LAUSR

In lightweight cryptographic primitives, round functions with only simple operations XOR, modular addition and rotation are widely used nowadays. This kind of ciphers is called ARX ciphers. For ARX ciphers, impossible differential cryptanalysis and zero-correlation linear cryptanalysis are among the most powerful attacks, and the key problems for these two attacks are discovering more and longer impossible differentials (IDs) and zero-correlation linear hulls (ZCLHs). However, finding new IDs and ZCLHs for ARX ciphers has been a manual work for a long time, which has been an obstacle in improving these two attacks. This paper proposes an automatic search method to improve the efficiency of finding new IDs and ZCLHs for ARX ciphers. In order to prove the efficiency of this new tool, we take HIGHT, LEA, SPECK three typical ARX algorithms as examples to explore their longer and new impossible differentials and zero-correlation linear hulls. To the best of our knowledge, this is the first application of automatic search method for ARX ciphers on finding new IDs and ZCLHs. For HIGHT, we find more 17 round IDs and multiple 17 round ZCLHs. This is the first discovery of 17 round ZCLHs for HIGHT. For LEA, we find extra four 10 round IDs and several 9 round ZCLHs. In the specification of LEA, the designers just identified three 10 round IDs and one 7 round ZCLH. For SPECK, we find thousands of 6 round IDs and forty-four 6 round ZCLHs. Neither IDs nor ZCLHs of SPECK has been proposed before. The successful application of our new tool shows great potential in improving the impossible differential cryptanalysis and zero-correlation linear cryptanalysis on ARX ciphers.