This chapter deals with provable security. It is desirable that mathematical proofs show that a given cryptosystem resists certain types of attacks. The security of cryptographic schemes and randomness are closely related. An encryption method provides secrecy only if the ciphertexts appear sufficiently random to the adversary. Therefore, probabilistic encryption algorithms are required. The pioneering work of Shannon on provable security, based on his information theory, is discussed in Section 9.1. For example, we prove that Vernam’s one-time pad is a perfectly secret encryption. Shannon’s notion of perfect secrecy may be interpreted in terms of probabilistic attacking algorithms that try to distinguish between two candidate plaintexts (Section 9.2).
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