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

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

Am einfachsten bin ich per email erreichbar:
e-mail:tanja@hyperelliptic.org

English version

• Binary Edwards Curves; siehe auch die Folien von der Eurocrypt Rump-Session und die Folien unseres Vortrags in Madrid.
• Explicit-Formulas Database
• Edwards coordinates
• EIPSI - Grand Opening April 21-22, 2008.
• DIAMANT-Summer School on Elliptic and Hyperelliptic Curve Cryptography 22-24 September 2008 in Eindhoven.
• The 12th Workshop on Elliptic Curve Cryptography (ECC 2008) Wir richten die nächste ECC in Utrecht aus und zwar 22.-24.09. 2008.
• Wir sind ein Knoten von ECRYPT - European Network of Excellence in Cryptology".
• CACE - Computer Aided Cryptography Engineering wird im 7. EU-Framework program gefördert.

• Pairing 2009
• Indocrypt 2008
• 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

• Peter Birkner
• Gaetan Bisson
• Michael Naehrig
• Christiane Peters
• Reza Rezaeian Farashahi
• Peter Schwabe

• 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,(mit A. Winterhof) Theoretical Computer Science 234 (2000), 301-308.
• Algorithms for factoring polynomials over arbitrary finite fields, (mit A. Winterhof) in 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, (mit C. Günther und 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, (mit A. Winterhof) in: Electronic Notes in Discrete Mathematics 6 als Proocedings von: 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, (mit A. Winterhof) Acta Arithmetica 101 (2002), 223-229.
• Linear Complexity of the Discrete Logarithm, (mit S. Konyagin und 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, (mit A. Winterhof), Discrete Applied Mathematics 128/1 (2003), 193 - 206.
• Polynomial Interpolation of the Elliptic Curve and XTR Discrete Logarithm, (mit 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 , (mit M. Ciet, F. Sica und J.-J. Quisquater ) in Proceedings of Eurocrypt 2003, LNCS 2656, 388-400.
• Interpolation of the Elliptic-Curve Diffie-Hellman Mapping, (mit A. Winterhof), Proceedings of AAECC 2003, LNCS 2643, 51-60.
• Trace-Zero Subvariety for Cryptosystems, erscheint in Journal of the Ramanujan Mathematical Society.
• On Using Expansions to the Base of $-2$, (mit R. Avanzi, G. Frey, und R. Oyono), erscheint in International Journal on Computer Mathematics vol 81 no 4, 2004.
• Montgomery Addition for Genus Two Curves, erscheint in Proceedings of ANTS 2004.
• Certain exponential sums and random walks on elliptic curves, (mit I. Shparlinski), eingereicht.
• Formulae for Arithmetic on Genus 2 Hyperelliptic Curves, erscheint in J. AAECC.
• Mathematical Background of Public Key Cryptography, (mit G. Frey ), siehe auch Preprint 10/2003 des IEM, Essen.
• Koblitz Curve Cryptosystems, erscheint in FFA.
• Collisions in Fast Generation of Ideal Classes and Points on Hyperelliptic and Elliptic Curves, (mit I. Shparlinski), erscheint in J. AAECC.

• Fast arithmetic on hyperelliptic Koblitz curves ,
  auf der MAGiC conference in Urbana/Champaign
  Abstract
  M1.ps M2.ps M3.ps Folien (leider 3 Files, da mit Zeichung)
  
  
• Speeding up the arithmetic on hyperelliptic Koblitz curves via Frobenius,
  Seminarvortrag im Information Protection Seminar in Urbana/Champaign
  Abstract
  Folien
  
  
• Schnelle Arithmetik auf hyperelliptischen Kurven,
  Seminarvortrag Oberseminar Algorithmische Mathematik in Paderborn
  Abstract
  Folien
  
  
• Hyperelliptische Kurven in der Kryptographie,
  Vortrag im Rahmen des ECC-Brainpool Workshops "Alternative Public-Key-Algorithmen"
  Folien
  
  
• Trace-Zero Subvariety for Cryptosystems,
  Vortrag auf YACC 2002
  Abstract
  Folien
  
  
• Efficient arithmetic on (hyper-)elliptic curves over finite fields,
  Vortrag im UCL Crypto Group - Seminar Series
  Folien
  
  
• Efficient arithmetic on (hyper-)elliptic curves over finite fields,
  Vortrag beim 2003 International Symposium on Next Generation Cryptography and Related Mathematics
  Folien
  
  
• Efficient arithmetic on (hyper-)elliptic curves over finite fields,
  Vortrag auf Computational Aspects of Algebraic Curves, and Cryptography, Gainesville
  Folien
  
  
• Efficient arithmetic on (hyper-)elliptic curves over finite fields,
  Vortrag im Cryptography Seminar in Rennes
  Folien
  
  
• Improved Algorithms for Efficient Arithmetic on Elliptic Curve using Fast Endomorphisms,
  Vortrag (gehalten von Francesco Sica) auf Eurocrypt 2003
  Folien in pdf
  
  
• Efficient arithmetic on (hyper-) elliptic curves over finite fields,
  Vortrag auf ECC 2003
  Slides
  
  
• Cryptographic Applications of Trace Zero Varieties,
  Vortrag auf Mathematics of Discrete Logarithms, Essen
  Slides
  
  
• Cryptographic Applications of Trace Zero Varieties,
  Vortrag auf Dagsthul Seminar -- Algorithms and Number Theory
  Slides
  
  
• Mathematical Countermeasures Against Side-Channel Attacks on ECC/HECC,
  Vortrag auf YACC 2004
  Slides
  
  
• Introduction to Side-Channel Attacks on elliptic and hyperelliptic curves,
  Vortrag auf ANTS VI 2004
  Slides
  
  
• Montgomery Addition for Genus Two Curves,
  Vortrag auf ANTS VI 2004
  Slides
  
  
• Mathematical Countermeasures against Side-Channel Attacks on Elliptic and Hyperelliptic Curves,
  Vortrag auf WARTACRYPT '04
  Slides
  
  
• Pseudorandom Number Generators Based on Elliptic Curves,
  Vortrag auf Number Theoretic Algorithms and Related Topics
  Slides
  
  
• Hyperelliptic curves in cryptography,
  Vortrag im "Seminar on zeta functions'' an der Technical University Tokyo
  Slides
  
  
• Efficient arithmetic on (hyper-)elliptic curves over finite fields,
  Vortrag im ``COSIC Seminar'', KU Leuven
  Slides
  
  
• Curve Cryptography - suitable primitives for embedded device ,
  Vortrag auf Cryptologie et Algorithmique En Normandie (CAEN'05)
  Slides
  
  
• Pairings on ordinary hyperelliptic curves,
  Vortrag auf Pairings in Cryptography
  Slides
  
  
• Arithmetic on Binary Genus $2$ Curves Suitable for Small Devices,
  Vortrag auf Workshop on RFID and Lightweight Crypto
  Slides
  
  
• Arithmetic of hyperelliptic curves over finite fields,
  Vortrag im Discrete Mathematics Seminar, University of Calgary
  Slides
  
  
• Efficient computation of pairings on non-supersingular hyperelliptic curves,
  Vortrag auf Number Theory Inspired by Cryptography, Banff
  Slides
  
  
• Efficient computation of pairings on non-supersingular hyperelliptic curves,
  Vortrag auf Algebraic Methods in Cryptography, Bochum
  Slides
  
  
• Cryptographic Applications of Trace Zero Varieties,
  Seminarvortrag am Cryptology Research Group at the Indian Statistical Institute, Kolkata
  Slides
  
  
• Pairings in Cryptography ,
  Tutorial auf ASIACRYPT 2005
  Slides
  
  
• Distribution of Some Sequences of Points on Elliptic Curves ,
  Vortrag in AMS Sectional Meeting Program by Special Session, Special Session on Number Theory
  Slides
  
  
• Arithmetic of hyperelliptic curves over finite fields , Teil des Tutorials auf der
  Summer School on "Computational Number Theory and Applications to Cryptography"
  Slides
  
  
• Pairing Based Cryptography , Teil des Tutrials auf der
  Summer School on "Computational Number Theory and Applications to Cryptography"
  Slides
  
  
• Analysis of pseudo-random number generators based on elliptic curves,
  Vortrag auf 31st Australasian Conference on Combinatorial Mathematics & Combinatorial Computing(ACCMCC)
  Slides
  
  
• Fast bilinear maps from the Tate-Lichtenbaum pairing on hyperelliptic curves,
  Vortrag auf ANTS VII, Berlin
  Slides
  
  
• Efficient arithmetic on (hyper-)elliptic curves over finite fields,
  Vortrag auf 2006 Workshop on Cryptography and Related Mathematics
  Slides
  
  
• Hyperelliptic Curves,
  Vortrag auf Information Security Summer School (ISSS) 2006. Taiwan.
  Slides
  
  
• Efficient arithmetic on hyperelliptic curves over finite fields,
  Vortrag auf Information Security Summer School (ISSS) 2006. Taiwan.
  Slides
  
  
• Pairing Based Cryptography,
  Vortrag auf Information Security Summer School (ISSS) 2006. Taiwan.
  Slides
  
  
• Public Key Cryptography - Performance Comparison and Benchmarking ,
  Keynote auf Simpósio Brasileiro em Segurança da Informação e de Sistemas Computacionais (SBSeg)
  Slides
  
  
• Index Calculus in Finite Fields & Hyperelliptic Curves ,
  Tutorial auf WCAP 2006 - III Workshop on Cryptographic Algorithms and Protocols
  Slides
  
  
• Efficient arithmetic on hyperelliptic curves over finite fields & Pairings,
  Tutorial auf WCAP 2006 - III Workshop on Cryptographic Algorithms and Protocols
  Slides
  
  
• Elliptic vs. hyperelliptic, part 2,
  Vortrag auf ECC 2006
  Folien und Folien in ps.gz
  
  Teil 1 des Kampfes wurde von Daniel J. Bernstein ausgetragen, seine Folien kann man hier finden.
  
  
• Open Problems in Pairings,
  Vortrag auf Number Theory and Cryptography - Open Problems
  Folien
  
  
• Tanja Lange,
  anläßlich der Vorstellung der neuen Mitarbeiter der Fakultät für Mathematik und Informatik an der Technische Universiteit Eindhoven
  Folien (pdf)
  
  
• Cryptographic applications of curves over finite fields,
  Vortrag im General Mathematical Colloquium Utrecht
  Folien
  
  
• Unified addition formulae for elliptic curves,
  Vortran in AMS Special Session on Mathematical Aspects of Cryptography, 2007 Spring AMS Eastern Section Meeting
  Folien
  
  
• Elliptic vs. hyperelliptic, part 2,
  Vortrag im EIDMA Seminar Combinatorial Theory
  Folien
  
  
• Mathematical Background of Pairings,
  Vortrag in ECRYPT PhD Summer School on Emerging Topics in Cryptographic Design and Cryptanalysis
  Folien
  
  
• Fast scalar multiplication on elliptic curves,
  Vortrag auf Conference on Algorithmic Number Theory
  Folien
  
  
• Elliptic vs. hyperelliptic, part 3 - Elliptic Strikes Back,
  Vortrag auf Eurocrypt 07 Rump Session
  Folien
  
  
• Side-channel attacks and countermeasures for curve based cryptography,
  Vortrag auf Quo vadis cryptology ? - Threat of Side-Channel Attacks
  Folien in ps
  Folien in pdf
  
  
• Fast scalar multiplication on elliptic curves,
  Vortrag auf 8th International Conference on Finite Fields and Applications
  Slides
  
  
• Elliptic vs. Hyperelliptic, part 3: Elliptic strikes back,
  Vortrag auf 11th Workshop on Elliptic Curve Cryptography 2007
  Folien für meine Hälfte
  Folien für Dan Bernsteins Hälfte
  
  
• The EFD thing,
  Vortrag in der Rump Session der CHES 2007 zusammen mit Dan Bernstein gehalten.
  Folien
  
  
• Edwards Curves for Cyptography,
  Vortrag in der EIDMA/DIAMANT Cryptography Working Group
  Folien
  
  
• Edwards coordinates for elliptic curves, part 1,
  Vortrag auf Explicit Methods in Number Theory In honour of Henri Cohen
  Folien
  Teil 2 wurde durch Dan Bernstein gehalten
  Dans Folien
  
  
• Edwards Coordinates for Elliptic Curves, part 1 ,
  Vortrag auf SAGE Days 6: Cryptology, Number theory, and Arithmetic Geometry
  Folien
  Teil 2 wurde von Dan Bernstein gehalten
  Dans Folien
• Edwards Curves for Cryptography,
  Vortrag auf dem Kolloquium über Kombinatorik
  Folien
  
  
• Faster Addition and Doubling on Elliptic Curves,
  gemeinsamer Vortrag mit Dan Bernstein auf der ASIACRYPT 2007
  Slides
  
  
• Edwards Coordinates,
  Vortrag auf Applied Algebra, Algebraic Algorithms, and Error Correcting Codes (AAECC-17)
  Folien
  
  
• The power of mathematics to protect data and to break data protection,
  Vortrag auf Research day at TU/e
  Folien
  
  
• Revisiting pairing based group key exchange,
  Vortrag auf Financial Cryptography and Data Security 2008
  Folien
  
  
• Binary Edwards Curves,
  Vortrag auf der Eurocrypt 2008 Rump Session
  Folien
  
  
• Faster arithmetic on elliptic curves -- blessing to ECC, harm to RSA,
  Vortrag auf EIPSI Grand Opening
  Folien
  
  
• Binary Edwards Curves,
  Vortrag im Seminario Matematico, Universidad Autonoma Madrid
  Folien
  
  
• Scalar Multiplication and Weierstrass Curves,
  Vortrag auf 3rd ECRYPT PhD SUMMER SCHOOL Advanced Topics in Cryptography
  Folien
  
  
• Shapes of Elliptic Curves,
  rump-session Vortrag auf der ANTS 2008
  Folien
  See also the zoo pictures.
  
  
• Binary Edwards Curves,
  Vortram im Séminaire de Cryptographie de Rennes
  Slides
  
  
• Binary Edwards Curves,
  Vortrag auf CHES 2008
  Slides
  
  

• 3rd ECRYPT PhD SUMMER SCHOOL "Advanced Topics in Cryptography"
• Mini-Kurs über Edwards Kurven
• 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 mehrere Vorträge (siehe oben für Folien)
• Information Security Summer School (ISSS) 2006. Taiwan mehrere Vorträge (siehe oben für Folien)
• Summer School on "Computational Number Theory and Applications to Cryptography" mehrere Vorträge (siehe oben für Folien)
• Advanced Cryptography an der DTU
  
• Tutorial on Pairings at ASIACRYPT 2005 (see above for slides)
• Applied Cryptography an er DTU (02232) zusammen mit 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"
  
  
  
• Links zu meinen alten Vorlesungen gibt es auf meiner alten homepage in Bochum.
• Leider sind die Seiten der Mathekids für Braunschweig und für Bochum nicht mehr im Netz.

Hyperelliptische Kurven mit schneller Arithmetik

Falls es Fragen gibt: tanja@hyperelliptic.org