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[原创]RSA公钥密码的破解
[这个贴子最后由天山草在 2011/11/13 10:12am 第 3 次编辑]
对(30n+17)*(30m+31)=695800000167999998647
或 900nm+930n+510m+527=695800000167999998647
求整数解,运行速度会慢得不可思议。
现代软件分解下面这个数(把上面的数四次排队)695800000167999998647695800000167999998647695800000167999998647695800000167999998647,仅用时 0.2 秒,结果是 {{7, 2}, {11, 1}, {13, 1}, {29, 1}, {101, 1}, {109, 1}, {127,1}, {281, 1}, {2689, 1}, {9901, 1}, {226549, 1}, {459691,1}, {909091, 1}, {121499449, 1}, {4458192223320340849, 1}, {6383486240073394483, 1}
原数进行八次排队(168位),分解用时为43秒,结果是:
695800000167999998647695800000167999998647695800000167999998647695800000167999998647695800000167999998647695800000167999998647695800000167999998647695800000167999998647 = 7×7×11×13×29×73×101×109×127×137×281×2689×7841×9901×226549×459691×909091×99990001×121499449×11189053009×603812429055411913×4458192223320340849×6383486240073394483×127522001020150503761×148029423400750506553
由此可见,“土办法”差距太大,思路不对。[br][br]-=-=-=-=- 以下内容由 天山草 在 时添加 -=-=-=-=-
如果分解一万位的大数,“洋办法”也无能为力了,可见破解 RSA 密码之难。再说,他的密码可能是一天一换,让你没有时间进行分解——虽然国家情报局的电脑比民间电脑厉害得多,那也是不行的。等到你行的时候,他会把数字弄到 100 万位。 |
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