The method of permutations generating for an arbitrary quantity of elements

Abstract

Every ciphering algorithm is based on two operations: substitution and permutation. So it is required to have a reliable permutations generator to construct a crypto- graphically strong cipher. The modern ciphers perform permutations only inside one separate block but not for the blocks among the whole message and this does not allow increasing the strength. Moreover the existing methods of permutations generating either do not allow generating a single pseudorandom permutation or having restrictions on the quantity of elements of the base set or do not provide the pseudorandom format of the permu­tations and they are difficult in the point of view of im­plementation. The developed method provides generating of a single pseudorandom permutation of an arbitrary quantity of elements and it is quite easy in implementation due to absence of complex computations. The method has eight variants which differ with the statistical charac­teristics of pseudorandomnicity evaluation. The algorithm of permutations generating, the mathematical model and the evaluation of comparison between the developed and existing methods are shown in this article.