1 #include "sc.h"
2 #include "crypto_int64.h"
3 #include "crypto_uint32.h"
4 #include "crypto_uint64.h"
5 
load_3(const unsigned char * in)6 static crypto_uint64 load_3(const unsigned char *in)
7 {
8   crypto_uint64 result;
9   result = (crypto_uint64) in[0];
10   result |= ((crypto_uint64) in[1]) << 8;
11   result |= ((crypto_uint64) in[2]) << 16;
12   return result;
13 }
14 
load_4(const unsigned char * in)15 static crypto_uint64 load_4(const unsigned char *in)
16 {
17   crypto_uint64 result;
18   result = (crypto_uint64) in[0];
19   result |= ((crypto_uint64) in[1]) << 8;
20   result |= ((crypto_uint64) in[2]) << 16;
21   result |= ((crypto_uint64) in[3]) << 24;
22   return result;
23 }
24 
25 /*
26 Input:
27   a[0]+256*a[1]+...+256^31*a[31] = a
28   b[0]+256*b[1]+...+256^31*b[31] = b
29   c[0]+256*c[1]+...+256^31*c[31] = c
30 
31 Output:
32   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
33   where l = 2^252 + 27742317777372353535851937790883648493.
34 */
35 
sc_muladd(unsigned char * s,const unsigned char * a,const unsigned char * b,const unsigned char * c)36 void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,const unsigned char *c)
37 {
38   crypto_int64 a0 = 2097151 & load_3(a);
39   crypto_int64 a1 = 2097151 & (load_4(a + 2) >> 5);
40   crypto_int64 a2 = 2097151 & (load_3(a + 5) >> 2);
41   crypto_int64 a3 = 2097151 & (load_4(a + 7) >> 7);
42   crypto_int64 a4 = 2097151 & (load_4(a + 10) >> 4);
43   crypto_int64 a5 = 2097151 & (load_3(a + 13) >> 1);
44   crypto_int64 a6 = 2097151 & (load_4(a + 15) >> 6);
45   crypto_int64 a7 = 2097151 & (load_3(a + 18) >> 3);
46   crypto_int64 a8 = 2097151 & load_3(a + 21);
47   crypto_int64 a9 = 2097151 & (load_4(a + 23) >> 5);
48   crypto_int64 a10 = 2097151 & (load_3(a + 26) >> 2);
49   crypto_int64 a11 = (load_4(a + 28) >> 7);
50   crypto_int64 b0 = 2097151 & load_3(b);
51   crypto_int64 b1 = 2097151 & (load_4(b + 2) >> 5);
52   crypto_int64 b2 = 2097151 & (load_3(b + 5) >> 2);
53   crypto_int64 b3 = 2097151 & (load_4(b + 7) >> 7);
54   crypto_int64 b4 = 2097151 & (load_4(b + 10) >> 4);
55   crypto_int64 b5 = 2097151 & (load_3(b + 13) >> 1);
56   crypto_int64 b6 = 2097151 & (load_4(b + 15) >> 6);
57   crypto_int64 b7 = 2097151 & (load_3(b + 18) >> 3);
58   crypto_int64 b8 = 2097151 & load_3(b + 21);
59   crypto_int64 b9 = 2097151 & (load_4(b + 23) >> 5);
60   crypto_int64 b10 = 2097151 & (load_3(b + 26) >> 2);
61   crypto_int64 b11 = (load_4(b + 28) >> 7);
62   crypto_int64 c0 = 2097151 & load_3(c);
63   crypto_int64 c1 = 2097151 & (load_4(c + 2) >> 5);
64   crypto_int64 c2 = 2097151 & (load_3(c + 5) >> 2);
65   crypto_int64 c3 = 2097151 & (load_4(c + 7) >> 7);
66   crypto_int64 c4 = 2097151 & (load_4(c + 10) >> 4);
67   crypto_int64 c5 = 2097151 & (load_3(c + 13) >> 1);
68   crypto_int64 c6 = 2097151 & (load_4(c + 15) >> 6);
69   crypto_int64 c7 = 2097151 & (load_3(c + 18) >> 3);
70   crypto_int64 c8 = 2097151 & load_3(c + 21);
71   crypto_int64 c9 = 2097151 & (load_4(c + 23) >> 5);
72   crypto_int64 c10 = 2097151 & (load_3(c + 26) >> 2);
73   crypto_int64 c11 = (load_4(c + 28) >> 7);
74   crypto_int64 s0;
75   crypto_int64 s1;
76   crypto_int64 s2;
77   crypto_int64 s3;
78   crypto_int64 s4;
79   crypto_int64 s5;
80   crypto_int64 s6;
81   crypto_int64 s7;
82   crypto_int64 s8;
83   crypto_int64 s9;
84   crypto_int64 s10;
85   crypto_int64 s11;
86   crypto_int64 s12;
87   crypto_int64 s13;
88   crypto_int64 s14;
89   crypto_int64 s15;
90   crypto_int64 s16;
91   crypto_int64 s17;
92   crypto_int64 s18;
93   crypto_int64 s19;
94   crypto_int64 s20;
95   crypto_int64 s21;
96   crypto_int64 s22;
97   crypto_int64 s23;
98   crypto_int64 carry0;
99   crypto_int64 carry1;
100   crypto_int64 carry2;
101   crypto_int64 carry3;
102   crypto_int64 carry4;
103   crypto_int64 carry5;
104   crypto_int64 carry6;
105   crypto_int64 carry7;
106   crypto_int64 carry8;
107   crypto_int64 carry9;
108   crypto_int64 carry10;
109   crypto_int64 carry11;
110   crypto_int64 carry12;
111   crypto_int64 carry13;
112   crypto_int64 carry14;
113   crypto_int64 carry15;
114   crypto_int64 carry16;
115   crypto_int64 carry17;
116   crypto_int64 carry18;
117   crypto_int64 carry19;
118   crypto_int64 carry20;
119   crypto_int64 carry21;
120   crypto_int64 carry22;
121 
122   s0 = c0 + a0*b0;
123   s1 = c1 + a0*b1 + a1*b0;
124   s2 = c2 + a0*b2 + a1*b1 + a2*b0;
125   s3 = c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0;
126   s4 = c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0;
127   s5 = c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0;
128   s6 = c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0;
129   s7 = c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0;
130   s8 = c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0;
131   s9 = c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0;
132   s10 = c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0;
133   s11 = c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0;
134   s12 = a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1;
135   s13 = a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2;
136   s14 = a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3;
137   s15 = a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4;
138   s16 = a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5;
139   s17 = a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6;
140   s18 = a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7;
141   s19 = a8*b11 + a9*b10 + a10*b9 + a11*b8;
142   s20 = a9*b11 + a10*b10 + a11*b9;
143   s21 = a10*b11 + a11*b10;
144   s22 = a11*b11;
145   s23 = 0;
146 
147   carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
148   carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
149   carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
150   carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
151   carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
152   carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
153   carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
154   carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
155   carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
156   carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21;
157   carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21;
158   carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21;
159 
160   carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
161   carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
162   carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
163   carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
164   carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
165   carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
166   carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
167   carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
168   carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21;
169   carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21;
170   carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21;
171 
172   s11 += s23 * 666643;
173   s12 += s23 * 470296;
174   s13 += s23 * 654183;
175   s14 -= s23 * 997805;
176   s15 += s23 * 136657;
177   s16 -= s23 * 683901;
178   s23 = 0;
179 
180   s10 += s22 * 666643;
181   s11 += s22 * 470296;
182   s12 += s22 * 654183;
183   s13 -= s22 * 997805;
184   s14 += s22 * 136657;
185   s15 -= s22 * 683901;
186   s22 = 0;
187 
188   s9 += s21 * 666643;
189   s10 += s21 * 470296;
190   s11 += s21 * 654183;
191   s12 -= s21 * 997805;
192   s13 += s21 * 136657;
193   s14 -= s21 * 683901;
194   s21 = 0;
195 
196   s8 += s20 * 666643;
197   s9 += s20 * 470296;
198   s10 += s20 * 654183;
199   s11 -= s20 * 997805;
200   s12 += s20 * 136657;
201   s13 -= s20 * 683901;
202   s20 = 0;
203 
204   s7 += s19 * 666643;
205   s8 += s19 * 470296;
206   s9 += s19 * 654183;
207   s10 -= s19 * 997805;
208   s11 += s19 * 136657;
209   s12 -= s19 * 683901;
210   s19 = 0;
211 
212   s6 += s18 * 666643;
213   s7 += s18 * 470296;
214   s8 += s18 * 654183;
215   s9 -= s18 * 997805;
216   s10 += s18 * 136657;
217   s11 -= s18 * 683901;
218   s18 = 0;
219 
220   carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
221   carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
222   carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
223   carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
224   carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
225   carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
226 
227   carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
228   carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
229   carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
230   carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
231   carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
232 
233   s5 += s17 * 666643;
234   s6 += s17 * 470296;
235   s7 += s17 * 654183;
236   s8 -= s17 * 997805;
237   s9 += s17 * 136657;
238   s10 -= s17 * 683901;
239   s17 = 0;
240 
241   s4 += s16 * 666643;
242   s5 += s16 * 470296;
243   s6 += s16 * 654183;
244   s7 -= s16 * 997805;
245   s8 += s16 * 136657;
246   s9 -= s16 * 683901;
247   s16 = 0;
248 
249   s3 += s15 * 666643;
250   s4 += s15 * 470296;
251   s5 += s15 * 654183;
252   s6 -= s15 * 997805;
253   s7 += s15 * 136657;
254   s8 -= s15 * 683901;
255   s15 = 0;
256 
257   s2 += s14 * 666643;
258   s3 += s14 * 470296;
259   s4 += s14 * 654183;
260   s5 -= s14 * 997805;
261   s6 += s14 * 136657;
262   s7 -= s14 * 683901;
263   s14 = 0;
264 
265   s1 += s13 * 666643;
266   s2 += s13 * 470296;
267   s3 += s13 * 654183;
268   s4 -= s13 * 997805;
269   s5 += s13 * 136657;
270   s6 -= s13 * 683901;
271   s13 = 0;
272 
273   s0 += s12 * 666643;
274   s1 += s12 * 470296;
275   s2 += s12 * 654183;
276   s3 -= s12 * 997805;
277   s4 += s12 * 136657;
278   s5 -= s12 * 683901;
279   s12 = 0;
280 
281   carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
282   carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
283   carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
284   carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
285   carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
286   carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
287 
288   carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
289   carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
290   carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
291   carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
292   carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
293   carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
294 
295   s0 += s12 * 666643;
296   s1 += s12 * 470296;
297   s2 += s12 * 654183;
298   s3 -= s12 * 997805;
299   s4 += s12 * 136657;
300   s5 -= s12 * 683901;
301   s12 = 0;
302 
303   carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
304   carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
305   carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
306   carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
307   carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
308   carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
309   carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
310   carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
311   carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
312   carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
313   carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
314   carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
315 
316   s0 += s12 * 666643;
317   s1 += s12 * 470296;
318   s2 += s12 * 654183;
319   s3 -= s12 * 997805;
320   s4 += s12 * 136657;
321   s5 -= s12 * 683901;
322   s12 = 0;
323 
324   carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
325   carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
326   carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
327   carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
328   carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
329   carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
330   carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
331   carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
332   carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
333   carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
334   carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
335 
336   s[0] = s0 >> 0;
337   s[1] = s0 >> 8;
338   s[2] = (s0 >> 16) | (s1 << 5);
339   s[3] = s1 >> 3;
340   s[4] = s1 >> 11;
341   s[5] = (s1 >> 19) | (s2 << 2);
342   s[6] = s2 >> 6;
343   s[7] = (s2 >> 14) | (s3 << 7);
344   s[8] = s3 >> 1;
345   s[9] = s3 >> 9;
346   s[10] = (s3 >> 17) | (s4 << 4);
347   s[11] = s4 >> 4;
348   s[12] = s4 >> 12;
349   s[13] = (s4 >> 20) | (s5 << 1);
350   s[14] = s5 >> 7;
351   s[15] = (s5 >> 15) | (s6 << 6);
352   s[16] = s6 >> 2;
353   s[17] = s6 >> 10;
354   s[18] = (s6 >> 18) | (s7 << 3);
355   s[19] = s7 >> 5;
356   s[20] = s7 >> 13;
357   s[21] = s8 >> 0;
358   s[22] = s8 >> 8;
359   s[23] = (s8 >> 16) | (s9 << 5);
360   s[24] = s9 >> 3;
361   s[25] = s9 >> 11;
362   s[26] = (s9 >> 19) | (s10 << 2);
363   s[27] = s10 >> 6;
364   s[28] = (s10 >> 14) | (s11 << 7);
365   s[29] = s11 >> 1;
366   s[30] = s11 >> 9;
367   s[31] = s11 >> 17;
368 }
369