Definition

Let 𝒦\mathcal{K} denote the key space, ℳ\mathcal{M} denote the message space, and 𝒞\mathcal{C} denote the cipher space.
An encryption scheme is a pair of polynomial time algorithms

Enc⁡:𝒦×ℳ→𝒞Enc⁡(k,m)=Enck⁡(m)Dec⁡:𝒦×ℳ→𝒞Dec⁡(k,m)=Deck⁡(m) \begin{aligned} \operatorname{Enc}: \mathcal{K} \times \mathcal{M} \to \mathcal{C} \qquad \operatorname{Enc}(k,m) = \operatorname{Enc}_k(m)\\ \operatorname{Dec}: \mathcal{K} \times \mathcal{M} \to \mathcal{C} \qquad \operatorname{Dec}(k,m) = \operatorname{Dec}_k(m) \end{aligned}

such that ∀k∈𝒦\forall k \in \mathcal{K}, ∀m∈ℳ\forall m \in \mathcal{M},

Dec⁡(k,Enc⁡(k,m))=m\operatorname{Dec}(k, \operatorname{Enc}(k,m)) = m

(correctness)

Encryption problem

Alice has a plaintext message mm, which she wants to send to Bob. It is encrypted with a key, kk, producing a ciphertext, cc, which is received by Bob, who decrypts it to recover mm. Eve, an eavesdropper, should not learn mm.

References

  1. https://intensecrypto.org/public/lec_01_introduction.html