素数主要用于密码学，因为确定一个给定的数是否是素数需要相当长的时间。对于黑客来说，如果任何算法都需要大量的时间来破解代码，那么它对他们来说就变得毫无用处

简单的?是的。

如果你把两个大素数相乘，你会得到一个只有两个(大)素数因数的巨大非素数。

分解这个数字是一个非平凡的操作，这一事实是许多密码学算法的来源。有关更多信息，请参阅单向函数。

附录: 再解释一下。两个质数的乘积可以用作公钥，而质数本身可以用作私钥。对数据所做的任何操作，如果只能通过知道这两个因素中的一个来撤销，那么解密起来就不是简单的了。

质数本身并不重要，重要的是处理质数的算法。特别是求一个数(任何一个数)的因式。

如你所知，任何数字至少有两个因数。质数有一个独特的性质，它只有两个因数:1和质数本身。

The reason factoring is so important is mathematicians and computer scientists don't know how to factor a number without simply trying every possible combination. That is, first try dividing by 2, then by 3, then by 4, and so forth. If you try to factor a prime number--especially a very large one--you'll have to try (essentially) every possible number between 2 and that large prime number. Even on the fastest computers, it will take years (even centuries) to factor the kinds of prime numbers used in cryptography.

事实上，我们不知道如何有效地分解一个大数字，这赋予了密码算法的优势。如果有一天，有人想出了如何做到这一点，我们目前使用的所有加密算法都将过时。这仍然是一个开放的研究领域。

我不是数学家或密码学家，所以这里有一个外行的观察(没有花哨的方程，抱歉)。

这整个线程充满了关于如何在密码学中使用质数的解释，很难在这个线程中找到任何人以简单的方式解释为什么使用质数…很可能是因为每个人都认为这些知识是理所当然的。

只有从外部看问题才能产生这样的反应;但是如果他们使用两个质数的和，为什么不创建一个列表，列出任何两个质数可以产生的所有可能的和呢?

在这个网站上有一个455,042,511个质数的列表，其中最高的质数是9,987,500,000(10位数字)。 已知的最大素数(截至2015年2月)是2的257,885,161 - 1次方，即17,425,170位数字。这意味着保留所有已知质数的列表是没有意义的，更不用说所有它们可能的和了。取一个数并检查它是否是质数更容易。

计算大质数本身就是一项艰巨的任务，所以密码学家和数学家都会说，反向计算两个相互相乘的质数已经足够困难了……今天。

Cryptographic algorithms generally rely for their security on having a "difficult problem". Most modern algorithms seem to use the factoring of very large numbers as their difficult problem - if you multiply two large numbers together, computing their factors is "difficult" (i.e. time-consuming). If those two numbers are prime numbers, then there is only one answer, which makes it even more difficult, and also guarantees that when you find the answer, it's the right one, not some other answer that just happens to give the same result.

最基本和一般的解释:密码学都是关于数论的，所有的整数(除了0和1)都是由质数组成的，所以你在数论中要处理很多质数。

More specifically, some important cryptographic algorithms such as RSA critically depend on the fact that prime factorization of large numbers takes a long time. Basically you have a "public key" consisting of a product of two large primes used to encrypt a message, and a "secret key" consisting of those two primes used to decrypt the message. You can make the public key public, and everyone can use it to encrypt messages to you, but only you know the prime factors and can decrypt the messages. Everyone else would have to factor the number, which takes too long to be practical, given the current state of the art of number theory.