Peter Birkner

About me

I am a postdoctoral researcher in the Laboratoire PRiSM at Université de Versailles Saint-Quentin-en-Yvelines. My research interests lie in the area of elliptic-curve and hyperelliptic-curve cryptography, in particular efficient arithmetic in Jacobians of hyperelliptic curves with small genus. I am also working on integer factorisation with the elliptic-curve method (ECM) and on elliptic curves in Edwards and twisted Edwards form.




Publications

  • Peter Birkner and Nicolas Thériault: Efficient Halving for Genus 3 Curves over Binary Fields. In: Advances in Mathematics of Communications, vol. 4, no. 1, pp. 23-47, 2010. (Details).

    An extended version with more curve types is available at the Cryptology ePrint Archive, Report 2009/157. A set of Magma files containing the implementation of our halving formulas can be found here.

  • Daniel V. Bailey, Brian Baldwin, Lejla Batina, Daniel J. Bernstein, Peter Birkner, Joppe W. Bos, Gauthier van Damme, Giacomo de Meulenaer, Junfeng Fan, Tim Güneysu, Frank Gurkaynak, Thorsten Kleinjung, Tanja Lange, Nele Mentens, Christof Paar, Francesco Regazzoni, Peter Schwabe, Leif Uhsadel: The Certicom Challenges ECC2-X. In: Workshop record of SHARCS'09 - Special-purpose Hardware for Attacking Cryptographic Systems, 2009. (PDF), (ePrint)

  • Peter Birkner and Tanja Lange: Efficient Arithmetic on Binary Genus-2 Curves. In: Workshop record of the Western European Workshop on Research in Cryptology (WEWoRC), 2009. (PDF)

  • Peter Birkner and Nicolas Thériault: Faster Halvings in Genus 2. In: Selected Areas in Cryptography (SAC 2008), Lecture Notes in Computer Science, vol. 5381, pp. 1-17, Springer, 2008. (PDF), (DOI)

  • Daniel J. Bernstein, Peter Birkner, Marc Joye, Tanja Lange and Christiane Peters: Twisted Edwards Curves. In: Progress in Cryptology – AFRICACRYPT 2008, Lecture Notes in Computer Science, vol. 5023, pp. 389-405, Springer, 2008. (PDF), (DOI)

  • Daniel J. Bernstein, Peter Birkner, Tanja Lange and Christiane Peters: Optimizing Double-Base Elliptic-Curve Single-Scalar Multiplication. In: Progress in Cryptology - INDOCRYPT 2007, Lecture Notes in Computer Science, vol. 4859, pp. 167-182, Springer, 2007. (PDF), (DOI)

  • Peter Birkner: Halbierungen von Divisorklassen in der Kryptographie. In: INFORMATIK 2007, Lecture Notes in Informatics, vol. P-110/2, pp. 189-194, Gesellschaft für Informatik, 2007. (PDF), (Proceedings)

  • Peter Birkner: Efficient Divisor Class Halving on Genus Two Curves. In: Selected Areas in Cryptography (SAC 2006), Lecture Notes in Computer Science, vol. 4356, pp. 317-326, Springer, 2007. (PDF), (DOI)

Preprints, Technical Reports, etc.

  • Daniel V. Bailey, Lejla Batina, Daniel J. Bernstein, Peter Birkner, Joppe W. Bos, Hsieh-Chung Chen, Chen-Mou Cheng, Gauthier Van Damme, Giacomo de Meulenaer, Luis Julian Dominguez Perez, Junfeng Fan, Tim Gueneysu, Frank Gurkaynak, Tanja Lange, Nele Mentens, Ruben Niederhagen, Christof Paar, Francesco Regazzoni, Peter Schwabe, Leif Uhsadel, Anthony Van Herrewege and Bo-Yin Yang: Breaking ECC2K-130. Cryptology ePrint Archive, Report 2009/541. (PDF), (ePrint)

  • Daniel J. Bernstein, Peter Birkner, Tanja Lange and Christiane Peters: ECM using Edwards Curves. Cryptology ePrint Archive, Report 2008/016. (PDF), (ePrint), (Good curves for ECM)



Presentations and Talks

2010

  • Edwards Curves and the ECM Factorisation Method. Seminar at Université de Versailles Saint-Quentin-en-Yvelines, France, 14th January 2010. (Slides)

2009

  • Edwards Curves and the ECM Factorisation Method. Seminar at Institute for Applied Information Processing and Communications (IAIK), Technische Universität Graz, Austria, 11th November 2009. (Slides)

  • Edwards Curves and the ECM Factorisation Method. Zahlentheoretisches Kolloquium, Institut für Mathematik A, Technische Universität Graz, Austria, 6th November 2009. (Slides)

  • Efficient Arithmetic on Binary Genus-2 Curves. Western European Workshop on Research in Cryptology (WEWoRC 2009), Graz, Austria, 9th July 2009. (Slides)

  • Efficient Arithmetic on Low-Genus Curves. Université de Versailles Saint-Quentin-en-Yvelines, France, 17th June 2009. (Slides)

  • Edwards Curves and the ECM Factorisation Method. Oberseminar Computational Mathematics, Universität Kassel, Germany, 26th May 2009. (Slides), (Seminar)

  • Edwards Curves and the ECM Factorisation Method. Fields Cryptography Retrospective Meeting, Fields Institute, Toronto, Canada, 12th May 2009. (Slides), (Workshop)

  • Edwards Curves and the ECM Factorisation Method. Oberseminar Algebra/Geometrie, Carl von Ossietzky Universität Oldenburg, Germany, 21st April 2009. (Slides), (Seminar)

2008

  • Edwards Curves and the ECM Factorisation Method. Seminar Codierungstheorie und Kryptographie, Universität Zürich, Switzerland, 29th October 2008. (Slides), (Seminar)

  • Edwards Curves and the ECM Factorisation Method. CADO workshop on Integer Factorization, Centre de recherche INRIA Nancy Grand-Est, France, 7th October 2008. (Slides), (Workshop)

  • Edwards Curves and the ECM Factorisation Method. The 12th Workshop on Elliptic Curve Cryptography (ECC 2008), Utrecht, Netherlands, 22nd September 2008. (Slides), (Workshop)

  • The Group Structure of Elliptic Curves. EIPSI Seminar, Technische Universiteit Eindhoven, Netherlands, 2nd July 2008. (Slides)

  • Edwards Curves and the ECM Factorisation Method. EIDMA Cryptography Working Group, Utrecht, Netherlands, 15th February 2008. (Slides)

2007

  • Edwards Curves for ECM. INRIA Seminar, Centre de recherche INRIA Nancy Grand-Est, France, 23rd November 2007.

  • Halbierungen von Divisorklassen in der Kryptographie.  Workshop “Kryptologie in Theorie und Praxis” (37. Jahrestagung der Gesellschaft für Informatik), Universität Bremen, Germany, 27th September 2007. (Slides)

  • Divisor Class Halving on Hyperelliptic Curves. EIDMA Seminar Combinatorial Theory, Technische Universiteit Eindhoven, Netherlands, 7th March 2007. (Slides)

2006

  • Divisor Class Halving on Hyperelliptic Curves. Elliptic Curve Symposium, Mount Allison University, Sackville, Canada, 24th November 2006. (Slides), (Workshop)

  • Divisor Class Halving on Hyperelliptic Curves. Cryptography Seminar, University of Waterloo, Canada, 18th October 2006. (Slides)

  • Efficient Divisor Class Halving on Genus Two Curves. SAC 2006 - The 13th Annual Workshop on Selected Areas in Cryptography, Concordia University, Montreal, Canada, 18th August 2006. (Slides), (SAC 2006)



Teaching

2009

  • Course on Selected Topics in Cryptography - Introduction to Elliptic Curves. Institute for Analysis and Computational Number Theory (Math A), Graz University of Technology, Austria, winter term 2009. (Details)

2008

  • Lecture on Hyperelliptic Curves. Summer School on Elliptic and Hyperelliptic Curve Cryptography, Technische Universiteit Eindhoven, Netherlands, 18th September 2008. (Slides), (Summer School)

  • Lecture on Elliptic Curves over Q. Summer School on Elliptic and Hyperelliptic Curve Cryptography, Technische Universiteit Eindhoven, Netherlands, 16th September 2008. (Slides), (Summer School)

  • Lecture on Edwards Curves. 3rd ECRYPT Summer School, Crete, Greece, 12th May 2008. (Slides)

2007

  • Lecture on Efficient Arithmetic on Elliptic and Hyperelliptic Curves. Tutorial on Elliptic and Hyperelliptic Curve Cryptography, Claude Shannon Institute, University College Dublin, Ireland, 4th September 2007. (Slides), (Tutorial)

2006

  • Lecture on Scalar Multiplication and Addition Chains. Summer School on Elliptic and Hyperelliptic Curve Cryptography, Fields Institute, Toronto, Canada, 11th September 2006. (Slides)



Theses

  • Efficient Arithmetic on Low-Genus Curves, PhD thesis, Technische Universiteit Eindhoven, Netherlands, 2009. (PDF)

  • Über die Bestimmung von Galoisgruppen (german), Diploma thesis, Universität Paderborn, Germany, 2004. (PDF)



Contact Information

Dr. Peter Birkner
Laboratoire PRiSM
Université de Versailles Saint-Quentin-en-Yvelines (Show location in Google Maps)
45 avenue des Etats-Unis
78035 Versailles Cedex
France

Room: 404 (Descartes building)
Email: pbirkner (at) fastmail.fm
Phone: +33 (0) 1 39 25 42 76





(Private)