在灌水版建立一个博弈版块如何？

无心人

85位的不对 还不如80的长

liangbch

signature^697=44583379684764213868431721926136605529750126332148393391083714467200675872771867145040612 (mod 195829895438658706737622283850473406883420690004301400096152802481984054576589511059194683)

RSA 不是很懂，问一下，44583379684764213868431721926136605529750126332148393391083714467200675872771867145040612 可是密文， 697 和 195829895438658706737622283850473406883420690004301400096152802481984054576589511059194683 可是公钥 E 和 P。 另外，可否推荐一块RSA 工具，可将密文用公钥解密。 网上说，129位（10进制）是一个临界值，n >129位，很难在合理的时间内分解，不知各位老大怎么看?

mathe

RSA解密很难，主要就是要对公钥进行因子分解。 无心人在BBS上已经提供了好几个因子分解的库文件（和源代码等），使用他们应该很不错。 而因子分解的时间复杂度是指数递增的，在n比较大的时候就很难成功了。这个无心人应该比较熟悉。比如他上面能够估计出分解那个90位整数大概需要1天时间。而他分解那个60位左右的数只用了数秒。从这些数据我们也可以猜测n稍微大一些分解已经很难了。

medie2005

我们这种平凡人,对于RSA破解,能做的也只是搜一些大牛开发的大数分解工具,借助这些工具来破解. 其实,也没什么意义了,都是别人嚼了又嚼的东西了

liangbch

我说的解密不是破解。解密是指 下文中的解密： 比如数字签名，信息发布者用私钥加密数据，信息阅读方用 信息发布者 提供的公钥解密数据 或者在通信中，发送方用接受方提供的公钥加密数据，接受方用用自己的私钥来解密数据

无心人

Tue May 06 10:56:05 2008 Tue May 06 10:56:05 2008 Tue May 06 10:56:05 2008 Msieve v. 0.88 Tue May 06 10:56:05 2008 random seeds: 49525ad0 79e91a8e Tue May 06 10:56:05 2008 factoring 23062496730092690709353215131843843057725682565268421456019 (59 digits) Tue May 06 10:56:05 2008 using multiplier of 19 Tue May 06 10:56:05 2008 using sieve block of 65536 Tue May 06 10:56:05 2008 using a sieve bound of 51941 (2647 primes) Tue May 06 10:56:05 2008 using large prime bound of 2389286 Tue May 06 10:57:12 2008 found 2752 relations (1457 full + 1295 partial), need 2743 Tue May 06 10:57:12 2008 begin with 11347 relations Tue May 06 10:57:12 2008 reduce to 2411 relations in 2 passes Tue May 06 10:57:12 2008 attempting to read 1457 full and 2411 partial relations Tue May 06 10:57:12 2008 recovered 1457 full and 2411 partial relations Tue May 06 10:57:12 2008 recovered 2886 polynomials Tue May 06 10:57:12 2008 attempting to build 1295 cycles Tue May 06 10:57:12 2008 found 1295 cycles in 1 passes Tue May 06 10:57:12 2008 distribution of cycle lengths: Tue May 06 10:57:12 2008 length 2 : 1295 Tue May 06 10:57:12 2008 largest cycle: 2 relations Tue May 06 10:57:12 2008 2647 x 2711 system, weight 66861 (avg 24.66/col) Tue May 06 10:57:12 2008 reduce to 2489 x 2553 in 3 passes Tue May 06 10:57:12 2008 lanczos halted after 41 iterations Tue May 06 10:57:12 2008 recovered 61 nontrivial dependencies Tue May 06 10:57:13 2008 prp29 factor: 78845314666500290207081997553 Tue May 06 10:57:13 2008 prp30 factor: 292503071712534603216698269123 Tue May 06 10:57:13 2008 elapsed time 00:01:08 Tue May 06 11:01:43 2008 Tue May 06 11:01:43 2008 Tue May 06 11:01:43 2008 Msieve v. 0.88 Tue May 06 11:01:43 2008 random seeds: 4493e188 546d9f56 Tue May 06 11:01:43 2008 factoring 19568751779704846894153757735636728037621270144025906037913319859 (65 digits) Tue May 06 11:01:43 2008 using multiplier of 31 Tue May 06 11:01:43 2008 using sieve block of 65536 Tue May 06 11:01:43 2008 using a sieve bound of 126551 (5933 primes) Tue May 06 11:01:43 2008 using large prime bound of 12401998 Tue May 06 11:03:29 2008 found 6485 relations (3130 full + 3355 partial), need 6029 Tue May 06 11:03:29 2008 begin with 34843 relations Tue May 06 11:03:29 2008 reduce to 6259 relations in 2 passes Tue May 06 11:03:29 2008 attempting to read 3130 full and 6259 partial relations Tue May 06 11:03:29 2008 recovered 3130 full and 6259 partial relations Tue May 06 11:03:29 2008 recovered 7883 polynomials Tue May 06 11:03:29 2008 attempting to build 3355 cycles Tue May 06 11:03:29 2008 found 3355 cycles in 1 passes Tue May 06 11:03:29 2008 distribution of cycle lengths: Tue May 06 11:03:29 2008 length 2 : 3355 Tue May 06 11:03:29 2008 largest cycle: 2 relations Tue May 06 11:03:29 2008 5933 x 5997 system, weight 158827 (avg 26.48/col) Tue May 06 11:03:29 2008 reduce to 5543 x 5607 in 3 passes Tue May 06 11:03:30 2008 lanczos halted after 89 iterations Tue May 06 11:03:30 2008 recovered 63 nontrivial dependencies Tue May 06 11:03:32 2008 prp32 factor: 67148917862769937322043077366873 Tue May 06 11:03:32 2008 prp33 factor: 291423188973750394352320153627883 Tue May 06 11:03:32 2008 elapsed time 00:01:49 Tue May 06 11:47:27 2008 Tue May 06 11:47:27 2008 Tue May 06 11:47:27 2008 Msieve v. 0.88 Tue May 06 11:47:27 2008 random seeds: 88881100 7e8768c6 Tue May 06 11:47:27 2008 factoring 3114737665614036551724192975736494577899839808364045105215740888438567 (70 digits) Tue May 06 11:47:27 2008 using multiplier of 35 Tue May 06 11:47:27 2008 using sieve block of 65536 Tue May 06 11:47:27 2008 using a sieve bound of 233881 (10467 primes) Tue May 06 11:47:27 2008 using large prime bound of 19178242 Tue May 06 11:51:36 2008 found 10753 relations (5598 full + 5155 partial), need 10563 Tue May 06 11:51:36 2008 begin with 51974 relations Tue May 06 11:51:36 2008 reduce to 9645 relations in 2 passes Tue May 06 11:51:36 2008 attempting to read 5598 full and 9645 partial relations Tue May 06 11:51:36 2008 recovered 5598 full and 9645 partial relations Tue May 06 11:51:36 2008 recovered 13216 polynomials Tue May 06 11:51:36 2008 attempting to build 5155 cycles Tue May 06 11:51:36 2008 found 5155 cycles in 1 passes Tue May 06 11:51:36 2008 distribution of cycle lengths: Tue May 06 11:51:36 2008 length 2 : 5155 Tue May 06 11:51:36 2008 largest cycle: 2 relations Tue May 06 11:51:36 2008 10467 x 10531 system, weight 299853 (avg 28.47/col) Tue May 06 11:51:37 2008 reduce to 9468 x 9532 in 3 passes Tue May 06 11:51:39 2008 lanczos halted after 151 iterations Tue May 06 11:51:39 2008 recovered 62 nontrivial dependencies Tue May 06 11:51:43 2008 prp35 factor: 24571843890568162730310908961971921 Tue May 06 11:51:43 2008 prp36 factor: 126760436843309930202877195135812727 Tue May 06 11:51:43 2008 elapsed time 00:04:16 Tue May 06 11:56:40 2008 Tue May 06 11:56:40 2008 Tue May 06 11:56:40 2008 Msieve v. 0.88 Tue May 06 11:56:40 2008 random seeds: 354216f0 8baf5ebe Tue May 06 11:56:40 2008 factoring 269239885904399464077666682592356844323423389153434388696172765128368027801 (75 digits) Tue May 06 11:56:41 2008 using multiplier of 1 Tue May 06 11:56:41 2008 using sieve block of 65536 Tue May 06 11:56:41 2008 using a sieve bound of 715679 (28599 primes) Tue May 06 11:56:41 2008 using large prime bound of 70852221 Tue May 06 12:04:54 2008 found 28715 relations (16018 full + 12697 partial), need 28695 Tue May 06 12:04:54 2008 begin with 143302 relations Tue May 06 12:04:54 2008 reduce to 23781 relations in 2 passes Tue May 06 12:04:54 2008 attempting to read 16018 full and 23781 partial relations Tue May 06 12:04:55 2008 recovered 16018 full and 23781 partial relations Tue May 06 12:04:55 2008 recovered 29559 polynomials Tue May 06 12:04:55 2008 attempting to build 12697 cycles Tue May 06 12:04:55 2008 found 12697 cycles in 1 passes Tue May 06 12:04:55 2008 distribution of cycle lengths: Tue May 06 12:04:55 2008 length 2 : 12697 Tue May 06 12:04:55 2008 largest cycle: 2 relations Tue May 06 12:04:55 2008 28599 x 28663 system, weight 793333 (avg 27.68/col) Tue May 06 12:04:56 2008 reduce to 24062 x 24126 in 4 passes Tue May 06 12:05:15 2008 lanczos halted after 382 iterations Tue May 06 12:05:16 2008 recovered 60 nontrivial dependencies Tue May 06 12:05:24 2008 prp37 factor: 8183269180297971111478441181493536633 Tue May 06 12:05:24 2008 prp38 factor: 32901262316119465396381940043223396897 Tue May 06 12:05:25 2008 elapsed time 00:08:45 Tue May 06 14:56:05 2008 Tue May 06 14:56:05 2008 Msieve v. 0.88 Tue May 06 14:56:05 2008 random seeds: 80a24078 e8556c46 Tue May 06 14:56:05 2008 factoring 24754629007703530595783597953118663273500649152609142573755968421157144229186131 (80 digits) Tue May 06 14:56:08 2008 using multiplier of 11 Tue May 06 14:56:08 2008 using sieve block of 65536 Tue May 06 14:56:08 2008 using a sieve bound of 1234969 (47647 primes) Tue May 06 14:56:08 2008 using large prime bound of 123496900 Tue May 06 15:38:29 2008 found 47885 relations (26202 full + 21683 partial), need 47743 Tue May 06 15:38:30 2008 begin with 245412 relations Tue May 06 15:38:30 2008 reduce to 40683 relations in 2 passes Tue May 06 15:38:30 2008 attempting to read 26202 full and 40683 partial relations Tue May 06 15:38:32 2008 recovered 26202 full and 40683 partial relations Tue May 06 15:38:32 2008 recovered 57409 polynomials Tue May 06 15:38:32 2008 attempting to build 21683 cycles Tue May 06 15:38:32 2008 found 21683 cycles in 1 passes Tue May 06 15:38:32 2008 distribution of cycle lengths: Tue May 06 15:38:32 2008 length 2 : 21683 Tue May 06 15:38:32 2008 largest cycle: 2 relations Tue May 06 15:38:33 2008 47647 x 47711 system, weight 1417651 (avg 29.71/col) Tue May 06 15:38:33 2008 reduce to 40343 x 40407 in 4 passes Tue May 06 15:40:44 2008 lanczos halted after 640 iterations Tue May 06 15:40:45 2008 recovered 60 nontrivial dependencies Tue May 06 15:41:19 2008 prp40 factor: 2698729977431574411732833294724178719161 Tue May 06 15:41:19 2008 prp40 factor: 9172695754935407463828342942914640433771 Tue May 06 15:41:19 2008 elapsed time 00:45:14 这是原始的二次筛运算记录Tue May 06 14:56:05 2008 59 1:08 65 1:49 70 4:16 75 8:45 80 45:14

mathe

原帖由 liangbch 于 2008-5-6 14:45 发表 我说的解密不是破解。解密是指 下文中的解密： 比如数字签名，信息发布者用私钥加密数据，信息阅读方用 信息发布者 提供的公钥解密数据 或者在通信中，发送方用接受方提供的公钥加密数据，接受方用用自己的 ...

gxqcn的HugeCalc里面有RSATool,可以用一用看。不过据medie2005说比较难看懂该怎么用(可能界面上提示比较少）

medie2005

我说的破解就是你说的解密.

无心人

Tue May 06 09:26:00 2008 Tue May 06 09:26:00 2008 Tue May 06 09:26:00 2008 Msieve v. 0.88 Tue May 06 09:26:00 2008 random seeds: 8b6f3420 bd53e1d8 Tue May 06 09:26:00 2008 factoring 195829895438658706737622283850473406883420690004301400096152802481984054576589511059194683 (90 digits) Tue May 06 09:26:04 2008 using multiplier of 7 Tue May 06 09:26:04 2008 using sieve block of 65536 Tue May 06 09:26:04 2008 using a sieve bound of 1572433 (59667 primes) Tue May 06 09:26:04 2008 using large prime bound of 125794640 Tue May 06 09:26:04 2008 using double large prime bound of 379657280734080 Tue May 06 14:44:36 2008 found 59796 relations (15600 full + 44196 partial), need 59763 Tue May 06 14:44:42 2008 begin with 634005 relations Tue May 06 14:44:43 2008 reduce to 130582 relations in 9 passes Tue May 06 14:44:43 2008 attempting to read 15600 full and 130582 partial relations Tue May 06 14:44:48 2008 recovered 15600 full and 130582 partial relations Tue May 06 14:44:48 2008 recovered 140385 polynomials Tue May 06 14:44:49 2008 attempting to build 44196 cycles Tue May 06 14:44:49 2008 found 44196 cycles in 6 passes Tue May 06 14:44:49 2008 distribution of cycle lengths: Tue May 06 14:44:49 2008 length 2 : 11437 Tue May 06 14:44:49 2008 length 3 : 10642 Tue May 06 14:44:49 2008 length 4 : 8117 Tue May 06 14:44:49 2008 length 5 : 5742 Tue May 06 14:44:49 2008 length 6 : 3668 Tue May 06 14:44:49 2008 length 7 : 2094 Tue May 06 14:44:49 2008 length 8 : 1187 Tue May 06 14:44:49 2008 length 9+: 1309 Tue May 06 14:44:49 2008 largest cycle: 20 relations Tue May 06 14:44:50 2008 59667 x 59731 system, weight 3451894 (avg 57.79/col) Tue May 06 14:44:50 2008 reduce to 58340 x 58404 in 3 passes Tue May 06 14:47:52 2008 lanczos halted after 924 iterations Tue May 06 14:47:53 2008 recovered 62 nontrivial dependencies Tue May 06 14:49:00 2008 prp45 factor: 193586843950321608506064410069661525156328021 Tue May 06 14:49:00 2008 prp46 factor: 1011586797132312935871084948418941679079526223 Tue May 06 14:49:00 2008 elapsed time 05:23:00 Tue May 06 15:00:31 2008 Tue May 06 15:00:31 2008 Tue May 06 15:00:31 2008 Msieve v. 0.88 Tue May 06 15:00:31 2008 random seeds: 79f173e0 94207b2c Tue May 06 15:00:31 2008 factoring 23062496730092690709353215131843843057725682565268421456019 (59 digits) Tue May 06 15:00:31 2008 using multiplier of 19 Tue May 06 15:00:31 2008 using sieve block of 65536 Tue May 06 15:00:31 2008 using a sieve bound of 51941 (2647 primes) Tue May 06 15:00:31 2008 using large prime bound of 2389286 Tue May 06 15:00:51 2008 found 3283 relations (1663 full + 1620 partial), need 2743 Tue May 06 15:00:51 2008 begin with 12784 relations Tue May 06 15:00:51 2008 reduce to 3001 relations in 2 passes Tue May 06 15:00:51 2008 attempting to read 1663 full and 3001 partial relations Tue May 06 15:00:51 2008 recovered 1663 full and 3001 partial relations Tue May 06 15:00:51 2008 recovered 3409 polynomials Tue May 06 15:00:51 2008 attempting to build 1620 cycles Tue May 06 15:00:51 2008 found 1620 cycles in 1 passes Tue May 06 15:00:51 2008 distribution of cycle lengths: Tue May 06 15:00:51 2008 length 2 : 1620 Tue May 06 15:00:51 2008 largest cycle: 2 relations Tue May 06 15:00:52 2008 2647 x 2711 system, weight 64391 (avg 23.75/col) Tue May 06 15:00:52 2008 reduce to 2453 x 2517 in 3 passes Tue May 06 15:00:52 2008 lanczos halted after 40 iterations Tue May 06 15:00:52 2008 recovered 64 nontrivial dependencies Tue May 06 15:00:53 2008 prp29 factor: 78845314666500290207081997553 Tue May 06 15:00:53 2008 prp30 factor: 292503071712534603216698269123 Tue May 06 15:00:53 2008 elapsed time 00:00:22 另外一台机器上的90位的结果，比预期的少很多 顺便测试了那个59位的做参考

mathe

原帖由 medie2005 于 2008-5-6 14:40 发表 我们这种平凡人,对于RSA破解,能做的也只是搜一些大牛开发的大数分解工具,借助这些工具来破解. 其实,也没什么意义了,都是别人嚼了又嚼的东西了

是的，其实对我们就是一种游戏而已