Konstantinos Limniotis

Properties of the Error Linear Complexity Spectrum

This paper studies the error linear complexity spectrum of binary sequences with period 2n. A precise categorization of those sequences having two distinct critical points in their spectra, as well as an enumeration of these sequences, is given. An upper bound on the maximum number of distinct critical points that the spectrum of a sequence can have is proved, and a construction which yields a lower bound on this number is given. In the process simpler proofs of some known results on the linear complexity and k-error linear complexity of sequences with period 2n are provided.

On the Nonlinear Complexity and Lempel–Ziv Complexity of Finite Length Sequences

The nonlinear complexity of binary sequences and its connections with Lempel-Ziv complexity is studied in this paper. A new recursive algorithm is presented, which produces the minimal nonlinear feedback shift register of a given binary sequence. Moreover, it is shown that the eigenvalue profile of a sequence uniquely determines its nonlinear complexity profile, thus establishing a connection between Lempel-Ziv complexity and nonlinear complexity. Furthermore, a lower bound for the Lempel-Ziv compression ratio of a given sequence is proved that depends on its nonlinear complexity.

A Design Technique for Energy Reduction in NORA CMOS Logic

In this work, a design technique to reduce the energy consumption in NO RAce (NORA) circuits is presented. The technique is based on a unidirectional switch topology combined with a new clocking scheme permitting both charge recycling between circuit nodes and elimination of the short circuit current. Calculations proved that energy savings higher than 20% can be achieved. Simulation results from NORA designs in a 0.18-mum CMOS technology are presented to demonstrate the effectiveness of the proposed technique to achieve both energy and energy-delay product reduction

Lower bounds on sequence complexity via generalised vandermonde determinants

Binary sequences generated by nonlinearly filtering maximal length sequences with period 2n–1 are studied in this paper. We focus on the particular class of equidistant filters and provide improved lower bounds on the linear complexity of the filtered sequences. This is achieved by first considering and proving properties of generalised Vandermonde determinants. Furthermore, it is shown that the methodology developed can be used for studying properties of any nonlinear filter.

Best Affine and Quadratic Approximations of Particular Classes of Boolean Functions

In this paper, we consider the problem of computing best low-order approximations of Boolean functions; we focus on the best quadratic approximations of a subclass of cubic functions with arbitrary number of variables and we provide formulas for their efficient calculation. Our methodology is developed upon properties of the best affine approximations of quadratic functions, for which formulas for their direct computation (not by means of the Walsh-Hadamard transform) are given. We determine the cubic functions in the above subclass that achieve the maximum second-order nonlinearity, thus yielding a lower bound for the covering radius of the second order Reed-Muller code ssr RM(2, n) in ssr RM(3, n). Simple extensions of these results to some special cases of higher degree functions, are seen to hold. Furthermore, a preliminary analysis of well-known constructions for bent functions, in terms of their second-order nonlinearity, is performed that indicates potential weaknesses if construction parameters are not properly chosen.

On the Linear Complexity of Sequences Obtained by State Space Generators

Binary sequences generated from finite state automata are studied in this correspondence by utilizing system theoretic concepts. We develop a new unified approach for analyzing the linear complexity of such sequences, via controllability and observability conditions. A vectorial trace representation of sequences with arbitrary period is provided, which leads to a new generalized discrete Fourier transform allowing the generation of sequences with prescribed linear complexity. Furthermore, we introduce new classes of nonlinear filters, using the proposed approach, which generalize currently known classes and guarantee the same lower bound on the linear complexity.

Nonlinear complexity of binary sequences and connections with lempel-ziv compression

The nonlinear complexity of binary sequences is studied in this paper. A new recursive algorithm is presented, which produces the minimal nonlinear feedback shift register of a given sequence. Further, a connection between the nonlinear complexity and the compression capability of a sequence is established. A lower bound for the Lempel-Ziv compression ratio that a given sequence can achieve is proved, which depends on its nonlinear complexity.

On the error linear complexity profiles of binary sequences of period 2 n

This paper studies the error linear complexity profiles of binary sequences with period 2n. We give a precise categorization of those sequences having 2 distinct critical points in their profiles, as well as an enumeration of these sequences. We also give an upper bound on the maximum number of distinct critical points that the profile of a sequence can have, along with several constructions for sequences having many distinct critical points.

Secondary constructions of Boolean functions with maximum algebraic immunity

The algebraic immunity of cryptographic Boolean functions with odd number of variables is studied in this paper. Proper modifications of functions with maximum algebraic immunity are proved that yield new functions whose algebraic immunity is also maximum. Several results are provided for both the multivariate and univariate representation, and their applicability is shown on known classes of Boolean functions. Moreover, new efficient algorithms to produce functions of guaranteed maximum algebraic immunity are developed, which further extend and generalize well-known constructions in this area. It is shown that high nonlinearity as well as good behavior against fast algebraic attacks are also achievable in several cases.

Constructing Boolean functions in odd number of variables with maximum algebraic immunity

The algebraic immunity of cryptographic Boolean functions with odd number of variables is studied in this paper. We prove that minor modifications of functions achieving maximum algebraic immunity yield functions which are bound to have maximum or almost maximum algebraic immunity. Based on this, a new efficient algorithm to produce functions of guaranteed maximum algebraic immunity is developed. Moreover, it is shown that known constructions of functions with maximum algebraic immunity may also be generalized by using the same concepts.