In this paper we analyze the general class of functions underlying the SIMON block cipher. In particular, we derive efficiently computable and easy to implement expressions for the exact differential and linear behavior of SIMON-like round function. Using those expressions we investigate a large set of natural SIMON variants with respect to the most important cryptographic criteria. Interestingly, the NSA\'s choice for the parameters are not always optimal.
Using a computer aided approach based on SAT/SMT solvers we are able to find both the optimal differential and linear characteristics for variants of SIMON and can also give better estimates on the
probability of differentials. As a result of this analysis we propose different sets of rotation constants, which feature better properties on some criteria, and might be interesting for further analysis.