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Papers in progress, Preprints, Submitted papers
- J. Gutierrez, A. Ibeas and A. Joux: Recovering a sum of two squares decomposition. Submitted, 2010.
- J. Gutierrez, D. Gomez-Perez, A. Ibeas, I. Shparlinski. Predicting Masked Linear Pseudorandom Number Generators over Finite Fields, submitted, 2011.
- A. Ibeas: Periodic lozenge tilings of the plane. Preprint, University of Cantabria, 2010.
- D. Gomez, J. Gutierrez, A. Ibeas. On the connectedness of finite distance graphs. Submitted 2011.
- J. Schicho and D. Sevilla: Tschirnhaus-Weirstrass curves. Preprint, Johann Radon Institute for Computational and Applied Mathematics, 2008.
- D. Gómez, J. Gutierrez, A. Ibeas. A strategy to recovering roots of bivariate polynomials modulo p. Preprint, Applied Mathematics and Computer Science Department, University of Cantabria, 2009.
- D. Gomez, J. Gutierrez, A. Ostafe. Hash functions from triangular Polynomial Systems. In progress 2011.
Publications in the past years
- D.
Gómez, J. Gutierrez, A. Ibeas. On
the Linear Complexity
in the
Naor-Reingold Sequence. Information Proccesing Letters, 111 (2011), 854-858.
- R. Sendra, D. Sevilla. Radical parametrizations of algebraic curves by adjoint curves. Journal of Symbolic Computation, 46-9(2011), 1030-1038.
- D. Sevilla and D. Wachsmuth:
Polynomial
integration on regions defined
by a triangle and a conic. Proceedings of the
International Symposium on Symbolic and Algebraic Computation, ISSAC
2010. p. 163-170. ISBN 978-1-4503-0150-3.
- Gomez, Domingo; Nicolás, Alejandro P. An estimate on the number of stable
quadratic polynomials. Finite Fields Appl. 16 (2010), no. 6,
401–405.
- A. Ibeas and A. Winterhof: Exponential sums and linear complexity of nonlinear pseudorandom number generators with polynomials of small p-weight degree. Uniform Distribution Theory 5 (2010), no. 1, pp. 79-93.
- J. Gutierrez and I. Shparlinski: Expansion of orbits of dynamical systems over finite fields. Bulletin of Australian Mathematical Scociety. 82 (2010), no. 2, 232–239.
- Cruz, Marcos; Gómez, Domingo; Sadornil, Daniel. On the linear complexity of the Naor-Reingold sequence with elliptic curves. Finite Fields Appl. 16 (2010), no. 5, 329–333.
- Gomez, Domingo; Winterhof, Arne. Waring's problem in finite fields with Dickson polynomials. Finite fields: theory and applications, 185–192, Contemp. Math., 518, Amer. Math. Soc., Providence, RI, 2010.
- D. Gómez, C. Chen, and A. Winterhof: Distribution of explicit digital inversive pseudorandom numbers and applications to some binay sequences. Monte Carlo and Quasi-Monte Carlo Methods 2008, to appear.
- D. Gómez, J. Gutierrez and A. Ibeas: Cryptographic aspects of some pseudorandom sequences . In "Nuevos Avances en Criptografía y Codificación de la Información". Eds: Policarpo Abascal et al. February 2009, pp. 77-85.
- D. Gómez and E. El-Mahassni: On the distribution of nonlinear congruential pseudorandom numbers of higher orders in residue rings. AAECC 2009. LNCS 5527, Pages: 195-203.
- D. Gómez, J. Gutierrez, A. Ibeas, and D. Sevilla: Common factors of resultants modulo p. Bulletin of the Australian Mathematical Society. Volume 79, Issue 2, April 2009, Pages: 299-302.
- A. Ibeas and A. Winterhof: Noisy interpolation of multivariate sparse polynomials in finite fields. In "AAECC 2009". Eds: M. Bras-Amorós and Tom Høholdt. LNCS 5527, pp. 169-178.
- D. Gómez and A. Winterhof: Character sums for sequences of iterations of Dickson polyomials. Finite fields and applications. Contemp. Math., 461. Pages: 147-151.
- D. Gómez, J.
Gutierrez, and A. Ibeas: An algorithm
for finding
small roots of
multivariate polynomials over the integers.
Proceedings of the
“Segundas Jornadas de Teoría de Números
2007”. Biblioteca de la
Revista Matemática Iberoamericana, 2008.
- A. Ibeas: On
the period of the Naor-Reingold generator.
Information Processing Letters. Volume 108, Issue 5, 15 November 2008,
Pages 304-307.
- J. McKay and D. Sevilla: Decomposing replicable functions. LMS J. of Computation and Mathematics 11(2008), pp. 146-171.
- J. Gutierrez and A. Winterhof: Exponential Sums of Nonlinear Congruential Pseudorandom Number Generators with Redei Functions. Finite Fields and their Applications 14 (2008) no. 2, pp. 410-416.
- D. Gómez and E. D. El-Mahassni: On the Distribution of Counter-Dependent Nonlinear Congruential Pseudorandom Number Generators in Residue Rings. International Journal of Number Theory. Volume: 4, Issue: 6 (December 2008) Page 1009 - 1018.
- D. Gómez, A. Winterhof: Multiplicative Character Sums of Recurring Sequences with Rédei Functions. Procc. SETA 2008. LNCS 5203, Springer, 175-181.
- J. Gutierrez, I. Shparlinski
: On
the distribution of rational funcitions on consecutive powers.
Uniform Distribution Theory 3 (2008), no.1, 85--91.
.
- J. Gutierrez and A. Ibeas: Inferring sequences produced by a linear congruential generator on elliptic curves missing high-order bits. Designs, Codes and Cryptography 41 (2007) no. 2, pp. 199-212.
- D. Gómez, J. Gutierrez, and A. Ibeas: Cayley Digraphs of Finite Abelian Groups and Monomial Ideals. SIAM Journal on Discrete Mathematics 21 (2007) no. 3, pp. 763-784.
- D. Gómez, J. Gutierrez, and A. Ibeas: Optimal Routing in Double Loop Networks. Theoretical Computer Science 381 (2007) no. 1-3, pp. 68-85.
- D. Sevilla and T. Shaska: Hyperelliptic curves with reduced automorphism group A5. Applicable Algebra In Engineering, Comunication and Computing 18 (2007) no. 1-2, pp. 3-20.
- D. Gómez, J. Gutierrez, and A. Ibeas: Attacking the Pollard Generator. IEEE Trans. Information Theory 52 (2006) no. 12, 2006, pp. 5518-5524.
- J. Gutierrez and D. Sevilla: On Ritt's decomposition Theorem in the case of finite fields. Finite Fields and Their Applications 12 (2006) no. 3, pp. 403-412.
- S. R. Blackburn, D. Gómez, J. Gutierrez, and I. Shparlinski: Reconstructing noisy polynomial evaluation in residue rings. Journal of Algorithms 61 (2006) no. 12, pp. 45-58.
- J. Gutierrez and D. Sevilla: On Decomposition of Tame Polynomials and Rational Functions. Proc. CASC 2006, LNCS 4194, Springer, pp. 219-227.
- D. Gómez, J. Gutierrez, and A. Ibeas: Integer Factoring with Extra Information. Proc. RECSI 2006, Barcelona, Spain, pp. 573-583.
- J. Gutierrez and D. Sevilla: Building Counterexamples to Generalizations for Rational Functions of Ritt's Decomposition Theorem. Journal of Algebra 303 (2006) no. 2, pp. 655-667.
- D. Gómez, J. Gutierrez, and I. Shparlinski: Exponential sums with Dickson polynomials. Finite Fields and Their Applications 12 (2006) no. 1, pp. 16-25.
- J. Gutierrez and D. Sevilla: Computation of Unirational Fields. Journal of Symbolic Computation 41 (2006) no. 11, pp. 1222-1244.
- D. Gómez, J. Gutierrez, and A. Ibeas: Cryptoanalysis of the Quadratic Generator. Proc. INDOCRYPT 2005, LNCS 3797, Springer, pp. 118-129.
- D. Gómez, J. Gutierrez, and A. Ibeas: Circulant Digraphs and Monomial Ideals. Proc. CASC 2005, LNCS 3718, Springer, pp. 196-207.
- J. Gutierrez and T. Shaska: Hyperelliptic curves with extra involutions. J. of Computation and Mathematics 8 (2005), LMS, pp. 102-115.
- S. R. Blackburn, D. Gómez, J. Gutierrez, and I. Shparlinski: Predicting Nonlinear Pseudorandom Number generators. Mathematics Computation 74 (2005) no. 251, AMS, pp. 1471-1494.
- C. Martinez, R. Beivide, E. Gabidulin, and J. Gutierrez: On the Weight Distribution of Gaussian Graphs with an Application to Coding Theory. Proc. IEEE 8th ISCTA 2005, HW Communications.
- J. Gutierrez and D. Sevilla: Computation of Unirational Fields. Proc. A3L (Algorithm Algebra and Logic 2005), ed. Dolzmann, Seidl, Sturm, pp 129-134.
- D. Gómez, J. Gutierrez, A. Ibeas, C. Martinez, and R. Beivide: On Finding a Shortest Path in Circulant Graphs with Two Jumps. Proc. COCOON 2005, LNCS 3595, Springer, pp. 777-786.
- C. Martinez, R. Beivide, J. Gutierrez, and E. Gabidulin: On the Perfect t-Dominating Set Problem in Circulant Graphs and Codes over Gaussian Integers. Proc. ISIT 2005, IEEE Computer Society Press.
- J. Gutierrez, D. Sevilla, and T. Shaska: Hyperelliptic Curves of Genus 3 with Prescribed Automorphism Group. Computational Aspects on Algebraic Curves, LNCS 13, Springer, pp. 109-123.
- Affine Algebraic Geometry. Proc. of the Special Session on Affine Algebraic Geometry in AMS-RSME 2003. Contemporary Mathematics 369, ed. J. Gutierrez, V. Shpilrain, and J-T. Yu.
- J. Gutierrez, D. Gómez, and A. Ibeas: Digrafos Circulantes e Ideales Monomiales. Proc. EGC 2005. Servicio de Publ. de la U. de Cantabria, pp. 54-67.
- D. Gómez, J. Gutierrez, A. Ibeas, C. Martinez, and R. Beivide: Encaminamiento en Grafos Dirigidos de Grado Cuatro. Proc. EACA 2004, pp. 155-159.
- D. Gómez, J.Gutierrez, A. Ibeas, and D. Sevilla: Prediciendo el Generador Cuadrático. Avances en Criptología y Seguridad de la Información (Proc. of RECSI 2004), Díaz de Santos, pp. 185-195.
- Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC 2004. ACM press, ed. J. Gutierrez.
- J. McKay and D. Sevilla: Aplicación de la Descomposición Racional Univariada a Monstruos Moonshine. Proc. EACA 2004, pp. 289-294.
- J. Gutierrez, R. Rubio, and J. von zur Gathen: Multivariate Polynomial Decomposition. Applicable Algebra in Engineering, Communication and Computing 14 (2003), no. 1, pp. 11-31.
- J. Gutierrez, I. Shparlinski, and A. Winterhof: On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators. IEEE Trans. on Information Theory 49 (2003), no. 1, pp. 60-64.
- R. Beivide, J.Gutierrez, C. Izu, and C. Martinez: Distance-Hereditary Embeddings of Circulant Graphs. Proc. International Conference on Coding and Computing ITCC 2003, IEEE Computer Society, pp. 320-325.
- S. R. Blackburn, D. Gómez, J. Gutierrez, and I. Shparlinski: Predicting the inversive generator. Proc. 9th IMA Intern. Conf on Cryptography and Coding (2003), LNCS 2898, Springer, pp. 264-275.
- R. Beivide, J. A. Gregorio, J. Gutierrez, C. Izu, C. Martinez, and J. Miguel-Alonso: Chordal Topologies for Interconnection Networks. Proc. 5th International Symposium on High Performance Computing ISHPC-V 2003, LNCS 2858, Springer, pp. 385-392.
- J. Gutierrez and A. Ibeas: Criptografía. Protocolos Criptográficos y Seguridad en Redes. Servicio de Publ. de la U. de Cantabria, pp. 63-85.
- J. Gutierrez: Las Redes Substitución-Permutación y el AES. Protocolos Criptográficos y Seguridad en Redes. Servicio de Publ. de la U. de Cantabria, pp. 86-102.
- Protocolos Criptográficos y Seguridad en Redes. Servicio de Publ. de la U. de Cantabria. Ed. J. Gutierrez and J. Tena.
- J. Gutierrez, R. Rubio, and J-T. Yu: D-Resultant for Rational Functions. Proc. AMS 130 (2002), no. 8, pp. 2237-2256.
- J. Gutierrez, R. Rubio, and J. Schicho: Polynomial Parametrization of Regular Curves. Computed Aided Geometric Design 19 (2002) no. 3, pp. 223-234.
- J. Gutierrez, R. Rubio, and D. Sevilla: On Multivariate Rational Function Decomposition. Journal of Symbolic Computation 33 (2002) no. 5, pp. 546-562.
- J. Gutierrez, R. Rubio, and D. Sevilla: Computing the Fixing Group of a Rational Function. Proc. of the 5th International Workshop on Computer Algebra in Scientific Computing CASC 2002, eds. V.G. Ganzha, E. Meyer, E. Vorozhtosov, pp. 159-164.
- J. Gutierrez, D. Kozen: Polynomial Decomposition. Computer Algebra Handbook, Springer-Verlag, pp. 22-26.
- C. Alonso, J. Gutierrez, and R. Rubio: On the Dimension of Parameters of a Unirational Variety. Cryptography and computational number theory (1999), pp. 3-9, Progr. Comput. Sci. Appl. Logic 20 (2001), Birkhäuser, pp. 3-11.
- J. Gutierrez and C. Ruiz de Velasco: Polynomial Near-rings in Several Variables. Proc. of Near-rings 1998, Kluwer Academic Publishers, pp. 94-102.
- J. Gutierrez and D. Gómez: Iterations of Multivariate Polynomials and Discrepancy of Pseudorandom Numbers. Proc. AAECC-14 2001, LNCS 2227, pp. 194-204.
- J. Gutierrez, R. Rubio, and D. Sevilla: Unirational Fields of Transcendence Degree One and Functional Decomposition. Proc. ISSAC 2001, ACM, pp. 167-175.
- J. Gutierrez, H. Niederreiter, and I. Shparlinski: On the Multidimensional Distribution of Inverse Congruential Pseudorandom Numbers in Parts of the Period. Monatshefe fur Mathematik 129 (2000), pp. 31-38.
- J. Gutierrez, T. Recio: Defining Degenerate Robots Symbolically. Mathematics and Computers in Simulation, 51 (2000), pp. 441-449.
- J. Gutierrez, R. Rubio: CADECOM: Computer Algebra software for functional DECOMposition. Proc. Computer Algebra in Scientific Computation CASC 2000, Springer-Verlag, pp. 233-249.
- J. Gutierrez: Computational Aspects on Lüroths Theorem. Joint conference AMS and HKMSociety.
- L. González-Vega, I. Necula, D. Sevilla: A Maple/Matlab Toolbox for Computed Aided Geometric Design. Proceedings of the 2000 Encuentro de Álgebra Computacional y Aplicaciones EACA 2000, pp. 239-256.
- L. González-Vega, I. Necula, D.Sevilla: A symbolic/numeric toolbox for Computed Aided Geometric Design. An. Univ. Timişoara Ser. Mat.-Inform. 38 no. 2 (2000), 2nd International Workshop on Symbolic and Numeric Algorithms in Scientific Computing (SYNASC 2000), pp. 73-99. ISSN 1224-970X.
- V. Drensky, J. Gutierrez, and J-T. Yu: Groebner Bases and the Nagata Automorphism. J. of Pure and Applied Algebra 135 (1999), no. 2, pp. 135-153.
- J. Gutierrez, R. Rubio, and J. von zur Gathen: On Multivariate Polynomial Decomposition. Proc. CASC 1999, Springer, pp. 463-479.
- J. Gutierrez: Maple Procedures for Simplifying Sine-Cosine Equations. Progress in Simulation, Modelling, Analysis and Synthesis of Modern Electrical and Electronic Devices and Systems. World Scientific Engineering Society, pp. 330-336.
- J. Gutierrez and R. Rubio: Cálculo de Subcuerpos en Extensiones Puramente Transcendentes. Proc. EACA 1999, pp. 277-282.
- J. Gutierrez and R. Rubio: Reduced Groebner Bases under Composition. Journal of Symbolic Computation 26 (1998), no. 4, pp. 433-444.
- J. Gutierrez and T. Recio: Advances on the Simplification of Sine-Cosine Equations. J. of Symbolic Computation 26 (1998), no. 1, pp. 31-70.
- C. Alonso, J. Gutierrez, and T. Recio: A Note on Separated Factors of Separated Polynomials. J. of Pure and Applied Algebra 121 (1997), no. 3, pp. 217-222.
- C. Alonso, J. Gutierrez, and T. Recio: An Implicitation Algorithm With Fewer Variables. Computed Aided Geometric Design 12 (1995), no. 3, pp. 251-258.
- C. Alonso, J. Gutierrez, and T. Recio: Reconsidering Algorithms for Real Parametric Curves. Aplicable Algebra and Engineering, Communication and Computing 6 (1995), no. 6, pp. 345-352.
- C. Alonso, J. Gutierrez, and T. Recio: A Rational Function Decomposition Algorithm by Near-Separated Polynomials. Journal of Symbolic Computation 19 (1995), no. 6, pp. 527-554.
- J. Gutierrez and C. Ruiz de Velasco: Ideals in the Near-Rings of Polynomials. Proc. of Near-rings, Oberwolfach 1989, pp. 91-95.
- C. Alonso, J. Gutierrez, and T. Recio: FRAC: A Maple Package for Computing in the Rational Function Field K(X). Maple V: Mathematics and its Application, Birkhäuser, pp. 107-115.
- C. Alonso, J. Gutierrez, and T. Recio: Trazado de Curvas Paramétricas sin Pérdida de Puntos en la Imagen. Proc. CEIG 1995, pp. 133-142.
