The Cryptography & Graphs Research Group (C&G) in Universitat de Lleida constitutes a well-established research team with a track record of more than 10 years of scientific activities. The team members in the C&G group are part of the Department of Mathematics and the Polytechnic Institute of Research and Innovation in Sustainability (InsPIReS). Most members of the C&G group teach in the degree and the master of Computer Science at the Escola Politècnica Superior (EPS). The research interests of the members in the C&G group lie between theory and applications, mainly in the following two areas: Cryptography and Graph Theory. In the area of Cryptography, our research focuses on computational aspects of algebraic curve cryptography and design of secure cryptographic protocols for RFID technology, smart cards and e-voting systems. In the area of Graph Theory, our research concerns open problems on dense and eccentric digraphs, extremal problems and privacy-preserving social network data analysis. [Més informació]

Recent Submissions

  • Distorting the volcano 

    Fouquet, Mireille; Miret, Josep M. (Josep Maria); Valera Martín, Javier (Elsevier, 2018)
    Volcanoes of ℓ–isogenies of elliptic curves are a special case of graphs with a cycle called crater. In this paper, given an elliptic curve E of a volcano of ℓ–isogenies, we present a condition over an endomorphism ϕ ...
  • Isogeny volcanoes of elliptic curves and sylow subgroups 

    Fouquet, Mireille; Miret, Josep M. (Josep Maria); Valera Martín, Javier (Springer International Publishing Switzerland, 2015)
    Given an ordinary elliptic curve over a finite field located in the floor of its volcano of ℓ-isogenies, we present an efficient procedure to take an ascending path from the floor to the level of stability and back to ...
  • MPI-based implementation of an enhanced algorithm to solve the LPN problem in a memory-constrained environment 

    Teixidó Torrelles, Ivan; Sebé Feixas, Francesc; Conde Colom, Josep; Solsona Tehàs, Francesc (Elsevier, 2014)
    In recent years, several lightweight cryptographic protocols whose security lies in the assumed intractability of the learning parity with noise (LPN) problem have been proposed. The LPN problem has been shown to be ...
  • Exploiting isogeny cordillera structure to obtain cryptographically good elliptic curves 

    Miret, Josep M. (Josep Maria); Tomàs, Rosana; Valls Marsal, Magda; Sadornil Renedo, Daniel; Tena Ayuso, Juan (Australian Computer Society Inc, 2008)
    The security of most elliptic curve cryptosystems is based on the intractability of the Elliptic Curve Discrete Logarithm Problem (ECDLP). Such a problem turns out to be computationally unfeasible when elliptic curves ...
  • On the ℓ-adic valuation of the cardinality of elliptic curves over finite extensions of Fq 

    Miret, Josep M. (Josep Maria); Pujolàs Boix, Jordi; Valera Martín, Javier (Springer Verlag, 2015)
    Let E be an elliptic curve defined over a finite field Fq of odd characteristic. Let l≠2 be a prime number different from the characteristic and dividing #E(Fq). We describe how the l-adic valuation of the number of points ...
  • Algorithms and cryptographic protocols using elliptic curves 

    Miret, Josep M. (Josep Maria); Moreno Chiral, Ramiro; Pujolàs Boix, Jordi; Valls Marsal, Magda (Institut d'Estudis Catalans. Secció de Ciències i Tecnologia, 2007)
    En els darrers anys, la criptografia amb corbes el.líptiques ha adquirit una importància creixent, fins a arribar a formar part en la actualitat de diferents estàndards industrials. Tot i que s'han dissenyat variants amb ...