Proofs of two conjectures on ternary weakly regular bent functions

We study ternary monomial functions of the form f(x)=\Tr_n(ax^d), where x\in \Ff_{3^n} and \Tr_n: \Ff_{3^n}\to \Ff_3 is the absolute trace function. Using a lemma of Hou \cite{hou}, Stickelberger's theorem on Gauss sums, and certain ternary weight inequalities, we show that certain ternary monomial functions arising from \cite{hk1} are weakly regular bent, settling a conjecture of Helleseth and Kholosha \cite{hk1}. We also prove that the Coulter-Matthews bent functions are weakly regular.Comment: 20 page

Clock-Controlled Shift Registers for Key-Stream Generation

In this paper we estimate the period of the sequence generated by a clock-controlled LFSR with an irreducible feedback polynomial and an arbitrary structure of the control sequence, as well as some randomness properties of this sequence including element distribution and the autocorrelation function. Also we construct and analyze a specific key-stream generator that applies clock-control. Finally, we present a comprehensive survey of known correlation attacks on clock-controlled registers and their memoryless combiners

Investigations in the design and analysis of key-stream generators

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Clock-Controlled Shift Registers for Key-Stream Generation

Abstract. In this paper we estimate the period of the sequence generated by a clock-controlled LFSR with an irreducible feedback polynomial and an arbitrary structure of the control sequence, as well as some randomness properties of this sequence including element distribution and the autocorrelation function. Also we construct and analyze a specific key-stream generator that applies clock-control. Finally, we present a comprehensive survey of known correlation attacks on clock-controlled registers and their memoryless combiners.

Tensor transform of Boolean functions and related algebraic and probabilistic properties

We introduce a tensor transform for Boolean functions that covers the algebraic normal and Walsh transforms but which also allows for the definition of new, probabilistic and weight transforms, relating a function to its bias polynomial and to the weights of its subfunctions respectively. Our approach leads to easy proofs for some known results and to new properties of the aforecited transforms. Finally, we present a new probabilistic characteristic of a Boolean function that is defined by its algebraic normal and probabilistic transforms over the reals