Improved Linear Hull Attack on Round-Reduced Simon with Dynamic Key-Guessing Techniques

Simon is a lightweight block cipher family proposed by NSA in 2013. It has drawn many cryptanalysts' attention and varieties of cryptanalysis results have been published, including differential, linear, impossible differential, integral cryptanalysis and so on. In this paper, we give the improved linear attacks on all reduced versions of Simon with dynamic key-guessing technique, which was proposed to improve the differential attack on Simon recently. By establishing the boolean function of parity bit in the linear hull distinguisher and reducing the function according to the property of AND operation, we can guess different subkeys or equivalent subkeys for different situations, which decrease the number of key bits involved in the attack and decrease the time complexity in a further step. As a result, 23-round Simon32/64, 24-round Simon48/72, 25-round Simon48/96, 30-round Simon64/96, 31-round Simon64/128, 37-round Simon96/96, 38-round Simon96/144, 49-round Simon128/128, 51-round Simon128/192 and 53-round Simon128/256 can be attacked. As far as we know, our attacks on most reduced versions of Simon are the best compared with the previous cryptanalysis results. However, this does not shake the security of Simon family with full rounds.