Accordingtothe JV theorem, a permutation can be associated to a positive integer. In particular, in order to obtain a permutation on the positions of a 192 bits string, we usually work on numbers of roughly �However, in this work, the Factorial theorem � which states that any permutation of length L can be built from 3 permutations on strings of length �where L is a multiple of 3 � is presented and proved. This results in a reduction of numbers, for 192 bits strings from �to roughly �This implies savings on time and computational resources.

JV theorem, factorial theorem, SPN criptosystem, 192-criptosystem, variable permutation.