Lecture Notes in Computer Science 5203 Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Alfred Kobsa University of California, Irvine, CA, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany
Solomon W. Golomb Matthew G. Parker Alexander Pott Arne Winterhof (Eds.) Sequences and Their Applications SETA 2008 5th International Conference Lexington, KY, USA, September 14-18, 2008 Proceedings 13
Volume Editors Solomon W. Golomb University of Southern California USC Viterbi School of Engineering Los Angeles, CA 90089-2565, USA E-mail: sgolomb@usc.edu Matthew G. Parker University of Bergen The Selmer Center, Department of Informatics 5020 Bergen, Norway E-mail: matthew.parker@ii.uib.no Alexander Pott Otto-von-Guericke-University Institute for Algebra and Geometry 39016 Magdeburg, Germany E-mail: alexander.pott@ovgu.de Arne Winterhof Johann Radon Institute for Computational and Applied Mathematics (RICAM) Austrian Academy of Sciences 4040 Linz, Austria E-mail: arne.winterhof@oeaw.ac.at Library of Congress Control Number: 2008933733 CR Subject Classification (1998): G.2, I.1, F.2, E.4, E.3 LNCS Sublibrary: SL 1 Theoretical Computer Science and General Issues ISSN 0302-9743 ISBN-10 3-540-85911-X Springer Berlin Heidelberg New York ISBN-13 978-3-540-85911-6 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com Springer-Verlag Berlin Heidelberg 2008 Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper SPIN: 12511037 06/3180 543210
Preface This volume contains the refereed proceedings papers of the Fifth International Conference on Sequences and their Applications (SETA 2008), held in Lexington, Kentucky (USA), September 14 18, 2008. The conference SETA is well established in the mathematics and computer science community. Topics of SETA include Randomness of sequences Correlation (periodic and aperiodic types) and combinatorial aspects of sequences (difference sets) Sequences with applications in coding theory and cryptography Sequences over finite fields/rings/function fields Linear and nonlinear feedback shift register sequences Sequences for radar distance ranging, synchronization, identification, and hardware testing Sequences for wireless communication Pseudorandom sequence generators Correlation and transformation of Boolean functions Multidimensional sequences and their correlation properties Linear and nonlinear complexity of sequences. This year s proceedings contain 32 contributed papers. All papers have been thoroughly refereed by at least two referees. Most of the refereeing was done by members of the program committee. We thank all of them for their help. We are also grateful to Serdar Boztaş, Nina Brandstätter, Nicolas Courtois, Fangwei Fu, Honggang Hu, Alexander Kholosha, Emmanuel Prouff, Martin Rötteler, Ayineedi Venkateswarlu and Bo-Yin Yang for their assistance in the reviewing process. In addition to the contributed papers, we had four invited lectures given by Claude Carlet (University of Paris 8, France), Pierre L Ecuyer (Université de Montréal, Canada), Guang Gong (University of Waterloo, Canada) and Robert McEliece (California Institute of Technology, USA). You find papers based on these invited talks in this volume. We would like to thank Ramakanth Kavuluru, Diane Mier, Paul Linton and Mark Goresky for their help in organizing this conference. We also thank Faruk Göloğlu and Tan Yin who helped to prepare this proceedings volume. July 2008 Solomon Golomb Matthew G. Parker Alexander Pott Arne Winterhof
Organization General Chair Andrew Klapper University of Kentucky, USA Program Co-chairs Solomon Golomb Alexander Pott University of Southern California, USA Otto-von-Guericke-University Magdeburg, Germany Conference Proceedings Co-editors Solomon Golomb Matthew G. Parker Alexander Pott Arne Winterhof University of Southern California, USA University of Bergen, Norway Otto-von-Guericke-University Magdeburg, Germany Austrian Academy of Sciences, Austria Program Committee K.T. Arasu Wright State University, USA Claude Carlet INRIA and University of Paris 8, France Pascale Charpin INRIA, France Habong Chung Hongik University, Korea Cunsheng Ding The Hong Kong University of Science and Technology, China Tuvi Etzion Technion Israel Institute of Technology, Israel Pingzhi Fan Southwest Jiaotong University, China Harold Fredricksen Naval Postgraduate School, USA Guang Gong University of Waterloo, Canada Mark Goresky Institute for Advanced Study, USA Tor Helleseth University of Bergen, Norway Kathryn Horadam RMIT, Australia Tom Høholdt Technical University of Denmark, Denmark Thomas Johansson Lunds Universitet, Sweden P. Vijay Kumar Indian Institute of Science, India Gohar Kyureghyan Otto-von-Guericke-University Magdeburg, Germany Wilfried Meidl Sabanci University, Turkey Oscar Moreno University of Puerto Rico, Puerto Rico
VIII Organization Jong-Seon No Udaya Parampalli Matthew G. Parker Bernhard Schmidt Hong-Yeop Song Arne Winterhof Kyeongcheol Yang Amr Youssef Seoul National University, Korea University of Melbourne, Australia University of Bergen, Norway Nanyang Technological University, Singapore Yonsei University, Korea Austrian Academy of Sciences, Austria Pohang University of Science and Technology, Korea Concordia University, Canada Sponsoring Institutions The University of Kentucky College of Engineering
Table of Contents Probabilistic Methods and Randomness Properties of Sequences Comparison of Point Sets and Sequences for Quasi-Monte Carlo and for Random Number Generation(Invited Paper)... 1 Pierre L Ecuyer On Independence and Sensitivity of Statistical Randomness Tests... 18 Meltem Sönmez Turan, Ali Doğanaksoy, and Serdar Boztaş New Distinguishers Based on Random Mappings against Stream Ciphers... 30 Meltem Sönmez Turan, Çağdaş Çalık, Nurdan Buz Saran, and Ali Doğanaksoy A Probabilistic Approach on Estimating the Number of Modular Sonar Sequences... 42 Ki-Hyeon Park and Hong-Yeop Song A Study on the Pseudorandom Properties of Sequences Generated Via the Additive Order... 51 Honggang Hu and Guang Gong On the Average Distribution of Power Residues and Primitive Elements in Inversive and Nonlinear Recurring Sequences... 60 Ayça Çeşmelioğlu and Arne Winterhof Correlation Some Results on the Arithmetic Correlation of Sequences (Extended Abstract)... 71 Mark Goresky and Andrew Klapper A Class of Nonbinary Codes and Sequence Families... 81 Xiangyong Zeng, Nian Li, and Lei Hu Results on the Crosscorrelation and Autocorrelation of Sequences... 95 Faruk Göloğlu and Alexander Pott m-sequences of Lengths 2 2k 1and2 k 1withatMostFour-Valued Cross Correlation... 106 Tor Helleseth and Alexander Kholosha
X Table of Contents On the Correlation Distribution of Kerdock Sequences... 121 Xiaohu Tang, Tor Helleseth, and Aina Johansen Two New Families of Low-Correlation Interleaved QAM Sequences... 130 Gagan Garg, P. Vijay Kumar, and C.E. Veni Madhavan Combinatorial and Algebraic Foundations The Combinatorics of Differentiation (Invited Paper)... 142 Anna S. Bertiger, Robert J. McEliece, and Sarah Sweatlock Group Representation Design of Digital Signals and Sequences... 153 Shamgar Gurevich, Ronny Hadani, and Nir Sochen Projective de Bruijn Sequences... 167 Yuki Ohtsuka, Makoto Matsumoto, and Mariko Hagita Multiplicative Character Sums of Recurring Sequences with Rédei Functions... 175 Domingo Gomez and Arne Winterhof On the Connection between Kloosterman Sums and Elliptic Curves... 182 Petr Lisoněk A Class of Optimal Frequency Hopping Sequences Based upon the Theory of Power Residues... 188 Daiyuan Peng, Tu Peng, Xiaohu Tang, and Xianhua Niu Security Aspects of Sequences Sequences, DFT and Resistance against Fast Algebraic Attacks (Invited Paper)... 197 Guang Gong Expected π-adic Security Measures of Sequences (Extended Abstract)... 219 Andrew Klapper Distance-Avoiding Sequences for Extremely Low-Bandwidth Authentication... 230 Michael J. Collins and Scott Mitchell On the Number of Linearly Independent Equations Generated by XL... 239 Sondre Rønjom and Håvard Raddum 2 n -Periodic Binary Sequences with Fixed k-error Linear Complexity for k =2or3... 252 Ramakanth Kavuluru
Table of Contents XI Generalized Joint Linear Complexity of Linear Recurring Multisequences... 266 Wilfried Meidl and Ferruh Özbudak Algorithms A Lattice-Based Minimal Partial Realization Algorithm... 278 Li-Ping Wang A Fast Jump Ahead Algorithm for Linear Recurrences in a Polynomial Space... 290 Hiroshi Haramoto, Makoto Matsumoto, and Pierre L Ecuyer Parallel Generation of l-sequences... 299 Cédric Lauradoux and Andrea Röck Correlation of Sequences over Rings Design of M-Ary Low Correlation Zone Sequence Sets by Interleaving... 313 Jin-Ho Chung and Kyeongcheol Yang The Peak to Sidelobe Level of the Most Significant Bit of Trace Codes over Galois Rings... 322 Patrick Solé and Dimitrii Zinoviev On Partial Correlations of Various Z 4 Sequence Families... 332 Parampalli Udaya and Serdar Boztaş Nonlinear Functions over Finite Fields On the Higher Order Nonlinearities of Boolean Functions and S-Boxes, and Their Generalizations (Invited Paper)... 345 Claude Carlet On a Class of Permutation Polynomials over F 2 n... 368 Pascale Charpin and Gohar M. Kyureghyan On 3-to-1 and Power APN S-Boxes... 377 Deepak Kumar Dalai Negabent Functions in the Maiorana McFarland Class... 390 Kai-Uwe Schmidt, Matthew G. Parker, and Alexander Pott New Perfect Nonlinear Multinomials over F p 2k for Any Odd Prime p... 403 Lilya Budaghyan and Tor Helleseth
XII Table of Contents A New Tool for Assurance of Perfect Nonlinearity... 415 Nuray At and Stephen D. Cohen Author Index... 421