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CurveFp
1. import random
2.
3. class CurveFp( object ):
4.   def __init__( self, p, a, b ):
5.     self.__p = p
6.     self.__a = a
7.     self.__b = b
8.
9.   def p( self ):
10.     return self.__p
11.
12.   def a( self ):
13.     return self.__a
14.
15.   def b( self ):
16.     return self.__b
17.
18.   def contains_point( self, x, y ):
19.     return ( y * y - ( x * x * x + self.__a * x + self.__b ) ) % self.__p == 0
20.
21. class Point( object ):
22.   def __init__( self, curve, x, y, order = none ):
23.     self.__curve = curve
24.     self.__x = x
25.     self.__y = y
26.     self.__order = order
27.     if self.__curve: assert self.__curve.contains_point( x, y )
28.     if order: assert self * order == INFINITY
29.
30.   def __add__( self, other ):
31.     if other == INFINITY: return self
32.     if self == INFINITY: return other
33.     assert self.__curve == other.__curve
34.     if self.__x == other.__x:
35.       if ( self.__y + other.__y ) % self.__curve.p() == 0:
36.         return INFINITY
37.       else:
38.         return self.double()
39.
40.     p = self.__curve.p()
41.     l = ( ( other.__y - self.__y ) *
42.           inverse_mod( other.__x - self.__x, p ) ) % p
43.     x3 = ( l * l - self.__x - other.__x ) % p
44.     y3 = ( l * ( self.__x - x3 ) - self.__y ) % p
45.     return Point( self.__curve, x3, y3 )
46.
47.   def __mul__( self, other ):
48.     def leftmost_bit( x ):
49.       assert x > 0
50.       result = 1L
51.       while result <= x: result = 2 * result
52.       return result / 2
53.
54.     e = other
55.     if self.__order: e = e % self.__order
56.     if e == 0: return INFINITY
57.     if self == INFINITY: return INFINITY
58.     assert e > 0
59.     e3 = 3 * e
60.     negative_self = Point( self.__curve, self.__x, -self.__y, self.__order )
61.     i = leftmost_bit( e3 ) / 2
62.     result = self
63.     while i > 1:
64.       result = result.double()
65.       if ( e3 & i ) != 0 and ( e & i ) == 0: result = result + self
66.       if ( e3 & i ) == 0 and ( e & i ) != 0: result = result + negative_self
67.       i = i / 2
68.     return result
69.
70.   def __rmul__( self, other ):
71.     return self * other
72.
73.   def __str__( self ):
74.     if self == INFINITY: return "infinity"
75.     return "(%d,%d)" % ( self.__x, self.__y )
76.
77.   def double( self ):
78.     if self == INFINITY:
79.       return INFINITY
80.
81.     p = self.__curve.p()
82.     a = self.__curve.a()
83.     l = ( ( 3 * self.__x * self.__x + a ) *
84.           inverse_mod( 2 * self.__y, p ) ) % p
85.     x3 = ( l * l - 2 * self.__x ) % p
86.     y3 = ( l * ( self.__x - x3 ) - self.__y ) % p
87.     return Point( self.__curve, x3, y3 )
88.
89.   def x( self ):
90.     return self.__x
91.
92.   def y( self ):
93.     return self.__y
94.
95.   def curve( self ):
96.     return self.__curve
97.
98.   def order( self ):
99.     return self.__order
100.
101. INFINITY = Point( none, none, none )
102.
103. def inverse_mod( a, m ):
104.   if a < 0 or m <= a: a = a % m
105.   c, d = a, m
106.   uc, vc, ud, vd = 1, 0, 0, 1
107.   while c != 0:
108.     q, c, d = divmod( d, c ) + ( c, )
109.     uc, vc, ud, vd = ud - q*uc, vd - q*vc, uc, vc
110.   assert d == 1
111.   if ud > 0: return ud
112.   else: return ud + m
113.
114. # secp256k1
115. _p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2FL
116. _r = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141L
117. _b = 0x0000000000000000000000000000000000000000000000000000000000000007L
118. _a = 0x0000000000000000000000000000000000000000000000000000000000000000L
119. _Gx = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798L
121.
122.
123. curve_256 = CurveFp( _p, _a, _b )
124. generator_256 = Point( curve_256, _Gx, _Gy, _r )
125. g = generator_256
126.
127. a = 40953105491513688516610281755790771311735293800933111307849947593713104200392
128. z = 1
129. z1 = 0x446ed63cb85160c28151e359de23cd336b8931f02cd737501fc2ed7a97e3796b
130. r = 0x571f6f5d9f91d8481b2d44e81f57dc6ee1345bae36658e34b0e375aae2bfe6a0
131. m = 115792089237316195423570985008687907852837564279074904382605163141518161494337
132. az1 = a + z
133. a1 = az1 % m
134. b1 = a1 - z1 % m
135. c1 = b1 * r % m
136. az2 = az1 + z
137. a2 = az2 % m
138. b2 = a2 - z1 % m
139. c2 = b2 * r % m
140. az3 = az2 + z
141. a3 = az3 % m
142. b3 = a3 - z1 % m
143. c3 = b3 * r % m
144. az4 = az3 + z
145. a4 = az4 % m
146. b4 = a4 - z1 % m
147. c4 = b4 * r % m
148. az5 = az4 + z
149. a5 = az5 % m
150. b5 = a5 - z1 % m
151. c5 = b5 * r % m
152. az6 = az5 + z
153. a6 = az6 % m
154. b6 = a6 - z1 % m
155. c6 = b6 * r % m
156. az7 = az6 + z
157. a7 = az7 % m
158. b7 = a7 - z1 % m
159. c7 = b7 * r % m
160. az8 = az7 + z
161. a8 = az8 % m
162. b8 = a8 - z1 % m
163. c8 = b8 * r % m
164. az9 = az8 + z
165. a9 = az9 % m
166. b9 = a9 - z1 % m
167. c9 = b9 * r % m
168. az10 = az9 + z
169. a10 = az10 % m
170. b10 = a10 - z1 % m
171. c10 = b10 * r % m
172. az11 = az10 + z
173. a11 = az11 % m
174. b11 = a11 - z1 % m
175. c11 = b11 * r % m
176. az12 = az11 + z
177. a12 = az12 % m
178. b12 = a12 - z1 % m
179. c12 = b12 * r % m
180. az13 = az12 + z
181. a13 = az13 % m
182. b13 = a13 - z1 % m
183. c13 = b13 * r % m
184. az14 = az13 + z
185. a14 = az14 % m
186. b14 = a14 - z1 % m
187. c14 = b14 * r % m
188. az15 = az14 + z
189. a15 = az15 % m
190. b15 = a15 - z1 % m
191. c15 = b15 * r % m
192. az16 = az15 + z
193. a16 = az16 % m
194. b16 = a16 - z1 % m
195. c16 = b16 * r % m
196. az17 = az16 + z
197. a17 = az17 % m
198. b17 = a17 - z1 % m
199. c17 = b17 * r % m
200. az18 = az17 + z
201. a18 = az18 % m
202. b18 = a18 - z1 % m
203. c18 = b18 * r % m
204. az19 = az18 + z
205. a19 = az19 % m
206. b19 = a19 - z1 % m
207. c19 = b19 * r % m
208. az20 = az19 + z
209. a20 = az20 % m
210. b20 = a20 - z1 % m
211. c20 = b20 * r % m
212. az21 = az20 + z
213. a21 = az21 % m
214. b21 = a21 - z1 % m
215. c21 = b21 * r % m
216. az22 = az21 + z
217. a22 = az22 % m
218. b22 = a22 - z1 % m
219. c22 = b22 * r % m
220. az23 = az22 + z
221. a23 = az23 % m
222. b23 = a23 - z1 % m
223. c23 = b23 * r % m
224. az24 = az23 + z
225. a24 = az24 % m
226. b24 = a24 - z1 % m
227. c24 = b24 * r % m
228. az25 = az24 + z
229. a25 = az25 % m
230. b25 = a25 - z1 % m
231. c25 = b25 * r % m
232. az26 = az25 + z
233. a26 = az26 % m
234. b26 = a26 - z1 % m
235. c26 = b26 * r % m
236. az27 = az26 + z
237. a27 = az27 % m
238. b27 = a27 - z1 % m
239. c27 = b27 * r % m
240. az28 = az27 + z
241. a28 = az28 % m
242. b28 = a28 - z1 % m
243. c28 = b28 * r % m
244. az29 = az28 + z
245. a29 = az29 % m
246. b29 = a29 - z1 % m
247. c29 = b29 * r % m
248. az30 = az29 + z
249. a30 = az30 % m
250. b30 = a30 - z1 % m
251. c30 = b30 * r % m
252. az31 = az30 + z
253. a31 = az31 % m
254. b31 = a31 - z1 % m
255. c31 = b31 * r % m
256. az32 = az31 + z
257. a32 = az32 % m
258. b32 = a32 - z1 % m
259. c32 = b32 * r % m
260. az33 = az32 + z
261. a33 = az33 % m
262. b33 = a33 - z1 % m
263. c33 = b33 * r % m
264. az34 = az33 + z
265. a34 = az34 % m
266. b34 = a34 - z1 % m
267. c34 = b34 * r % m
268. az35 = az34 + z
269. a35 = az35 % m
270. b35 = a35 - z1 % m
271. c35 = b35 * r % m
272. az36 = az35 + z
273. a36 = az36 % m
274. b36 = a36 - z1 % m
275. c36 = b36 * r % m
276. az37 = az36 + z
277. a37 = az7 % m
278. b37 = a37 - z1 % m
279. c37 = b37 * r % m
280. az38 = az37 + z
281. a38 = az38 % m
282. b38 = a38 - z1 % m
283. c38 = b38 * r % m
284. az39 = az38 + z
285. a39 = az39 % m
286. b39 = a39 - z1 % m
287. c39 = b39 * r % m
288. az40 = az39 + z
289. a40 = az40 % m
290. b40 = a40 - z1 % m
291. c40 = b40 * r % m
292. az41 = az40 + z
293. a41 = az41 % m
294. b41 = a41 - z1 % m
295. c41 = b41 * r % m
296. az42 = az41 + z
297. a42 = az42 % m
298. b42 = a42 - z1 % m
299. c42 = b42 * r % m
300. az43 = az42 + z
301. a43 = az43 % m
302. b43 = a43 - z1 % m
303. c43 = b43 * r % m
304. az44 = az43 + z
305. a44 = az44 % m
306. b44 = a44 - z1 % m
307. c44 = b44 * r % m
308. az45 = az44 + z
309. a45 = az45 % m
310. b45 = a45 - z1 % m
311. c45 = b45 * r % m
312. az46 = az45 + z
313. a46 = az46 % m
314. b46 = a46 - z1 % m
315. c46 = b46 * r % m
316. az47 = az46 + z
317. a47 = az47 % m
318. b47 = a47 - z1 % m
319. c47 = b47 * r % m
320. az48 = az47 + z
321. a48 = az48 % m
322. b48 = a48 - z1 % m
323. c48 = b48 * r % m
324. az49 = az48 + z
325. a49 = az49 % m
326. b49 = a49 - z1 % m
327. c49 = b49 * r % m
328. az50 = az49 + z
329. a50 = az50 % m
330. b50 = a50 - z1 % m
331. c50 = b50 * r % m
332. Laz1 = az50 + z
333. La1 = Laz1 % m
334. Lb1 = La1 - z1 % m
335. Lc1 = Lb1 * r % m
336. Laz2 = Laz1 + z
337. La2 = Laz2 % m
338. Lb2 = La2 - z1 % m
339. Lc2 = Lb2 * r % m
340. Laz3 = Laz2 + z
341. La3 = Laz3 % m
342. Lb3 = La3 - z1 % m
343. Lc3 = Lb3 * r % m
344. Laz4 = Laz3 + z
345. La4 = Laz4 % m
346. Lb4 = La4 - z1 % m
347. Lc4 = Lb4 * r % m
348. Laz5 = Laz4 + z
349. La5 = Laz5 % m
350. Lb5 = La5 - z1 % m
351. Lc5 = Lb5 * r % m
352. Laz6 = Laz5 + z
353. La6 = Laz6 % m
354. Lb6 = La6 - z1 % m
355. Lc6 = Lb6 * r % m
356. Laz7 = Laz6 + z
357. La7 = Laz7 % m
358. Lb7 = La7 - z1 % m
359. Lc7 = Lb7 * r % m
360. Laz8 = Laz7 + z
361. La8 = Laz8 % m
362. Lb8 = La8 - z1 % m
363. Lc8 = Lb8 * r % m
364. Laz9 = Laz8 + z
365. La9 = Laz9 % m
366. Lb9 = La9 - z1 % m
367. Lc9 = Lb9 * r % m
368. Laz10 = Laz9 + z
369. La10 = Laz10 % m
370. Lb10 = La10 - z1 % m
371. Lc10 = Lb10 * r % m
372. Laz11 = Laz10 + z
373. La11 = Laz11 % m
374. Lb11 = La11 - z1 % m
375. Lc11 = Lb11 * r % m
376. Laz12 = Laz11 + z
377. La12 = Laz12 % m
378. Lb12 = La12 - z1 % m
379. Lc12 = Lb12 * r % m
380. Laz13 = Laz12 + z
381. La13 = Laz13 % m
382. Lb13 = La13 - z1 % m
383. Lc13 = Lb13 * r % m
384. Laz14 = Laz13 + z
385. La14 = Laz14 % m
386. Lb14 = La14 - z1 % m
387. Lc14 = Lb14 * r % m
388. Laz15 = Laz14 + z
389. La15 = Laz15 % m
390. Lb15 = La15 - z1 % m
391. Lc15 = Lb15 * r % m
392. Laz16 = Laz15 + z
393. La16 = Laz16 % m
394. Lb16 = La16 - z1 % m
395. Lc16 = Lb16 * r % m
396. Laz17 = Laz16 + z
397. La17 = Laz17 % m
398. Lb17 = La17 - z1 % m
399. Lc17 = Lb17 * r % m
400. Laz18 = Laz17 + z
401. La18 = Laz18 % m
402. Lb18 = La18 - z1 % m
403. Lc18 = Lb18 * r % m
404. Laz19 = Laz18 + z
405. La19 = Laz19 % m
406. Lb19 = La19 - z1 % m
407. Lc19 = Lb19 * r % m
408. Laz20 = Laz19 + z
409. La20 = Laz20 % m
410. Lb20 = La20 - z1 % m
411. Lc20 = Lb20 * r % m
412. Laz21 = Laz20 + z
413. La21 = Laz21 % m
414. Lb21 = La21 - z1 % m
415. Lc21 = Lb21 * r % m
416. Laz22 = Laz21 + z
417. La22 = Laz22 % m
418. Lb22 = La22 - z1 % m
419. Lc22 = Lb22 * r % m
420. Laz23 = Laz22 + z
421. La23 = Laz23 % m
422. Lb23 = La23 - z1 % m
423. Lc23 = Lb23 * r % m
424. Laz24 = Laz23 + z
425. La24 = Laz24 % m
426. Lb24 = La24 - z1 % m
427. Lc24 = Lb24 * r % m
428. Laz25 = Laz24 + z
429. La25 = Laz25 % m
430. Lb25 = La25 - z1 % m
431. Lc25 = Lb25 * r % m
432. Laz26 = Laz25 + z
433. La26 = Laz26 % m
434. Lb26 = La26 - z1 % m
435. Lc26 = Lb26 * r % m
436. Laz27 = Laz26 + z
437. La27 = Laz27 % m
438. Lb27 = La27 - z1 % m
439. Lc27 = Lb27 * r % m
440. Laz28 = Laz27 + z
441. La28 = Laz28 % m
442. Lb28 = La28 - z1 % m
443. Lc28 = Lb28 * r % m
444. Laz29 = Laz28 + z
445. La29 = Laz29 % m
446. Lb29 = La29 - z1 % m
447. Lc29 = Lb29 * r % m
448. Laz30 = Laz29 + z
449. La30 = Laz30 % m
450. Lb30 = La30 - z1 % m
451. Lc30 = Lb30 * r % m
452. Laz31 = Laz30 + z
453. La31 = Laz31 % m
454. Lb31 = La31 - z1 % m
455. Lc31 = Lb31 * r % m
456. Laz32 = Laz31 + z
457. La32 = Laz32 % m
458. Lb32 = La32 - z1 % m
459. Lc32 = Lb32 * r % m
460. Laz33 = Laz32 + z
461. La33 = Laz33 % m
462. Lb33 = La33 - z1 % m
463. Lc33 = Lb33 * r % m
464. Laz34 = Laz33 + z
465. La34 = Laz34 % m
466. Lb34 = La34 - z1 % m
467. Lc34 = Lb34 * r % m
468. Laz35 = Laz34 + z
469. La35 = Laz35 % m
470. Lb35 = La35 - z1 % m
471. Lc35 = Lb35 * r % m
472. Laz36 = Laz35 + z
473. La36 = Laz36 % m
474. Lb36 = La36 - z1 % m
475. Lc36 = Lb36 * r % m
476. Laz37 = Laz36 + z
477. La37 = Laz7 % m
478. Lb37 = La37 - z1 % m
479. Lc37 = Lb37 * r % m
480. Laz38 = Laz37 + z
481. La38 = Laz38 % m
482. Lb38 = La38 - z1 % m
483. Lc38 = Lb38 * r % m
484. Laz39 = Laz38 + z
485. La39 = Laz39 % m
486. Lb39 = La39 - z1 % m
487. Lc39 = Lb39 * r % m
488. Laz40 = Laz39 + z
489. La40 = Laz40 % m
490. Lb40 = La40 - z1 % m
491. Lc40 = Lb40 * r % m
492. Laz41 = Laz40 + z
493. La41 = Laz41 % m
494. Lb41 = La41 - z1 % m
495. Lc41 = Lb41 * r % m
496. Laz42 = Laz41 + z
497. La42 = Laz42 % m
498. Lb42 = La42 - z1 % m
499. Lc42 = Lb42 * r % m
500. Laz43 = Laz42 + z
501. La43 = Laz43 % m
502. Lb43 = La43 - z1 % m
503. Lc43 = Lb43 * r % m
504. Laz44 = Laz43 + z
505. La44 = Laz44 % m
506. Lb44 = La44 - z1 % m
507. Lc44 = Lb44 * r % m
508. Laz45 = Laz44 + z
509. La45 = Laz45 % m
510. Lb45 = La45 - z1 % m
511. Lc45 = Lb45 * r % m
512. Laz46 = Laz45 + z
513. La46 = Laz46 % m
514. Lb46 = La46 - z1 % m
515. Lc46 = Lb46 * r % m
516. Laz47 = Laz46 + z
517. La47 = Laz47 % m
518. Lb47 = La47 - z1 % m
519. Lc47 = Lb47 * r % m
520. Laz48 = Laz47 + z
521. La48 = Laz48 % m
522. Lb48 = La48 - z1 % m
523. Lc48 = Lb48 * r % m
524. Laz49 = Laz48 + z
525. La49 = Laz49 % m
526. Lb49 = La49 - z1 % m
527. Lc49 = Lb49 * r % m
528. Laz50 = Laz49 + z
529. La50 = Laz50 % m
530. Lb50 = La50 - z1 % m
531. Lc50 = Lb50 * r % m
532. p1 = c1 * g
533. r = p1.x()
534. if r == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes1')
535. p2 = c2 * g
536. r2 = p2.x()
537. if r2 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes2')
538. p3 = c3 * g
539. r3 = p3.x()
540. if r3 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes3')
541. p4 = c4 * g
542. r4 = p4.x()
543. if r4 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes4')
544. p5 = c5 * g
545. r5 = p5.x()
546. if r5 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes5')
547. p6 = c6 * g
548. r6 = p6.x()
549. if r6 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes6')
550. p7 = c7 * g
551. r7 = p7.x()
552. if r7 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes7')
553. p8 = c8 * g
554. r8 = p8.x()
555. if r8 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes8')
556. p9 = c9 * g
557. r9 = p9.x()
558. if r9 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes9')
559. p9 = c9 * g
560. r9 = p9.x()
561. if r9 == 0: print('yes9')
562. p10 = c10 * g
563. r10 = p10.x()
564. if r10 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes10')
565. p11 = c11 * g
566. r11 = p11.x()
567. if r11 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes11')
568. p12 = c12 * g
569. r12 = p12.x()
570. if r12 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes12')
571. p13 = c13 * g
572. r13 = p13.x()
573. if r13 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes13')
574. p14 = c14 * g
575. r14 = p14.x()
576. if r14 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes14')
577. p15 = c15 * g
578. r15 = p15.x()
579. if r15 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes15')
580. p16 = c16 * g
581. r16 = p16.x()
582. if r16 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes16')
583. p17 = c17 * g
584. r17 = p17.x()
585. if r17 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes17')
586. p18 = c18 * g
587. r18 = p18.x()
588. if r18 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes18')
589. p19 = c19 * g
590. r19 = p19.x()
591. if r19 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes19')
592. p20 = c20 * g
593. r20 = p20.x()
594. if r20 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes20')
595. p21 = c21 * g
596. r21 = p21.x()
597. if r21 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes21')
598. p22 = c22 * g
599. r22 = p22.x()
600. if r22 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes22')
601. p23 = c23 * g
602. r23 = p23.x()
603. if r23 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes23')
604. p24 = c24 * g
605. r24 = p24.x()
606. if r24 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes24')
607. p25 = c25 * g
608. r25 = p25.x()
609. if r2 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes25')
610. p26 = c26 * g
611. r26 = p26.x()
612. if r26 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes26')
613. p27 = c27 * g
614. r27 = p27.x()
615. if r27 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes27')
616. p28 = c28 * g
617. r28 = p28.x()
618. if r28 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes28')
619. p29 = c29 * g
620. r29 = p29.x()
621. if r29 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes29')
622. p30 = c30 * g
623. r30 = p30.x()
624. if r30 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes30')
625. p31 = c31 * g
626. r31 = p31.x()
627. if r31 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes31')
628. p32 = c32 * g
629. r32 = p32.x()
630. if r32 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes32')
631. p33 = c33 * g
632. r33 = p33.x()
633. if r33 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes33')
634. p34 = c34 * g
635. r34 = p34.x()
636. if r34 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes34')
637. p35 = c35 * g
638. r35 = p35.x()
639. if r35 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes35')
640. p36 = c36 * g
641. r36 = p36.x()
642. if r36 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes36')
643. p37 = c37 * g
644. r37 = p37.x()
645. if r37 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes37')
646. p38 = c38 * g
647. r38 = p38.x()
648. if r38 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes38')
649. p39 = c39 * g
650. r39 = p39.x()
651. if r39 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes39')
652. p40 = c40 * g
653. r40 = p40.x()
654. if r40 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes40')
655. p41 = c41 * g
656. r41 = p41.x()
657. if r41 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes41')
658. p42 = c42 * g
659. r42 = p42.x()
660. if r42 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes42')
661. p43 = c43 * g
662. r43 = p43.x()
663. if r43 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes43')
664. p45 = c45 * g
665. r45 = p45.x()
666. if r45 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes45')
667. p46 = c46 * g
668. r46 = p46.x()
669. if r46 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes46')
670. p47 = c47 * g
671. r47 = p47.x()
672. if r47 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes47')
673. p48 = c48 * g
674. r48 = p48.x()
675. if r48 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes48')
676. p49 = c49 * g
677. r49 = p49.x()
678. if r49 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes49')
679. p50 = c50 * g
680. r50 = p50.x()
681. if r50 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yes50')
682. Lp1 = Lc1 * g
683. Lr = Lp1.x()
684. if Lr == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL1')
685. Lp2 = Lc2 * g
686. Lr2 = Lp2.x()
687. if Lr2 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL2')
688. Lp3 = Lc3 * g
689. Lr3 = Lp3.x()
690. if Lr3 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL3')
691. Lp4 = Lc4 * g
692. Lr4 = Lp4.x()
693. if Lr4 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL4')
694. Lp5 = Lc5 * g
695. Lr5 = Lp5.x()
696. if Lr5 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL5')
697. Lp6 = Lc6 * g
698. Lr6 = Lp6.x()
699. if Lr6 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL6')
700. Lp7 = Lc7 * g
701. Lr7 = Lp7.x()
702. if Lr7 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL7')
703. Lp8 = Lc8 * g
704. Lr8 = Lp8.x()
705. if Lr8 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL8')
706. Lp9 = Lc9 * g
707. Lr9 = Lp9.x()
708. if Lr9 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL9')
709. Lp10 = Lc10 * g
710. Lr10 = Lp10.x()
711. if Lr10 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL10')
712. Lp11 = Lc11 * g
713. Lr11 = Lp11.x()
714. if Lr11 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL11')
715. Lp12 = Lc12 * g
716. Lr12 = Lp12.x()
717. if Lr12 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL12')
718. Lp13 = Lc13 * g
719. Lr13 = Lp13.x()
720. if Lr13 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL13')
721. Lp14 = Lc14 * g
722. Lr14 = Lp14.x()
723. if r14 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL14')
724. Lp15 = Lc15 * g
725. Lr15 = Lp15.x()
726. if Lr15 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL15')
727. Lp16 = Lc16 * g
728. Lr16 = Lp16.x()
729. if Lr16 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL16')
730. Lp17 = Lc17 * g
731. Lr17 = Lp17.x()
732. if Lr17 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL17')
733. Lp18 = Lc18 * g
734. Lr18 = Lp18.x()
735. if Lr18 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL18')
736. Lp19 = Lc19 * g
737. Lr19 = Lp19.x()
738. if Lr19 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL19')
739. Lp20 = Lc20 * g
740. Lr20 = Lp20.x()
741. if Lr20 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL20')
742. Lp21 = Lc21 * g
743. Lr21 = Lp21.x()
744. if Lr21 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL21')
745. Lp22 = Lc22 * g
746. Lr22 = Lp22.x()
747. if Lr22 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL22')
748. Lp23 = Lc23 * g
749. Lr23 = Lp23.x()
750. if Lr23 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL23')
751. Lp24 = Lc24 * g
752. Lr24 = Lp24.x()
753. if Lr24 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL24')
754. Lp25 = Lc25 * g
755. Lr25 = Lp25.x()
756. if Lr2 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL25')
757. Lp26 = Lc26 * g
758. Lr26 = Lp26.x()
759. if Lr26 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL26')
760. Lp27 = Lc27 * g
761. Lr27 = Lp27.x()
762. if Lr27 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL27')
763. Lp28 = Lc28 * g
764. Lr28 = Lp28.x()
765. if Lr28 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL28')
766. Lp29 = Lc29 * g
767. Lr29 = Lp29.x()
768. if Lr29 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL29')
769. Lp30 = Lc30 * g
770. Lr30 = Lp30.x()
771. if Lr30 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL30')
772. Lp31 = Lc31 * g
773. Lr31 = Lp31.x()
774. if Lr31 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL31')
775. Lp32 = Lc32 * g
776. Lr32 = Lp32.x()
777. if Lr32 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL32')
778. Lp33 = Lc33 * g
779. Lr33 = Lp33.x()
780. if Lr33 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL33')
781. Lp34 = Lc34 * g
782. Lr34 = Lp34.x()
783. if Lr34 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL34')
784. Lp35 = Lc35 * g
785. Lr35 = Lp35.x()
786. if Lr35 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL35')
787. Lp36 = Lc36 * g
788. Lr36 = Lp36.x()
789. if Lr36 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL36')
790. Lp37 = Lc37 * g
791. Lr37 = Lp37.x()
792. if Lr37 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL37')
793. Lp38 = Lc38 * g
794. Lr38 = Lp38.x()
795. if Lr38 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL38')
796. Lp39 = Lc39 * g
797. Lr39 = Lp39.x()
798. if Lr39 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL39')
799. Lp40 = Lc40 * g
800. Lr40 = Lp40.x()
801. if Lr40 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL40')
802. Lp41 = Lc41 * g
803. Lr41 = Lp41.x()
804. if Lr41 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL41')
805. Lp42 = Lc42 * g
806. Lr42 = Lp42.x()
807. if Lr42 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL42')
808. Lp43 = Lc43 * g
809. Lr43 = Lp43.x()
810. if Lr43 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL43')
811. Lp45 = Lc45 * g
812. Lr45 = Lp45.x()
813. if Lr45 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL45')
814. Lp46 = Lc46 * g
815. Lr46 = Lp46.x()
816. if Lr46 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL46')
817. Lp47 = Lc47 * g
818. Lr47 = Lp47.x()
819. if Lr47 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL47')
820. Lp48 = Lc48 * g
821. Lr48 = Lp48.x()
822. if Lr48 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL48')
823. Lp49 = Lc49 * g
824. Lr49 = Lp49.x()
825. if Lr49 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL49')
826. Lp50 = Lc50 * g
827. Lr50 = Lp50.x()
828. if Lr50 == 0x7146f0e0fcb3139947cf0beb870fe251930ca10d4545793d31033e801b5219ab: print('yesL50')
829. print(Laz50)
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