Application of LFSRs in time/memory trade-off cryptanalysis

Time/memory trade-off (TMTO) attacks require the generation of a sequence of functions which are obtained as minor modifications of a one-way function to be inverted. We carefully examine the requirements for such function generation. A counter based method is used to generate the functions for the rainbow method. We show that there are functions for which the counter method fails. This is similar to the example given by Fiat and Naor for the Heilman TMTO. Our main contribution is to suggest the use of LFSR sequences for function generation to be used in the rainbow TMTO. Properties of LFSR sequences such as long period, pseudorandomness properties and efficient forward and backward generation make such sequences useful for the intended application. One specific advantage is that it is not possible to a priori construct a Fiat-Naor type example for the LFSR based rainbow method.