_epu32(r9 , s[4].v), _mm_add_epi64(_mm_mul_epu32(r8, s[5].v), _mm_add_epi64(_mm_mul_epu32(r7 , s[6].v), _mm_add_epi64(_mm_mul_epu32(r6, s[7].v), _mm_add_epi64(_mm_mul_epu32(r5 , s[8].v), _mm_mul_epu32(r4, s[9].v)))))));
310  out[4].v = _mm_add_epi64(out[4].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[5].v), _mm_add_epi64(_mm_mul_epu32(r8, s[6].v), _mm_add_epi64(_mm_mul_epu32(r7_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r6, s[8].v), _mm_mul_epu32(r5_2, s[9].v))))));
311  out[5].v = _mm_add_epi64(out[5].v, _mm_add_epi64(_mm_mul_epu32(r9 , s[6].v), _mm_add_epi64(_mm_mul_epu32(r8, s[7].v), _mm_add_epi64(_mm_mul_epu32(r7 , s[8].v), _mm_mul_epu32(r6, s[9].v)))));
312  out[6].v = _mm_add_epi64(out[6].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r8, s[8].v), _mm_mul_epu32(r7_2, s[9].v))));
313  out[7].v = _mm_add_epi64(out[7].v, _mm_add_epi64(_mm_mul_epu32(r9 , s[8].v), _mm_mul_epu32(r8, s[9].v)));
314  out[8].v = _mm_add_epi64(out[8].v, _mm_mul_epu32(r9_2, s[9].v));
315 
316  c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
317  c1 = _mm_srli_epi64(out[1].v, 25); c2 = _mm_srli_epi64(out[5].v, 25); out[1].v = _mm_and_si128(out[1].v, packedmask25.v); out[5].v = _mm_and_si128(out[5].v, packedmask25.v); out[2].v = _mm_add_epi64(out[2].v, c1); out[6].v = _mm_add_epi64(out[6].v, c2);
318  c1 = _mm_srli_epi64(out[2].v, 26); c2 = _mm_srli_epi64(out[6].v, 26); out[2].v = _mm_and_si128(out[2].v, packedmask26.v); out[6].v = _mm_and_si128(out[6].v, packedmask26.v); out[3].v = _mm_add_epi64(out[3].v, c1); out[7].v = _mm_add_epi64(out[7].v, c2);
319  c1 = _mm_srli_epi64(out[3].v, 25); c2 = _mm_srli_epi64(out[7].v, 25); out[3].v = _mm_and_si128(out[3].v, packedmask25.v); out[7].v = _mm_and_si128(out[7].v, packedmask25.v); out[4].v = _mm_add_epi64(out[4].v, c1); out[8].v = _mm_add_epi64(out[8].v, c2);
320  c2 = _mm_srli_epi64(out[8].v, 26); out[8].v = _mm_and_si128(out[8].v, packedmask26.v); out[9].v = _mm_add_epi64(out[9].v, c2);
321  c2 = _mm_srli_epi64(out[9].v, 25); out[9].v = _mm_and_si128(out[9].v, packedmask25.v); out[0].v = _mm_add_epi64(out[0].v, _mm_mul_epu32(c2, packednineteen.v));
322  c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
323 }
324 
325 /* multiply a bignum */
326 void
327 curve25519_mul(bignum25519 out, const bignum25519 r, const bignum25519 s) {
328  xmmi m01,m23,m45,m67,m89;
329  xmmi m0123,m4567;
330  xmmi s0123,s4567;
331  xmmi s01,s23,s45,s67,s89;
332  xmmi s12,s34,s56,s78,s9;
333  xmmi r0,r2,r4,r6,r8;
334  xmmi r1,r3,r5,r7,r9;
335  xmmi r119,r219,r319,r419,r519,r619,r719,r819,r919;
336  xmmi c1,c2,c3;
337 
338  s0123 = _mm_load_si128((xmmi*)s + 0);
339  s01 = _mm_shuffle_epi32(s0123,_MM_SHUFFLE(3,1,2,0));
340  s12 = _mm_shuffle_epi32(s0123, _MM_SHUFFLE(2,2,1,1));
341  s23 = _mm_shuffle_epi32(s0123,_MM_SHUFFLE(3,3,2,2));
342  s4567 = _mm_load_si128((xmmi*)s + 1);
343  s34 = _mm_unpacklo_epi64(_mm_srli_si128(s0123,12),s4567);
344  s45 = _mm_shuffle_epi32(s4567,_MM_SHUFFLE(3,1,2,0));
345  s56 = _mm_shuffle_epi32(s4567, _MM_SHUFFLE(2,2,1,1));
346  s67 = _mm_shuffle_epi32(s4567,_MM_SHUFFLE(3,3,2,2));
347  s89 = _mm_load_si128((xmmi*)s + 2);
348  s78 = _mm_unpacklo_epi64(_mm_srli_si128(s4567,12),s89);
349  s89 = _mm_shuffle_epi32(s89,_MM_SHUFFLE(3,1,2,0));
350  s9 = _mm_shuffle_epi32(s89, _MM_SHUFFLE(3,3,2,2));
351 
352  r0 = _mm_load_si128((xmmi*)r + 0);
353  r1 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(1,1,1,1));
354  r1 = _mm_add_epi64(r1, _mm_and_si128(r1, sse2_top64bitmask.v));
355  r2 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(2,2,2,2));
356  r3 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(3,3,3,3));
357  r3 = _mm_add_epi64(r3, _mm_and_si128(r3, sse2_top64bitmask.v));
358  r0 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(0,0,0,0));
359  r4 = _mm_load_si128((xmmi*)r + 1);
360  r5 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(1,1,1,1));
361  r5 = _mm_add_epi64(r5, _mm_and_si128(r5, sse2_top64bitmask.v));
362  r6 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(2,2,2,2));
363  r7 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(3,3,3,3));
364  r7 = _mm_add_epi64(r7, _mm_and_si128(r7, sse2_top64bitmask.v));
365  r4 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(0,0,0,0));
366  r8 = _mm_load_si128((xmmi*)r + 2);
367  r9 = _mm_shuffle_epi32(r8, _MM_SHUFFLE(3,1,3,1));
368  r9 = _mm_add_epi64(r9, _mm_and_si128(r9, sse2_top64bitmask.v));
369  r8 = _mm_shuffle_epi32(r8, _MM_SHUFFLE(3,0,3,0));
370 
371  m01 = _mm_mul_epu32(r1,s01);
372  m23 = _mm_mul_epu32(r1,s23);
373  m45 = _mm_mul_epu32(r1,s45);
374  m67 = _mm_mul_epu32(r1,s67);
375  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r3,s01));
376  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r3,s23));
377  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r3,s45));
378  m89 = _mm_mul_epu32(r1,s89);
379  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r5,s01));
380  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r5,s23));
381  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r3,s67));
382  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r7,s01));
383  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r5,s45));
384  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r7,s23));
385  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r9,s01));
386 
387  /* shift up */
388  m89 = _mm_unpackhi_epi64(m67,_mm_slli_si128(m89,8));
389  m67 = _mm_unpackhi_epi64(m45,_mm_slli_si128(m67,8));
390  m45 = _mm_unpackhi_epi64(m23,_mm_slli_si128(m45,8));
391  m23 = _mm_unpackhi_epi64(m01,_mm_slli_si128(m23,8));
392  m01 = _mm_unpackhi_epi64(_mm_setzero_si128(),_mm_slli_si128(m01,8));
393 
394  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r0,s01));
395  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r0,s23));
396  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r0,s45));
397  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r0,s67));
398  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r2,s01));
399  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r2,s23));
400  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r4,s23));
401  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r0,s89));
402  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r4,s01));
403  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r2,s45));
404  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r2,s67));
405  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r6,s01));
406  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r4,s45));
407  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r6,s23));
408  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r8,s01));
409 
410  r219 = _mm_mul_epu32(r2, packednineteen.v);
411  r419 = _mm_mul_epu32(r4, packednineteen.v);
412  r619 = _mm_mul_epu32(r6, packednineteen.v);
413  r819 = _mm_mul_epu32(r8, packednineteen.v);
414  r119 = _mm_shuffle_epi32(r1,_MM_SHUFFLE(0,0,2,2)); r119 = _mm_mul_epu32(r119, packednineteen.v);
415  r319 = _mm_shuffle_epi32(r3,_MM_SHUFFLE(0,0,2,2)); r319 = _mm_mul_epu32(r319, packednineteen.v);
416  r519 = _mm_shuffle_epi32(r5,_MM_SHUFFLE(0,0,2,2)); r519 = _mm_mul_epu32(r519, packednineteen.v);
417  r719 = _mm_shuffle_epi32(r7,_MM_SHUFFLE(0,0,2,2)); r719 = _mm_mul_epu32(r719, packednineteen.v);
418  r919 = _mm_shuffle_epi32(r9,_MM_SHUFFLE(0,0,2,2)); r919 = _mm_mul_epu32(r919, packednineteen.v);
419 
420  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r919,s12));
421  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r919,s34));
422  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r919,s56));
423  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r919,s78));
424  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r719,s34));
425  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r719,s56));
426  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r719,s78));
427  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r719,s9));
428  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r519,s56));
429  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r519,s78));
430  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r519,s9));
431  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r819,s89));
432  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r319,s78));
433  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r319,s9));
434  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r619,s89));
435  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r919,s9));
436  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r819,s23));
437  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r819,s45));
438  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r819,s67));
439  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r619,s45));
440  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r619,s67));
441  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r419,s67));
442  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r419,s89));
443  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r219,s89));
444  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r119,s9));
445 
446  r0 = _mm_unpacklo_epi64(m01, m45);
447  r1 = _mm_unpackhi_epi64(m01, m45);
448  r2 = _mm_unpacklo_epi64(m23, m67);
449  r3 = _mm_unpackhi_epi64(m23, m67);
450  r4 = _mm_unpacklo_epi64(m89, m89);
451  r5 = _mm_unpackhi_epi64(m89, m89);
452 
453  c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
454  c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8);
455  c1 = _mm_srli_epi64(r4, 26); r4 = _mm_and_si128(r4, packedmask26.v); r5 = _mm_add_epi64(r5, c1);
456  c1 = _mm_srli_epi64(r5, 25); r5 = _mm_and_si128(r5, packedmask25.v); r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3));
457  c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
458 
459  m0123 = _mm_unpacklo_epi32(r0, r1);
460  m4567 = _mm_unpackhi_epi32(r0, r1);
461  m0123 = _mm_unpacklo_epi64(m0123, _mm_unpacklo_epi32(r2, r3));
462  m4567 = _mm_unpacklo_epi64(m4567, _mm_unpackhi_epi32(r2, r3));
463  m89 = _mm_unpackhi_epi32(r4, r5);
464 
465  _mm_store_si128((xmmi*)out + 0, m0123);
466  _mm_store_si128((xmmi*)out + 1, m4567);
467  _mm_store_si128((xmmi*)out + 2, m89);
468 }
469 
470 typedef struct bignum25519mulprecomp_t {
471  xmmi r0,r2,r4,r6,r8;
472  xmmi r1,r3,r5,r7,r9;
473  xmmi r119,r219,r319,r419,r519,r619,r719,r819,r919;
474 } bignum25519mulprecomp;
475 
476 /* precompute a constant to multiply by */
477 inline void
478 curve25519_mul_precompute(bignum25519mulprecomp *pre, const bignum25519 r) {
479  pre->r0 = _mm_load_si128((xmmi*)r + 0);
480  pre->r1 = _mm_shuffle_epi32(pre->r0, _MM_SHUFFLE(1,1,1,1));
481  pre->r1 = _mm_add_epi64(pre->r1, _mm_and_si128(pre->r1, sse2_top64bitmask.v));
482  pre->r2 = _mm_shuffle_epi32(pre->r0, _MM_SHUFFLE(2,2,2,2));
483  pre->r3 = _mm_shuffle_epi32(pre->r0, _MM_SHUFFLE(3,3,3,3));
484  pre->r3 = _mm_add_epi64(pre->r3, _mm_and_si128(pre->r3, sse2_top64bitmask.v));
485  pre->r0 = _mm_shuffle_epi32(pre->r0, _MM_SHUFFLE(0,0,0,0));
486  pre->r4 = _mm_load_si128((xmmi*)r + 1);
487  pre->r5 = _mm_shuffle_epi32(pre->r4, _MM_SHUFFLE(1,1,1,1));
488  pre->r5 = _mm_add_epi64(pre->r5, _mm_and_si128(pre->r5, sse2_top64bitmask.v));
489  pre->r6 = _mm_shuffle_epi32(pre->r4, _MM_SHUFFLE(2,2,2,2));
490  pre->r7 = _mm_shuffle_epi32(pre->r4, _MM_SHUFFLE(3,3,3,3));
491  pre->r7 = _mm_add_epi64(pre->r7, _mm_and_si128(pre->r7, sse2_top64bitmask.v));
492  pre->r4 = _mm_shuffle_epi32(pre->r4, _MM_SHUFFLE(0,0,0,0));
493  pre->r8 = _mm_load_si128((xmmi*)r + 2);
494  pre->r9 = _mm_shuffle_epi32(pre->r8, _MM_SHUFFLE(3,1,3,1));
495  pre->r9 = _mm_add_epi64(pre->r9, _mm_and_si128(pre->r9, sse2_top64bitmask.v));
496  pre->r8 = _mm_shuffle_epi32(pre->r8, _MM_SHUFFLE(3,0,3,0));
497 
498  pre->r219 = _mm_mul_epu32(pre->r2, packednineteen.v);
499  pre->r419 = _mm_mul_epu32(pre->r4, packednineteen.v);
500  pre->r619 = _mm_mul_epu32(pre->r6, packednineteen.v);
501  pre->r819 = _mm_mul_epu32(pre->r8, packednineteen.v);
502  pre->r119 = _mm_shuffle_epi32(pre->r1,_MM_SHUFFLE(0,0,2,2)); pre->r119 = _mm_mul_epu32(pre->r119, packednineteen.v);
503  pre->r319 = _mm_shuffle_epi32(pre->r3,_MM_SHUFFLE(0,0,2,2)); pre->r319 = _mm_mul_epu32(pre->r319, packednineteen.v);
504  pre->r519 = _mm_shuffle_epi32(pre->r5,_MM_SHUFFLE(0,0,2,2)); pre->r519 = _mm_mul_epu32(pre->r519, packednineteen.v);
505  pre->r719 = _mm_shuffle_epi32(pre->r7,_MM_SHUFFLE(0,0,2,2)); pre->r719 = _mm_mul_epu32(pre->r719, packednineteen.v);
506  pre->r919 = _mm_shuffle_epi32(pre->r9,_MM_SHUFFLE(0,0,2,2)); pre->r919 = _mm_mul_epu32(pre->r919, packednineteen.v);
507 }
508 
509 
510 /* multiply a bignum by a pre-computed constant */
511 inline void
512 curve25519_mul_precomputed(bignum25519 out, const bignum25519 s, const bignum25519mulprecomp *r) {
513  xmmi m01,m23,m45,m67,m89;
514  xmmi m0123,m4567;
515  xmmi s0123,s4567;
516  xmmi s01,s23,s45,s67,s89;
517  xmmi s12,s34,s56,s78,s9;
518  xmmi r0,r1,r2,r3,r4,r5;
519  xmmi c1,c2,c3;
520 
521  s0123 = _mm_load_si128((xmmi*)s + 0);
522  s01 = _mm_shuffle_epi32(s0123,_MM_SHUFFLE(3,1,2,0));
523  s12 = _mm_shuffle_epi32(s0123, _MM_SHUFFLE(2,2,1,1));
524  s23 = _mm_shuffle_epi32(s0123,_MM_SHUFFLE(3,3,2,2));
525  s4567 = _mm_load_si128((xmmi*)s + 1);
526  s34 = _mm_unpacklo_epi64(_mm_srli_si128(s0123,12),s4567);
527  s45 = _mm_shuffle_epi32(s4567,_MM_SHUFFLE(3,1,2,0));
528  s56 = _mm_shuffle_epi32(s4567, _MM_SHUFFLE(2,2,1,1));
529  s67 = _mm_shuffle_epi32(s4567,_MM_SHUFFLE(3,3,2,2));
530  s89 = _mm_load_si128((xmmi*)s + 2);
531  s78 = _mm_unpacklo_epi64(_mm_srli_si128(s4567,12),s89);
532  s89 = _mm_shuffle_epi32(s89,_MM_SHUFFLE(3,1,2,0));
533  s9 = _mm_shuffle_epi32(s89, _MM_SHUFFLE(3,3,2,2));
534 
535  m01 = _mm_mul_epu32(r->r1,s01);
536  m23 = _mm_mul_epu32(r->r1,s23);
537  m45 = _mm_mul_epu32(r->r1,s45);
538  m67 = _mm_mul_epu32(r->r1,s67);
539  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r3,s01));
540  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r3,s23));
541  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r3,s45));
542  m89 = _mm_mul_epu32(r->r1,s89);
543  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r5,s01));
544  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r5,s23));
545  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r3,s67));
546  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r7,s01));
547  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r5,s45));
548  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r7,s23));
549  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r9,s01));
550 
551  /* shift up */
552  m89 = _mm_unpackhi_epi64(m67,_mm_slli_si128(m89,8));
553  m67 = _mm_unpackhi_epi64(m45,_mm_slli_si128(m67,8));
554  m45 = _mm_unpackhi_epi64(m23,_mm_slli_si128(m45,8));
555  m23 = _mm_unpackhi_epi64(m01,_mm_slli_si128(m23,8));
556  m01 = _mm_unpackhi_epi64(_mm_setzero_si128(),_mm_slli_si128(m01,8));
557 
558  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r0,s01));
559  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r0,s23));
560  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r0,s45));
561  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r0,s67));
562  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r2,s01));
563  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r2,s23));
564  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r4,s23));
565  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r0,s89));
566  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r4,s01));
567  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r2,s45));
568  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r2,s67));
569  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r6,s01));
570  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r4,s45));
571  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r6,s23));
572  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r8,s01));
573  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r919,s12));
574  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r919,s34));
575  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r919,s56));
576  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r919,s78));
577  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r719,s34));
578  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r719,s56));
579  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r719,s78));
580  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r719,s9));
581  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r519,s56));
582  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r519,s78));
583  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r519,s9));
584  m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r819,s89));
585  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r319,s78));
586  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r319,s9));
587  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r619,s89));
588  m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r919,s9));
589  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r819,s23));
590  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r819,s45));
591  m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r819,s67));
592  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r619,s45));
593  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r619,s67));
594  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r419,s67));
595  m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r419,s89));
596  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r219,s89));
597  m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r119,s9));
598 
599  r0 = _mm_unpacklo_epi64(m01, m45);
600  r1 = _mm_unpackhi_epi64(m01, m45);
601  r2 = _mm_unpacklo_epi64(m23, m67);
602  r3 = _mm_unpackhi_epi64(m23, m67);
603  r4 = _mm_unpacklo_epi64(m89, m89);
604  r5 = _mm_unpackhi_epi64(m89, m89);
605 
606  c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
607  c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8);
608  c1 = _mm_srli_epi64(r4, 26); r4 = _mm_and_si128(r4, packedmask26.v); r5 = _mm_add_epi64(r5, c1);
609  c1 = _mm_srli_epi64(r5, 25); r5 = _mm_and_si128(r5, packedmask25.v); r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3));
610  c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
611 
612  m0123 = _mm_unpacklo_epi32(r0, r1);
613  m4567 = _mm_unpackhi_epi32(r0, r1);
614  m0123 = _mm_unpacklo_epi64(m0123, _mm_unpacklo_epi32(r2, r3));
615  m4567 = _mm_unpacklo_epi64(m4567, _mm_unpackhi_epi32(r2, r3));
616  m89 = _mm_unpackhi_epi32(r4, r5);
617 
618  _mm_store_si128((xmmi*)out + 0, m0123);
619  _mm_store_si128((xmmi*)out + 1, m4567);
620  _mm_store_si128((xmmi*)out + 2, m89);
621 }
622 
623 /* square a bignum 'count' times */
624 #define curve25519_square(r,x) curve25519_square_times(r,x,1)
625 
626 void
627 curve25519_square_times(bignum25519 r, const bignum25519 in, int count) {
628  xmmi m01,m23,m45,m67,m89;
629  xmmi r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
630  xmmi r0a,r1a,r2a,r3a,r7a,r9a;
631  xmmi r0123,r4567;
632  xmmi r01,r23,r45,r67,r6x,r89,r8x;
633  xmmi r12,r34,r56,r78,r9x;
634  xmmi r5619;
635  xmmi c1,c2,c3;
636 
637  r0123 = _mm_load_si128((xmmi*)in + 0);
638  r01 = _mm_shuffle_epi32(r0123,_MM_SHUFFLE(3,1,2,0));
639  r23 = _mm_shuffle_epi32(r0123,_MM_SHUFFLE(3,3,2,2));
640  r4567 = _mm_load_si128((xmmi*)in + 1);
641  r45 = _mm_shuffle_epi32(r4567,_MM_SHUFFLE(3,1,2,0));
642  r67 = _mm_shuffle_epi32(r4567,_MM_SHUFFLE(3,3,2,2));
643  r89 = _mm_load_si128((xmmi*)in + 2);
644  r89 = _mm_shuffle_epi32(r89,_MM_SHUFFLE(3,1,2,0));
645 
646  do {
647  r12 = _mm_unpackhi_epi64(r01, _mm_slli_si128(r23, 8));
648  r0 = _mm_shuffle_epi32(r01, _MM_SHUFFLE(0,0,0,0));
649  r0 = _mm_add_epi64(r0, _mm_and_si128(r0, sse2_top64bitmask.v));
650  r0a = _mm_shuffle_epi32(r0,_MM_SHUFFLE(3,2,1,2));
651  r1 = _mm_shuffle_epi32(r01, _MM_SHUFFLE(2,2,2,2));
652  r2 = _mm_shuffle_epi32(r23, _MM_SHUFFLE(0,0,0,0));
653  r2 = _mm_add_epi64(r2, _mm_and_si128(r2, sse2_top64bitmask.v));
654  r2a = _mm_shuffle_epi32(r2,_MM_SHUFFLE(3,2,1,2));
655  r3 = _mm_shuffle_epi32(r23, _MM_SHUFFLE(2,2,2,2));
656  r34 = _mm_unpackhi_epi64(r23, _mm_slli_si128(r45, 8));
657  r4 = _mm_shuffle_epi32(r45, _MM_SHUFFLE(0,0,0,0));
658  r4 = _mm_add_epi64(r4, _mm_and_si128(r4, sse2_top64bitmask.v));
659  r56 = _mm_unpackhi_epi64(r45, _mm_slli_si128(r67, 8));
660  r5619 = _mm_mul_epu32(r56, packednineteen.v);
661  r5 = _mm_shuffle_epi32(r5619, _MM_SHUFFLE(1,1,1,0));
662  r6 = _mm_shuffle_epi32(r5619, _MM_SHUFFLE(3,2,3,2));
663  r78 = _mm_unpackhi_epi64(r67, _mm_slli_si128(r89, 8));
664  r6x = _mm_unpacklo_epi64(r67, _mm_setzero_si128());
665  r7 = _mm_shuffle_epi32(r67, _MM_SHUFFLE(2,2,2,2));
666  r7 = _mm_mul_epu32(r7, packed3819.v);
667  r7a = _mm_shuffle_epi32(r7, _MM_SHUFFLE(3,3,3,2));
668  r8x = _mm_unpacklo_epi64(r89, _mm_setzero_si128());
669  r8 = _mm_shuffle_epi32(r89, _MM_SHUFFLE(0,0,0,0));
670  r8 = _mm_mul_epu32(r8, packednineteen.v);
671  r9 = _mm_shuffle_epi32(r89, _MM_SHUFFLE(2,2,2,2));
672  r9x = _mm_slli_epi32(_mm_shuffle_epi32(r89, _MM_SHUFFLE(3,3,3,2)), 1);
673  r9 = _mm_mul_epu32(r9, packed3819.v);
674  r9a = _mm_shuffle_epi32(r9, _MM_SHUFFLE(2,2,2,2));
675 
676  m01 = _mm_mul_epu32(r01, r0);
677  m23 = _mm_mul_epu32(r23, r0a);
678  m45 = _mm_mul_epu32(r45, r0a);
679  m45 = _mm_add_epi64(m45, _mm_mul_epu32(r23, r2));
680  r23 = _mm_slli_epi32(r23, 1);
681  m67 = _mm_mul_epu32(r67, r0a);
682  m67 = _mm_add_epi64(m67, _mm_mul_epu32(r45, r2a));
683  m89 = _mm_mul_epu32(r89, r0a);
684  m89 = _mm_add_epi64(m89, _mm_mul_epu32(r67, r2a));
685  r67 = _mm_slli_epi32(r67, 1);
686  m89 = _mm_add_epi64(m89, _mm_mul_epu32(r45, r4));
687  r45 = _mm_slli_epi32(r45, 1);
688 
689  r1 = _mm_slli_epi32(r1, 1);
690  r3 = _mm_slli_epi32(r3, 1);
691  r1a = _mm_add_epi64(r1, _mm_and_si128(r1, sse2_bot64bitmask.v));
692  r3a = _mm_add_epi64(r3, _mm_and_si128(r3, sse2_bot64bitmask.v));
693 
694  m23 = _mm_add_epi64(m23, _mm_mul_epu32(r12, r1));
695  m45 = _mm_add_epi64(m45, _mm_mul_epu32(r34, r1a));
696  m67 = _mm_add_epi64(m67, _mm_mul_epu32(r56, r1a));
697  m67 = _mm_add_epi64(m67, _mm_mul_epu32(r34, r3));
698  r34 = _mm_slli_epi32(r34, 1);
699  m89 = _mm_add_epi64(m89, _mm_mul_epu32(r78, r1a));
700  r78 = _mm_slli_epi32(r78, 1);
701  m89 = _mm_add_epi64(m89, _mm_mul_epu32(r56, r3a));
702  r56 = _mm_slli_epi32(r56, 1);
703 
704  m01 = _mm_add_epi64(m01, _mm_mul_epu32(_mm_slli_epi32(r12, 1), r9));
705  m01 = _mm_add_epi64(m01, _mm_mul_epu32(r34, r7));
706  m23 = _mm_add_epi64(m23, _mm_mul_epu32(r34, r9));
707  m01 = _mm_add_epi64(m01, _mm_mul_epu32(r56, r5));
708  m23 = _mm_add_epi64(m23, _mm_mul_epu32(r56, r7));
709  m45 = _mm_add_epi64(m45, _mm_mul_epu32(r56, r9));
710  m01 = _mm_add_epi64(m01, _mm_mul_epu32(r23, r8));
711  m01 = _mm_add_epi64(m01, _mm_mul_epu32(r45, r6));
712  m23 = _mm_add_epi64(m23, _mm_mul_epu32(r45, r8));
713  m23 = _mm_add_epi64(m23, _mm_mul_epu32(r6x, r6));
714  m45 = _mm_add_epi64(m45, _mm_mul_epu32(r78, r7a));
715  m67 = _mm_add_epi64(m67, _mm_mul_epu32(r78, r9));
716  m45 = _mm_add_epi64(m45, _mm_mul_epu32(r67, r8));
717  m67 = _mm_add_epi64(m67, _mm_mul_epu32(r8x, r8));
718  m89 = _mm_add_epi64(m89, _mm_mul_epu32(r9x, r9a));
719 
720  r0 = _mm_unpacklo_epi64(m01, m45);
721  r1 = _mm_unpackhi_epi64(m01, m45);
722  r2 = _mm_unpacklo_epi64(m23, m67);
723  r3 = _mm_unpackhi_epi64(m23, m67);
724  r4 = _mm_unpacklo_epi64(m89, m89);
725  r5 = _mm_unpackhi_epi64(m89, m89);
726 
727  c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
728  c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8);
729  c1 = _mm_srli_epi64(r4, 26); r4 = _mm_and_si128(r4, packedmask26.v); r5 = _mm_add_epi64(r5, c1);
730  c1 = _mm_srli_epi64(r5, 25); r5 = _mm_and_si128(r5, packedmask25.v); r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3));
731  c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
732 
733  r01 = _mm_unpacklo_epi64(r0, r1);
734  r45 = _mm_unpackhi_epi64(r0, r1);
735  r23 = _mm_unpacklo_epi64(r2, r3);
736  r67 = _mm_unpackhi_epi64(r2, r3);
737  r89 = _mm_unpackhi_epi64(r4, r5);
738  } while (--count);
739 
740  r0123 = _mm_shuffle_epi32(r23, _MM_SHUFFLE(2,0,3,3));
741  r4567 = _mm_shuffle_epi32(r67, _MM_SHUFFLE(2,0,3,3));
742  r0123 = _mm_or_si128(r0123, _mm_shuffle_epi32(r01, _MM_SHUFFLE(3,3,2,0)));
743  r4567 = _mm_or_si128(r4567, _mm_shuffle_epi32(r45, _MM_SHUFFLE(3,3,2,0)));
744  r89 = _mm_shuffle_epi32(r89, _MM_SHUFFLE(3,3,2,0));
745 
746  _mm_store_si128((xmmi*)r + 0, r0123);
747  _mm_store_si128((xmmi*)r + 1, r4567);
748  _mm_store_si128((xmmi*)r + 2, r89);
749 }
750 
751 /* square two packed bignums */
752 inline void
753 curve25519_square_packed64(packedelem64 *out, const packedelem64 *r) {
754  xmmi r0,r1,r2,r3;
755  xmmi r1_2,r3_2,r4_2,r5_2,r6_2,r7_2;
756  xmmi d5,d6,d7,d8,d9;
757  xmmi c1,c2;
758 
759  r0 = r[0].v;
760  r1 = r[1].v;
761  r2 = r[2].v;
762  r3 = r[3].v;
763 
764  out[0].v = _mm_mul_epu32(r0, r0);
765  r0 = _mm_slli_epi32(r0, 1);
766  out[1].v = _mm_mul_epu32(r0, r1);
767  r1_2 = _mm_slli_epi32(r1, 1);
768  out[2].v = _mm_add_epi64(_mm_mul_epu32(r0, r2 ), _mm_mul_epu32(r1, r1_2));
769  r1 = r1_2;
770  out[3].v = _mm_add_epi64(_mm_mul_epu32(r0, r3 ), _mm_mul_epu32(r1, r2 ));
771  r3_2 = _mm_slli_epi32(r3, 1);
772  out[4].v = _mm_add_epi64(_mm_mul_epu32(r0, r[4].v), _mm_add_epi64(_mm_mul_epu32(r1, r3_2 ), _mm_mul_epu32(r2, r2)));
773  r2 = _mm_slli_epi32(r2, 1);
774  out[5].v = _mm_add_epi64(_mm_mul_epu32(r0, r[5].v), _mm_add_epi64(_mm_mul_epu32(r1, r[4].v), _mm_mul_epu32(r2, r3)));
775  r5_2 = _mm_slli_epi32(r[5].v, 1);
776  out[6].v = _mm_add_epi64(_mm_mul_epu32(r0, r[6].v), _mm_add_epi64(_mm_mul_epu32(r1, r5_2 ), _mm_add_epi64(_mm_mul_epu32(r2, r[4].v), _mm_mul_epu32(r3, r3_2 ))));
777  r3 = r3_2;
778  out[7].v = _mm_add_epi64(_mm_mul_epu32(r0, r[7].v), _mm_add_epi64(_mm_mul_epu32(r1, r[6].v), _mm_add_epi64(_mm_mul_epu32(r2, r[5].v), _mm_mul_epu32(r3, r[4].v))));
779  r7_2 = _mm_slli_epi32(r[7].v, 1);
780  out[8].v = _mm_add_epi64(_mm_mul_epu32(r0, r[8].v), _mm_add_epi64(_mm_mul_epu32(r1, r7_2 ), _mm_add_epi64(_mm_mul_epu32(r2, r[6].v), _mm_add_epi64(_mm_mul_epu32(r3, r5_2 ), _mm_mul_epu32(r[4].v, r[4].v)))));
781  out[9].v = _mm_add_epi64(_mm_mul_epu32(r0, r[9].v), _mm_add_epi64(_mm_mul_epu32(r1, r[8].v), _mm_add_epi64(_mm_mul_epu32(r2, r[7].v), _mm_add_epi64(_mm_mul_epu32(r3, r[6].v), _mm_mul_epu32(r[4].v, r5_2 )))));
782 
783  d5 = _mm_mul_epu32(r[5].v, packedthirtyeight.v);
784  d6 = _mm_mul_epu32(r[6].v, packednineteen.v);
785  d7 = _mm_mul_epu32(r[7].v, packedthirtyeight.v);
786  d8 = _mm_mul_epu32(r[8].v, packednineteen.v);
787  d9 = _mm_mul_epu32(r[9].v, packedthirtyeight.v);
788 
789  r4_2 = _mm_slli_epi32(r[4].v, 1);
790  r6_2 = _mm_slli_epi32(r[6].v, 1);
791  out[0].v = _mm_add_epi64(out[0].v, _mm_add_epi64(_mm_mul_epu32(d9, r1 ), _mm_add_epi64(_mm_mul_epu32(d8, r2 ), _mm_add_epi64(_mm_mul_epu32(d7, r3 ), _mm_add_epi64(_mm_mul_epu32(d6, r4_2), _mm_mul_epu32(d5, r[5].v))))));
792  out[1].v = _mm_add_epi64(out[1].v, _mm_add_epi64(_mm_mul_epu32(d9, _mm_srli_epi32(r2, 1)), _mm_add_epi64(_mm_mul_epu32(d8, r3 ), _mm_add_epi64(_mm_mul_epu32(d7, r[4].v), _mm_mul_epu32(d6, r5_2 )))));
793  out[2].v = _mm_add_epi64(out[2].v, _mm_add_epi64(_mm_mul_epu32(d9, r3 ), _mm_add_epi64(_mm_mul_epu32(d8, r4_2), _mm_add_epi64(_mm_mul_epu32(d7, r5_2 ), _mm_mul_epu32(d6, r[6].v)))));
794  out[3].v = _mm_add_epi64(out[3].v, _mm_add_epi64(_mm_mul_epu32(d9, r[4].v ), _mm_add_epi64(_mm_mul_epu32(d8, r5_2), _mm_mul_epu32(d7, r[6].v))));
795  out[4].v = _mm_add_epi64(out[4].v, _mm_add_epi64(_mm_mul_epu32(d9, r5_2 ), _mm_add_epi64(_mm_mul_epu32(d8, r6_2), _mm_mul_epu32(d7, r[7].v))));
796  out[5].v = _mm_add_epi64(out[5].v, _mm_add_epi64(_mm_mul_epu32(d9, r[6].v ), _mm_mul_epu32(d8, r7_2 )));
797  out[6].v = _mm_add_epi64(out[6].v, _mm_add_epi64(_mm_mul_epu32(d9, r7_2 ), _mm_mul_epu32(d8, r[8].v)));
798  out[7].v = _mm_add_epi64(out[7].v, _mm_mul_epu32(d9, r[8].v));
799  out[8].v = _mm_add_epi64(out[8].v, _mm_mul_epu32(d9, r[9].v));
800 
801  c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
802  c1 = _mm_srli_epi64(out[1].v, 25); c2 = _mm_srli_epi64(out[5].v, 25); out[1].v = _mm_and_si128(out[1].v, packedmask25.v); out[5].v = _mm_and_si128(out[5].v, packedmask25.v); out[2].v = _mm_add_epi64(out[2].v, c1); out[6].v = _mm_add_epi64(out[6].v, c2);
803  c1 = _mm_srli_epi64(out[2].v, 26); c2 = _mm_srli_epi64(out[6].v, 26); out[2].v = _mm_and_si128(out[2].v, packedmask26.v); out[6].v = _mm_and_si128(out[6].v, packedmask26.v); out[3].v = _mm_add_epi64(out[3].v, c1); out[7].v = _mm_add_epi64(out[7].v, c2);
804  c1 = _mm_srli_epi64(out[3].v, 25); c2 = _mm_srli_epi64(out[7].v, 25); out[3].v = _mm_and_si128(out[3].v, packedmask25.v); out[7].v = _mm_and_si128(out[7].v, packedmask25.v); out[4].v = _mm_add_epi64(out[4].v, c1); out[8].v = _mm_add_epi64(out[8].v, c2);
805  c2 = _mm_srli_epi64(out[8].v, 26); out[8].v = _mm_and_si128(out[8].v, packedmask26.v); out[9].v = _mm_add_epi64(out[9].v, c2);
806  c2 = _mm_srli_epi64(out[9].v, 25); out[9].v = _mm_and_si128(out[9].v, packedmask25.v); out[0].v = _mm_add_epi64(out[0].v, _mm_mul_epu32(c2, packednineteen.v));
807  c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
808 }
809 
810 /* make [nqx+nqz,nqpqx+nqpqz], [nqpqx-nqpqz,nqx-nqz] from [nqx+nqz,nqpqx+nqpqz], [nqx-nqz,nqpqx-nqpqz] */
811 inline void
812 curve25519_make_nqpq(packedelem64 *primex, packedelem64 *primez, const packedelem32 *pqx, const packedelem32 *pqz) {
813  primex[0].v = _mm_shuffle_epi32(pqx[0].v, _MM_SHUFFLE(1,1,0,0));
814  primex[1].v = _mm_shuffle_epi32(pqx[0].v, _MM_SHUFFLE(3,3,2,2));
815  primex[2].v = _mm_shuffle_epi32(pqx[1].v, _MM_SHUFFLE(1,1,0,0));
816  primex[3].v = _mm_shuffle_epi32(pqx[1].v, _MM_SHUFFLE(3,3,2,2));
817  primex[4].v = _mm_shuffle_epi32(pqx[2].v, _MM_SHUFFLE(1,1,0,0));
818  primex[5].v = _mm_shuffle_epi32(pqx[2].v, _MM_SHUFFLE(3,3,2,2));
819  primex[6].v = _mm_shuffle_epi32(pqx[3].v, _MM_SHUFFLE(1,1,0,0));
820  primex[7].v = _mm_shuffle_epi32(pqx[3].v, _MM_SHUFFLE(3,3,2,2));
821  primex[8].v = _mm_shuffle_epi32(pqx[4].v, _MM_SHUFFLE(1,1,0,0));
822  primex[9].v = _mm_shuffle_epi32(pqx[4].v, _MM_SHUFFLE(3,3,2,2));
823  primez[0].v = _mm_shuffle_epi32(pqz[0].v, _MM_SHUFFLE(0,0,1,1));
824  primez[1].v = _mm_shuffle_epi32(pqz[0].v, _MM_SHUFFLE(2,2,3,3));
825  primez[2].v = _mm_shuffle_epi32(pqz[1].v, _MM_SHUFFLE(0,0,1,1));
826  primez[3].v = _mm_shuffle_epi32(pqz[1].v, _MM_SHUFFLE(2,2,3,3));
827  primez[4].v = _mm_shuffle_epi32(pqz[2].v, _MM_SHUFFLE(0,0,1,1));
828  primez[5].v = _mm_shuffle_epi32(pqz[2].v, _MM_SHUFFLE(2,2,3,3));
829  primez[6].v = _mm_shuffle_epi32(pqz[3].v, _MM_SHUFFLE(0,0,1,1));
830  primez[7].v = _mm_shuffle_epi32(pqz[3].v, _MM_SHUFFLE(2,2,3,3));
831  primez[8].v = _mm_shuffle_epi32(pqz[4].v, _MM_SHUFFLE(0,0,1,1));
832  primez[9].v = _mm_shuffle_epi32(pqz[4].v, _MM_SHUFFLE(2,2,3,3));
833 }
834 
835 /* make [nqx+nqz,nqx-nqz] from [nqx+nqz,nqpqx+nqpqz], [nqx-nqz,nqpqx-nqpqz] */
836 inline void
837 curve25519_make_nq(packedelem64 *nq, const packedelem32 *pqx, const packedelem32 *pqz) {
838  nq[0].v = _mm_unpacklo_epi64(pqx[0].v, pqz[0].v);
839  nq[1].v = _mm_unpackhi_epi64(pqx[0].v, pqz[0].v);
840  nq[2].v = _mm_unpacklo_epi64(pqx[1].v, pqz[1].v);
841  nq[3].v = _mm_unpackhi_epi64(pqx[1].v, pqz[1].v);
842  nq[4].v = _mm_unpacklo_epi64(pqx[2].v, pqz[2].v);
843  nq[5].v = _mm_unpackhi_epi64(pqx[2].v, pqz[2].v);
844  nq[6].v = _mm_unpacklo_epi64(pqx[3].v, pqz[3].v);
845  nq[7].v = _mm_unpackhi_epi64(pqx[3].v, pqz[3].v);
846  nq[8].v = _mm_unpacklo_epi64(pqx[4].v, pqz[4].v);
847  nq[9].v = _mm_unpackhi_epi64(pqx[4].v, pqz[4].v);
848 }
849 
850 /* compute [nqx+nqz,nqx-nqz] from nqx, nqz */
851 inline void
852 curve25519_compute_nq(packedelem64 *nq, const bignum25519 nqx, const bignum25519 nqz) {
853  xmmi x0,x1,x2;
854  xmmi z0,z1,z2;
855  xmmi a0,a1,a2;
856  xmmi s0,s1,s2;
857  xmmi r0,r1;
858  xmmi c1,c2;
859  x0 = _mm_load_si128((xmmi*)nqx + 0);
860  x1 = _mm_load_si128((xmmi*)nqx + 1);
861  x2 = _mm_load_si128((xmmi*)nqx + 2);
862  z0 = _mm_load_si128((xmmi*)nqz + 0);
863  z1 = _mm_load_si128((xmmi*)nqz + 1);
864  z2 = _mm_load_si128((xmmi*)nqz + 2);
865  a0 = _mm_add_epi32(x0, z0);
866  a1 = _mm_add_epi32(x1, z1);
867  a2 = _mm_add_epi32(x2, z2);
868  s0 = _mm_add_epi32(x0, packed2p0.v);
869  s1 = _mm_add_epi32(x1, packed2p1.v);
870  s2 = _mm_add_epi32(x2, packed2p2.v);
871  s0 = _mm_sub_epi32(s0, z0);
872  s1 = _mm_sub_epi32(s1, z1);
873  s2 = _mm_sub_epi32(s2, z2);
874  r0 = _mm_and_si128(_mm_shuffle_epi32(s0, _MM_SHUFFLE(2,2,0,0)), sse2_bot32bitmask.v);
875  r1 = _mm_and_si128(_mm_shuffle_epi32(s0, _MM_SHUFFLE(3,3,1,1)), sse2_bot32bitmask.v);
876  c1 = _mm_srli_epi32(r0, 26);
877  c2 = _mm_srli_epi32(r1, 25);
878  r0 = _mm_and_si128(r0, packedmask26.v);
879  r1 = _mm_and_si128(r1, packedmask25.v);
880  r0 = _mm_add_epi32(r0, _mm_slli_si128(c2, 8));
881  r1 = _mm_add_epi32(r1, c1);
882  s0 = _mm_unpacklo_epi64(_mm_unpacklo_epi32(r0, r1), _mm_unpackhi_epi32(r0, r1));
883  s1 = _mm_add_epi32(s1, _mm_srli_si128(c2, 8));
884  nq[0].v = _mm_unpacklo_epi64(a0, s0);
885  nq[2].v = _mm_unpackhi_epi64(a0, s0);
886  nq[4].v = _mm_unpacklo_epi64(a1, s1);
887  nq[6].v = _mm_unpackhi_epi64(a1, s1);
888  nq[8].v = _mm_unpacklo_epi64(a2, s2);
889  nq[1].v = _mm_shuffle_epi32(nq[0].v, _MM_SHUFFLE(3,3,1,1));
890  nq[3].v = _mm_shuffle_epi32(nq[2].v, _MM_SHUFFLE(3,3,1,1));
891  nq[5].v = _mm_shuffle_epi32(nq[4].v, _MM_SHUFFLE(3,3,1,1));
892  nq[7].v = _mm_shuffle_epi32(nq[6].v, _MM_SHUFFLE(3,3,1,1));
893  nq[9].v = _mm_shuffle_epi32(nq[8].v, _MM_SHUFFLE(3,3,1,1));
894 }
895 
896 
897 /* compute [x+z,x-z] from [x,z] */
898 inline void
899 curve25519_addsub_packed64(packedelem64 *r) {
900  packed32bignum25519 x,z,add,sub;
901 
902  x[0].v = _mm_unpacklo_epi64(r[0].v, r[1].v);
903  z[0].v = _mm_unpackhi_epi64(r[0].v, r[1].v);
904  x[1].v = _mm_unpacklo_epi64(r[2].v, r[3].v);
905  z[1].v = _mm_unpackhi_epi64(r[2].v, r[3].v);
906  x[2].v = _mm_unpacklo_epi64(r[4].v, r[5].v);
907  z[2].v = _mm_unpackhi_epi64(r[4].v, r[5].v);
908  x[3].v = _mm_unpacklo_epi64(r[6].v, r[7].v);
909  z[3].v = _mm_unpackhi_epi64(r[6].v, r[7].v);
910  x[4].v = _mm_unpacklo_epi64(r[8].v, r[9].v);
911  z[4].v = _mm_unpackhi_epi64(r[8].v, r[9].v);
912 
913  curve25519_add_packed32(add, x, z);
914  curve25519_sub_packed32(sub, x, z);
915 
916  r[0].v = _mm_unpacklo_epi64(add[0].v, sub[0].v);
917  r[1].v = _mm_unpackhi_epi64(add[0].v, sub[0].v);
918  r[2].v = _mm_unpacklo_epi64(add[1].v, sub[1].v);
919  r[3].v = _mm_unpackhi_epi64(add[1].v, sub[1].v);
920  r[4].v = _mm_unpacklo_epi64(add[2].v, sub[2].v);
921  r[5].v = _mm_unpackhi_epi64(add[2].v, sub[2].v);
922  r[6].v = _mm_unpacklo_epi64(add[3].v, sub[3].v);
923  r[7].v = _mm_unpackhi_epi64(add[3].v, sub[3].v);
924  r[8].v = _mm_unpacklo_epi64(add[4].v, sub[4].v);
925  r[9].v = _mm_unpackhi_epi64(add[4].v, sub[4].v);
926 }
927 
928 /* compute [x,z] * [121666,121665] */
929 inline void
930 curve25519_121665_packed64(packedelem64 *out, const packedelem64 *in) {
931  xmmi c1,c2;
932 
933  out[0].v = _mm_mul_epu32(in[0].v, packed121666121665.v);
934  out[1].v = _mm_mul_epu32(in[1].v, packed121666121665.v);
935  out[2].v = _mm_mul_epu32(in[2].v, packed121666121665.v);
936  out[3].v = _mm_mul_epu32(in[3].v, packed121666121665.v);
937  out[4].v = _mm_mul_epu32(in[4].v, packed121666121665.v);
938  out[5].v = _mm_mul_epu32(in[5].v, packed121666121665.v);
939  out[6].v = _mm_mul_epu32(in[6].v, packed121666121665.v);
940  out[7].v = _mm_mul_epu32(in[7].v, packed121666121665.v);
941  out[8].v = _mm_mul_epu32(in[8].v, packed121666121665.v);
942  out[9].v = _mm_mul_epu32(in[9].v, packed121666121665.v);
943 
944  c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
945  c1 = _mm_srli_epi64(out[1].v, 25); c2 = _mm_srli_epi64(out[5].v, 25); out[1].v = _mm_and_si128(out[1].v, packedmask25.v); out[5].v = _mm_and_si128(out[5].v, packedmask25.v); out[2].v = _mm_add_epi64(out[2].v, c1); out[6].v = _mm_add_epi64(out[6].v, c2);
946  c1 = _mm_srli_epi64(out[2].v, 26); c2 = _mm_srli_epi64(out[6].v, 26); out[2].v = _mm_and_si128(out[2].v, packedmask26.v); out[6].v = _mm_and_si128(out[6].v, packedmask26.v); out[3].v = _mm_add_epi64(out[3].v, c1); out[7].v = _mm_add_epi64(out[7].v, c2);
947  c1 = _mm_srli_epi64(out[3].v, 25); c2 = _mm_srli_epi64(out[7].v, 25); out[3].v = _mm_and_si128(out[3].v, packedmask25.v); out[7].v = _mm_and_si128(out[7].v, packedmask25.v); out[4].v = _mm_add_epi64(out[4].v, c1); out[8].v = _mm_add_epi64(out[8].v, c2);
948  c2 = _mm_srli_epi64(out[8].v, 26); out[8].v = _mm_and_si128(out[8].v, packedmask26.v); out[9].v = _mm_add_epi64(out[9].v, c2);
949  c2 = _mm_srli_epi64(out[9].v, 25); out[9].v = _mm_and_si128(out[9].v, packedmask25.v); out[0].v = _mm_add_epi64(out[0].v, _mm_mul_epu32(c2, packednineteen.v));
950  c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
951 }
952 
953 /* compute [sq.x,sqscalar.x-sqscalar.z] * [sq.z,sq.x-sq.z] */
954 inline void
955 curve25519_final_nq(packedelem64 *nq, const packedelem64 *sq, const packedelem64 *sq121665) {
956  packed32bignum25519 x, z, sub;
957  packed64bignum25519 t, nqa, nqb;
958 
959  x[0].v = _mm_or_si128(_mm_unpacklo_epi64(sq[0].v, sq[1].v), _mm_slli_si128(_mm_unpacklo_epi64(sq121665[0].v, sq121665[1].v), 4));
960  z[0].v = _mm_or_si128(_mm_unpackhi_epi64(sq[0].v, sq[1].v), _mm_slli_si128(_mm_unpackhi_epi64(sq121665[0].v, sq121665[1].v), 4));
961  x[1].v = _mm_or_si128(_mm_unpacklo_epi64(sq[2].v, sq[3].v), _mm_slli_si128(_mm_unpacklo_epi64(sq121665[2].v, sq121665[3].v), 4));
962  z[1].v = _mm_or_si128(_mm_unpackhi_epi64(sq[2].v, sq[3].v), _mm_slli_si128(_mm_unpackhi_epi64(sq121665[2].v, sq121665[3].v), 4));
963  x[2].v = _mm_or_si128(_mm_unpacklo_epi64(sq[4].v, sq[5].v), _mm_slli_si128(_mm_unpacklo_epi64(sq121665[4].v, sq121665[5].v), 4));
964  z[2].v = _mm_or_si128(_mm_unpackhi_epi64(sq[4].v, sq[5].v), _mm_slli_si128(_mm_unpackhi_epi64(sq121665[4].v, sq121665[5].v), 4));
965  x[3].v = _mm_or_si128(_mm_unpacklo_epi64(sq[6].v, sq[7].v), _mm_slli_si128(_mm_unpacklo_epi64(sq121665[6].v, sq121665[7].v), 4));
966  z[3].v = _mm_or_si128(_mm_unpackhi_epi64(sq[6].v, sq[7].v), _mm_slli_si128(_mm_unpackhi_epi64(sq121665[6].v, sq121665[7].v), 4));
967  x[4].v = _mm_or_si128(_mm_unpacklo_epi64(sq[8].v, sq[9].v), _mm_slli_si128(_mm_unpacklo_epi64(sq121665[8].v, sq121665[9].v), 4));
968  z[4].v = _mm_or_si128(_mm_unpackhi_epi64(sq[8].v, sq[9].v), _mm_slli_si128(_mm_unpackhi_epi64(sq121665[8].v, sq121665[9].v), 4));
969 
970  curve25519_sub_packed32(sub, x, z);
971 
972  t[0].v = _mm_shuffle_epi32(sub[0].v, _MM_SHUFFLE(1,1,0,0));
973  t[1].v = _mm_shuffle_epi32(sub[0].v, _MM_SHUFFLE(3,3,2,2));
974  t[2].v = _mm_shuffle_epi32(sub[1].v, _MM_SHUFFLE(1,1,0,0));
975  t[3].v = _mm_shuffle_epi32(sub[1].v, _MM_SHUFFLE(3,3,2,2));
976  t[4].v = _mm_shuffle_epi32(sub[2].v, _MM_SHUFFLE(1,1,0,0));
977  t[5].v = _mm_shuffle_epi32(sub[2].v, _MM_SHUFFLE(3,3,2,2));
978  t[6].v = _mm_shuffle_epi32(sub[3].v, _MM_SHUFFLE(1,1,0,0));
979  t[7].v = _mm_shuffle_epi32(sub[3].v, _MM_SHUFFLE(3,3,2,2));
980  t[8].v = _mm_shuffle_epi32(sub[4].v, _MM_SHUFFLE(1,1,0,0));
981  t[9].v = _mm_shuffle_epi32(sub[4].v, _MM_SHUFFLE(3,3,2,2));
982 
983  nqa[0].v = _mm_unpacklo_epi64(sq[0].v, t[0].v);
984  nqb[0].v = _mm_unpackhi_epi64(sq[0].v, t[0].v);
985  nqa[1].v = _mm_unpacklo_epi64(sq[1].v, t[1].v);
986  nqb[1].v = _mm_unpackhi_epi64(sq[1].v, t[1].v);
987  nqa[2].v = _mm_unpacklo_epi64(sq[2].v, t[2].v);
988  nqb[2].v = _mm_unpackhi_epi64(sq[2].v, t[2].v);
989  nqa[3].v = _mm_unpacklo_epi64(sq[3].v, t[3].v);
990  nqb[3].v = _mm_unpackhi_epi64(sq[3].v, t[3].v);
991  nqa[4].v = _mm_unpacklo_epi64(sq[4].v, t[4].v);
992  nqb[4].v = _mm_unpackhi_epi64(sq[4].v, t[4].v);
993  nqa[5].v = _mm_unpacklo_epi64(sq[5].v, t[5].v);
994  nqb[5].v = _mm_unpackhi_epi64(sq[5].v, t[5].v);
995  nqa[6].v = _mm_unpacklo_epi64(sq[6].v, t[6].v);
996  nqb[6].v = _mm_unpackhi_epi64(sq[6].v, t[6].v);
997  nqa[7].v = _mm_unpacklo_epi64(sq[7].v, t[7].v);
998  nqb[7].v = _mm_unpackhi_epi64(sq[7].v, t[7].v);
999  nqa[8].v = _mm_unpacklo_epi64(sq[8].v, t[8].v);
1000  nqb[8].v = _mm_unpackhi_epi64(sq[8].v, t[8].v);
1001  nqa[9].v = _mm_unpacklo_epi64(sq[9].v, t[9].v);
1002  nqb[9].v = _mm_unpackhi_epi64(sq[9].v, t[9].v);
1003 
1004  curve25519_mul_packed64(nq, nqa, nqb);
1005 }
1006 
1007 /*
1008  * In: b = 2^5 - 2^0
1009  * Out: b = 2^250 - 2^0
1010  */
1011 void
1012 curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
1013  ALIGN(16) bignum25519 t0,c;
1014 
1015  /* 2^5 - 2^0 */ /* b */
1016  /* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
1017  /* 2^10 - 2^0 */ curve25519_mul(b, t0, b);
1018  /* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
1019  /* 2^20 - 2^0 */ curve25519_mul(c, t0, b);
1020  /* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
1021  /* 2^40 - 2^0 */ curve25519_mul(t0, t0, c);
1022  /* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
1023  /* 2^50 - 2^0 */ curve25519_mul(b, t0, b);
1024  /* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
1025  /* 2^100 - 2^0 */ curve25519_mul(c, t0, b);
1026  /* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
1027  /* 2^200 - 2^0 */ curve25519_mul(t0, t0, c);
1028  /* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
1029  /* 2^250 - 2^0 */ curve25519_mul(b, t0, b);
1030 }
1031 
1032 /*
1033  * z^(p - 2) = z(2^255 - 21)
1034  */
1035 void
1036 curve25519_recip(bignum25519 out, const bignum25519 z) {
1037  ALIGN(16) bignum25519 a, t0, b;
1038 
1039  /* 2 */ curve25519_square(a, z); /* a = 2 */
1040  /* 8 */ curve25519_square_times(t0, a, 2);
1041  /* 9 */ curve25519_mul(b, t0, z); /* b = 9 */
1042  /* 11 */ curve25519_mul(a, b, a); /* a = 11 */
1043  /* 22 */ curve25519_square(t0, a);
1044  /* 2^5 - 2^0 = 31 */ curve25519_mul(b, t0, b);
1045  /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
1046  /* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
1047  /* 2^255 - 21 */ curve25519_mul(out, b, a);
1048 }
1049 
1050 ANONYMOUS_NAMESPACE_END
1051 
1052 NAMESPACE_BEGIN(CryptoPP)
1053 NAMESPACE_BEGIN(Donna)
1054 
1055 int curve25519_mult_SSE2(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
1056 {
1057  FixedSizeSecBlock<byte, 32> e;
1058  for (size_t i = 0;i < 32;++i)
1059  e[i] = secretKey[i];
1060  e[0] &= 0xf8; e[31] &= 0x7f; e[31] |= 0x40;
1061 
1062  ALIGN(16) bignum25519 nqx = {1}, nqpqz = {1}, nqz = {0}, nqpqx, zmone;
1063  packed32bignum25519 qx, qz, pqz, pqx;
1064  packed64bignum25519 nq, sq, sqscalar, prime, primex, primez, nqpq;
1065  bignum25519mulprecomp preq;
1066  size_t bit=0;
1067 
1068  curve25519_expand(nqpqx, othersKey);
1069  curve25519_mul_precompute(&preq, nqpqx);
1070 
1071  /* do bits 254..3 */
1072  for (size_t i = 254, lastbit=0; i >= 3; i--) {
1073  bit = (e[i/8] >> (i & 7)) & 1;
1074  curve25519_swap_conditional(nqx, nqpqx, (word32)(bit ^ lastbit));
1075  curve25519_swap_conditional(nqz, nqpqz, (word32)(bit ^ lastbit));
1076  lastbit = bit;
1077 
1078  curve25519_tangle32(qx, nqx, nqpqx); /* qx = [nqx,nqpqx] */
1079  curve25519_tangle32(qz, nqz, nqpqz); /* qz = [nqz,nqpqz] */
1080 
1081  curve25519_add_packed32(pqx, qx, qz); /* pqx = [nqx+nqz,nqpqx+nqpqz] */
1082  curve25519_sub_packed32(pqz, qx, qz); /* pqz = [nqx-nqz,nqpqx-nqpqz] */
1083 
1084  curve25519_make_nqpq(primex, primez, pqx, pqz); /* primex = [nqx+nqz,nqpqx+nqpqz], primez = [nqpqx-nqpqz,nqx-nqz] */
1085  curve25519_mul_packed64(prime, primex, primez); /* prime = [nqx+nqz,nqpqx+nqpqz] * [nqpqx-nqpqz,nqx-nqz] */
1086  curve25519_addsub_packed64(prime); /* prime = [prime.x+prime.z,prime.x-prime.z] */
1087  curve25519_square_packed64(nqpq, prime); /* nqpq = prime^2 */
1088  curve25519_untangle64(nqpqx, nqpqz, nqpq);
1089  curve25519_mul_precomputed(nqpqz, nqpqz, &preq); /* nqpqz = nqpqz * q */
1090 
1091  /* (((sq.x-sq.z)*121665)+sq.x) * (sq.x-sq.z) is equivalent to (sq.x*121666-sq.z*121665) * (sq.x-sq.z) */
1092  curve25519_make_nq(nq, pqx, pqz); /* nq = [nqx+nqz,nqx-nqz] */
1093  curve25519_square_packed64(sq, nq); /* sq = nq^2 */
1094  curve25519_121665_packed64(sqscalar, sq); /* sqscalar = sq * [121666,121665] */
1095  curve25519_final_nq(nq, sq, sqscalar); /* nq = [sq.x,sqscalar.x-sqscalar.z] * [sq.z,sq.x-sq.z] */
1096  curve25519_untangle64(nqx, nqz, nq);
1097  };
1098 
1099  /* it's possible to get rid of this swap with the swap in the above loop
1100  at the bottom instead of the top, but compilers seem to optimize better this way */
1101  curve25519_swap_conditional(nqx, nqpqx, (word32)bit);
1102  curve25519_swap_conditional(nqz, nqpqz, (word32)bit);
1103 
1104  /* do bits 2..0 */
1105  for (size_t i = 0; i < 3; i++) {
1106  curve25519_compute_nq(nq, nqx, nqz);
1107  curve25519_square_packed64(sq, nq); /* sq = nq^2 */
1108  curve25519_121665_packed64(sqscalar, sq); /* sqscalar = sq * [121666,121665] */
1109  curve25519_final_nq(nq, sq, sqscalar); /* nq = [sq.x,sqscalar.x-sqscalar.z] * [sq.z,sq.x-sq.z] */
1110  curve25519_untangle64(nqx, nqz, nq);
1111  }
1112 
1113  curve25519_recip(zmone, nqz);
1114  curve25519_mul(nqz, nqx, zmone);
1115  curve25519_contract(sharedKey, nqz);
1116 
1117  return 0;
1118 }
1119 
1120 NAMESPACE_END // Donna
1121 NAMESPACE_END // CryptoPP
1122 
1123 #endif // CRYPTOPP_CURVE25519_SSE2
FixedSizeSecBlock
Fixed size stack-based SecBlock.
Definition: secblock.h:1246
config.h
Library configuration file.
sword64
signed long long sword64
64-bit signed datatype
Definition: config_int.h:109
byte
unsigned char byte
8-bit unsigned datatype
Definition: config_int.h:66
sword32
signed int sword32
32-bit signed datatype
Definition: config_int.h:91
word32
unsigned int word32
32-bit unsigned datatype
Definition: config_int.h:72
word64
unsigned long long word64
64-bit unsigned datatype
Definition: config_int.h:101
LittleEndian
EnumToType< ByteOrder, LITTLE_ENDIAN_ORDER > LittleEndian
Provides a constant for LittleEndian.
Definition: cryptlib.h:155
misc.h
Utility functions for the Crypto++ library.
CryptoPP
Crypto++ library namespace.
pch.h
Precompiled header file.
secblock.h
Classes and functions for secure memory allocations.
swap
void swap(::SecBlock< T, A > &a, ::SecBlock< T, A > &b)
Swap two SecBlocks.
Definition: secblock.h:1289
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