Calculate the Number of active s boxes I really want to learn how to calculate the number of active s _boxes for block cipher cryptographic algorithms.
I want to do that manually after running each round of an algorithm such as LED algorithm, what should I notice or compare in order to calculate the number of active s_boxes ?
I read that definition ".You run the algorithm with two different plaintexts (whose difference is usually small – just a few bits, everything else being equal).

Wherever these plaintexts lead to different inputs to an S-box (in any layer/round of the algorithm), we call this S-Box “active” (since the other S-boxes produce the same result for both plaintexts, they are called “passive” and are not considered further)"", and want to learn how to calculate the number of differential active s_boxes?
If you want to do this manually as stated in your question the approach would be similar to this:


choose an input difference $\alpha$ compute the active input sboxes $n_0$ as the number of sboxes that have a non-zero input difference,
when $\alpha$ is the input difference
choose an plaintext $p_0$ and $p_1 = p_0 \oplus \alpha$


compute one round of encryption to get $t^1_0$, and $t^1_1$
compute $\gamma_1 = t^1_0 \oplus t^1_1$, which is the output difference after one encryption round.
compute the active sboxes after one round $n_1$ as the number of sboxes that have a non-zero input difference, regarding $\gamma_1$
repeat for number of rounds $r$ you want to cover

the number of active sboxes for input difference $\alpha$ is $n(\alpha) = \sum_i n_i$
repeat the full procedure for every possible $\alpha$
the minimum number of active sboxes is $\min_\alpha n(\alpha)$.


Of course, there are more sophisticated ways than this, but if you want to do this manually, it might be a good start to understand the concept.