University of Calgary
Renate Scheidler
- Professor
- Mathematics
Research Interests
Number Theory:
General:
Currently Teaching
| W2021 - MATH 318 - Introduction to Cryptography | ||||||||||
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Postdoctoral Fellows
- Jack Klys (2018-2020)
- Ha Tran (2016-2018)
- Felix Fontein (2009-2010)
- Qingquan Wu (2008-2010)
- Pieter Rozenhart (2009)
- Eric Landquist (2009)
- Stephane Lemieux (2004-2006)
- Roger Patterson (2004-2006)
Graduate Students
- Qinglong Luo, PhD, Mathematics, Calgary (expected 2024)
- Edgar Pacheco Castan, PhD Mathematics, Calgary (expected 2022)
- Pedro Jose Sobrevilla Moreno, PhD, Mathematics, Calgary (expected 2022)
- Sumin Leem, PhD, Mathematics, Calgary (expected 2021)
- Jonathan Webster, MSc, Computer Science, Calgary (expected 2021)
- Evan MacNeil, MSc, Mathematics, Calgary (2019)
- Qinglong Luo, MSc, Mathematics, Calgary (2019)
- Parthasarathi Das, MSc, Computer Science, Calgary (2019)
- Perlas Caranay, PhD, Mathematics, Calgary 2018
- Hongyuan Wang, MSc, Mathematics, Calgary 2016
- Monireh Rezai Rad, PhD, Mathematics, Calgary 2016
- Colin Weir, PhD, Mathematics, Calgary 2013
- Vanessa Dixon, MSc, Mathematics, Calgary 2011
- Adrian Tang, PhD, Mathematics, Calgary 2011
- Perlas Caranay, MSc, Mathematics, Calgary 2009
- Pieter Rozenhart, PhD, Mathematics, Calgary 2009
- Eric Landquist, PhD, Mathematics, University of Illinois 2008
- Manisha Parmar, MSc, Computer Science, Calgary 2008
- Qingquan Wu, PhD, Mathematics, University of Illinois 2007
- Karel Bergmann, MSc, Computer Science, Calgary 2007
- Taysia Krivoruchko, MSc, Computer Science, Calgary 2007
- Nick Sullivan, MSc, Mathematics, Calgary 2007
- Daniel Weimer, Diplom, Mathematics, Technical University of Darmstadt 2004
- Richard Cannings, MSc, Mathematics & Computer Science, Calgary 2004
- Brendan Oseen, MSc, Mathematics, Calgary 2003
Undergraduate Students
Boonyarit (Ken) Intiyot, BSc Honors, Mathematics, University of Delaware, 1998
Madelin Entz, BSc Honours, Mathematics, University of Calgary, 2020
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
Scholar Profiles
Publications
Book Chapter
- Caranay, Perlas, Greenberg., Matthew and Scheidler, Renate. "Computing modular polynomials and isogenies of rank two Drinfeld modules over finite fields" 75 Years Mathematics of Computation Ed. Brenner, S, Shparlinski, I., Shu, S.-W. and Szyld, D. B. Providence: Contemporary Mathematics, vol. 754, American Mathematical Society, 2020. 283-313. Print.
- MacNeil, Evan, Jacobson Jr, Michael J. and Scheidler, Renate. "Divisor class group arithmetic on C_{3,4} curves" Proceedings of the Fourteenth Algorithmic Number Theory Symposium (ANTS-XIV) Ed. Galbraith, Steven D. Berkeley, California: Mathematical Sciences Publishers, 2020. 317-334. Print.
- Das, Parthasarathi, Jacobson Jr., Michael J. and Scheidler, Renate. "Improved efficiency of a linearly homomorphic cryptosystem" Codes, Cryptology and Information Security, Third International Conference (C2SI 2019), Lecture Notes in Computer Science, vol. 11445 Ed. Carlet, C., Guilley, S., Nitaj, A. and Souidi, E.M. Springer, 2019. 349-368. Print.
- Rezai Rad, Monireh, Jacobson Jr., Michael J. and Scheidler, Renate. "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 Ed. Gueye, C.T., Persichetti, E., Cayrel, P.-L. and Buchmann, J. Springer, 2019. 183-203. Print.
- 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.
- Weir, Colin, Scheidler, Renate and Howe, Everett W.. "Constructing and tabulating dihedral function fields" Proceedings of the Tenth Algorithmic Number Theory Symposium (ANTS-X), The Open Book Series, vol. 1 Ed. Howe, Everett W. and Kedlaya, Kiran S. Berkeley, California: Mathematical Science Publishers, 2013. 557-585. Print.
- Scheidler, Renate and Jacobson Jr., Michael J.. "Section 12.4 Hyperelliptic Curves" Handbook of Finite Fields Chapman & Hall/CRC, 2013. Print.
- Dixon, Vanessa, Jacobson Jr., Michael J. and Scheidler, Renate. "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 Ed. Hevia, Alejandro and Neven, Gregory Springer-Verlag Berlin Heidelberg, 2012. 214-233. 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 Jr., Michael J., Scheidler, Renate and Weimer, Daniel. "An adaptation of the NICE cryptosystem to real quadratic orders" Progress in Cryptology - AFRICACRYPT 2008, Lecture Notes in Computer Science, vol. 5023 Ed. Vaudenay, Serge Springer-Verlag Berlin Heidelberg, 2008. 191-208. Print.
- Rozenhart, Pieter and Scheidler, Renate. "Tabulation of cubic function fields with imaginary and unusual Hessian" Proceedings of the Eighth Algorithmic Number Theory Symposium (ANTS-VIII), Lecture Notes in Computer Science, vol. 5011 Ed. van der Poorten, Alfred J. and Stein, Andreas Springer-Verlag Berlin Heidelberg, 2008. 357-370. Print.
- Bergmann, Karel, Scheidler, Renate and Jacob, Christian. "Cryptanalysis using genetic algorithms (abstract)" GECCO '08: Proceedings of the 10th annual conference on Genetic and Evolutionary Computation Ed. Keijzer, Maarten New York, NY: Association for Computing Machinery, 2008. 1099-1100. Print.
- 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.
- Scheidler, Renate. "Algorithmic aspects of cubic function fields" Proceedings of the Sixth Algorithmic Number Theory Symposium (ANTS-VI), Lecture Notes in Computer Science, vol. 3976 Ed. Buell, Duncan Springer-Verlag Berlin Heidelberg, 2004. 395-410. Print.
- Scheidler, Renate and Williams, Hugh C.. "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.
- Scheidler, Renate. "Reduction in purely cubic function fields of unit rank one" Proceedings of the Fourth Algorithmic Number Theory Symposium(ANTS-IV), Lecture Notes in Computer Science, vol. 1838 Ed. Buhler, Joe P Springer-Verlag Berlin Heidelberg, 2000. 515-532. Print.
- Scheidler, Renate and Stein, Andreas. "Unit computation in purely cubic function fields of unit rank 1 (extended abstract)" Proceedings of the Third Algorithmic Number Theory Symposium (ANTS-III), Lecture Notes in Computer Science, vol. 1423 Ed. Buhler, Joe P Springer-Verlag Berlin Heidelberg, 1998. 592-606. Print.
- Scheidler, Renate. "Cryptography in real quadratic congruence function fields" Proceedings of the First International Conference on the Theory and Applications of Crytology (PRAGOCRYPT'96) Ed. Pribyl, Jiri Prague (Czech Republic): CTU Publishing House, 1996. 109-128. Print.
- Scheidler, Renate. "Compact representation in real quadratic congruence function fields" Proceedings of the Second Algorithmic Number Theory Symposium (ANTS-II), Lecture Notes in Computer Science, vol. 1122 Ed. Cohen, Henri Springer-Verlag Berlin Heidelberg, 1996. 323-336. Print.
- Scheidler, Renate, Buchmann, Johannes A. and Williams, Hugh C.. "Implementation of a key exchange protocol using real quadratic fields (extended abstract)" Advances in Cryptology - EUROCRYPT '90, Lecture Notes in Computer Science, vol. 473 Springer-Verlag Berlin Heidelberg, 1991. 98-109. Print.
Edited Book
- Scheidler, Renate and Sorenson, Jonathan (eds). Proceedings of the Thirteenth Algorithmic Number Theory Symposium (ANTS-XIII), The Open Book Series, vol. 2 Berkeley, California: Mathematical Science Publishers, 2019. Print.
- Cojocaru, Alina, Lauter, Kristin, Pries, Rachel and Scheidler, Renate (eds). WIN - Women in Numbers: Research Directions in Number Theory, Fields Institute Communications, vol. 60 Providence: American Mathematical Society, 2011. Print.
Journal Article
- Scheidler, Renate and Woodrow, Robert. "Richard Kenneth Guy (1916-2020)". CMS Notes 52.4 (2020). Print.
- Scheidler, Renate, Jacobson Jr. Michael J., Lee, Yoonjin 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.
- Rozenhart, Pieter, Jacobson Jr., Michael J. and Scheidler, Renate. "Computing quadratic function fields with high 3-rank via cubic field tabulation". Rocky Mountain Journal of Mathematics 45.6 (2015): 1985-2022. Print.
- Scheidler, Renate and Jacobson Jr., Michael J.. "Infrastructure: structure inside the class group of a real quadratic field". Notices of the American Mathematical Society 61.1 (2014): 36-46. Print.
- Rezai Rad, Monireh, Jacobson Jr., Michael J. 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 J. 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 Jr., Michael J., Scheidler, Renate and Stein. Andreas. "Cryptographic aspects of real hyperelliptic curves". Tatra Mountains Mathematical Publications 40.5 (2010): 1-35. Print.
- Bauer, Mark, 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 J., 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, Michael J., Scheidler, Renate and Williams, Hugh C.. "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 C.. "Further tabulation of the Erdos-Selfridge function". Mathematics of Computation 66.220 (1997): 1709-1717. Print.
- Scheidler, Renate, Stein, Andreas and Williams, Hugh C.. "Key-exchange in real quadratic congruence function fields". Designs, Codes and Cryptography 7.1-2 (1996): 153-174. Print.
- Scheidler, Renate and Williams, Hugh C.. "A public-key cryptosystem utilizing cyclotomic fields". Designs, Codes and Cryptography 6.2 (1995): 117-131. Print.
- Scheidler, Renate, Buchmann, Johannes and Williams, Hugh C.. "A key exchange protocol using real quadratic fields". Journal of Cryptology 7.3 (1994): 171-199. Print.
- Scheidler, Renate and Williams, Hugh C.. "A method of tabulating the number-theoretic function g(k)". Mathematics of Computation 59.199 (1992): 251-257. Print.
M.Sc. Thesis
- Scheidler, Renate. On the Algebra and Arithmetic of Cubic Forms and Cubic Number Fields (in German) 1987.
Ph.D. Thesis
- Scheidler, Renate. Applications of Algebraic Number Theory to Cryptography 1993.
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