Abstract

In this study, we generalize the conception of orthomorphisms and obtain a counting formula on the generalized linear orthomorphisms over the Galois field with the arbitrary prime number p as the characteristic. Thus the partial generation algorithm of generalized linear orthomorphisms is achieved. The counting formula of the linear orthomorphisms over the finite field with characteristic 2 is the special case in our results. Furthermore, the generalized linear orthomorphisms generated and discussed in this study can gain the maximum branch number when they are designed as P-permutations.

Keywords:

Block cipher, generalized linear orthomorphism, p-permutation, the branch number,

References

Competing interests

The authors have no competing interests.

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Copyright

The authors have no competing interests.