Cipher

A cipher is defined over the spaces of:

All Keys, K

All Messages, M

All Cipher texts, C

Cipher (defined as a triple, (K,M,C)) as a pair of algorithms (E,D) where E represents the encryption algorithm and D represents the decryption algorithm.

E:K×M→C

and

D:K×C→M

Such that:

∀m∈M,k∈K:D(k,E(k,m))=m

E is often randomized

D is always deterministic

A cipher (E,D) has perfect secrecy if:

∀m0,m1∈M(|m0|=|m1|)and∀c∈C Pr[E(k,m0)=c]=Pr[E(k,m1)=c]

where k←K (k is a randomly distributed key from K)

In other words, if I was given a particular cipher text (encrypted message), I will have no idea which message originally created it since it could be any other message with equal probability.