Coding Theory and Cryptology
Eindhoven Institute for the Protection of Information
Department of Mathematics and Computer Science
Room HG 9.92
Technische Universiteit Eindhoven
P.O. Box 513
5600 MB Eindhoven
Netherlands

Phone: +31 (0) 40 247 4764
Fax.: +31 (0)40 243 5810

The easiest ways to reach me whereever I am:
e-mail:tanja@hyperelliptic.org

Seite auf deutsch

• Binary Edwards Curves; also have a look at the Slides from the Eurocrypt Rump-Session
• Explicit-Formulas Database
• Edwards coordinates
• EIPSI - Grand Opening April 21-22, 2008.
• The 12th Workshop on Elliptic Curve Cryptography (ECC 2008)We are organizing the next ECC in Utrecht, September 22-24, 2008.
  We plan to host a summer school on Elliptic Curve Cryptography the week before ECC.
• We are a node of ECRYPT - European Network of Excellence in Cryptology".
• CACE - Computer Aided Cryptography Engineering got funding in the 7th EU-Framework program.

• ASIACRYPT 2008
• PQCrypto 2008
• The 12th Workshop on Elliptic Curve Cryptography (ECC 2008) (Organizer)
• Pairing 2008
• 8th Central European Conference on Cryptography - Graz 2008
• The 13th Australasian Conference on Information Security and Privacy (ACISP 2008)
• AfricaCrypt 2008
• SHARCS'07 - Special-purpose Hardware for Attacking Cryptographic Systems (Program Co-Chair)
• 11th Workshop on Elliptic Curve Cryptography (ECC 2007)
• Tutorial on Elliptic and Hyperelliptic Curve Cryptography 2007 (Organizer)
• CRYPTO 2007
• The 14th Annual Workshop on Selected Areas in Cryptography
• CNIS 2007
• SECRYPT 2007
• Pairing2007
• International Workshop on the Arithmetic of Finite Fields (WAIFI 2007)
• SPEED - Software Performance Enhancement for Encryption and Decryption (Organizer)
• 2th Australasian Conference on Information Security and Privacy
• INDOCRYPT 2006 (Program Co-Chair)
• ASIACRYPT2006
• The 10th Workshop on Elliptic Curve Cryptography (ECC 2006)
• Summer School on Elliptic and Hyperelliptic Curve Cryptography (Organizer)
• SECRYPT 2006
• PQCrypto 2006: International Workshop on Post-Quantum Cryptography
• SHARCS'06 - Special-purpose Hardware for Attacking Cryptographic Systems (Program Co-Chair)
• ACISP 2006
• Indocrypt 2005
• Asiacrypt 2005
• 4th International Conference on CRYPTOLOGY AND NETWORK SECURITY
• The 9th Workshop on Elliptic Curve Cryptography (ECC 2005) (Organizer)
• FICS-Summer School on "Elliptic Curves in Cryptography" (Organizer)
• Cryptologie et Algorithmique En Normandie (CAEN'05)
• EIDMA Mini-Course "Computational Methods in Public Key Cryptology" (Co-Organizer)
• Pairings in Cryptography
• Applied Cryptography and Network Security 2005
• Information Security & Hiding (ISH '05)
• SHARCS'05 - Special-purpose Hardware for Attacking Cryptographic Systems (Program Co-Chair)
• WCC - Workshop on Coding and Cryptography
• Cryptographers' Track of the RSA Conference, CT-RSA 2005
• Indocrypt 2004
• Oberwolfach Seminar: Arithmetic Geometry and Public Key Cryptography (Co-Organizer)
• The 8th Workshop on Elliptic Curve Cryptography (ECC 2004) (Co-Organizer)
• ECRYPT Summer School on "Elliptic Curves in Cryptography" (Organizer)
• SCN 2004, the fourth edition of the Conference on Security in Communication Networks '04
• CHES 2004

• CACE Computer Aided Cryptography Engineering
• ECRYPT Network of Excellence in Cryptology
• STORK Strategic Roadmap for Crypto
• AREHCC - Advanced Research on Elliptic and Hyperelliptic Curve Cryptography

• Factoring polynomials over arbitrary finite fields,(with A. Winterhof) Theoretical Computer Science 234 (2000), 301-308.
• Algorithms for factoring polynomials over arbitrary finite fields, (with A. Winterhof), Proceedings of the Fifth International Conference on Finite Fields and Applications 2000, (Springer 2001), 319-328.
• Speeding up the Arithmetic on Hyperelliptic Koblitz Curves of Genus 2, (with C. Günther and A. Stein) Selected Areas in Cryptography, SAC 2001, Lecture Notes in Computer Science 2012, (Springer 2001), 106-117.
• Interpolation of the Discrete Logarithm in Finite Fields by Boolean Functions, (with A. Winterhof) in: Electronic Notes in Discrete Mathematics 6 as Proocedings of: International Workshop on Coding and Cryptography (WCC 2001).
• Incomplete character sums over finite fields and their applications to the interpolation of the discrete logarithm by Boolean functions, (with A. Winterhof) Acta Arithmetica 101 (2002), 223-229.
• Linear Complexity of the Discrete Logarithm, (with S. Konyagin and I. Shparlinski), Designs, Codes and Cryptography 28 (2003), 135-146.
• Interpolation of the Discrete Logarithm in F_q by Boolean Functions and by Polynomials in Several Variables Modulo a Divisor of q-1, (with A. Winterhof), Discrete Applied Mathematics 128/1 (2003), 193 - 206.
• Polynomial Interpolation of the Elliptic Curve and XTR Discrete Logarithm, (with A. Winterhof) Proceedings of the 8th Annual International Computing and Combinatorics Conference (COCOON'02) (Singapore, 2002), LNCS 2387, 137-143.
• Koblitz Curve Cryptosystems, STJournal of System Research 4 (2003), 29-36.
• Improved Algorithms for Efficient Arithmetic on Elliptic Curve using Fast Endomorphisms, (with M. Ciet, F. Sica and J.-J. Quisquater ) Proceedings of Eurocrypt 2003, LNCS 2656, 388-400.
• Interpolation of the Elliptic-Curve Diffie-Hellman Mapping, (with A. Winterhof), Proceedings of AAECC 2003, LNCS 2643, 51-60.
• Trace-Zero Subvariety for Cryptosystems, to appear in Journal of the Ramanujan Mathematical Society.
• On Using Expansions to the Base of $-2$, (with R. Avanzi, G. Frey, and R. Oyono), to appear in International Journal on Computer Mathematics vol 81 no 4, 2004.
• Montgomery Addition for Genus Two Curves, to appear in Proceedings of ANTS 2004.
• Certain exponential sums and random walks on elliptic curves, (with I. Shparlinski), submitted.
• Formulae for Arithmetic on Genus 2 Hyperelliptic Curves, to appear in J. AAECC.
• Mathematical Background of Public Key Cryptography, (with G. Frey ), see also Preprint 10/2003 of the IEM, Essen.
• Koblitz Curve Cryptosystems, to appear in FFA.
• Collisions in Fast Generation of Ideal Classes and Points on Hyperelliptic and Elliptic Curves, (with I. Shparlinski), to appear in J. AAECC.
• tbc.

• Fast arithmetic on hyperelliptic Koblitz curves ,
  at the MAGiC conference in Urbana/Champaign
  Abstract
  M1.ps M2.ps M3.ps Slides (3 files, middle one containing picture of Diffie-Hellman key-exchange)
  
  
• Efficient arithmetic on (hyper-)elliptic curves over finite fields,
  talk at UCL Crypto Group - Seminar Series
  Slides
  
  
• Efficient arithmetic on (hyper-)elliptic curves over finite fields,
  talk at 2003 International Symposium on Next Generation Cryptography and Related Mathematics, Japan
  Slides
  
  
• Efficient arithmetic on (hyper-)elliptic curves over finite fields,
  talk at Computational Aspects of Algebraic Curves, and Cryptography, Gainesville
  Slides
  
  
• Efficient arithmetic on (hyper-)elliptic curves over finite fields,
  talk at Cryptography Seminar in Rennes
  Slides
  
  
• Improved Algorithms for Efficient Arithmetic on Elliptic Curve using Fast Endomorphisms,
  talk given by Francesco Sica at Eurocrypt 2003
  Slides in pdf
  
  
• Efficient arithmetic on (hyper-) elliptic curves over finite fields,
  talk at ECC 2003
  Slides
  
  
• Cryptographic Applications of Trace Zero Varieties,
  talk at Mathematics of Discrete Logarithms, Essen
  Slides
  
  
• Cryptographic Applications of Trace Zero Varieties,
  talk at Dagsthul Seminar -- Algorithms and Number Theory
  Slides
  
  
• Mathematical Countermeasures Against Side-Channel Attacks on ECC/HECC,
  talk at YACC 2004
  Slides
  
  
• Introduction to Side-Channel Attacks on elliptic and hyperelliptic curves,
  talk at ANTS VI 2004
  Slides
  
  
• Montgomery Addition for Genus Two Curves,
  talk at ANTS VI 2004
  Slides
  
  
• Mathematical Countermeasures against Side-Channel Attacks on Elliptic and Hyperelliptic Curves,
  talk at WARTACRYPT '04
  Slides
  
  
• Pseudorandom Number Generators Based on Elliptic Curves,
  talk at Number Theoretic Algorithms and Related Topics
  Slides
  
  
• Hyperelliptic curves in cryptography,
  talk at the "Seminar on zeta functions'' at the Technical University Tokyo
  Slides
  
  
• Efficient arithmetic on (hyper-)elliptic curves over finite fields,
  talk at the ``COSIC Seminar'', KU Leuven
  Slides
  
  
• Curve Cryptography - suitable primitives for embedded device ,
  talk at Cryptologie et Algorithmique En Normandie (CAEN'05)
  Slides
  
  
• Pairings on ordinary hyperelliptic curves,
  talk at Pairings in Cryptography
  Slides
  
  
• Arithmetic on Binary Genus $2$ Curves Suitable for Small Devices,
  talk at Workshop on RFID and Lightweight Crypto
  Slides
  
  
• Arithmetic of hyperelliptic curves over finite fields,
  talk at Discrete Mathematics Seminar, University of Calgary
  Slides
  
  
• Efficient computation of pairings on non-supersingular hyperelliptic curves,
  talk at Number Theory Inspired by Cryptography, Banff
  Slides
  
  
• Efficient computation of pairings on non-supersingular hyperelliptic curves,
  talk at Algebraic Methods in Cryptography, Bochum
  Slides
  
  
• Cryptographic Applications of Trace Zero Varieties,
  seminar talk at Cryptology Research Group at the Indian Statistical Institute, Kolkata
  Slides
  
  
• Pairings in Cryptography ,
  tutorial at ASIACRYPT 2005
  Slides
  
  
• Distribution of Some Sequences of Points on Elliptic Curves ,
  talk at AMS Sectional Meeting Program by Special Session, Special Session on Number Theory
  Slides
  
  
• Arithmetic of hyperelliptic curves over finite fields , part of lecture at
  Summer School on "Computational Number Theory and Applications to Cryptography"
  Slides
  
  
• Pairing Based Cryptography , part of lecture at
  Summer School on "Computational Number Theory and Applications to Cryptography"
  Slides
  
  
• Analysis of pseudo-random number generators based on elliptic curves,
  talk at 31st Australasian Conference on Combinatorial Mathematics & Combinatorial Computing(ACCMCC)
  Slides
  
  
• Fast bilinear maps from the Tate-Lichtenbaum pairing on hyperelliptic curves,
  talk at ANTS VII, Berlin
  Slides
  
  
• Efficient arithmetic on (hyper-)elliptic curves over finite fields,
  talk at 2006 Workshop on Cryptography and Related Mathematics
  Slides
  
  
• Hyperelliptic Curves,
  talk at Information Security Summer School (ISSS) 2006. Taiwan.
  Slides
  
  
• Efficient arithmetic on hyperelliptic curves over finite fields,
  talk at Information Security Summer School (ISSS) 2006. Taiwan.
  Slides
  
  
• Pairing Based Cryptography,
  talk at Information Security Summer School (ISSS) 2006. Taiwan.
  Slides
  
  
• Public Key Cryptography - Performance Comparison and Benchmarking ,
  keynote at Simpósio Brasileiro em Segurança da Informação e de Sistemas Computacionais (SBSeg)
  Slides
  
  
• Index Calculus in Finite Fields & Hyperelliptic Curves ,
  tutorial at WCAP 2006 - III Workshop on Cryptographic Algorithms and Protocols
  Slides
  
  
• Efficient arithmetic on hyperelliptic curves over finite fields & Pairings,
  tutorial at WCAP 2006 - III Workshop on Cryptographic Algorithms and Protocols
  Slides
  
  
• Elliptic vs. hyperelliptic, part 2,
  talk at ECC 2006
  Slides and Slides in ps.gz
  Part 1 of the fight was excecuted by Daniel J. Bernstein, his slides can be found here.
  
  
• Open Problems in Pairings,
  talk at Number Theory and Cryptography - Open Problems
  Slides
  
  
• Tanja Lange,
  on the occasion of presentating the new employees of the faculty for mathematics and computer science of the Technische Universiteit Eindhoven
  Slides (pdf)
  
  
• Cryptographic applications of curves over finite fields,
  talk at General Mathematical Colloquium Utrecht
  Slides
  
  
• Unified addition formulae for elliptic curves,
  talk at AMS Special Session on Mathematical Aspects of Cryptography, 2007 Spring AMS Eastern Section Meeting
  Slides
  
  
• Elliptic vs. hyperelliptic, part 2,
  talk at EIDMA Seminar Combinatorial Theory
  Slides
  
  
• Mathematical Background of Pairings,
  talk at ECRYPT PhD Summer School on Emerging Topics in Cryptographic Design and Cryptanalysis
  Slides
  
  
• Fast scalar multiplication on elliptic curves,
  talk at Conference on Algorithmic Number Theory
  Slides
  
  
• Elliptic vs. hyperelliptic, part 3 - Elliptic Strikes Back,
  talk at Eurocrypt 07 Rump Session
  Slides
  
  
• Side-channel attacks and countermeasures for curve based cryptography,
  talk at Quo vadis cryptology ? - Threat of Side-Channel Attacks
  Slides in ps
  Slides in pdf
  
  
• Fast scalar multiplication on elliptic curves,
  talk at 8th International Conference on Finite Fields and Applications
  Slides
  
  
• Elliptic vs. Hyperelliptic, part 3: Elliptic strikes back,
  talk at 11th Workshop on Elliptic Curve Cryptography 2007
  Slides for my half
  Slides for Dan Bernstein's half
  
  
• The EFD thing,
  presentation at the rump session of CHES 2007 given jointly with Dan Bernstein
  Slides
  
  
• Edwards Curves for Cyptography,
  presentation at EIDMA/DIAMANT Cryptography Working Group
  Slides
  
  
• Edwards coordinates for elliptic curves, part 1,
  presentation at Explicit Methods in Number Theory In honour of Henri Cohen
  Slides
  Part 2 was given by Dan Bernstein
  Dan's slides
  
  
• Edwards Coordinates for Elliptic Curves, part 1 ,
  presentation at SAGE Days 6: Cryptology, Number theory, and Arithmetic Geometry
  Slides
  Part 2 was given by Dan Bernstein
  Dan's slides
  
  
• Edwards Curves for Cryptography,
  presentation at Kolloquium über Kombinatorik
  Slides
  
  
• Faster Addition and Doubling on Elliptic Curves,
  joint presentation with Dan Bernstein at ASIACRYPT 2007
  Slides
  
  
• Edwards Coordinates,
  presentation at Applied Algebra, Algebraic Algorithms, and Error Correcting Codes (AAECC-17)
  Slides
  
  
• The power of mathematics to protect data and to break data protection,
  presentation at Research day at TU/e
  Slides
  
  
• Revisiting pairing based group key exchange,
  presentation at Financial Cryptography and Data Security 2008
  Slides
  
  
• Binary Edwards Curves,
  presentation at the Eurocrypt 2008 Rump Session
  Slides
  
  
• Faster arithmetic on elliptic curves -- blessing to ECC, harm to RSA,
  presentation at EIPSI Grand Opening
  Slides
  
  
• Binary Edwards Curves,
  presentation at Seminario Matematico, Universidad Autonoma Madrid
  Slides
  
  

• 3rd ECRYPT PhD SUMMER SCHOOL "Advanced Topics in Cryptography"
• Minicours on Edwards curves; material
• Tutorial on Elliptic and Hyperelliptic Curve Cryptography 2007
• ECRYPT PhD SUMMER SCHOOL "Emerging Topics in Cryptographic Design and Cryptanalysis" Tutorial on Mathematical Background of Pairings
• Summer School on Elliptic and Hyperelliptic Curve Cryptography
• WCAP 2006 - III Workshop on Cryptographic Algorithms and Protocols several talks (see above for slides)
• Information Security Summer School (ISSS) 2006. Taiwan several talks (see above for slides)
• Summer School on "Computational Number Theory and Applications to Cryptography" several talks (see above for slides)
• Advanced Cryptography at DTU
  
• Tutorial on Pairings at ASIACRYPT 2005 (see above for slides)
• Applied Cryptography at DTU (02232) together with Christian Damsgaard Jensen
• FICS-Summer School on "Elliptic Curves in Cryptography"
• Oberwolfach Seminar: Arithmetic Geometry and Public Key Cryptography
• ECRYPT Summer School on "Elliptic Curves in Cryptography"
  
  
  
• Older courses are linked from my old homepage in Bochum.
• You find the homepage of the Mathekids Bochum here (only in german).

Hyperelliptic Curves allowing fast Arithmetic

I was a member of the Graduate School on "Cryptography". I organized the Workshop on applied cryptography in Bedlewo, Poland, in 2001.

Old homepage containing cours material (german) for courses given in Braunschweig.

Homepage der Mathekids (Braunschweig), only in german.

e-mail tanja@hyperelliptic.org