Arithmetic of Finite Fields: 6th International Workshop, WAIFI 2016, Ghent, Belgium, July 13-15, 2016, Revised Selected Papers

274 Pages·2016·5.01 MB·English

by  Sylvain Duquesne

Sylvain Duquesne
Svetla Petkova-Nikova (Eds.)
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Arithmetic of Finite Fields
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6th International Workshop, WAIFI 2016
Ghent, Belgium, July 13–15, 2016
Revised Selected Papers
123
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Sylvain Duquesne Svetla Petkova-Nikova (Eds.)
(cid:129)
Arithmetic of Finite Fields
6th International Workshop, WAIFI 2016
–
Ghent, Belgium, July 13 15, 2016
Revised Selected Papers
123
Editors
Sylvain Duquesne Svetla Petkova-Nikova
University of Rennes KULeuven
Rennes Leuven
France Belgium
ISSN 0302-9743 ISSN 1611-3349 (electronic)
Lecture Notesin Computer Science
ISBN 978-3-319-55226-2 ISBN978-3-319-55227-9 (eBook)
DOI 10.1007/978-3-319-55227-9
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Preface
These are the proceedings of WAIFI 2016, the 6th International Workshop on the
ArithmeticofFiniteFields,heldinGhent,Belgium,duringJuly13–15,2016.Thefive
previous editions of this workshop were held in Madrid, Spain (WAIFI 2007), Siena,
Italy (WAIFI 2008), Istanbul, Turkey (WAIFI 2010), Bochum, Germany (WAIFI
2012),andGebze,Turkey(WAIFI2014).Springerhaspublishedallpreviousvolumes
of the WAIFI proceedings in the LNCS series.
Since 2008, WAIFI has been held every even year, bringing together mathemati-
cians, computer scientists, engineers, and physicists who conduct research in different
areas offinite field arithmetic.
Theprogramconsistedofthreeinvitedtalksand17contributedpapers.Theinvited
speakerswereSwastikKopparty(RutgersUniversity,USA),SimeonBall (Universitat
Politècnica de Catalunya, Spain) and Razvan Barbulescu (CNRS, Paris 6 and 7,
France). The papers supporting the two last invited talks were also included in the
proceedings. The contributed talks were selected from 38 submissions, each of which
wasassignedtoatleastthree committeemembers orexternal reviewerschosen bythe
members. Additionally, the Program Committee had a significant online discussion
phaseforseveraldays.Threeadditionalpresentationsweremadeduringtheworkshop
but are not part of these proceedings.
WeareverygratefultothemembersoftheProgramCommitteefortheirdedication,
professionalism, and careful work with the review and selection process. We also
sincerely thank the external reviewers who contributed with their special expertise to
review papers for this workshop.
We deeply thank the general co-chairs, Vincent Rijmen and Leo Storme, for their
supportoftheProgramCommitteeandtheirhardworkinleadingtheoverallorganization
of the workshop helped by the Organizing Committee. Wewould also liketo sincerely
thank members of the Steering Committee of the workshop series for their constant
supportandencouragementinoureffortstocreateastimulatingscientificprogramleading
tothisvolume. Furthermore,wethank Jean-JacquesQuisquaterfor his valuablehelpin
publicityandwearealsoverygratefultoJoséLuisImañaandJandeBeulefordiligently
maintaining the workshop website. As with the previous volumes, Springer agreed to
publishtherevisedandexpandedversionsoftheWAIFI2016papersasanLNCSvolume.
WethankAlfredHoffmanandAnnaKramerfromSpringerformakingthispossible.
The submission and selection of papers were done using the EasyChair conference
managementsystem. Hence,thankyouEasyChair!Wewould alsoliketoacknowledge
theFoundationCompositioMathematicaandFWOforbeingsponsorsoftheworkshop.
Finally, but most importantly, we deeply thank all the authors who submitted their
papers to the workshop and the participants all over the world who chose to honor us
with their attendance.
February 2017 Sylvain Duquesne
Svetla Petkova-Nikova
Organization
Steering Committee
Berk Sunar Worcester Polytechnic Institute, USA
Anwar Hasan University of Waterloo, Canada
Çetin Kaya Koç University of California Santa Barbara, USA
Jean-Jacques Quisquater Université Catholique de Louvain, Belgium
Christof Paar Ruhr-Universität Bochum, Germany
Gustavo Sutter Autonomous University of Madrid, Spain
José Luis Imaña Complutense University of Madrid, Spain
Francisco CINVESTAV-IPN, Mexico
Rodriguez-Henriquez
Ferruh Ozbudak Middle East Technical University, Turkey
Sihem Mesnager University of Paris 8, France
Erkay Savaş Sabanci University, Turkey
Claude Carlet University of Paris 8, France
General Co-chairs
Vincent Rijmen KU Leuven, Belgium
Leo Storme Ghent University, Belgium
Local Organizing Committee
Daniele Bartoli Ghent University, Belgium
Wouter Castryck Ghent University, Belgium
Maarten De Boeck Ghent University, Belgium
John Sheekey Ghent University, Belgium
Leo Storme Ghent University, Belgium
Peter Vandendriessche Ghent University, Belgium
Geertrui Van de Voorde Ghent University, Belgium
Jan De Beule Vrije Universiteit Brussel, Belgium
Vincent Rijmen KU Leuven, Belgium
Bart Preneel KU Leuven, Belgium
Jan Tuitman KU Leuven, Belgium
Jean-Jacques Quisquater Université Catholique de Louvain, Belgium
Joost Vercruysse Université Libre de Bruxelles, Belgium
Program Co-chairs
Sylvain Duquesne University of Rennes 1, France
Svetla Petkova-Nikova KU Leuven, Belgium
VIII Organization
Publicity Chair
Jean-Jacques Quisquater Université Catholique de Louvain, Belgium
Program Committee
Tsonka Baicheva Bulgarian Academy of Sciences, Bulgaria
Jean-Claude Bajard University Pierre et Marie Curie, France
Josep Balasch KU Leuven, Belgium
Anne Canteaut Inria Rocquencourt, France
Claude Carlet University of Paris 8, France
Luca De Feo University of Versailles-Saint Quentin, France
Sylvain Duquesne University Rennes 1, France
Tor Helleseth University of Bergen, Norway
Sophie Huczynska University of St. Andrews, UK
Alexander Kholosha University of Bergen, Norway
Miroslav Knezevic KU Leuven and NXP Semiconductors, Belgium
Gohar Kyureghyan University of Magdeburg, Germany
Ivan Landzhev New Bulgarian University, Bulgaria
Gregor Leander Ruhr University Bochum, Germany
Sihem Mesnager University of Paris 8, France
Amir Moradi Ruhr University Bochum, Germany
Gary Mullen Penn State University, USA
Svetla Petkova-Nikova KU Leuven, Belgium
Daniel Panario Carleton University, Canada
Ruud Pellikaan Technical University Eindhoven, The Netherlands
Alexander Pott Otto von Guericke University, Germany
Christophe Ritzenthaler University of Rennes 1, France
Leo Storme Ghent University, Belgium
Arnaud Tisserand CNRS, University of Rennes 1, France
Frederik Vercauteren KU Leuven, Belgium
Paul Zimmermann Inria Nancy - Grand Est, France
Additional Reviewers
Domingo Gomez University of Cantabria, Spain
Sujoy Sinha Roy KU Leuven, Belgium
Valentin Suder University of Versailles Saint-Quentin, France
Nicolas Estibals University of Rennes 1, France
Kanat Abdukhalikov United Arab Emirates University, UAE
Alina Ostafe University of New South Wales, Australia
Karim Bigou University of Brest, France
Wilfried Meidl Sabanci University, Turkey
Yi Lu University of Bergen, Norway
Omran Ahmadi Institute for Research in Fundamental Sciences, Iran
Zhixiong Chen Mercy College, USA
Organization IX
Wouter Castryck Ghent University, Belgium
Qiang Wang Carleton University, Canada
Aurore Guillevic Inria Nancy, Grand Est, France
Audrey Lucas University of Rennes 1, France
Ayoub Otmani University of Rouen, France
Ayça ÇeŞmelioglu Istanbul Kemerburgaz University, Turkey
Nicolas Sendrier Inria Paris, France
Gregoire Lecerf Ecole Polytechnique, France
Gabriel Gallin University of Rennes 1, France
Arthur Beckers KU Leuven, Belgium
Tobias Oder Ruhr-Universität Bochum, Germany
Contents
Invited Talk I
A Brief History of Pairings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Razvan Barbulescu
Elliptic Curves
Differential Addition on Binary Elliptic Curves. . . . . . . . . . . . . . . . . . . . . . 21
Reza Rezaeian Farashahi and Seyed Gholamhossein Hosseini
Adequate Elliptic Curves for Computing the Product of n Pairings . . . . . . . . 36
Loubna Ghammam and Emmanuel Fouotsa
On Pseudorandom Properties of Certain Sequences of Points
on Elliptic Curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
László Mérai
Applications
Linear Complexity and Expansion Complexity of Some Number
Theoretic Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Richard Hofer and Arne Winterhof
Irreducible Polynomials
On Sets of Irreducible Polynomials Closed by Composition. . . . . . . . . . . . . 77
Andrea Ferraguti, Giacomo Micheli, and Reto Schnyder
A Note on the Brawley-Carlitz Theorem on Irreducibility of Composed
Products of Polynomials over Finite Fields. . . . . . . . . . . . . . . . . . . . . . . . . 84
Akihiro Munemasa and Hiroko Nakamura
Invited Talk II
On Arcs and Quadrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Simeon Ball
Applications to Cryptography
A Generalised Successive Resultants Algorithm . . . . . . . . . . . . . . . . . . . . . 105
James H. Davenport, Christophe Petit, and Benjamin Pring