Basics of encryption

Definition. An encryption system consists of:

• a message space M
• a ciphertext space C
• a key space K
• an indexed set of functions E_k:M->C, k in K
• an indexed set of functions D_k:C->M, k in K

such that for all k in K, and for all m in M, D_k(E_k(m)) = m

Example Define M and C to be strings of letters from the alphabet Z/nZ, and let K=Z/nZ. Define e_k(x) = x+k mod n., and

e_k(m₁m₂...m_l) = ( e_k(m₁),e_k(m₂),...,e_k(m_l))

Example (One time pad) In the previous example, take k=(k₁,...,k_l), and define

E_k(m_{1 m2 ... ml) = (ek1}(m1), ek2}(m2), ... ekl(ml))}