Renate Scheidler


Contact information

Courses

  • MATH 211 - Linear Methods I
  • CPSC 313 - Introduction to Computability
  • PMAT 315 - Algebra I
  • PMAT 317 - Honours Algebra I
  • MATH 318/CPSC 418 - Introduction to Cryptography
  • MATH 401 - Topics in Cryptography
  • CPSC 413 - Design and Analysis of Algorithms I
  • CPSC 429 - Applied Cryptography
  • PMAT 429 - Cryptography - Design and Analysis of Cryptosystems
  • CPSC 502 - Research Project
  • PMAT 503.04 - Modern Cryptography and Cryptanalysis
  • PMAT 529/649 Advanced - Cryptography and Cryptanalysis
  • CPSC/PMAT 629 - Elliptic Curves and Cryptography
  • CPSC/PMAT 669 - Cryptography

Research and teaching

Research areas

  • Algorithmic Number Theory
  • Mathematical cryptology

Publications

Book chapter

  • Scheidler, Renate. "Construction of All Cubic Fields of a Fixed Fundamental Discriminant" Cubic Fields With Geometry Ed. Hambleton, Samuel and Williams, Hugh C. Heidelberg: Springer International Publishing, 2018. 173-203. Print.
  • Scheidler, Renate, Bouw, Irene, Ho, Wei, Malmskog, Beth, Srinivasan, Padmavathi and Vincent,Christelle. "Zeta functions of a class of Artin-Schreier curves with many automorphisms" Directions in Number Theory Ed. Eischen, Ellen, Long, Ling, Pries, Rachel and Stange, Katherine (eds) Springer, 2016. 87-124. Print.
  • Scheidler, Renate. "An Introduction to hyperelliptic curve arithmetic" Contemporary Developments in Finite Fields and Applications Ed. Canteaut, Anne, Effinger, Gove, Huczynska, Panario, Daniel and Storme, Leo (eds) World Scientific, 2016. 321-340. Print.
  • Jacobson, Michael John Jr. and Scheidler, Renate. "Section 12.4 Hyperelliptic Curves" Handbook of Finite Fields Chapman & Hall/CRC, 2013. Print.
  • Berger, Lisa, Hoelscher, Jing Long, Lee, Yoonjin, Paulhus, Jennifer and Scheidler, Renate. "The l-rank structure of a global function field" WIN--Women in Numbers: Research Directions in Number Theory Ed. Cojocaru, Alina, Lauter, Kristin and Pries, Rachel (eds) Providence: American Mathematical Society, 2011. Fields Institute Communications, vol. 60, 145-166. Print.
  • Jacobson, Michael, Scheidler, Renate and Stein, Andreas. "Fast arithmetic on hyperelliptic curves via continued fraction expansions" Advances in Coding Theory and Cryptology, Series on Coding Theory and Cryptology 3 Ed. Shaska, T., Huffman, W. C. and Ustimenko, V. Hackensack, New Jersey: World Scientific Publishing Co. Pte. Ltd., 2007. 201-244. Print.
  • Jacobson, Michael, Scheidler, Renate and Williams, Hugh. "The efficiency and security of a real quadratic field-based key exchange protocol" Public-Key Cryptography and Computational Number Theory Berlin: de Gruyter & Co. Publishers, 2001. 89-112. Print.

Conference proceedings

  • Scheidler, Renate, Parthasarati Das and Michael J. Jacobson Jr. Improved Efficiency of a Linearly Homomorphic Cryptosystem 2019.
  • Weir, Colin, Scheidler, Renate and Howe, Everett. Construction and tabulation of dihedral function fields 2013.
  • Dixon, Vanessa, Jacobson, Michael John Jr. and Scheidler, Renate. Improved exponentiation and key agreement in the infrastructure of a real quadratic field 2013.
  • Scheidler, Renate, Bergmann, Karel and Jacob, Christian. Cryptanalysis using genetic algorithms 2008.
  • Rozenhart, Pieter and Scheidler, Renate. Tabulation of cubic function fields with imaginary and unusual Hessian 2008.
  • Jacobson, Michael, Scheidler, Renate and Weimer, Daniel. An adaptation of the NICE cryptosystem to real quadratic orders 2008.
  • Scheidler, Renate. Algorithmic aspects of cubic function fields 2004.
  • Scheidler, Renate. Reduction in purely cubic function fields of unit rank one 2000.
  • Scheidler, Renate and Stein, Andreas. Unit computation in purely cubic function fields of unit rank 1 (extended abstract) 1998.
  • Scheidler, Renate. Compact representation in real quadratic congruence function fields 1996.
  • Scheidler, Renate. Cryptography in real quadratic congruence function fields 1996.
  • Scheidler, Renate, Buchmann, Johannes and Williams, Hugh. Implementation of a key exchange protocol using real quadratic fields (extended abstract) 1991.

Journal article

  • Jacobson, Michael J., Jr., Lee, Yoonjin, Scheidler, Renate and Williams, Hugh C.. "Construction of all cubic function fields of a given square-free discriminant". International Journal of Number Theory 11.6 (2015): 1839-1885. Print.
  • Scheidler, Renate, Jacobson, Michael John Jr and Rozenhart, Pieter. "Computing quadratic function fields with high 3-rank via cubic field tabulation". Rocky Mountain Journal of Mathematics 45.6 (2015): 1985-2022. Print.
  • Jacobson, Michael J. Jr. and Scheidler, Renate. "Infrastructure: structure inside the class group of a real quadratic field". Notices of the American Mathematical Society 61.1 (2014): 36-46. Print.
  • Jacobson, Michael J., Jr., Rezai Rad, Monireh and Scheidler, Renate. "Comparison of scalar multiplication on real hyperelliptic curves". Advances in Mathematics of Communications 8.4 (2014): 389-406. Print.
  • Cheng, Kell Hiu-Fai, Guy, Richard K., Scheidler, Renate and Williams, Hugh C.. "Classification and symmetries of a family of continued fractions with bounded period length". Journal of the Australian Mathematical Society 93.1-2 (2013): 53-76. Print.
  • Bembom, Tobias, Scheidler, Renate and Wu, Qingquan. "Prime decomposition and class number factors for certain function fields". Annales de Sciences Mathématiques du Québec 36.2 (2013): 325-348. Print.
  • Rozenhart, Pieter, Jacobson Jr, Michael John and Scheidler, Renate. "Tabulation of cubic function fields via polynomial binary cubic forms". Mathematics of Computation 81. (2012): 2335-2359. Print.
  • Avanzi, Roberto, Jacobson Jr, Michael John and Scheidler, Renate. "Efficient reduction of large divisors on hyperelliptic curves". Advances in Mathematics of Communications 4.2 (2010): 261-279. Print.
  • Landquist, Eric, Rozenhart, Pieter, Scheidler, Renate, Webster, Jonathan and Wu, Qingquan. "An explicit treatment of cubic function fields with applications". Canadian Journal of Mathematics 62.4 (2010): 787-807. Print.
  • Caranay, Perlas and Scheidler, Renate. "An efficient seventh power residue symbol algorithm". International Journal of Number Theory 6.8 (2010): 1831-1853. Print.
  • Wu, Qingquan and Scheidler, Renate. "The ramification groups and different of a compositum of Artin-Schreier extensions". International Journal of Number Theory 6.7 (2010): 1542-1564. Print.
  • Jacobson, Michael, Scheidler, Renate and Stein, Andreas. "Cryptographic aspects of real hyperelliptic curves". Tatra Mountains Mathematical Publications 40.5 (2010): 1-35. Print.
  • Bauer, Mark, Jacobson, Michael, Lee, Yoonjin and Scheidler, Renate. "Construction of hyperelliptic function fields of high three-rank". Mathematics of Computation 77.261 (2008): 503-530. Print.
  • Scheidler, Renate and Stein, Andreas. "Approximating Euler products and class number computation in algebraic function fields". Rocky Mountain Journal of Mathematics 40.5 (2008): 1689-1727. Print.
  • Jacobson, Michael, Scheidler, Renate and Stein, Andreas. "Cryptographic protocols on real hyperelliptic curves". Advances in Mathematics of Communications 1.2 (2007): 197-221. Print.
  • Scheidler, Renate and Stein, Andreas. "Class number approximation in cubic function fields". Contributions to Discrete Mathematics 2.2 (2007): 107-132. Print.
  • Wu, Qingquan and Scheidler, Renate. "An explicit treatment of biquadratic function fields". Contributions to Discrete Mathematics 2.1 (2007): 43-60. Print.
  • Jacobson, M.J., Scheidler, Renate and Williams, Hugh. "An improved real quadratic field based key exchange procedure". Journal of Cryptology. The Journal of the International Association for Cryptologic Research 19.2 (2006): 211-239. Print.
  • Lee, Yoonjin, Scheidler, Renate and Yarrish, Christopher. "Computation of the fundamental units and the regulator of a cyclic cubic function field". Experimental Mathematics 12.2 (2003): 211-225. Print.
  • Scheidler, Renate. "Cryptography in quadratic function fields". Designs, Codes and Cryptography 22.3 (2001): 239-264. Print.
  • Scheidler, Renate. "Ideal arithmetic and infrastructure in purely cubic function fields". Journal de Theorie des Nombres de Bordeaux 13.2 (2001): 609-631. Print.
  • Scheidler, Renate. "Purely cubic complex function fields with small units". Acta Arithmetica 95.4 (2000): 289-304. Print.
  • Scheidler, Renate. "Decision problems in quadratic function fields of high genus". Journal of Complexity 16.2 (2000): 411-423. Print.
  • Scheidler, Renate and Stein, Andreas. "Voronoi's algorithm in purely cubic congruence function fields of unit rank 1". Mathematics of Computation 69.231 (2000): 1245-1266. Print.
  • Scheidler, Renate. "Purely cubic function fields with short periods". Publicationes Mathematicae Debrecen 54.3-4 (1999): 497-511. Print.
  • Scheidler, Renate. "A public-key cryptosystem using purely cubic fields". Journal of Cryptology. The Journal of the International Association for Cryptologic Research 11.2 (1998): 109-124. Print.
  • Lukes, Richard F., Scheidler, Renate and Williams, Hugh. "Further tabulation of the Erdos-Selfridge function". Mathematics of Computation 66.220 (1997): 1709-1717. Print.
  • Scheidler, Renate, Stein, Andreas and Williams, Hugh. "Key-exchange in real quadratic congruence function fields". Designs, Codes and Cryptography 7.1-2 (1996): 153-174. Print.
  • Scheidler, Renate and Williams, Hugh. "A public-key cryptosystem utilizing cyclotomic fields". Designs, Codes and Cryptography 6.2 (1995): 117-131. Print.
  • Scheidler, Renate, Buchmann, Johannes and Williams, Hugh. "A key exchange protocol using real quadratic fields". Journal of Cryptology 7.3 (1994): 171-199. Print.
  • Scheidler, Renate and Williams, Hugh. "A method of tabulating the number-theoretic function g(k)". Mathematics of Computation 59.199 (1992): 251-257. Print.

MSc thesis

  • Scheidler, Renate. On the Algebra and Arithmetic of Cubic Forms and Cubic Number Fields (in German) 2008.

PhD thesis

  • Scheidler, Renate. Applications of Algebraic Number Theory to Cryptography 1993.