Improvement and Analysis of VDP Method in Time/Memory Tradeoff Applications
In many cases, cryptanalysis of a cryptographic system can be interpreted as the process of inverting a one-way function. TMTO is designed to be a generic approach that can be used on any one-way function independent of the structure of the specific target system. It was first introduced to attack block ciphers by Hellman in 1980. The distinguished point (DP) method is a technique that reduces the number of table look-ups performed by Hellman’s algorithm. A variant of the DP (VDP) method is introduced to reduce the amount of memory required to store the pre-computed tables while maintaining the same success rate and online time. Both the DP method and VDP method can be applied to Hellman tradeoff or rainbow tradeoff.
We carefully examine the technical details of the VDP method and find that it is possible to construct functions for which the original method fails. Based on the analysis, we propose a modification of the VDP method. Furthermore, we present an accurate version of the tradeoff curve that does not ignore the effect of false alarms and takes storage reduction techniques into consideration. We find optimal parameter sets of this new method by minimizing the tradeoff coefficient. A more exact and fair comparison between tradeoff algorithms is also given, which shows that our method applied to the Hellman tradeoff performs best among them.
KeywordsFalse Alarm Distinguished Point Success Probability Block Cipher Time Memory
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- 1.Borst, J., Preneel, B., Vandewalle, J.: On the time-memory tradeoff between exhaustive key search and table precomputation. In: Symposium on Information Theory in the Benelux, pp. 111–118. Citeseer (1998)Google Scholar
- 2.Fiat, A., Naor, M.: Rigorous time/space tradeoffs for inverting functions. In: Proceedings of the Twenty-third Annual ACM Symposium on Theory of Computing, pp. 534–541. ACM (1991)Google Scholar
- 5.Hong, J., Moon, S.: A comparison of cryptanalytic tradeoff algorithms. Technical report, Cryptology ePrint Archive, Report 2010/176 (2010)Google Scholar
- 6.Kim, I.J., Matsumoto, T.: Achieving higher success probability in time-memory trade-off cryptanalysis without increasing memory size. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 82(1), 123–129 (1999)Google Scholar