MILP‐based automatic differential search for LEA and HIGHT block ciphers

Abstract

The authors use the mixed-integer linear programming (MILP) technique for the automatic search for differential characteristics of LEA and HIGHT ciphers. They show that the MILP model of the differential property of modular addition with one constant input can be represented with a much lesser number of linear inequalities compared to the general case. Benefiting from this model for HIGHT block cipher, they can achieve a reduction of 112r out of 480r in the total number of linear constraints for the MILP model of r-round of HIGHT. This saving accelerates the searching process of HIGHT about twice as fast. They enjoy the MILP model to investigate the differential effect of these ciphers and provide a more accurate estimation for the differential probability. Their observations show that despite HIGHT, LEA exhibits a strong differential effect. The results gained by this method improve/extend the previous results as follows. For LEA block cipher, they found more efficient 12- and 13-round differentials whose probabilities are better than the best previous 12- and 13-round differentials for a factor of about 26 and 27, respectively. In the case of HIGHT block cipher, they found new 12- and 13-round differentials, though with the same best-reported probabilities.