Algebraic cryptanalysis of round-reduced lightweight ciphers Simon and Speck

This paper presents algebraic attacks on Simon and Speck, two families of lightweight block ciphers having LRX- and ARX-structures respectively. They were presented by the U.S. National Security Agency in 2013 and later standardized by ISO as a part of the RFID air interface standard. The ciphers are algebraically encoded, and the resulting systems of Boolean equations are solved with different SAT solvers as well as methods based on the linearization. For the first time, the approaches that use the sparsity of systems of Boolean equations are applied to these ciphers. The linearization parameters in systems of equations for both of the ciphers are estimated. A comparison of the efficiency of the used methods is provided.The results of the algebraic analysis show that the inclusion of additional nonlinear operations significantly increases the attack time and the amount of memory used. Therefore, the methods considered are more effective for cryptanalysis of the Simon cipher than Speck.