Differential Analysis of the Nonlinear Functions of SHACAL-2 Algorithm and the Application

SHACAL-2 algorithm is one of the standard block ciphers recommended by European NESSIE plan. It includes two kinds of nonlinear functions, the choice function and the major function. This paper studies mainly differential properties of the two nonlinear functions, and it is shown that the number of solutions of the differential equation is only related with the weight of the input difference when the difference only appears at the first position of the choice function, or only appears at the first or the second position of the major function. This observation is applied to the differential fault analysis on SHACAL-2. The results demonstrate that at least 160 random faults are needed to obtain 512 bit key with successful probability more than 60%, while at least 240 random faults are needed to obtain 512 bit key with successful probability more than 98%.