A Comparison of Cryptanalytic Tradeoff Algorithms

Abstract

Three time memory tradeoff algorithms are compared in this paper. Specifically, the classical tradeoff algorithm by Hellman, the distinguished point tradeoff method, and the rainbow table method, in their non-perfect table versions, are treated.We show that, under parameters and assumptions that are typically considered in theoretic discussions of the tradeoff algorithms, Hellman and distinguished point tradeoffs perform very close to each other and that the rainbow table method performs somewhat better than the other two algorithms. Our method of comparison can easily be applied to other situations, where the conclusions could be different.The analysis of tradeoff efficiency presented in this paper does not ignore the effects of false alarms and also covers techniques for reducing storage, such as ending point truncations and index tables. Our comparison of algorithms takes the success probabilities and pre-computation efforts fully into account.

Analysis of the Parallel Distinguished Point Tradeoff

“…The two inversion objectives clearly require different amounts of resources to achieve. If applications of the tradeoff technique to password recovery from sufficiently long password hashes are to be considered, the second version is the correct inversion problem to study [11]. In the interest of practical applicability, the current paper deals with the second inversion problem.…”

“…However, these can be resolved in exactly the same way as with the exiting false alarms. Using the analysis given in [11], one can maintain the side effects of additional false alarms to a manageable level by controlling the degree of truncation. 5.…”

“…Suppose that the online chain has become a DP chain of length i and has produced an alarm. When regenerating the associated pre-computation chain to resolve the alarm, one need not continue any further thant−i iterations [11].…”

“…In a recent work [11], that builds on the works [1,10], the value of X tc was accurately computed for the Hellman, DP, and rainbow tradeoffs, and then the tradeoff coefficients of the three algorithms were compared against each other. Unlike previous attempts, the comparison of [11] took the inversion success rate, pre-computation cost, and the number of bits required to store each table entry fully into account. Their conclusion, in oversimplified terms, was that the classical Hellman and the DP tradeoffs perform comparable to each other and that the rainbow table method outperforms these two.…”

“…In this work, we give a treatment analogous to [11] of the DP tradeoff variant that processes its multiple pre-computation tables in parallel. We present an accurate theoretic online time complexity analysis of the parallel DP tradeoff and compare its performance with that of the rainbow tradeoff.…”