如何计算x ^ y mod z? [英] How to calculate x^y mod z?

问题描述

我想知道如何计算x ^ y mod z. x和y非常大(无法容纳64位整数)，而z将容纳64位整数. 一件事不给出答案，例如x ^ y mod z与(x mod z)^ y mod z相同.

I am wondering how to calculate x^y mod z. x and y are very large (can't fit in 64 bit integer) and z will fit 64 bit integer. And one thing don't give answers like x^y mod z is same as (x mod z)^y mod z.

推荐答案

以下是标准方法，采用伪代码:

Here is the standard method, in pseudo-code:

function powerMod(b, e, m)
    x := 1
    while e > 0
        if e % 2 == 1
            x := (b * x) % m
            e := e - 1
        else
            b := (b * b) % m
            e := e / 2
    return x

该算法称为通过平方求幂"或平方乘"方法.

The algorithm is known as exponentiation by squaring or the square and multiply method.

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