Efficient implementation of generalized Maiorana–McFarland class of cryptographic functions

Recently, a class of cryptographic Boolean functions called generalized Maiorana–McFarland (GMM) functions was proposed in Zhang and Pasalic (IEEE Trans Inf Theory 60(10):6681–6695, 2014). In particular, it was demonstrated that certain subclasses within the GMM class satisfy all the relevant cryptographic criteria including a good resistance to (fast) algebraic cryptanalysis. However, the issue of efficient hardware implementation, which is essentially of crucial importance when such a function is used as a filtering function in certain stream cipher encryption schemes, has not been addressed in Zhang and Pasalic (2014). In this article, we analyze the complexity of hardware implementation of these subclasses and provide some exact estimates in terms of the number of elementary circuits needed. It turns out that these classes of cryptographically strong functions are also characterized with a very low hardware implementation cost, making these functions attractive candidates for the use in certain stream cipher schemes.