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.

Comparison of perfect table cryptanalytic tradeoff algorithms

The computing power of graphics processing units (GPU) has increased rapidly, and there has been extensive research on general-purpose computing on GPU (GPGPU) for cryptographic algorithms such as RSA, ECC, NTRU, and AES With the rise of GPGPU, commodity computers have become complex heterogeneous GPU+CPU systems This new architecture poses new challenges and opportunities in high-performance computing In this paper, we present high-speed parallel implementations of the rainbow method, which is known as the most efficient time-memory tradeoff, in the heterogeneous GPU+CPU system We give a complete analysis of the effect of multiple checkpoints on reducing the cost of false alarms, and take advantage of it for load balancing between GPU and CPU Our implementation with multiple checkpoints requires no more time on average for resolving false alarms and it actually finishes earlier than generating all online chains unlike other implementations on GPU

/pdf/high-speed-parallel-implementations-of-the-rainbow-method-in-kwimqpcevu.pdf

High-Speed Parallel Implementations of the Rainbow Method in a Heterogeneous System

The computing power of graphics processing units GPU has increased rapidly, and there has been extensive research on general-purpose computing on GPU GPGPU for cryptographic algorithms such as RSA, Elliptic Curve Cryptosystem ECC, NTRU, and Advanced Encryption Standard. With the rise of GPGPU, commodity computers have become complex heterogeneous GPU+CPU systems. This new architecture poses new challenges and opportunities in high-performance computing. In this paper, we present high-speed parallel implementations of the rainbow method based on perfect tables, which is known as the most efficient time-memory trade-off, in the heterogeneous GPU+CPU system. We give a complete analysis of the effect of multiple checkpoints on reducing the cost of false alarms and take advantage of it for load balancing between GPU and CPU. For GTX460, our implementation is about 1.86 and 3.25 times faster than other GPU-accelerated implementations, RainbowCrack and Cryptohaze, respectively, and for GTX580, 1.53 and 2.40 times faster. Copyright © 2014 John Wiley & Sons, Ltd.

/pdf/high-speed-parallel-implementations-of-the-rainbow-method-353m6x5ai1.pdf

High-speed parallel implementations of the rainbow method based on perfect tables in a heterogeneous system

/pdf/issledovanie-slozhnosti-metoda-raduzhnykh-tablits-s-1pxb00ow6o.pdf

Исследование сложности метода радужных таблиц с маркерами цепочек

High-speed implementation of rainbow table method on heterogeneous multi-device architecture

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.

/pdf/improvement-and-analysis-of-vdp-method-in-time-memory-42gvzaxh1b.pdf

Improvement and analysis of VDP method in time/memory tradeoff applications

Time memory tradeoff (TMTO) attack has proven to be an effective cryptanalysis method against block ciphers and stream ciphers. Since it was first proposed in 1980s, many new ideas have come out to reduce the false alarms during the online phase, among which rainbow table introduced by Oechslin and perfect table introduced by Borst et al. are notable landmarks. Avoine et al. introduced the checkpoints technique to detect false alarms using little additional memory without regenerating the pre-computed chain. In this paper, we revisit the analysis of multiple checkpoints in rainbow tradeoff. For non-perfect table we give a new sight to the computation of the expected decreasing number of chain regenerations at the k-th iteration. This helps to better understand the real nature of false alarms and leads us to the same results as the work of Jung Woo Kim et al. at Indocrypt 2012. For perfect rainbow tradeoff we give the first way to find optimal positions of multiple checkpoints. The results are better than previous work of Avoine et al., which only applies when the perfect table has the maximum number of chains. All the results are verified through meticulous experiments.

/pdf/analysis-of-multiple-checkpoints-in-non-perfect-and-perfect-4vsivzgiui.pdf

Analysis of Multiple Checkpoints in Non-perfect and Perfect Rainbow Tradeoff Revisited

In this paper, we present a rigorous evaluation of Thing and Ying's attack (TY attack) [11] along with practical implementations. We find that the cryptanalysis time of their attack is too high to be practical. We also propose a more general time memory trade-off by combining the distinguished points strategy with TY attack. Both theoretical analysis and experimental results show that our new design can save about 53.7% cryptanalysis time compared to TY attack and can reduce about 35.2% storage requirement compared to the original rainbow attack.

https://link.springer.com/content/pdf/10.1007/978-3-642-34129-8_28.pdf

A new variant of time memory trade-off on the improvement of thing and ying's attack

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Improvement and analysis of VDP method in time/memory tradeoff applications

Analysis of Multiple Checkpoints in Non-perfect and Perfect Rainbow Tradeoff Revisited

A new variant of time memory trade-off on the improvement of thing and ying's attack