Analysis of the Parallel Distinguished Point Tradeoff

Cryptanalytic time memory tradeoff algorithms are tools for quickly inverting one-way functions and many consider the rainbow table method to be the most efficient tradeoff algorithm. However, it was recently announced, mostly based on experiments, that the parallelization of the perfect distinguished point tradeoff algorithm brings about an algorithm that is 50\% more efficient than the perfect rainbow table method. Motivated by this claim, while noting that the massive pre-computation associated with any tradeoff algorithm makes the non-perfect forms of tradeoff algorithms more practical, we provide an accurate theoretic analysis of the parallel version of the non-perfect distinguished point tradeoff algorithm. Performance differences between different tradeoff algorithms are usually not very large, but even these small differences can be crucial in practice. So we take care not to ignore the side effects of false alarms in providing an online time complexity analysis of the parallel distinguished point tradeoff algorithm. Our complexity results are used to compare the parallel non-perfect distinguished point tradeoff against the non-perfect rainbow table method. The two algorithms are compared under identical success rate requirements and the pre-computation efforts are also taken into account. Contrary to our anticipation, we find that the rainbow table method is superior in typical situations, even though the parallelization did have a positive effect on the efficiency of the distinguished point tradeoff algorithm

Blockchain as cryptanalytic tool

One approach for blockchain based applications to provide a proof-of-work is the computation of hash-values. In our opinion these computations are a waste of energy. It would be highly desirable to find an alternative method that generates useful output. We show how to substitute hashing by performing multiplications on Elliptic Curves in order to find distinguished points that can then be used to solve the discrete logarithm problem on a chosen curve. Today\u27s digital infrastructures rely on only a few curves. We argue that the advent of blockchain based technologies makes the use of only few standardised curves questionable. In principle all cryptanalytic algorithms that use Rabin\u27s idea of distinguished points can be used in blockchain based attacks. Similar ideas can be used for the number field sieve

A Comparison of Perfect Table Cryptanalytic Tradeoff Algorithms

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 preceding paper are of more practical value. Comparisons that take both the cost of pre-computation and the efficiency of the online phase into account, at parameters that achieve a common success rate, can now be carried out with ease. Comparisons can be based on the expected execution complexities rather than the worst case complexities, and details such as the effects of false alarms and various storage optimization techniques need no longer be ignored. A significant portion of this paper is allocated to accurately 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 Cryptanalytic Time Memory Tradeoff Algorithms with Focus on Some Rainbow Variants

학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 2. 홍진.Cryptanalytic time memory tradeoff algorithms are tools for inverting one-way functions, and they are used to recover passwords from unsalted password hashes. There are many publicly known tradeoff algorithms, and the rainbow tradeoff algorithm, which is widely believed to be the best tradeoff algorithm, at least among implementers, has been the most popular method. In this thesis, we provide accurate complexity analyses of the thick rainbow tradeoff algorithm and the non-perfect and perfect table fuzzy rainbow tradeoff algorithms. These are algorithms that have not yet received much attention. Our analyses show that, when the pre-computation cost and the online execution efficiency are both taken into consideration, the perfect table fuzzy rainbow tradeoff can be seen as performing the best among the three algorithms considered and actually even better than the original rainbow tradeoff. The computational complexities for some time memory data tradeoff methods are also analyzed. The multi-target tradeoffs that we cover are the classical Hellman, distinguished point, and fuzzy rainbow methods, both in their non-perfect and perfect table versions for the latter two methods. We find that their execution complexities are no different from the complexities of the corresponding single-target algorithms executed under certain matching parameters. As in the single-target case, we conclude that the perfect table fuzzy rainbow tradeoff algorithm is the most preferable among the multi-target tradeoff algorithms we have considered.Chapter 1 Introduction 1 Chapter 2 Preliminaries 5 2.1 Previous Results of Major Algorithms 7 2.1.1 Hellman Tradeoff 7 2.1.2 DP Tradeoff 8 2.1.3 Rainbow Tradeoff 10 2.2 Some Rainbow Variants 11 2.2.1 Thick Rainbow Tradeoff 12 2.2.2 Non-Perfect Table Fuzzy Rainbow Tradeoff 13 2.2.3 Perfect Table Fuzzy Rainbow Tradeoff 15 Chapter 3 Analyses of the Three Rainbow Variants 18 3.1 Thick Rainbow Tradeoff 18 3.1.1 Probability of Success 18 3.1.2 Online Complexity 21 3.2 Non-Perfect Table Fuzzy Rainbow Tradeoff 25 3.2.1 Probability of Success 25 3.2.2 Online Complexity 31 3.3 Perfect Table Fuzzy Rainbow Tradeoff 37 3.3.1 Probability of Success 37 3.3.2 Online Complexity 41 Chapter 4 Storage Optimization 49 4.1 The Degree of Ending Point Truncation 50 4.1.1 Thick Rainbow Tradeoff 50 4.1.2 Non-Perfect Table Fuzzy Rainbow Tradeoff 52 4.1.3 Perfect Table Fuzzy Rainbow Tradeoff 54 Chapter 5 Comparison of Algorithms 56 5.1 Adjustment Factors for Tradeoff Coefficients 56 5.2 Some Observations concerning Fuzzy Rainbow Tradeoffs 58 5.3 Comparison 63 Chapter 6 Time Memory Data Tradeoff Algorithms 67 6.1 Algorithms 67 6.2 Analysis 69 Chapter 7 Experiments 72 7.1 Thick Rainbow Tradeoff 72 7.2 Non-Perfect Table Fuzzy Rainbow Tradeoff 74 7.3 Perfect Table Fuzzy Rainbow Tradeoff 78 7.4 Time Memory Data Tradeoff Algorithms 84 Chapter 8 Conclusion 86 Abstract (in Korean) 91Docto