Question

Let G be a secure pseudorandom generator with expansion factor α. Please describe a computationally secure symmetric key encryption scheme based on such G.

Answer 1

Q.Let G be a secure pseudorandom generator with expansion factor α. Please describe a computationally secure symmetric key encryption scheme based on such G.

Answer:

Gen: On input 1ⁿ, choose k {0, 1}ⁿ uniformly at random and output it as the key.

• Enc: On input a key k ∈  {0, 1}ⁿ and a message m ∈ {0, 1}⁽ⁿ⁾. output the ciphertext

c := G(k) m.

• Dec: On input a key k ∈  {0, 1}ⁿ and a ciphertext c∈ {0, 1}⁽ⁿ⁾, output the plaintext message

m := G(k) c.