Choosing Parameters to Achieve a Higher Success Rate for Hellman Time Memory Trade Off Attack

In 1980, Hellman proposed the Time Memory Trade Off (TMTO) attack and applied it on block cipher DES (Data Encryption Standard). Time Memory Trade Off attack is one of the methods that inverts a one way function. The resistance to TMTO attacks is an important criterion in the design of a modern cipher. Unlike the exhaustive search and table lookup methods, TMTO is a probabilistic method, that is, the search operation may not find a preimage even if there exists one. Up to now, there are some approximate bounds for success rates of Hellman table by Hellman and Kusuda et al. In this study, we give a more precise approximation for the coverage of a single Hellman table. There is no precise guideline in the literature that points out how to choose parameters for Hellman TMTO. We present a detailed analysis of the success rate of Hellman table via new parameters and also show how to choose parameters to achieve a higher success rate. The results are experimentally confirmed. We also discuss the Hellman's TMTO Curve.