Studies on the cryptanalytic time memory trade-offs

Abstract

A time memory trade-off is a generic method to invert a given one-way function and can be applied to analyze many cryptographical systems, for example, to find a key of a block or stream cipher or to acquire a valid password from an encrypted password. Since the Hellman method was introduced, many methods and techniques have been suggested so that we happen to know some general properties. However for a long time, the analyses on the TMTO have been proceeded with inaccurate manners. For example, the success probability of the Hellman table has been underestimated and the exact portion of the efforts for verifying false alarms had not been computed. In recent years, some accurate computations on the TMTO have been tried and we executed accurate analyses on the TMTO in this context. In this thesis, we give an estimate formula for the success probability of the Hellman table and analyze false alarm behaviors accurately. We suggest a new TMTO method, named variable distinguished point or VDP. Our ultimate objective is finding an efficient way to use the TMTO by quantitative understandings. We suggest such an efficient way with a new technique of endpoint cutting.