Post quantum cryptography based on non-commutative group is a hot topic in cryptography. The order of the group ensures the difficulty of inverse operation to some extent. We mainly study the algebraic proposition of order of transitive permutation groups g1

?g2 generated by two elements g1

?g2

give a necessary and sufficient conditions of transitive permutation group

and get a lower bound estimation of order of transitive permutation groups generated by two elements. In the process of the instantiation for generating g1

g2 which enables the order of transitive permutation groups g1

?g2 to satisfy the corresponding lower bound value

we give a method expressing a class of special n?order cycles as the product of two n?ary permutations and a corresponding design algorithm on transitive permutation groups g1

?g2 generated by two elements. In the end

this paper describes the application of transitive permutation group in symmetric cryptography.