How can I calculate the minimum number of active s_boxes for block cipher algorithms such as present algorithm? I have read in that, but I couldn't understand the meaning of branch number.
Present cipher is bit based permutation cipher. The branch number is calculated based on the minimum number of hamming weight sum of input and output in the difference distribution table(DDT) or linearity approximation table (LAT) of the sbox. in case of present cipher the 4-bit sbox , the differential branch number (BR) is 3.
to apply the differential BR on the whole present cipher , I advice you to apply mixed integer linear programming. this link contains the MILP model of different ciphers including present in sage, you can start from here.