Publications of Renate Scheidler

  1. K. H .F. Cheng, R. K. Guy, R. Scheidler and H. C. Williams Classificaton and symmetries of a family of continued fractions with bounded period length. To appear in Journal of the Australian Mathematical Society.

  2. P. Rozenhart, M. J. Jacobson, Jr. and R. Scheidler, Tabulation of cubic function fields via polynomial binary cubic forms. To appear in Mathematics of Computation.

  3. L. Berger, J. L. Hoelscher, Y. Lee, J. Paulhus and R. Scheidler, The l-rank structure of a global function field. In WIN--Women in Numbers: Research Directions in Number Theory Fields Institute Communications, vol. 60, American Mathematical Society, Providence, Rhode Island, 2011, 145-166.

  4. P. Caranay and R. Scheidler, An efficient seventh power residue symbol algorithm. International Journal of Number Theory 6(8) (2010), 1831-1853.

  5. Q. Wu and R. Scheidler, The ramification groups and different of a compositum of Artin-Schreier extensions. International Journal of Number Theory 6(7) (2010), 1541-1564.

  6. R. Scheidler and A. Stein, Approximating Euler products and class number computation in algebraic function fields. Rocky Mountain Journal of Mathematics 40(5) (2010), 1689-1727.

  7. M. J. Jacobson, Jr., R. Scheidler and A. Stein, Cryptographic aspects of real hyperelliptic curves. Tatra Mountains Mathematical Publications 45 (2010), 1-35.

  8. E. Landquist, P. Rozenhart, R. Scheidler, J. Webster and Q. Wu, An explicit treatment of cubic function fields with applications. Canadian Journal of Mathematics 62(4) (2010), 787-807.

  9. R. Avanzi, M. J. Jacobson, Jr. and R. Scheidler Efficient reduction of large divisors on hyperelliptic curves. Advances in Mathematics of Communications 4(2) (2010), 261-279.

  10. M. J. Jacobson, Jr, R. Scheidler and D. Weimer, An adaptation of the NICE cryptosystem to real quadratic orders. In Progress in Cryptology - AFRICACRYPT 2008, Lecture Notes in Computer Science, vol. 5023, Springer, Berlin 2008, 191-208.

  11. P. Rozenhart and R. Scheidler, Tabulation of cubic function fields with imaginary and unusual Hessian. In Proceedings of the Eighth Algorithmic Number Theory Symposium ANTS-VIII, Lecture Notes in Computer Science, vol. 5011, Springer, Berlin 2008, 357-370.

  12. M. L. Bauer, M. J. Jacobson, Jr., Y. Lee and R. Scheidler, Construction of hyperelliptic function fields of high three-rank. Mathematics of Computation 77(261) (2008), 503-530.

  13. R. Scheidler and A. Stein, Class number approximation in cubic function fields. Contributions to Discrete Mathematics 2(2) (2007), 107-132.

  14. M. J. Jacobson, Jr., R. Scheidler and A. Stein, Cryptographic protocols on real hyperelliptic curves. Advances in Mathematics of Communications 1(2) (2007), 197-221.

  15. M. J. Jacobson, Jr., R. Scheidler and A. Stein, Fast arithmetic on hyperelliptic curves via continued fraction expansions. Invited paper, in Advances in Coding Theory and Cryptology, Series on Coding Theory and Cryptology, vol. 3, World Scientific Publishing Co. Pte. Ltd., Hackensack, New Jersey 2007, 201-244.

  16. Q. Wu and R. Scheidler, An explicit treatment of biquadratic function fields. Contributions to Discrete Mathematics 2(1) (2007), 43-60.

  17. M. J. Jacobson, Jr., R. Scheidler and H. C. Williams, An improved real quadratic field based key exchange procedure. Journal of Cryptology 19(2) (2006), 211 - 239.

  18. R. Scheidler, Algorithmic aspects of cubic function fields. In Proceedings of the Sixth Algorithmic Number Theory Symposium ANTS-VI, Lecture Notes in Computer Science, vol 3976, Springer, Berlin 2004, 395-410.

  19. Y. Lee, R. Scheidler and C. Yarrish, Computation of the fundamental units and the regulator of a cyclic cubic function field. Experimental Mathematics 12(2) (2003), 211-225.

  20. R. Scheidler, Ideal arithmetic and infrastructure in purely cubic function fields. Journal de Théorie des Nombres de Bordeaux 13(2) (2001), 609-631.
    Corrigendum to Lemma 4.2.

  21. M. J. Jacobson, Jr., R. Scheidler and H. C. Williams, The efficiency and security of a real quadratic field-based key exchange protocol. In Public-Key Cryptography and Computational Number Theory (Warsaw, 2000), de Gruyter & Co. Publishers, Berlin 2001, 89-112.

  22. R. Scheidler, Cryptography in quadratic function fields. Designs, Codes and Cryptography 22(3) (2001), 239-264.

  23. R. Scheidler, Purely cubic complex function fields with small units. Acta Arithmetica XCV.4 (2000), 289-304.

  24. R. Scheidler, Decision problems in quadratic function fields of high genus. Journal of Complexity 16(2) (2000), 411-423.

  25. R. Scheidler and A. Stein, Voronoi's algorithm in purely cubic congruence function fields of unit rank 1. Mathematics of Computation 69(231) (2000), 1245-1266.

  26. R. Scheidler, Reduction in purely cubic function fields of unit rank one. In Proceedings of the Fourth Algorithmic Number Theory Symposium ANTS-IV, Lecture Notes in Computer Science, vol. 1838, Springer, Berlin 2000, 515-532.

  27. R. Scheidler, Purely cubic function fields with short periods. Publicationes Mathematicae Debreçen 54(3-4) (1999), 497-511.

  28. R. Scheidler and A. Stein, Unit computation in purely cubic function fields of unit rank 1 (extended abstract). In Proceedings of the Third Algorithmic Number Theory Symposium ANTS-III, Lecture Notes in Computer Science, vol. 1423, Springer, Berlin 1998, 592-606.

  29. R. Scheidler, A public-key cryptosystem using purely cubic fields. Journal of Cryptology 11(2) (1998), 109-124.

  30. R. F. Lukes, R. Scheidler and H. C. Williams, Further tabulation of the Erdös-Selfridge function. Mathematics of Computation 66(220) (1997), 1709-1717.

  31. R. Scheidler, Cryptography in real quadratic congruence function fields. In Proceedings of Pragocrypt, CTU Publishing House, Prague (Czech Republic) 1996, 109-128.

  32. R. Scheidler, Compact representation in real quadratic congruence function fields. In Proceedings of the Second Algorithmic Number Theory Symposium ANTS-II, Lecture Notes in Computer Science, vol. 1122, Springer, Berlin 1996, 323-336.

  33. R. Scheidler, A. Stein and H. C. Williams, Key exchange in real quadratic congruence function fields. Designs, Codes and Cryptography 7(1-2) (1996), 153-174.

  34. R. Scheidler and H. C. Williams, A public-key cryptosystem utilizing cyclotomic fields. Designs Codes and Cryptography 6(2) (1995), 117-131.

  35. R. Scheidler, J. A. Buchmann and H.C. Williams, A key exchange protocol using real quadratic fields. Journal of Cryptology 7(3) (1994), 171-199.

  36. R. Scheidler and H. C. Williams, A method of tabulating the number theoretic function g(k) Mathematics of Computation 59(199) (1992), 251-257.

  37. R. Scheidler, J. A. Buchmann and H. C. Williams, Implementation of a key exchange protocol using real quadratic fields (extended abstract). In Advances in Cryptology - EUROCRYPT '90, Lecture Notes in Computer Science, vol. 473, Springer, Berlin 1991, 98-109.

Doctoral Dissertation:
Applications of Algebraic Number Theory to Cryptography
Department of Computer Science, University of Manitoba (Canada) 1993.
Advisor: Dr. H.C. Williams

Diplomarbeit (Master's Thesis):
On the Algebra and Arithmetic of Cubic Forms and Cubic Number Fields (in German)
Department of Mathematics, University of Cologne (Germany) 1987.
Advisor: Prof. W. Jehne

Renate Scheidler's home page
Renate Scheidler's biographical information