Partly-Pseudo-Linear Cryptanalysis of Reduced-Round S peck

We apply McKay’s pseudo-linear approximation of addition modular 2n to lightweight ARX block ciphers with large words, specifically the S peck family. We demonstrate that a pseudo-linear approximation can be combined with a linear approximation using the meet-in-the-middle attack technique to recover several key bits. Thus we illustrate improvements to S peck linear distinguishers based solely on Cho–Pieprzyk approximations by combining them with pseudo-linear approximations, and propose key recovery attacks.