Class notes for my spring 2006 course Advanced Cryptography are available now.

This page is no longer updated. Please visit http://www.hyperelliptic.org/tanja/.

Room 152
Phone: +45 4525 3007
Voice mail: +45 3696 7248
Fax.: +45 4588 1399
e-mail:tanja@hyperelliptic.org

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After the big success last year, the The 9th Workshop on Elliptic Curve Cryptography (ECC 2005) is also apreceeded by a Summer School on Elliptic Curve Cryptography.

• CHES 2004
• SCN 2004, the fourth edition of the Conference on Security in Communication Networks '04
• The 8th Workshop on Elliptic Curve Cryptography (ECC 2004)
• Indocrypt 2004
• Cryptographers' Track of the RSA Conference, CT-RSA 2005
• WCC - Workshop on Coding and Cryptography
• SHARCS - Special-purpose Hardware for Attacking Cryptographic Systems
• The 9th Workshop on Elliptic Curve Cryptography (ECC 2005)
• PQCrypto 2006: International Workshop on Post-Quantum 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
  
  

• This term I'm teaching Advanced Cryptography at DTU. Class notes are available now.
  
• 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