New construction of single-cycle T-function families

The single cycle T-function is a particular permutation function with complex algebraic structures, maximum period and efficient implementation in software and hardware. In this paper, on the basis of existing methods, we present a new construction using a class of single cycle T-functions meeting certain conditions to construct a family of new single cycle T-functions, and we also give the numeration lower bound for the newly constructed single cycle T- functions

New construction of single cycle T-function families

The single cycle T-function is a particular permutation function with complex algebraic structures, maximum period and efficient implementation in software and hardware. In this paper, on the basis of existing methods, by using a class of single cycle T-functions that satisfy some certain conditions, we first present a new construction of single cycle T-function families. Unlike the previous approaches, this method can construct multiple single cycle T-functions at once. Then the mathematical proof of the feasibility is given. Next the numeration for the newly constructed single cycle T-functions is also investigated. Finally, this paper is end up with a discussion of the properties which these newly constructed functions preserve, such as linear complexity and stability (k-error complexity), as well as a comparison with previous construction methods

T-functions revisited: New criteria for bijectivity/transitivity

The paper presents new criteria for bijectivity/transitivity of T-functions and fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz $p$-adic functions and to study measure-preservation/ergodicity of these