2. Perfect Secret Encryption

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Presentation transcript:

2. Perfect Secret Encryption CIS 5371 Cryptography 2. Perfect Secret Encryption

Encryption Plaintext Ciphertext Encryption Decryption encryption key decryption key Encryption Plaintext Ciphertext Decryption

Encryption schemes

Encryption schemes Definition An encryption scheme (Gen,Enc,Dec) over message space M is perfectly secret if for every probability distribution over M, every message mM, and every ciphertext cC for which Pr[C = c]  0: Pr[M = m | C = c] = Pr[M = m] Convention: We consider only probability distributions over M, C that assign non-zero probabilities to all mM and cC.

Encryption schemes Lemma 1 An encryption scheme (Gen,Enc,Dec) over message space M is perfectly secret if and only if for every probability distribution over M, every message mM, and every ciphertext cC: Pr[C = c | M = m] = Pr[C = c]

Encryption schemes

Encryption schemes An equivalent definition for perfect secrecy

Encryption schemes

Shannon’s Theorem Theorem Let (Gen,Enc,Dec) be an encryption scheme over a message space M for which |M|= |K|=|C|. The scheme is perfectly secret if and only if: Every key kK is chosen with equal probability 1/|K| by algorithm Gen. For every mM and every cC there is a unique key kK such that Enck(m) outputs c

Encryption algorithms

Encryption schemes Theorem The one time pad encryption scheme is perfectly secret.

Limitations to perfect secrecy Theorem Let (Gen,Enc,Dec) be a perfectly secret encryption scheme over message space M, and let K be the key space as determined by Gen. Then |K|  |M| .