Observations on the SIMON block cipher family, by Stefan Kölbl and Gregor Leander and Tyge Tiessen

In this paper we analyse the general class of functions underly- ing the Simon block cipher. In particular, we derive efficiently computable and easily implementable expressions for the exact differential and linear behaviour of Simon-like round functions. Following up on this, we use those expressions for a computer aided approach based on SAT/SMT solvers to find both optimal differential and linear characteristics for Simon. Furthermore, we are able to find all characteristics contributing to the probability of a differential for Simon32 and give better estimates for the probability for other variants. Finally, we investigate a large set of Simon variants using different rotation constants with respect to their resistance against differential and linear cryptanalysis. Interestingly, the default parameters seem to be not always optimal.