ON SINGLE CYCLE T-FUNCTIONS GENERATED BY SOME ELEMENTS

The Single Cycle T-functions

In this paper the single cycle T-functions are studied. Making use of the explicit formulas of sum and product of 2-adic integers, we present the necessary and sufficient conditions on the generalized polynomial p̃(x) = a0⊕a1x + ⊕ · · · + ⊕adx d(mod2n) being a single cycle T-function. Furthermore, for any given generalized polynomial, we can deduce some expressions about its coefficients by whic...

A New Class of Single Cycle T-Functions

T-function is a relatively new cryptographic building block suitable for streamciphers. It has the potential of becoming a substitute for LFSRs, and those that correspond to maximum length LFSRs are called single cycle T-functions. We present a family of single cycle T-functions, previously unknown. An attempt at building a hardware oriented streamcipher based on this new T-function is given.

SOME QUOTIENTS ON A BCK-ALGEBRA GENERATED BY A FUZZY SET

First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra  X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quo...

On Lie algebras generated by few extremal elements

Permutation groups generated by short elements

This document was provoked by a question on the SEQFAN mailing list, which was passed on to me by Simone Severini. We consider the following four questions. How many subgroups of the symmetric group Sn are generated by • transpositions; • 3-cycles; • transpositions and 3-cycles, • products of pairs of transpositions? For each of the four questions there are three ways of counting the subgroups:...