The Rainbow Attack on Stream Ciphers Based on Maiorana-McFarland Functions

In this paper, we present the rainbow attack on stream ciphers filtered by Maiorana-McFarland functions. This can be considered as a generalization of the time-memory-data trade-off attack of Mihaljevic and Imai on Toyocrypt. First, we substitute the filter function in Toyocrypt (which has the same size as the LFSR) with a general MaioranaMcFarland function. This allows us to apply the attack to a wider class of stream ciphers. Moreover, our description replaces the time-memory-data trade-off attack with the rainbow attack of Oeshlin, which offers better performance and implementation advantages. Second, we highlight how the choice of different Maiorana-McFarland functions can affect the effectiveness of our attack. Third, we show that the attack can be modified to apply on filter functions which are smaller than the LFSR or on filtercombiner stream ciphers. This allows us to cryptanalyze other configurations commonly found in practice. Finally, filter functions with vector output are sometimes used in stream ciphers to improve the throughput. Therefore the case when the Maiorana-McFarland functions have vector output is investigated. We found that the extra speed comes at the price of additional weaknesses which make the attacks easier.