Differential Properties of LRX-analogues of Small Constant Multiplication

In this work, we consider a class of mappings over bit vectors which imitate the multiplication by small constants with pure logic operations and non-cyclic shifts. Such mappings can provide non-linearity and strengthen the design of LRX-cryptosystems, which are widely used in lightweight cryptography, due to their apparent benefits: a simple implementation and the absence of internal rotational symmetry, which increases security against rotational attacks. We examine the security of these mappings against differential cryptanalysis. We provide an explicit easy-to-calculate expression of differential probabilities for several versions of LRX-analogues of small constant multiplication with different operations and shift values.