对称和公钥加密 [英] Symmetric and public key encryption

问题描述

假设N个人想要使用对称密钥加密与N-1个其他人进行通信。任何两个人i和j之间的所有交流对于这个N组中的所有其他人都是可见的，并且该组中的任何其他人都不应该能够解码他们的通信。整个系统需要多少个键？现在假设使用公钥加密。在这种情况下需要多少个密钥？

我已经找到两个对称的答案，即状态是n（n-1）/ 2或n（n-1） ），前者对我来说是最有意义的。

对于公开我找到2N键或N键。再次，前者对我来说是最有意义的。

有人可以对正确答案有所了解吗？

解决方案

这是超出了SO的范围，我建议你将来看看crypto.stackexchange.com。此外，这个问题在某些方面是模糊的，你没有解释你的理性。我鼓励你下次更多的信息。说...

要使用对称密钥加密进行通信，每对人都必须共享一个密钥。这导致 N（N-1）/ 2 方程式。然而，大多数系统将假设您的密钥是单向的，因此每个发送者具有每个接收者的唯一密钥，将密钥数量的两倍增加到 N（N-1）。

要使用非对称加密技术进行通信，不计算任何类型的证书颁发机构，每个用户都有一个公钥/私钥对。每个用户两个密钥导致 2N 值。然而，如果你认为每个对只是一个键，那么我可以理解一个合理的人称这个 N 键（他们甚至可能意味着 code> N 键或 O（N）键）。

Suppose N people want to communicate with each of N- 1 other people using symmetric key encryption. All communication between any two people, i and j, is visible to all other people in this group of N, and no other person in this group should be able to decode their communication. How many keys are required in the system as a whole? Now suppose that public key encryption is used. How many keys are required in this case?

I have found two answers for symmetric that state it is either n(n-1)/2 or n(n-1), the former makes most sense to me.

For public I have found either 2N keys or N keys. Again the former makes most sense to me here.

Could someone shed some light on the correct answers?

解决方案

This is out of scope for SO, I suggest you look at crypto.stackexchange.com in the future. Also, the question is vague in some ways and you fail to explain your rational. I encourage you to include more information next time. That said...

To communicate using symmetric key cryptography each pair of people must share a key. This leads to the N(N-1)/2 equation. However, most systems will assume your keys are uni-directional so each sender has a unique key for each receiver, this doubles the number of keys to N(N-1).

To communicate using asymmetric cryptography, and not counting any sort of certificate authority, each user has a public/private key pair. Two keys per user leads to the 2N value. If, however, you consider each "pair" to be just one key then I could understand a reasonable person calling this N keys (they might even mean "on the order of N keys", or O(N) keys).

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