New Integral distinguishers for I - Present™, TANGRAM and CHAM

Integral analysis is one of the most effective analysis methods for lightweight block ciphers. In this paper, the integral property are evaluated to three ciphers, I-Present™, TANGRAM and CHAM. The model of bit-based division property is established and solved by SAT and Gurobi solver. We obtain several new or improved bit-based division distinguishers for I-Present™, TANGRAM and CHAM. Furthermore, we get the 10-round integral distinguisher of Present™, with the improved data complexity about 2⁵⁶. For TANGRAM-128, we find 13-round integral distinguisher, which is the longest distinguisher with more lower data complexity at present. This also shows that the use of SAT solver for integral analysis can attack more block ciphers. At the same time, the integral analysis by using Gurobi solver of CHAM is also carried out, and 19-round and 21-round integral distinguisher of CHAM-64 and CHAM-128 are obtained respectively, which are five rounds and three rounds more than those of the designer.