Publications

Preprints

Papers in journals

47. L. Mérai, I. E. Shparlinski, A. Winterhof, Character sums over sparse elements of finite fields, Bull. Lond. Math. Soc., (2024) doi:  10.1112/blms.13008

46. L. Mérai, I. E. Shparlinski, Distribution of recursive matrix pseudorandom number generator modulo prime powers, Math. Comp. 93 (2024), 1355-1370, doi: 10.1090/mcom/3895

45. L. Mérai, On divisors of sums of polynomials, Finite Fields Appl. 83 (2022) Paper No. 102090, doi: 10.1016/j.ffa.2022.102090

44. N. Anbar , T. Kalaycı, W. Meidl, L. Mérai, On functions with the maximal number of bent components, IEEE Trans. Inform. Theory 68 no. 9 (2022), 6174-6186. doi: 10.1109/TIT.2022.3174672

43. L. Mérai, A. Winterhof, Pseudorandom sequences derived from automatic sequences,  Cryptogr. Commun. 14, 783–815 (2022) doi: 10.1007/s12095-022-00556-9

42. B. Kerr, L. Mérai, I. E. Shparlinski, On digits of Mersenne numbers, Rev. Mat. Iberoam.  38 (2022), no. 6, 1901–1925, doi: 10.4171/RMI/1316

41. F. Barroero, L. Capuano, L. Mérai, A. Ostafe, M. Sha, Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes, Int. Math. Res. Not. (2022), no. 20, 16094–16137. doi: 10.1093/imrn/rnab171

40. V. Anupindi, L. Mérai, Linear complexity of some sequences derived from hyperelliptic curves of genus 2, Cryptogr. Commun. 14 (2022) 117-134. doi: 10.1007/s12095-021-00521-y

39. C. Dartyge, L. Mérai, A. Winterhof, On the distribution of the Rudin-Shapiro function for finite fields, Proc. Amer. Math. Soc. 149 (2021), no. 12, 5013–5023. doi: 10.1090/proc/15668 

38. L. Mérai, I. E. Shparlinski, On the dynamical system generated by the Möbius transformation at prime times, Res. Math. Sci. 8 (2021), no. 1, Paper No. 10, 12 pp.  doi: 10.1007/s40687-021-00249-4

37. L. Mérai, A. Ostafe, I. E. Shparlinski, Dynamical irreducibility of polynomials in reduction modulo primes. Math. Z.  298 (2021), no. 3-4, 1187–1199. doi: 10.1007/s00209-020-02630-5

36. L. Mérai, I. E. Shparlinski, Unlikely intersections over finite fields: polynomial orbits in small subgroups. Discrete Contin. Dyn. Syst. 40, (2020) no.2, 1065-1073, doi: 10.3934/dcds.2020070

35. D. Gómez-Pérez, L. Mérai, Algebraic dependence in generating functions and expansion complexity. Adv. Math. Commun. 14 (2020) no. 2, 307-318, doi: 10.3934/amc.2020022

34. L. Mérai, I. E. Shparlinski, Distribution of short subsequences of inversive congruential pseudorandom numbers modulo 2^t. Math. Comp. 89 (2020), no. 322, 911-922, doi: 10.1090/mcom/3467

33. D. Gómez-Pérez, L. Mérai, I. E. Shparlinski, On the complexity of exact counting of dynamically irreducible polynomials.  J. Symbolic Comput. 99(2020), 231-241, doi: 10.1016/j.jsc.2019.06.001

32. L. Mérai, Values of rational functions in small subgroups of finite fields and the identity testing problem from powers. Int. J. Number Theory. 16 (2020), no. 2, 219-231, doi: 10.1142/S1793042120500128

31. L. Mérai, I. E. Shparlinski, Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields. Acta Arith. 188 (2019), 401-411.doi: 10.4064/aa180307-20-8

30. M. Karpinski, L. Mérai, I. E. Shparlinski, Identity testing and interpolation from high powers of polynomials of large degree over finite fields. J. Complexity, 49 (2018) 74-84, doi: 10.1016/j.jco.2018.07.006

29. L. Mérai, J. Rivat, A. Sárközy, The measures of pseudorandomness and the NIST tests. Lecture Notes in Comput. Sci., 10737, Springer, Cham, 2018, 197-216 doi: 10.1007/978-3-319-76620-1_12

28. D. Gómez-Pérez, L. Mérai, H. Niederreiter, On the expansion complexity of sequences over finite fields. IEEE Trans. Inform. Theory 64 no. 6 (2018), 4228-4232. doi: 10.1109/TIT.2018.2792490

27. L. Mérai, A. Winterhof, On the Nth linear complexity of automatic sequences. J. Number Theory. 187 (2018), 415-429. doi: 10.1016/j.jnt.2017.11.008

26. L. Mérai, A. Winterhof, On the pseudorandomness of automatic sequences. Cryptogr. Commun. 10 (2018), no. 6, 1013-1022. doi: 10.1007/s12095-017-0260-7

25. L. Mérai, On the elliptic curve endomorphism generator.  Des. Codes Cryptogr. 86 (2018) no. 5, 1113-1129. doi: 10.1007/s10623-017-0382-0

24. R. Hofer, L. Mérai, A. Winterhof, Measures of pseudorandomness: Arithmetic autocorrelation and correlation measure. In: C. Elsholtz, P. Grabner (Eds.), Number Theory - Diophantine problems, uniform distribution and applications, Festschrift in honour of Robert F. Tichy's 60th birthday.: Springer, 303–312, Springer, Cham, 2017 doi: 10.1007/978-3-319-55357-3_15

23. L. Mérai, On pseudorandom properties of certain sequences of points on elliptic curve. Lecture Notes in Comput. Sci., 10064, Springer, Berlin, 2016, 54-63 doi: 10.1007/978-3-319-55227-9_4

22. L. Mérai, Predicting the elliptic curve congruential generator. Appl. Algebra Eng. Commun. Comput. 28 (2017) no. 3, 193-203 doi: 10.1007/s00200-016-0303-x

21. L. Mérai, H. Niederreiter, A. Winterhof, Expansion complexity and linear complexity of sequences over finite fields. Cryptogr. Commun. 9 (2017) no. 4, 501-509 doi: 10.1007/s12095-016-0189-2

20. L. Mérai, The cross-correlation measure of families of finite binary sequences: limiting distributions and minimal values. Discrete Appl. Math. 214 (2016) 153–168. doi: 10.1016/j.dam.2016.06.024

19. L. Mérai, On the typical values of the cross-correlation measure. Monatsh. Math. 180 (2016) no. 1, 83-99, doi: 10.1007/s00605-016-0886-0

18. L. Mérai, A. Winterhof, On the pseudorandomness of the Liouville function of polynomials over a finite field. Unif. Distrib. Theory, 11 (2016), no. 1, 47-58.

17. L. Mérai, A. Winterhof, On the linear complexity profile of some sequences derived from elliptic curves. Des. Codes Cryptogr., 81 (2016) no. 2, 259-267, doi: 10.1007/s10623-015-0140-0

16. L. Mérai, O. Yayla, Improving results on the pseudorandomness of sequences generated via the additive order. Discrete Math. 338 (2015), 2020-2025, doi: 10.1016/j.disc.2015.04.015

15. L. Mérai, Pseudorandomness of binary sequences derived from linear recursions. Periodica Math. Hungar. 71 (2015) 64-77, doi: 10.1007/s10998-015-0085-0

14. L. Mérai, On the elliptic curve power generator. Unif. Distrib. Theory, 9 (2014) no. 2, 59-65.

13. L. Mérai, The higher dimensional analogue of certain estimates of Roth and Sárközy. Periodica Math. Hungar. 68 (2014) 77-91, doi: 0.1007/s10998-014-0016-5

12. M. Bárász, P. Ligeti, K. Lónya, L. Mérai, D. A. Nagy, An another twist in the Dining Cryptographers' protocol. Tatra Mt. Math. Publ. 57 (2013) 85-99, doi: 10.2478/tmmp-2013-0037

11. M. Bárász, P. Ligeti, L. Mérai, D. A. Nagy, Anonymous sealed bid auction protocol based on a variant of the Dining Cryptographers' protocol. Periodica Math. Hungar. 65 (2012), no. 2, 167-176, doi: 10.1007/s10998-012-6512-6

10. L. Mérai, Remarks on pseudorandom binary sequences over elliptic curves. Fund. Inform. 114 (2012) no. 3-4, 301-308.

 9. L. Mérai, Construction of pseudorandom binary sequences over elliptic curves using multiplicative characters. Publ. Math. Debrecen, 80 (2012) no. 1-2, 199-213.

 8. L. Mérai, Construction of pseudorandom binary lattices using elliptic curves. Proc. Amer. Math. Soc. 139 (2011), no. 2, 407-420.

 7. L. Mérai, On finite pseudorandom lattices of k symbols. Monatsh. Math. 161 (2010), no. 2, 173-191.

 6. L. Mérai, Construction of pseudorandom binary lattices based on multiplicative characters. Periodica Math. Hungar. 59 (2009) 43-51.

 5. L. Mérai, A construction of pseudorandom binary sequences using both additive and multiplicative characters. Acta Arith. 139 (2009), 241-252.

 4. L. Mérai, A construction of pseudorandom binary sequences using rational functions. Unif. Distrib. Theory, 4 (2009), no. 1, 35-49.

 3. L. Mérai, Construction of large families of pseudorandom binary sequences. Ramanujan J. 18 (2009), 341-349, the original publication is available at www.springerlink.com.

 2. G. Horváth, L. Mérai, The complexity of checking identities over non-solvable groups (in Hungarian). Mat. Lapok 13 (2006/07), no. 2, 20-27 (2008).

 1. G. Horváth, J. Lawrence, L. Mérai, Cs. Szabó, The complexity of the equivalence problem for nonsolvable groups. Bull. Lond. Math. Soc. 39 (2007), no. 3, 433-438.

Patents