Automatic Search of Linear Trails in ARX with Applications to SPECK and Chaskey

In this paper, we study linear cryptanalysis of the ARX structure by means of automatic search. To evaluate the security of ARX designs against linear cryptanalysis, it is crucial to find (round-reduced) linear trails with maximum correlation. We model the problem of finding optimal linear trails by the boolean satisfiability problem (SAT), translate the propagation of masks through ARX operations into bitwise expressions and constraints, and then solve the problem using a SAT solver. We apply the method to find optimal linear trails for roundreduced versions of the block cipher SPECK and the MAC algorithm Chaskey. For SPECK with block size 32/48/64/96/128, we can find optimal linear trails for 22/11/13/9/9 rounds respectively, which largely improves previous results, especially on larger versions. A 3-round optimal linear trail of Chaskey is presented for the first time as far as we know. In addition, our method can be used to enumerate the trails in a linear hull, and we present two linear hulls with the distributions of trails for round-reduced SPECK32. Our work provides designers with more accurate evaluation against linear cryptanalysis on ARX designs, especially for primitives with large block sizes and many rounds.