Let (Gen, Enc, Dec) be a private-key encryption scheme that satisfies correctness, and produces ciphertexts that...

 

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Let (Gen, Enc, Dec) be a private-key encryption scheme that satisfies correctness, and produces ciphertexts that are equal in length to the messages. That is, for some key space K and positive integer n: • Gen samples a key k € K. . Enc(k, m) takes as input a key k and an n-bit message m, and outputs an n-bit ciphertext c. • Dec(k, c) takes as input a key k and an n-bit ciphertext c, and outputs an n-bit message. We would like to know how the security is affected if we encrypt messages twice, with two independently generated keys. Formally, define a new encryption scheme (Gen',Enc', Dec') as follows: • Gen' independently samples two keys k1← Gen and k2 ← Gen, and outputs (k1, k2) € K x K as the key. 3 . • Enc' ((k1, k2), m) = Enc(k2, Enc(k1, m)) for any message m = {0, 1} n and key (k1, k2). . Dec' (c, m) = Dec(k1, Dec(k2, c)) for any ciphertext c = {0, 1} n and key (k1, k2). Prove that if (Gen, Enc, Dec) satisfies one-time perfect security, then (Gen',Enc', Dec') also satisfies one-time perfect security. Let (Gen, Enc, Dec) be a private-key encryption scheme that satisfies correctness, and produces ciphertexts that are equal in length to the messages. That is, for some key space K and positive integer n: • Gen samples a key k € K. . Enc(k, m) takes as input a key k and an n-bit message m, and outputs an n-bit ciphertext c. • Dec(k, c) takes as input a key k and an n-bit ciphertext c, and outputs an n-bit message. We would like to know how the security is affected if we encrypt messages twice, with two independently generated keys. Formally, define a new encryption scheme (Gen',Enc', Dec') as follows: • Gen' independently samples two keys k1← Gen and k2 ← Gen, and outputs (k1, k2) € K x K as the key. 3 . • Enc' ((k1, k2), m) = Enc(k2, Enc(k1, m)) for any message m = {0, 1} n and key (k1, k2). . Dec' (c, m) = Dec(k1, Dec(k2, c)) for any ciphertext c = {0, 1} n and key (k1, k2). Prove that if (Gen, Enc, Dec) satisfies one-time perfect security, then (Gen',Enc', Dec') also satisfies one-time perfect security.

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Definition An encryption scheme Gen EncDec with message spac... View the full answer