In Section 9.3, we give important examples of probabilistic encryption algorithms that are practical. Unfortunately, Vernam’s one-time pad is not practical in most situations. Shannon’s notion of perfect secrecy may be interpreted in terms of probabilistic attacking algorithms, which try to distinguish between two candidate plaintexts (Section 9.2). For example, we prove that Vernam’s one-time pad is a perfectly secret encryption. The pioneering work of Shannon on provable security, based on his information theory, is discussed in Section 9.1. Therefore, probabilistic encryption algorithms are required.
An encryption method provides secrecy only if the ciphertexts appear sufficiently random to the adversary. The security of cryptographic schemes and randomness are closely related. It is desirable that mathematical proofs show that a given cryptosystem resists certain types of attacks. This chapter deals with provable security.
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