Paper 2006/127

A New Cryptanalytic Time/Memory/Data Trade-off Algorithm

Sourav Mukhopadhyay and Palash Sarkar

Abstract

In 1980, Hellman introduced a time/memory trade-off (TMTO) algorithm satisfying the TMTO curve $TM^2=N^2$, where $T$ is the online time, $M$ is the memory and $N$ is the size of the search space. Later work by Biryukov-Shamir incorporated multiple data to obtain the curve $TM^2D^2=N^2$, where $D$ is the number of data points. In this paper, we describe a new table structure obtained by combining Hellman's structure with a structure proposed by Oechslin. Using the new table structure, we design a new multiple data TMTO algorithm both with and without the DP method. The TMTO curve for the new algorithm is obtained to be $T^3M^7D^8=N^7$. This curve is based on a conjecture on the number of distinct points covered by the new table. Support for the conjecture has been obtained through some emperical observations. For $D>N^{1/4}$, we show that the trade-offs obtained by our method are better than the trade-offs obtained by the BS method.