PUBLICATIONS   -   Renate Scheidler

  1. J. Duque-Rosero, H. Goodson, E. Lorenzo Garcia, B. Malmskog and R. Scheidler, On invariants of Artin-Schreier curves, arXiv:2401.08843 [math.NT], to appear in Women in Numbers 6 - Research Directions in Number Theory, Association for Women in Mathematics Series.

  2. S. Leem, M. J. Jacobson and R. Scheidler, Solving Norm Equations in Global Function Fields, to appear in Proceedings of the 16th Algorithmic Number Theory Symposium (ANTS XVI), Research in Number Theory, Springer 2024.

  3. S. Arpin, M. Chen, K. E. Lauter, R. Scheidler, K. E. Stange and H. T. N. Tran, Orientations and cycles in supersingular isogeny graphs, Women in Numbers 5 - Research Directions in Number Theory, Association for Women in Mathematics Series, vol. 33, Springer 2024, 25-87.

  4. C. Bagshaw, M. J. Jacobson Jr., R. Scheidler, and N. Rollick, Improved methods for finding imaginary quadratic fields with high n-rank, LuCaNT: LMFDB, Computation, and Number Theory, Contemporary Mathematics, vol. 796, American Mathematical Society, Providence, Rhode Island 2024, 1-28.

  5. R. Scheidler, Women in Numbers, CMS Notes 56 (2024), no. 2, online.

  6. S. Arpin, M. Chen, K. E. Lauter, R. Scheidler, K. E. Stange and H. T. N. Tran, Orienteering with one endomorphism, La Matematica 2 (2023), 523-582

  7. E. P. White, R. K. Guy and R. Scheidler, Difference necklaces, Journal of Integer Sequences 25 (2022), Article 22.5.3, 21pp, online.

  8. J. Korbas, R. Scheidler and P. Zvengrowski, The cup-length of Stiefel and projective Stiefel manifolds, The Graduate Journal of Mathematics 6 (2021), no. 1, 27-34.

  9. E. MacNeil, M. J. Jacobson Jr. and R. Scheidler, Divisor class group arithmetic on C3,4 curves, Proceedings of the 14th Algorithmic Number Theory Symposium (ANTS-XIV), The Open Book Series, vol. 4, Mathematical Science Publishers, Berkeley, California 2020, pp. 317-334.

  10. R. Scheidler, Foreword to "Fibonacci plays Billiards" by E. Berlekamp and R. Guy, Crux Mathematicorum 48 (2020), no. 8, Special issue dedicated to Richard Guy, p. 334.

  11. R. Scheidler and R. Woodrow, Richard Kenneth Guy (1916-2020), English and French version, CMS Notes 52 (2020), no. 4, online

  12. P. Caranay, M. Greenberg and R. Scheidler, Computing modular polynomials and isogenies of rank two Drinfeld modules over finite fields, 75 Years Mathematics of Computation, Contemporary Mathematics, vol. 754, American Mathematical Society, Providence, Rhode Island 2020, 283-313.

  13. M. Rezai Rad, M. J. Jacobson, Jr. and R. Scheidler, Jacobian versus infrastructure in split hyperelliptic curves, First International Conference on Algebra, Codes and Cryptography, A2C 2019, Communications in Computer and Information Science, vol. 1133, Springer 2019, 183-203.

  14. P. Das, M. J. Jacobson, Jr. and R. Scheidler, Improved efficiency of a linearly homomorphic cryptosystem, Codes, Cryptology and Information Security, Third International Conference, C2SI 2019, Lecture Notes in Computer Science, vol. 11445, Springer 2019, 349-368.

  15. R. Scheidler, Construction of all cubic fields of a fixed fundamental discriminant. In Cubic Fields With Geometry (S. Hambleton & H. C. Williams, authors), CMS Books in Mathematics, Springer International Publishing, New York, 2018, 173-302.

  16. R. Scheidler, An Introduction to hyperelliptic curve arithmetic. Invited paper, in Contemporary Developments in Finite Fields and Applications, World Scientific Publishers, Singapore 2016, 321-340.

  17. I. Bouw, W. Ho, B. Malmskog, R. Scheidler, P. Srinivasan and C. Vincent, Zeta functions of a class of Artin-Schreier curves with many automorphisms. In Directions in Number Theory - Proceedings of the 2014 WIN3 Workshop, Association for Women in Mathematics Series, vol. 3, Springer, Switzerland 2016, 87-124.

  18. P. Rozenhart, M. J. Jacobson, Jr. and R. Scheidler, Computing quadratic function fields with high 3-rank via cubic field tabulation. Rocky Mountain Journal of Mathematics 45 (2015), no. 6, 1985-2022.

  19. M. J. Jacobson, Jr., Y. Lee, R. Scheidler and H. C. Williams, Construction of all cubic function fields of a given square-free discriminant. International Journal of Number Theory 11 (2015), no. 6, 1839-1885.

  20. M. J. Jacobson, Jr., M. Rezai Rad and R. Scheidler, Comparison of scalar multiplication on real hyperelliptic curves. Advances in Mathematics of Communications 8 (2014), no. 4, special issue dedicated to GEOCRYPT 2013, 389-406.

  21. M. J. Jacobson, Jr. and R. Scheidler, Infrastructure: structure inside the class group of a real quadratic field. Notices of the American Mathematical Society 61 (2014), no. 1, 36-46.

  22. C. Weir, R. Scheidler and E. W. Howe, Constructing and tabulating dihedral function fields. Proceedings of the Tenth Algorithmic Number Theory Symposium (ANTS-X 2012), The Open Book Series, vol. 1, Mathematical Science Publishers, Berkeley, California 2013, pp. 557-585.

  23. M. J. Jacobson, Jr. and R. Scheidler, Hyperelliptic Curves. Section 12.4 of Handbook of Finite Fields, Chapman & Hall/CRC, Boca Raton, Florida 2013, pp. 447-456.

  24. K. H. F. Cheng, R. K. Guy, R. Scheidler and H. C. Williams, Classification and symmetries of a family of continued fractions with bounded period length. Journal of the Australian Mathematical Society 93 (2013), no. 1-2, 53-76.

  25. T. Bembom, R. Scheidler and Q. Wu, Prime decomposition and class number factors for certain function fields. Annales de Sciences Mathematiques du Quebec 36 (2012), no. 2, 325-348.

  26. V. Dixon, M. J. Jacobson, Jr. and R. Scheidler, Improved exponentiation and key agreement in the infrastructure of a real quadratic field. Progress in Cryptology - Proceedings of Latincrypt 2012, Lecture Notes in Computer Science, vol. 7533, Springer, Berlin 2012, 214-233.

  27. P. Rozenhart, M. J. Jacobson, Jr. and R. Scheidler, Tabulation of cubic function fields via polynomial binary cubic forms. Mathematics of Computation 81 (2012), no. 280, 2335-2359.

  28. 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.

  29. P. Caranay and R. Scheidler, An efficient seventh power residue symbol algorithm. International Journal of Number Theory 6 (2010), no. 8, 1831-1853.

  30. Q. Wu and R. Scheidler, The ramification groups and different of a compositum of Artin-Schreier extensions. International Journal of Number Theory 6 (2010), no. 7, 1541-1564.

  31. R. Scheidler and A. Stein, Approximating Euler products and class number computation in algebraic function fields. Rocky Mountain Journal of Mathematics 40 (2010), no. 5, 1689-1727.

  32. M. J. Jacobson, Jr., R. Scheidler and A. Stein, Cryptographic aspects of real hyperelliptic curves. Tatra Mountains Mathematical Publications 47 (2010), no. 1, 31-65.

  33. 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 (2010), no. 4, 787-807.

  34. R. Avanzi, M. J. Jacobson, Jr. and R. Scheidler Efficient reduction of large divisors on hyperelliptic curves. Advances in Mathematics of Communications 4 (2010), no. 2, 261-279.

  35. 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.

  36. 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.

  37. 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 (2008), no. 261, 503-530.

  38. K. Bergmann, R. Scheidler and C. Jacob, Cryptanalysis using genetic algorithms (abstract). In Proceedings of the 10th Genetic and Evolutionary Computation Conference (GECCO 2008) July 2008, pp. 1099-1100 (2008).

  39. R. Scheidler and A. Stein, Class number approximation in cubic function fields. Contributions to Discrete Mathematics 2 (2007), no. 2, 107-132.

  40. M. J. Jacobson, Jr., R. Scheidler and A. Stein, Cryptographic protocols on real hyperelliptic curves. Advances in Mathematics of Communications 1 (2007), no. 2, 197-221.

  41. 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.

  42. Q. Wu and R. Scheidler, An explicit treatment of biquadratic function fields. Contributions to Discrete Mathematics 2 (2007), no. 1, 43-60.

  43. M. J. Jacobson, Jr., R. Scheidler and H. C. Williams, An improved real quadratic field based key exchange procedure. Journal of Cryptology 19 (2006), no. 2, 211 - 239.

  44. 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.

  45. Y. Lee, R. Scheidler and C. Yarrish, Computation of the fundamental units and the regulator of a cyclic cubic function field. Experimental Mathematics 12 (2003), no 2, 211-225.

  46. R. Scheidler, Ideal arithmetic and infrastructure in purely cubic function fields. Journal de Théorie des Nombres de Bordeaux 13 (2001), no. 2, 609-631.
    Corrigendum to Lemma 4.2.

  47. 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.

  48. R. Scheidler, Cryptography in quadratic function fields. Designs, Codes and Cryptography 22 (2001), no. 3, 239-264.

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

  50. R. Scheidler, Decision problems in quadratic function fields of high genus. Journal of Complexity 16 (2000), no. 2, 411-423.

  51. R. Scheidler and A. Stein, Voronoi's algorithm in purely cubic congruence function fields of unit rank 1. Mathematics of Computation 69 (2000), no. 231, 1245-1266.

  52. 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.

  53. R. Scheidler, Purely cubic function fields with short periods. Publicationes Mathematicae Debrecen 54 (1999), no. 3-4, 497-511.

  54. 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.

  55. R. Scheidler, A public-key cryptosystem using purely cubic fields. Journal of Cryptology 11 (1998), no. 2, 109-124.

  56. R. F. Lukes, R. Scheidler and H. C. Williams, Further tabulation of the Erdos-Selfridge function. Mathematics of Computation 66 (1997), no. 220, 1709-1717.

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

  58. 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.

  59. R. Scheidler, A. Stein and H. C. Williams, Key exchange in real quadratic congruence function fields. Designs, Codes and Cryptography 7 (1996), , no. 1-2, 153-174.

  60. R. Scheidler and H. C. Williams, A public-key cryptosystem utilizing cyclotomic fields. Designs Codes and Cryptography 6 (1995), no. 2, 117-131.

  61. R. Scheidler, J. A. Buchmann and H.C. Williams, A key exchange protocol using real quadratic fields. Journal of Cryptology 7 (1994), no. 3, 171-199.

  62. R. Scheidler and H. C. Williams, A method of tabulating the number theoretic function g(k) Mathematics of Computation 59 (1992), no. 199, 251-257.

  63. 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 Curriculum Vitae