Introduction of TMTO attack on Hash Functions

In this article, we introduce Time Memory Trade Off attack and a method for finding near collisions in a hash function. By considering hash computations, it is easy to compute a lower bound for the complexity of near-collision algorithms, and to construct matching algorithm. However, this algorithm needs a lot of memory, and uses memory accesses. Recently, some algorithms have been proposed that do not require this amount of memory. They need more hash evaluation, but this attack is actually more practical. These algorithms can be divided in two main group: the first group is based on truncation and the second group is based on covering codes. In this paper, we consider the first group that is based on truncation. For practical implementation, it can be assumed that some memory is available, Leurent [10] showed that it is possible to reduce the complexity significantly by using this memory. In the next step, Sasaki et al. [9] proposed improvement of most popular Time Memory Trade off for K-tree algorithm by using multi-collision based on Helman’s table. As a result, they obtained new trade off curve that for k=4 the tradeoff curve will be . In this article, at the first the methods of TMTO, and then the method of finding near-collision by using TMTO are explained.