Comparison of perfect table cryptanalytic tradeoff algorithms

Abstract

The performances of three major time memory tradeoff algorithms were compared in a recent paper. The algorithms considered there were the classical Hellman tradeoff and the non-perfect table versions of the distinguished point method and the rainbow table method. This paper adds the perfect table versions of the distinguished point method and the rainbow table method to the list, so that all the major tradeoff algorithms may now be compared against each other. Even though there are existing claims as to the superiority of one tradeoff algorithm over another algorithm, the algorithm performance comparisons provided by the current work and the recent paper mentioned above are of higher practical value. We provide comparisons of algorithms at parameters that achieve a common success rate of inversion and which take both the cost of pre-computation and the efficiency of the online phase into account. The comparisons are based on the average case execution behaviors rather than the worst case situations, and non-negligible details such as the effects of false alarms and various storage optimization techniques are no longer ignored. A large portion of this paper is allocated to analyzing the execution behavior of the perfect table distinguished point method. In particular, we obtain a closed-form formula for the average length of chains associated with a perfect distinguished point table.