Choosing Parameters to Achieve a Higher Success Rate for Hellman Time Memory Trade Off Attack

Abstract

In 1980, Hellman proposed the Time Memory Trade Off (TMTO) attack and applied it on block cipher DES (Data Encryption Standard). Time Memory Trade Off attack is one of the methods that inverts a one way function. The resistance to TMTO attacks is an important criterion in the design of a modern cipher. Unlike the exhaustive search and table lookup methods, TMTO is a probabilistic method, that is, the search operation may not find a preimage even if there exists one. Up to now, there are some approximate bounds for success rates of Hellman table by Hellman and Kusuda et al. In this study, we give a more precise approximation for the coverage of a single Hellman table.There is no precise guideline in the literature that points out how to choose parameters for Hellman TMTO. We present a detailed analysis of the success rate of Hellman table via new parameters and also show how to choose parameters to achieve a higher success rate. The results are experimentally confirmed. We also discuss the Hellman's TMTO Curve.

A Comparison of Cryptanalytic Tradeoff Algorithms

“…As was previously noted through (28) and (27), when under a fixed probability of success requirement, both (25) and (26).…”

“…This result is copied as Proposition 21 in the main body of the current paper. Success probability of the Hellman tradeoff was also studied in [26]. However, the inversion problem considered there is different from that considered by the current paper.…”

“…In the strict sense, previous graphs for the DP and Hellman tradeoffs were also discrete set of points, but unless N is very small, the points are extremely close to each other. Unlike our comparison between DP and Hellman tradeoffs, the parts that depend on R ps appearing in the expressions (31) and (30) are not identical to those appearing in the cor- responding expressions (28), (27), (25), and (26). Hence, separate graphs need to be drawn for each success rate.…”

“…Some discussions may be found in [1,26]. However, generating a perfect Hellman table is costly and its use is not considered to be practical.…”

On a probabilistic approach to the estimation of reliability of the Hellman method

“…Получению оценок надежности метода Хеллмана в рамках того или иного теоретико-вероятностного подхода посвящен ряд работ [1,[8][9][10]. В данных работах оценка надежности метода Хеллмана сводится к оценке среднего значения случайной величины ξ(m, t, N ), моделирующей число различных элементов множества X, задействованных при построении одной таблицы из m записей для цепочек вычислений длины t.…”