Impossible differential and zero-correlation linear cryptanalysis of Marx, Marx2, Chaskey and Speck32

ARX symmetric ciphers use three operations: Additional, Rotational, and XOR in their structures. The SPECK, MARX, MARX2, and CHASKEY are examples of ARX block ciphers. In this paper, we consider the zero-correlation linear cryptanalysis of MARX, MARX2 and impossible differential cryptanalysis of MARX, MARX2, and CHASKEY.To our knowledge, this cryptanalysis has not been performed on any of the mentioned ciphers so far. Among the available methods for finding the best impossible differential and zero correlation characteristic in the corresponding cryptanalysis, we use Mixed Integer Linear Programming (MILP). The MILP is an automated search method to find the best differential (linear) characteristics of a cipher with a specified number of rounds. Thanks to the MILP method, for the CHASKEY cipher, we find 4-round impossible differential characteristics. For MARX, we present a 13-round attack by using a 10-round impossible differential characteristic. Also, for MARX2, we find 7-round impossible differential characteristics that cause the 11 rounds attack. Moreover, we apply zero-correlation linear cryptanalysis on 10 and 7-round of MARX and MARX2, respectively.