Showing papers by "Harald Niederreiter published in 2009"

Algebraic Geometry in Coding Theory and Cryptography

Abstract: This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available.Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books

Joint linear complexity of multisequences consisting of linear recurring sequences

Abstract: The linear complexity of sequences is one of the important security measures for stream cipher systems. Recently, in the study of vectorized stream cipher systems, the joint linear complexity of multisequences has been investigated. In this paper, we study the joint linear complexity of multisequences consisting of linear recurring sequences. The expectation and variance of the joint linear complexity of random multisequences consisting of linear recurring sequences are determined. These results extend the corresponding results on the expectation and variance of the joint linear complexity of random periodic multisequences. Then we enumerate the multisequences consisting of linear recurring sequences with fixed joint linear complexity. A general formula for the appropriate counting function is derived. Some convenient closed-form expressions for the counting function are determined in special cases. Furthermore, we derive tight upper and lower bounds on the counting function in general. Some interesting relationships among the counting functions of certain cases are established. The generating polynomial for the distribution of joint linear complexities is determined. The proofs use new methods that enable us to obtain results of great generality.

Construction Algorithms for Good Extensible Lattice Rules

Abstract: Extensible (polynomial) lattice rules have the property that the number N of points in the node set may be increased while retaining the existing points. It was shown by Hickernell and Niederreiter in a nonconstructive manner that there exist generating vectors for extensible integration lattices of excellent quality for N=b,b2,b3,…, where b is a given integer greater than 1. Similar results were proved by Niederreiter for polynomial lattices. In this paper we provide construction algorithms for good extensible lattice rules. We treat the classical as well as the polynomial case.

On the gowers norm of pseudorandom binary sequences

Abstract: We study the Gowers norm for periodic binary sequences and relate it to correlation measures for such sequences. The case of periodic binary sequences derived from inversive pseudorandom numbers is considered in detail.