为什么素数在密码学中很重要？ [英] Why are primes important in cryptography?

问题描述

有一件事总是作为一个非密码学家注意我：为什么使用总数是如此重要？是什么使得他们在加密技术中如此特别？

One thing that always strikes me as a non-cryptographer: Why is it so important to use Prime numbers? What makes them so special in cryptography?

有没有人有简单的简短说明？ （我知道有很多引物，应用密码学是圣经，但正如所说：我不是想实现我自己的加密算法，我发现的东西只是使我的大脑爆炸 - 没有10页的数学公式请：:)）

Does anyone have a simple short explanation? (I am aware that there are many primers and that Applied Cryptography is the Bible, but as said: I am not looking to implement my own cryptographic algorithm, and the stuff that I found just made my brain explode - no 10 pages of math formulas please :))

感谢。

推荐答案

最基本和一般的解释：密码学是全部关于数论，所有整数（0和1除外）都由素数组成，所以你在数论中处理素数很多。

Most basic and general explanation: cryptography is all about number theory, and all integer numbers (except 0 and 1) are made up of primes, so you deal with primes a lot in number theory.

更具体地说，一些重要的加密算法如 RSA 关键取决于素因子分解大数字需要很长时间。基本上，你有一个公钥，由用于加密消息的两个大素数的乘积组成，以及由用于解密消息的两个素数组成的秘密密钥。你可以使公共密钥公开，每个人都可以使用它来加密消息给你，但只有你知道的主要因素，并可以解密消息。每个人都必须考虑数字，考虑到数字理论的当前状态，这需要太长的时间才能实用。

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.

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