如何找到大量muliplication模100000007 [英] how to find muliplication of large numbers modulo 100000007

问题描述

据我们所知1000000007是一个大素数。
我如何才能找到两个大数的乘法模1000000007

As we know 1000000007 is a large prime number. How can I find multiplication of two large numbers modulo 1000000007

例如，如果我想找到78627765 * 67527574mod1000000007，我怎么能做到这一点。

For example if I want to find 78627765*67527574 mod 1000000007, how can I do it.

至少如果有人告诉我，我的程序应尽量

At least if anyone tell me the procedure I shall try

请注意：请让我知道有如int，long或long long基本数据类型的解决方案
在此先感谢

Note: pls let me know the solution with primitive datatypes like int,long or long long Thanks in advance

推荐答案

模链接的作品与那些推你的数字补偿空间的限制合理的数字：

Modulo chaining works with reasonable numbers that are pushing the limits of your numerical comp-space:

(A * B) % C == ((A % C) * (B % C)) % C.

这个证明是pretty直线前进，有数以千计的关于密码的网站在世界各地的例子。一个简单的例子：

The proof for this is pretty straight forward and there are literally thousands of examples on cryptography websites all over the world. A simple sample:

（7 * 8）％5 = 56％5 = 1

(7 * 8) % 5 = 56 % 5 = 1

和

((7 % 5) * (8 % 5)) % 5 = (2 * 3) % 5 = 6 % 5 = 1

我希望这有助于。显然，当A和B都已经被推到您的最高端平台的限制，但仍小于C，它变得毫无意义，但它可以很方便的时候不是这种情况下（即当A> C和/或B> C ）。

I hope this helps. Obviously when A and B are already pushed to your top-end platform limits and are still smaller than C, it gets pointless, but it can be very handy when this is not the case (I.e. when A > C and/or B > C).

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