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Research

Research interests :

Public-key cryptography. Algorithmic number theory. Discrete logarithm problem. Algebraic curves and applications in cryptography. Pairing based cryptography. APN functions. Modular curves.

Publications :
  • E. Ferard, R. Oyono, F. Rodier: Some More Functions That Are Not APN Infinitely Often. The Case of Gold and Kasami exponents, accepted in Proceedings of AGCT 13, March 2012.
  • F. Luca, R. Oyono: An exponential Diophantine equation related to powers of two consecutive Fibonacci numbers, Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 4 (2011), 45-50.
  • R. Oyono, C. Ritzenthaler: On rationality of the intersection points of a line with a plane quartic, proceeding of the international workshop WAIFI 2010 (International Workshop on the Arithmetic of Finite Fields), LNCS 6087, 224-237, 2010.
  • E. Gonzalez-Jimenez, R. Oyono: Non-hyperelliptic modular curves of genus 3, Journal of Number Theory, 130 (2010), pp. 862-878.
  • R. Oyono: Non-hyperelliptic modular Jacobians of dimension 3, Mathematics of Computation, 78 (2009), no. 266, 1173-1191.
  • S. Flon, R. Oyono, C. Ritzenthaler: Fast addition on non-hyperelliptic genus 3 curves, Algebraic geometry and its applications, Proceedings of the first SAGA conference, Ser. Number theory and its applications, World Sci. Publ., Hackensack, NJ, pp. 1 -- 28, 2008.
  • R. Granger, F. Hess, R. Oyono, N. Theriault, F. Vercauteren: Ate Pairing on Hyperelliptic curves, Advances in Cryptology, EUROCRYPT 2007, volume 4515 of LNCS, pp. 419-436.
  • R. Avanzi, T. Lange, G. Frey, R. Oyono: On Using Expansions to the Base of -2, Int. J. of. Comp. Math., pp403-406, 2004.
  • S. Flon, R. Oyono: Fast arithmetic on Jacobians of Picard curves, PKC 2004, LNCS 2947, pp. 55-68, 2004.
Preprints :

  • R. Oyono, N. Thériault: Group Arithmetic on C_{3,5} curves, submitted in November 2011.
Theses :

  • Phd thesis, Universität Essen, 2006: Arithmetik nicht-hyperelliptischer Kurven des Geschlechts 3 und ihre Anwendung in der Kryptographie.

  • Master thesis, Universität Gießen, 2000: Buekenhout-Metz Unitalen in PG(2,q^2).

Programs

Data on modular Curves / Jacobians