3.2 Cryptographic keys
We saw in the last section that keys are extremely important because they are the only things that are supposed to be secret in a cryptosystem. But what exactly is a key?
A cryptographic key K comes from a large (but finite) set 𝒦. This large set is called the key space. If we assume that K is some bit sequence of length N, then 𝒦 = {0,1}N and the size of 𝒦 is 2N.
Figure 3.1: A cryptographic key k, the shared secret between Alice and Bob that ensures the security of their communication, is an element of a large (but finite) key space 𝒦. If the length of the key is N bits, then the size of 𝒦 is 2N
Naturally, we only want Alice and Bob to know the key, so Eve should neither be able to guess K, nor should she be able to eavesdrop on K when it is exchanged or obtain K by other means. These other means can be anything from a malware attack on Alice or Bob to spying on the electromagnetic radiation emanating from their...