Research interests:

 

       Number Theory, Algebraic Geometry and its Applications in Cryptography and Coding Theory. 

 

 

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RESEARCH

1. Points rationnels sur Q de la jacobienne de la courbe modulaire X0(81), C. R. Acad. Sc. Paris, t. 298, Série I, no 18 (1984), 433-436.

2. Points rationnels de la courbe modulaire X0(125) et de sa jacobienne, J. Number Theory, 25 (1987), 112-131.

3. Evaluation d'une somme cubique de caractères, J. Number Theory, 27 (1987), 41-45.

4. On the homomorphisms of a family of finite rings, Bull. Greek Math. Soc. 30 (1989), 43- 48.

5. Solutions entières de l'équation  Ym = f(X), Sém. Th. des Nombres Bordeaux 3 (1991), 187-199.

6. Points entiers sur les courbes hyperelliptiques, Acta Arithmetica, 62 (1992), 25-43.

7. Solutions entières de l'équation  f(X,Y) a = p(X)g(X,Y), C. R. Acad. Sc. Paris 315 (1992), 963-968.

8. Courbes elliptiques et 2-extensions Abéliennes, Bull. Greek Math. Soc. 34 (1992), 155-160.

9. Points entiers sur les courbes de genre 0, Colloquim Mathematicum, LXVI (1993), 1-7.

10. Points entiers et modèles des courbes algébriques, Monatshefte für Mathematik 118 (1994), 111-143.

11. Estimation effective des points entiers d'une famille de courbes algébriques, Annales de la Faculté de Sciences de Toulouse, V, no 4, (1996), 691-725.

12. Integer points on algebraic curves with exceptional units, J. Austr. Math. Soc. 63 (1997), 145-164.

13. Polynomial bounds for the solutions of a class of Diophantine equations J. Number Theory 66 (1997), 271-281.

14. Bounds for the size of integral solutions to Ym = f(X), Proc. Edinburgh Math. Soc. 42 (1999), 127-141.

15. A simple method for solving the diophantine equation y2 = x4+ax3+bx2+cx+d, Elemente der Mathematik 54 (1999), 32-36.

16. Bounds for the minimal solutions of the genus zero diophantine equations, Acta Arithmetica, LXXXVI.1 (1998) 51-90.

            17. The number of solutions of the Mordell equation, Acta Arithmetica LXXXVIII.2 (1999), 173-179. Corrigendum, Acta Arithmetica XCII.4 (2000), 387-8.

            18. Sur la réduction modulo p des polynômes absolument irréductibles, Monatshefte für Mathematik 129 (2000), 139-145.

            19. Sur la réduction modp des courbes algébriques lisses, Archiv der Mathematik 75 (2000), 342-345.

            20. Bounds for the size of integral points on curves of genus 0, Acta Mathematica Hungarica, 93 (4) (2001), 327-346.

            21. (with E. Voskos) On the practical solution of genus zero diophantine equations, Journal of Symbolic Computation, 30 (2000), 573-582.

            22. (with E. Voskos) Solving genus zero diophantine equations with at most two infinite valuations, Journal of Symbolic Computation, 33 (2002), 479-491.

            23. Affine curves with infinitely many integral points, Proc. Amer. Math. Soc.131, 5 (2002), 1357-1359.

            24. (with E. Voskos) On the distribution of integer points of rational curves, Periodica Math. Hungarica, 46 (1) (2003), 99-111.

            25. Bounds for the smallest integer point of a rational curve, Acta Arith. 107.3 (2003), 251-268.

            26. (σε συνεργασία με τον M. Laurent) On the global distance between two algebraic points on a curve, J. Number Theory 104 (2004), 210-254.

            27. Integer points on rational curves with fixed gcd, Publicationes Mathematicae Debrecen, 64, 3-4 (2004), 369-379.

            28. (with G. Walsh) A note on the Diophantine equation x2-dy4 = 1 with prime discriminant, C. R. Math. Rep.Acad. Sci. Canada, 27 no. 2 (2005), 54-57.

29. (with G. Walsh) A note on the Diophantine equation x2-dy4 = 1 with prime discriminant II, Colloquium Mathematicum 105, No.1 (2006), 51-55.

30. (with Κ. Draziotis) Practical solution of the Diophantine equation y2 = x(x+2apb)(x-2apb), Mathematics of Computation, Vol. 75, no 255 (2006), 1585-1593.

            31. (with Κ. Draziotis) Explicit Chevalley-Weil Theorem for Affine Plane Curves, Rocky Mountain Journal of Mathematics, 39(1) (2009), 49-70.

            32. (with Κ. Draziotis) Solving the Diophantine equation  y2 =   x(x2- n2), Journal of Number Theory  129 (2009), 102-121.

            33. On the rational solutions of the equation f(X,Y)a = h(X)g(X,Y), Canadian Mathematical Bulletin, 52 (1) (2009), 117-126.

            34. (with P. Alvanos and Y. Bilu) Characterizing Algebraic Curves with Infinitely Many Integral Points, International Journal of Number Theory 5, no. 4 (2009), 585 - 590.

            35. A variant of Digital Signature Algorithm, Designs, Codes and Cryptography 51, No. 1 (2009), 99-104. Erratum Designs, Codes and Cryptography 58, No. 2, (2011), 219.

36.  (with P. Alvanos) Solving Norm Form Equations over Number Fields, Algebraic Informatics, Third International Conference, CAI 2009, Thessaloniki, Greece, May 19-22, 2009, Proceedings,  Lecture Notes in Computer Science  5725, pp 136-146.

            37. A public key encryption scheme based on factoring and discrete logarithm, Journal of Discrete Mathematical Sciences & Cryptography, 12 (2009) No 6, 745-752.

            38. (with Κ. Draziotis) An Effective Version of Chevalley-Weil Theorem  for Projective Plane Curves, Houston Journal of Mathematics, Mathematics Vol. 38, No. 1 ( 2012), 29-39.

            39. (with P. Alvanos) Solving genus zero Diophantine equations over number fields, Journal of Symbolic Computation  46 (2011), 54-69.

            40. (with  G. Karagiorgos)  An algorithm for computing a basis of a finite Abelian group, 4rd International Conference on Algebraic Informatics, Linz, Austria, June 21-24, 2011. LNCS 6742, Springer, Berlin, (2011) 174-184.

            41. (with G. Karagiorgos)  Linear Time Algorithms for the Basis of Abelian Groups, 17th Annual International Conference in Computing and Combinatorics COCOON 2011, Dallas TX, USA, August 14-16, 2011. LNCS 6842, Springer, Berlin Heidelberg (2011), 456-466.

42. Some Lattice Attacks on DSA and ECDSA, Applicable Algebra in Engineering, Communication and Computing, (2011) 22:347–358.

43. (with G. Karagiorgos) Efficient Algorithms for the Basis of Finite Abelian Groups, Discrete  Mathematics, Algorithms and Applications, Vol. 3, No 4  (2011) 537-552.

44. On the Cryptographic Long Term Security, Journal of Applied Mathematics & Bioinformatics, vol.3, no.1, 2013, 1-15.

45. (with Κ. Draziotis) Lattice Attacks on DSA schemes based on Lagrange’s Algorithm, 5rd International Conference on Algebraic Informatics, Island Porcquerolles, France, September 3-6, 2013. LNCS 8080, Springer, Berlin, (2013) 121-133.

 46. (with R. Rolland) A Digital Signature Scheme for Long-Term Security Cryptology ePrint Archive: Report 2012/134.