1 #include "fixedint.h"
2 #include "sc.h"
3 
4 #ifndef ED25519_LOAD_BYTES
5 #define ED25519_LOAD_BYTES
6 
load_3(const unsigned char * in)7 static uint64_t load_3(const unsigned char *in) {
8     uint64_t result;
9 
10     result = (uint64_t) in[0];
11     result |= ((uint64_t) in[1]) << 8;
12     result |= ((uint64_t) in[2]) << 16;
13 
14     return result;
15 }
16 
load_4(const unsigned char * in)17 static uint64_t load_4(const unsigned char *in) {
18     uint64_t result;
19 
20     result = (uint64_t) in[0];
21     result |= ((uint64_t) in[1]) << 8;
22     result |= ((uint64_t) in[2]) << 16;
23     result |= ((uint64_t) in[3]) << 24;
24 
25     return result;
26 }
27 
28 #endif
29 
30 /*
31 Input:
32   s[0]+256*s[1]+...+256^63*s[63] = s
33 
34 Output:
35   s[0]+256*s[1]+...+256^31*s[31] = s mod l
36   where l = 2^252 + 27742317777372353535851937790883648493.
37   Overwrites s in place.
38 */
39 
sc_reduce(unsigned char * s)40 void sc_reduce(unsigned char *s) {
41     int64_t s0 = 2097151 & load_3(s);
42     int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
43     int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
44     int64_t s3 = 2097151 & (load_4(s + 7) >> 7);
45     int64_t s4 = 2097151 & (load_4(s + 10) >> 4);
46     int64_t s5 = 2097151 & (load_3(s + 13) >> 1);
47     int64_t s6 = 2097151 & (load_4(s + 15) >> 6);
48     int64_t s7 = 2097151 & (load_3(s + 18) >> 3);
49     int64_t s8 = 2097151 & load_3(s + 21);
50     int64_t s9 = 2097151 & (load_4(s + 23) >> 5);
51     int64_t s10 = 2097151 & (load_3(s + 26) >> 2);
52     int64_t s11 = 2097151 & (load_4(s + 28) >> 7);
53     int64_t s12 = 2097151 & (load_4(s + 31) >> 4);
54     int64_t s13 = 2097151 & (load_3(s + 34) >> 1);
55     int64_t s14 = 2097151 & (load_4(s + 36) >> 6);
56     int64_t s15 = 2097151 & (load_3(s + 39) >> 3);
57     int64_t s16 = 2097151 & load_3(s + 42);
58     int64_t s17 = 2097151 & (load_4(s + 44) >> 5);
59     int64_t s18 = 2097151 & (load_3(s + 47) >> 2);
60     int64_t s19 = 2097151 & (load_4(s + 49) >> 7);
61     int64_t s20 = 2097151 & (load_4(s + 52) >> 4);
62     int64_t s21 = 2097151 & (load_3(s + 55) >> 1);
63     int64_t s22 = 2097151 & (load_4(s + 57) >> 6);
64     int64_t s23 = (load_4(s + 60) >> 3);
65     int64_t carry0;
66     int64_t carry1;
67     int64_t carry2;
68     int64_t carry3;
69     int64_t carry4;
70     int64_t carry5;
71     int64_t carry6;
72     int64_t carry7;
73     int64_t carry8;
74     int64_t carry9;
75     int64_t carry10;
76     int64_t carry11;
77     int64_t carry12;
78     int64_t carry13;
79     int64_t carry14;
80     int64_t carry15;
81     int64_t carry16;
82 
83     s11 += s23 * 666643;
84     s12 += s23 * 470296;
85     s13 += s23 * 654183;
86     s14 -= s23 * 997805;
87     s15 += s23 * 136657;
88     s16 -= s23 * 683901;
89     s23 = 0;
90     s10 += s22 * 666643;
91     s11 += s22 * 470296;
92     s12 += s22 * 654183;
93     s13 -= s22 * 997805;
94     s14 += s22 * 136657;
95     s15 -= s22 * 683901;
96     s22 = 0;
97     s9 += s21 * 666643;
98     s10 += s21 * 470296;
99     s11 += s21 * 654183;
100     s12 -= s21 * 997805;
101     s13 += s21 * 136657;
102     s14 -= s21 * 683901;
103     s21 = 0;
104     s8 += s20 * 666643;
105     s9 += s20 * 470296;
106     s10 += s20 * 654183;
107     s11 -= s20 * 997805;
108     s12 += s20 * 136657;
109     s13 -= s20 * 683901;
110     s20 = 0;
111     s7 += s19 * 666643;
112     s8 += s19 * 470296;
113     s9 += s19 * 654183;
114     s10 -= s19 * 997805;
115     s11 += s19 * 136657;
116     s12 -= s19 * 683901;
117     s19 = 0;
118     s6 += s18 * 666643;
119     s7 += s18 * 470296;
120     s8 += s18 * 654183;
121     s9 -= s18 * 997805;
122     s10 += s18 * 136657;
123     s11 -= s18 * 683901;
124     s18 = 0;
125     carry6 = (s6 + (1 << 20)) >> 21;
126     s7 += carry6;
127     s6 -= carry6 << 21;
128     carry8 = (s8 + (1 << 20)) >> 21;
129     s9 += carry8;
130     s8 -= carry8 << 21;
131     carry10 = (s10 + (1 << 20)) >> 21;
132     s11 += carry10;
133     s10 -= carry10 << 21;
134     carry12 = (s12 + (1 << 20)) >> 21;
135     s13 += carry12;
136     s12 -= carry12 << 21;
137     carry14 = (s14 + (1 << 20)) >> 21;
138     s15 += carry14;
139     s14 -= carry14 << 21;
140     carry16 = (s16 + (1 << 20)) >> 21;
141     s17 += carry16;
142     s16 -= carry16 << 21;
143     carry7 = (s7 + (1 << 20)) >> 21;
144     s8 += carry7;
145     s7 -= carry7 << 21;
146     carry9 = (s9 + (1 << 20)) >> 21;
147     s10 += carry9;
148     s9 -= carry9 << 21;
149     carry11 = (s11 + (1 << 20)) >> 21;
150     s12 += carry11;
151     s11 -= carry11 << 21;
152     carry13 = (s13 + (1 << 20)) >> 21;
153     s14 += carry13;
154     s13 -= carry13 << 21;
155     carry15 = (s15 + (1 << 20)) >> 21;
156     s16 += carry15;
157     s15 -= carry15 << 21;
158     s5 += s17 * 666643;
159     s6 += s17 * 470296;
160     s7 += s17 * 654183;
161     s8 -= s17 * 997805;
162     s9 += s17 * 136657;
163     s10 -= s17 * 683901;
164     s17 = 0;
165     s4 += s16 * 666643;
166     s5 += s16 * 470296;
167     s6 += s16 * 654183;
168     s7 -= s16 * 997805;
169     s8 += s16 * 136657;
170     s9 -= s16 * 683901;
171     s16 = 0;
172     s3 += s15 * 666643;
173     s4 += s15 * 470296;
174     s5 += s15 * 654183;
175     s6 -= s15 * 997805;
176     s7 += s15 * 136657;
177     s8 -= s15 * 683901;
178     s15 = 0;
179     s2 += s14 * 666643;
180     s3 += s14 * 470296;
181     s4 += s14 * 654183;
182     s5 -= s14 * 997805;
183     s6 += s14 * 136657;
184     s7 -= s14 * 683901;
185     s14 = 0;
186     s1 += s13 * 666643;
187     s2 += s13 * 470296;
188     s3 += s13 * 654183;
189     s4 -= s13 * 997805;
190     s5 += s13 * 136657;
191     s6 -= s13 * 683901;
192     s13 = 0;
193     s0 += s12 * 666643;
194     s1 += s12 * 470296;
195     s2 += s12 * 654183;
196     s3 -= s12 * 997805;
197     s4 += s12 * 136657;
198     s5 -= s12 * 683901;
199     s12 = 0;
200     carry0 = (s0 + (1 << 20)) >> 21;
201     s1 += carry0;
202     s0 -= carry0 << 21;
203     carry2 = (s2 + (1 << 20)) >> 21;
204     s3 += carry2;
205     s2 -= carry2 << 21;
206     carry4 = (s4 + (1 << 20)) >> 21;
207     s5 += carry4;
208     s4 -= carry4 << 21;
209     carry6 = (s6 + (1 << 20)) >> 21;
210     s7 += carry6;
211     s6 -= carry6 << 21;
212     carry8 = (s8 + (1 << 20)) >> 21;
213     s9 += carry8;
214     s8 -= carry8 << 21;
215     carry10 = (s10 + (1 << 20)) >> 21;
216     s11 += carry10;
217     s10 -= carry10 << 21;
218     carry1 = (s1 + (1 << 20)) >> 21;
219     s2 += carry1;
220     s1 -= carry1 << 21;
221     carry3 = (s3 + (1 << 20)) >> 21;
222     s4 += carry3;
223     s3 -= carry3 << 21;
224     carry5 = (s5 + (1 << 20)) >> 21;
225     s6 += carry5;
226     s5 -= carry5 << 21;
227     carry7 = (s7 + (1 << 20)) >> 21;
228     s8 += carry7;
229     s7 -= carry7 << 21;
230     carry9 = (s9 + (1 << 20)) >> 21;
231     s10 += carry9;
232     s9 -= carry9 << 21;
233     carry11 = (s11 + (1 << 20)) >> 21;
234     s12 += carry11;
235     s11 -= carry11 << 21;
236     s0 += s12 * 666643;
237     s1 += s12 * 470296;
238     s2 += s12 * 654183;
239     s3 -= s12 * 997805;
240     s4 += s12 * 136657;
241     s5 -= s12 * 683901;
242     s12 = 0;
243     carry0 = s0 >> 21;
244     s1 += carry0;
245     s0 -= carry0 << 21;
246     carry1 = s1 >> 21;
247     s2 += carry1;
248     s1 -= carry1 << 21;
249     carry2 = s2 >> 21;
250     s3 += carry2;
251     s2 -= carry2 << 21;
252     carry3 = s3 >> 21;
253     s4 += carry3;
254     s3 -= carry3 << 21;
255     carry4 = s4 >> 21;
256     s5 += carry4;
257     s4 -= carry4 << 21;
258     carry5 = s5 >> 21;
259     s6 += carry5;
260     s5 -= carry5 << 21;
261     carry6 = s6 >> 21;
262     s7 += carry6;
263     s6 -= carry6 << 21;
264     carry7 = s7 >> 21;
265     s8 += carry7;
266     s7 -= carry7 << 21;
267     carry8 = s8 >> 21;
268     s9 += carry8;
269     s8 -= carry8 << 21;
270     carry9 = s9 >> 21;
271     s10 += carry9;
272     s9 -= carry9 << 21;
273     carry10 = s10 >> 21;
274     s11 += carry10;
275     s10 -= carry10 << 21;
276     carry11 = s11 >> 21;
277     s12 += carry11;
278     s11 -= carry11 << 21;
279     s0 += s12 * 666643;
280     s1 += s12 * 470296;
281     s2 += s12 * 654183;
282     s3 -= s12 * 997805;
283     s4 += s12 * 136657;
284     s5 -= s12 * 683901;
285     s12 = 0;
286     carry0 = s0 >> 21;
287     s1 += carry0;
288     s0 -= carry0 << 21;
289     carry1 = s1 >> 21;
290     s2 += carry1;
291     s1 -= carry1 << 21;
292     carry2 = s2 >> 21;
293     s3 += carry2;
294     s2 -= carry2 << 21;
295     carry3 = s3 >> 21;
296     s4 += carry3;
297     s3 -= carry3 << 21;
298     carry4 = s4 >> 21;
299     s5 += carry4;
300     s4 -= carry4 << 21;
301     carry5 = s5 >> 21;
302     s6 += carry5;
303     s5 -= carry5 << 21;
304     carry6 = s6 >> 21;
305     s7 += carry6;
306     s6 -= carry6 << 21;
307     carry7 = s7 >> 21;
308     s8 += carry7;
309     s7 -= carry7 << 21;
310     carry8 = s8 >> 21;
311     s9 += carry8;
312     s8 -= carry8 << 21;
313     carry9 = s9 >> 21;
314     s10 += carry9;
315     s9 -= carry9 << 21;
316     carry10 = s10 >> 21;
317     s11 += carry10;
318     s10 -= carry10 << 21;
319 
320     s[0] = (unsigned char) (s0 >> 0);
321     s[1] = (unsigned char) (s0 >> 8);
322     s[2] = (unsigned char) ((s0 >> 16) | (s1 << 5));
323     s[3] = (unsigned char) (s1 >> 3);
324     s[4] = (unsigned char) (s1 >> 11);
325     s[5] = (unsigned char) ((s1 >> 19) | (s2 << 2));
326     s[6] = (unsigned char) (s2 >> 6);
327     s[7] = (unsigned char) ((s2 >> 14) | (s3 << 7));
328     s[8] = (unsigned char) (s3 >> 1);
329     s[9] = (unsigned char) (s3 >> 9);
330     s[10] = (unsigned char) ((s3 >> 17) | (s4 << 4));
331     s[11] = (unsigned char) (s4 >> 4);
332     s[12] = (unsigned char) (s4 >> 12);
333     s[13] = (unsigned char) ((s4 >> 20) | (s5 << 1));
334     s[14] = (unsigned char) (s5 >> 7);
335     s[15] = (unsigned char) ((s5 >> 15) | (s6 << 6));
336     s[16] = (unsigned char) (s6 >> 2);
337     s[17] = (unsigned char) (s6 >> 10);
338     s[18] = (unsigned char) ((s6 >> 18) | (s7 << 3));
339     s[19] = (unsigned char) (s7 >> 5);
340     s[20] = (unsigned char) (s7 >> 13);
341     s[21] = (unsigned char) (s8 >> 0);
342     s[22] = (unsigned char) (s8 >> 8);
343     s[23] = (unsigned char) ((s8 >> 16) | (s9 << 5));
344     s[24] = (unsigned char) (s9 >> 3);
345     s[25] = (unsigned char) (s9 >> 11);
346     s[26] = (unsigned char) ((s9 >> 19) | (s10 << 2));
347     s[27] = (unsigned char) (s10 >> 6);
348     s[28] = (unsigned char) ((s10 >> 14) | (s11 << 7));
349     s[29] = (unsigned char) (s11 >> 1);
350     s[30] = (unsigned char) (s11 >> 9);
351     s[31] = (unsigned char) (s11 >> 17);
352 }
353 
354 
355 
356 /*
357 Input:
358   a[0]+256*a[1]+...+256^31*a[31] = a
359   b[0]+256*b[1]+...+256^31*b[31] = b
360   c[0]+256*c[1]+...+256^31*c[31] = c
361 
362 Output:
363   s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
364   where l = 2^252 + 27742317777372353535851937790883648493.
365 */
366 
sc_muladd(unsigned char * s,const unsigned char * a,const unsigned char * b,const unsigned char * c)367 void sc_muladd(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) {
368     int64_t a0 = 2097151 & load_3(a);
369     int64_t a1 = 2097151 & (load_4(a + 2) >> 5);
370     int64_t a2 = 2097151 & (load_3(a + 5) >> 2);
371     int64_t a3 = 2097151 & (load_4(a + 7) >> 7);
372     int64_t a4 = 2097151 & (load_4(a + 10) >> 4);
373     int64_t a5 = 2097151 & (load_3(a + 13) >> 1);
374     int64_t a6 = 2097151 & (load_4(a + 15) >> 6);
375     int64_t a7 = 2097151 & (load_3(a + 18) >> 3);
376     int64_t a8 = 2097151 & load_3(a + 21);
377     int64_t a9 = 2097151 & (load_4(a + 23) >> 5);
378     int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
379     int64_t a11 = (load_4(a + 28) >> 7);
380     int64_t b0 = 2097151 & load_3(b);
381     int64_t b1 = 2097151 & (load_4(b + 2) >> 5);
382     int64_t b2 = 2097151 & (load_3(b + 5) >> 2);
383     int64_t b3 = 2097151 & (load_4(b + 7) >> 7);
384     int64_t b4 = 2097151 & (load_4(b + 10) >> 4);
385     int64_t b5 = 2097151 & (load_3(b + 13) >> 1);
386     int64_t b6 = 2097151 & (load_4(b + 15) >> 6);
387     int64_t b7 = 2097151 & (load_3(b + 18) >> 3);
388     int64_t b8 = 2097151 & load_3(b + 21);
389     int64_t b9 = 2097151 & (load_4(b + 23) >> 5);
390     int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
391     int64_t b11 = (load_4(b + 28) >> 7);
392     int64_t c0 = 2097151 & load_3(c);
393     int64_t c1 = 2097151 & (load_4(c + 2) >> 5);
394     int64_t c2 = 2097151 & (load_3(c + 5) >> 2);
395     int64_t c3 = 2097151 & (load_4(c + 7) >> 7);
396     int64_t c4 = 2097151 & (load_4(c + 10) >> 4);
397     int64_t c5 = 2097151 & (load_3(c + 13) >> 1);
398     int64_t c6 = 2097151 & (load_4(c + 15) >> 6);
399     int64_t c7 = 2097151 & (load_3(c + 18) >> 3);
400     int64_t c8 = 2097151 & load_3(c + 21);
401     int64_t c9 = 2097151 & (load_4(c + 23) >> 5);
402     int64_t c10 = 2097151 & (load_3(c + 26) >> 2);
403     int64_t c11 = (load_4(c + 28) >> 7);
404     int64_t s0;
405     int64_t s1;
406     int64_t s2;
407     int64_t s3;
408     int64_t s4;
409     int64_t s5;
410     int64_t s6;
411     int64_t s7;
412     int64_t s8;
413     int64_t s9;
414     int64_t s10;
415     int64_t s11;
416     int64_t s12;
417     int64_t s13;
418     int64_t s14;
419     int64_t s15;
420     int64_t s16;
421     int64_t s17;
422     int64_t s18;
423     int64_t s19;
424     int64_t s20;
425     int64_t s21;
426     int64_t s22;
427     int64_t s23;
428     int64_t carry0;
429     int64_t carry1;
430     int64_t carry2;
431     int64_t carry3;
432     int64_t carry4;
433     int64_t carry5;
434     int64_t carry6;
435     int64_t carry7;
436     int64_t carry8;
437     int64_t carry9;
438     int64_t carry10;
439     int64_t carry11;
440     int64_t carry12;
441     int64_t carry13;
442     int64_t carry14;
443     int64_t carry15;
444     int64_t carry16;
445     int64_t carry17;
446     int64_t carry18;
447     int64_t carry19;
448     int64_t carry20;
449     int64_t carry21;
450     int64_t carry22;
451 
452     s0 = c0 + a0 * b0;
453     s1 = c1 + a0 * b1 + a1 * b0;
454     s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
455     s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
456     s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
457     s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
458     s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
459     s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
460     s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
461     s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
462     s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
463     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;
464     s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
465     s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
466     s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
467     s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
468     s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
469     s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
470     s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
471     s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
472     s20 = a9 * b11 + a10 * b10 + a11 * b9;
473     s21 = a10 * b11 + a11 * b10;
474     s22 = a11 * b11;
475     s23 = 0;
476     carry0 = (s0 + (1 << 20)) >> 21;
477     s1 += carry0;
478     s0 -= carry0 << 21;
479     carry2 = (s2 + (1 << 20)) >> 21;
480     s3 += carry2;
481     s2 -= carry2 << 21;
482     carry4 = (s4 + (1 << 20)) >> 21;
483     s5 += carry4;
484     s4 -= carry4 << 21;
485     carry6 = (s6 + (1 << 20)) >> 21;
486     s7 += carry6;
487     s6 -= carry6 << 21;
488     carry8 = (s8 + (1 << 20)) >> 21;
489     s9 += carry8;
490     s8 -= carry8 << 21;
491     carry10 = (s10 + (1 << 20)) >> 21;
492     s11 += carry10;
493     s10 -= carry10 << 21;
494     carry12 = (s12 + (1 << 20)) >> 21;
495     s13 += carry12;
496     s12 -= carry12 << 21;
497     carry14 = (s14 + (1 << 20)) >> 21;
498     s15 += carry14;
499     s14 -= carry14 << 21;
500     carry16 = (s16 + (1 << 20)) >> 21;
501     s17 += carry16;
502     s16 -= carry16 << 21;
503     carry18 = (s18 + (1 << 20)) >> 21;
504     s19 += carry18;
505     s18 -= carry18 << 21;
506     carry20 = (s20 + (1 << 20)) >> 21;
507     s21 += carry20;
508     s20 -= carry20 << 21;
509     carry22 = (s22 + (1 << 20)) >> 21;
510     s23 += carry22;
511     s22 -= carry22 << 21;
512     carry1 = (s1 + (1 << 20)) >> 21;
513     s2 += carry1;
514     s1 -= carry1 << 21;
515     carry3 = (s3 + (1 << 20)) >> 21;
516     s4 += carry3;
517     s3 -= carry3 << 21;
518     carry5 = (s5 + (1 << 20)) >> 21;
519     s6 += carry5;
520     s5 -= carry5 << 21;
521     carry7 = (s7 + (1 << 20)) >> 21;
522     s8 += carry7;
523     s7 -= carry7 << 21;
524     carry9 = (s9 + (1 << 20)) >> 21;
525     s10 += carry9;
526     s9 -= carry9 << 21;
527     carry11 = (s11 + (1 << 20)) >> 21;
528     s12 += carry11;
529     s11 -= carry11 << 21;
530     carry13 = (s13 + (1 << 20)) >> 21;
531     s14 += carry13;
532     s13 -= carry13 << 21;
533     carry15 = (s15 + (1 << 20)) >> 21;
534     s16 += carry15;
535     s15 -= carry15 << 21;
536     carry17 = (s17 + (1 << 20)) >> 21;
537     s18 += carry17;
538     s17 -= carry17 << 21;
539     carry19 = (s19 + (1 << 20)) >> 21;
540     s20 += carry19;
541     s19 -= carry19 << 21;
542     carry21 = (s21 + (1 << 20)) >> 21;
543     s22 += carry21;
544     s21 -= carry21 << 21;
545     s11 += s23 * 666643;
546     s12 += s23 * 470296;
547     s13 += s23 * 654183;
548     s14 -= s23 * 997805;
549     s15 += s23 * 136657;
550     s16 -= s23 * 683901;
551     s23 = 0;
552     s10 += s22 * 666643;
553     s11 += s22 * 470296;
554     s12 += s22 * 654183;
555     s13 -= s22 * 997805;
556     s14 += s22 * 136657;
557     s15 -= s22 * 683901;
558     s22 = 0;
559     s9 += s21 * 666643;
560     s10 += s21 * 470296;
561     s11 += s21 * 654183;
562     s12 -= s21 * 997805;
563     s13 += s21 * 136657;
564     s14 -= s21 * 683901;
565     s21 = 0;
566     s8 += s20 * 666643;
567     s9 += s20 * 470296;
568     s10 += s20 * 654183;
569     s11 -= s20 * 997805;
570     s12 += s20 * 136657;
571     s13 -= s20 * 683901;
572     s20 = 0;
573     s7 += s19 * 666643;
574     s8 += s19 * 470296;
575     s9 += s19 * 654183;
576     s10 -= s19 * 997805;
577     s11 += s19 * 136657;
578     s12 -= s19 * 683901;
579     s19 = 0;
580     s6 += s18 * 666643;
581     s7 += s18 * 470296;
582     s8 += s18 * 654183;
583     s9 -= s18 * 997805;
584     s10 += s18 * 136657;
585     s11 -= s18 * 683901;
586     s18 = 0;
587     carry6 = (s6 + (1 << 20)) >> 21;
588     s7 += carry6;
589     s6 -= carry6 << 21;
590     carry8 = (s8 + (1 << 20)) >> 21;
591     s9 += carry8;
592     s8 -= carry8 << 21;
593     carry10 = (s10 + (1 << 20)) >> 21;
594     s11 += carry10;
595     s10 -= carry10 << 21;
596     carry12 = (s12 + (1 << 20)) >> 21;
597     s13 += carry12;
598     s12 -= carry12 << 21;
599     carry14 = (s14 + (1 << 20)) >> 21;
600     s15 += carry14;
601     s14 -= carry14 << 21;
602     carry16 = (s16 + (1 << 20)) >> 21;
603     s17 += carry16;
604     s16 -= carry16 << 21;
605     carry7 = (s7 + (1 << 20)) >> 21;
606     s8 += carry7;
607     s7 -= carry7 << 21;
608     carry9 = (s9 + (1 << 20)) >> 21;
609     s10 += carry9;
610     s9 -= carry9 << 21;
611     carry11 = (s11 + (1 << 20)) >> 21;
612     s12 += carry11;
613     s11 -= carry11 << 21;
614     carry13 = (s13 + (1 << 20)) >> 21;
615     s14 += carry13;
616     s13 -= carry13 << 21;
617     carry15 = (s15 + (1 << 20)) >> 21;
618     s16 += carry15;
619     s15 -= carry15 << 21;
620     s5 += s17 * 666643;
621     s6 += s17 * 470296;
622     s7 += s17 * 654183;
623     s8 -= s17 * 997805;
624     s9 += s17 * 136657;
625     s10 -= s17 * 683901;
626     s17 = 0;
627     s4 += s16 * 666643;
628     s5 += s16 * 470296;
629     s6 += s16 * 654183;
630     s7 -= s16 * 997805;
631     s8 += s16 * 136657;
632     s9 -= s16 * 683901;
633     s16 = 0;
634     s3 += s15 * 666643;
635     s4 += s15 * 470296;
636     s5 += s15 * 654183;
637     s6 -= s15 * 997805;
638     s7 += s15 * 136657;
639     s8 -= s15 * 683901;
640     s15 = 0;
641     s2 += s14 * 666643;
642     s3 += s14 * 470296;
643     s4 += s14 * 654183;
644     s5 -= s14 * 997805;
645     s6 += s14 * 136657;
646     s7 -= s14 * 683901;
647     s14 = 0;
648     s1 += s13 * 666643;
649     s2 += s13 * 470296;
650     s3 += s13 * 654183;
651     s4 -= s13 * 997805;
652     s5 += s13 * 136657;
653     s6 -= s13 * 683901;
654     s13 = 0;
655     s0 += s12 * 666643;
656     s1 += s12 * 470296;
657     s2 += s12 * 654183;
658     s3 -= s12 * 997805;
659     s4 += s12 * 136657;
660     s5 -= s12 * 683901;
661     s12 = 0;
662     carry0 = (s0 + (1 << 20)) >> 21;
663     s1 += carry0;
664     s0 -= carry0 << 21;
665     carry2 = (s2 + (1 << 20)) >> 21;
666     s3 += carry2;
667     s2 -= carry2 << 21;
668     carry4 = (s4 + (1 << 20)) >> 21;
669     s5 += carry4;
670     s4 -= carry4 << 21;
671     carry6 = (s6 + (1 << 20)) >> 21;
672     s7 += carry6;
673     s6 -= carry6 << 21;
674     carry8 = (s8 + (1 << 20)) >> 21;
675     s9 += carry8;
676     s8 -= carry8 << 21;
677     carry10 = (s10 + (1 << 20)) >> 21;
678     s11 += carry10;
679     s10 -= carry10 << 21;
680     carry1 = (s1 + (1 << 20)) >> 21;
681     s2 += carry1;
682     s1 -= carry1 << 21;
683     carry3 = (s3 + (1 << 20)) >> 21;
684     s4 += carry3;
685     s3 -= carry3 << 21;
686     carry5 = (s5 + (1 << 20)) >> 21;
687     s6 += carry5;
688     s5 -= carry5 << 21;
689     carry7 = (s7 + (1 << 20)) >> 21;
690     s8 += carry7;
691     s7 -= carry7 << 21;
692     carry9 = (s9 + (1 << 20)) >> 21;
693     s10 += carry9;
694     s9 -= carry9 << 21;
695     carry11 = (s11 + (1 << 20)) >> 21;
696     s12 += carry11;
697     s11 -= carry11 << 21;
698     s0 += s12 * 666643;
699     s1 += s12 * 470296;
700     s2 += s12 * 654183;
701     s3 -= s12 * 997805;
702     s4 += s12 * 136657;
703     s5 -= s12 * 683901;
704     s12 = 0;
705     carry0 = s0 >> 21;
706     s1 += carry0;
707     s0 -= carry0 << 21;
708     carry1 = s1 >> 21;
709     s2 += carry1;
710     s1 -= carry1 << 21;
711     carry2 = s2 >> 21;
712     s3 += carry2;
713     s2 -= carry2 << 21;
714     carry3 = s3 >> 21;
715     s4 += carry3;
716     s3 -= carry3 << 21;
717     carry4 = s4 >> 21;
718     s5 += carry4;
719     s4 -= carry4 << 21;
720     carry5 = s5 >> 21;
721     s6 += carry5;
722     s5 -= carry5 << 21;
723     carry6 = s6 >> 21;
724     s7 += carry6;
725     s6 -= carry6 << 21;
726     carry7 = s7 >> 21;
727     s8 += carry7;
728     s7 -= carry7 << 21;
729     carry8 = s8 >> 21;
730     s9 += carry8;
731     s8 -= carry8 << 21;
732     carry9 = s9 >> 21;
733     s10 += carry9;
734     s9 -= carry9 << 21;
735     carry10 = s10 >> 21;
736     s11 += carry10;
737     s10 -= carry10 << 21;
738     carry11 = s11 >> 21;
739     s12 += carry11;
740     s11 -= carry11 << 21;
741     s0 += s12 * 666643;
742     s1 += s12 * 470296;
743     s2 += s12 * 654183;
744     s3 -= s12 * 997805;
745     s4 += s12 * 136657;
746     s5 -= s12 * 683901;
747     s12 = 0;
748     carry0 = s0 >> 21;
749     s1 += carry0;
750     s0 -= carry0 << 21;
751     carry1 = s1 >> 21;
752     s2 += carry1;
753     s1 -= carry1 << 21;
754     carry2 = s2 >> 21;
755     s3 += carry2;
756     s2 -= carry2 << 21;
757     carry3 = s3 >> 21;
758     s4 += carry3;
759     s3 -= carry3 << 21;
760     carry4 = s4 >> 21;
761     s5 += carry4;
762     s4 -= carry4 << 21;
763     carry5 = s5 >> 21;
764     s6 += carry5;
765     s5 -= carry5 << 21;
766     carry6 = s6 >> 21;
767     s7 += carry6;
768     s6 -= carry6 << 21;
769     carry7 = s7 >> 21;
770     s8 += carry7;
771     s7 -= carry7 << 21;
772     carry8 = s8 >> 21;
773     s9 += carry8;
774     s8 -= carry8 << 21;
775     carry9 = s9 >> 21;
776     s10 += carry9;
777     s9 -= carry9 << 21;
778     carry10 = s10 >> 21;
779     s11 += carry10;
780     s10 -= carry10 << 21;
781 
782     s[0] = (unsigned char) (s0 >> 0);
783     s[1] = (unsigned char) (s0 >> 8);
784     s[2] = (unsigned char) ((s0 >> 16) | (s1 << 5));
785     s[3] = (unsigned char) (s1 >> 3);
786     s[4] = (unsigned char) (s1 >> 11);
787     s[5] = (unsigned char) ((s1 >> 19) | (s2 << 2));
788     s[6] = (unsigned char) (s2 >> 6);
789     s[7] = (unsigned char) ((s2 >> 14) | (s3 << 7));
790     s[8] = (unsigned char) (s3 >> 1);
791     s[9] = (unsigned char) (s3 >> 9);
792     s[10] = (unsigned char) ((s3 >> 17) | (s4 << 4));
793     s[11] = (unsigned char) (s4 >> 4);
794     s[12] = (unsigned char) (s4 >> 12);
795     s[13] = (unsigned char) ((s4 >> 20) | (s5 << 1));
796     s[14] = (unsigned char) (s5 >> 7);
797     s[15] = (unsigned char) ((s5 >> 15) | (s6 << 6));
798     s[16] = (unsigned char) (s6 >> 2);
799     s[17] = (unsigned char) (s6 >> 10);
800     s[18] = (unsigned char) ((s6 >> 18) | (s7 << 3));
801     s[19] = (unsigned char) (s7 >> 5);
802     s[20] = (unsigned char) (s7 >> 13);
803     s[21] = (unsigned char) (s8 >> 0);
804     s[22] = (unsigned char) (s8 >> 8);
805     s[23] = (unsigned char) ((s8 >> 16) | (s9 << 5));
806     s[24] = (unsigned char) (s9 >> 3);
807     s[25] = (unsigned char) (s9 >> 11);
808     s[26] = (unsigned char) ((s9 >> 19) | (s10 << 2));
809     s[27] = (unsigned char) (s10 >> 6);
810     s[28] = (unsigned char) ((s10 >> 14) | (s11 << 7));
811     s[29] = (unsigned char) (s11 >> 1);
812     s[30] = (unsigned char) (s11 >> 9);
813     s[31] = (unsigned char) (s11 >> 17);
814 }
815