Provable security of modes of operation for symmetric-key cryptography considering initial vectors

摘要

The study of the security of symmetric-key cryptography is classified into two areas, namely the security evaluation of schemes and that of the cryptographic primitives. Assuming the security of cryptographic primitives, the security of the scheme is proven. The security proof also requires limitations of adversary's ability and the IV generation. So far all symmetric-key schemes are proven by IV generations based on secret randomness or internal counters. Otherwise, it is known that all schemes are fail to achieve the strongest notions, e.g. Left-or-Right sense. In this paper, we discuss the relationship between IV generation and security of the symmetric-key cryptography. First we give the formalization of a block cipher and a stream cipher. For each of two mechanisms, we discuss the relationship between the IV and security. We put a special interest to specific modes of a block cipher. That mode requires very strict conditions to achieve the Left-or-Right sense security. In contrast, the mode can achieve the weaker security notions by the weakest IV generation, while securities of many schemes in symmetric-key cryptography suddenly fail to hide information by that IV generation.