Dr.
László Merai
Senior Scientist Applied Discrete Mathematics and Cryptography
Contact
Email: Laszlo.Merai(at)oeaw.ac.at
Telephone: +43 732 2468 5236
Biographical sketch
- 2001 - 2006: BSc and MCs in Applied Mathematics, Eötvös Loránd University
- 2006 - 2011: PhD in Mathematics, Eötvös Loránd University
FORMER AND CURRENT POSITIONS
- 2009 - 2012: Young researcher at the Rényi Institute, Budapest
- 2012 - present: Assistant professor at Eötvös Loránd University, Budapest
- 2014 - 01/2018: Research Scientist at RICAM, Linz
- 08/2018 - present: Research Scientist at RICAM, Linz
Teaching
- Discrete Mathematics Research Seminar (SS 2020)
Research Projects
Research interests
- Number theory
- Pseudorandom numbers
- Finite fields
- Cryptography
Publications
Peer Reviewed Journal Publication (28)
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Barroero, F.; Capuano, L.; Mérai, L.; Ostafe, A.; Sha, M. (2021) Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes. International Mathematics Research Notices, Bd. to appear, S. 23.
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Anupindi, V.; Merai, L. (2021) Linear complexity of some sequences derived from hyperelliptic curves of genus 2. Cryptography and Communications, Bd. to appear, S. 19.
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Dartyge, C.; Merai, L.; Winterhof, A. (2021) On the distribution of the Rudin-Shapiro function for finite fields. Proceedings of the American Mathematical Society, Bd. to appear, S. 1-14.
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Mérai, L.; Shparlinski, I.E. . (2021) On the dynamical system generated by the Möbius transformation at prime times. Research in Mathematical Sciences, Bd. to appear, S. 1-10.
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Mérai, L.; Ostafe, A.; Shparlinski, I.E. (2020) Dynamical irreducibility of polynomials in reduction modulo primes. Mathematische Zeitschrift, Bd. to appear, S. 15.
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Merai, L. (2020) Values of rational functions in small subgroups of finite fields and the identity testing problem from powers. Int. J. Number Theory, Bd. 16 (2), S. 219-–231.
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Gómez-Pérez, D.; Mérai, L. (2020) Algebraic dependence in generating functions and expansion complexity. Adv. Math. Commun., Bd. 14 (2), S. 307-–318.
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Gomez-Perez, D.; Merai, L.; Shparlinski, I.E. (2020) On the complexity of exact counting of dynamically irreducible polynomials. Journal of Symbolic Computation, Bd. 99, S. 231--241.
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L. Merai, I.E. Shparlinski (2020) Unlikely intersections over finite fields: polynomial orbits in small subgroups. Discrete Contin. Dyn. Syst., Bd. 40 (2), S. 1065--1073.
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L. Mérai, I. E. Shparlinski (2020) Distribution of short subsequences of inversive congruential pseudorandom number generator. Math. Comp. Math. Comp., Bd. 89 (322), S. 911--922.
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Merai, L.; Shparlinski, I.E. (2019) Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields. Acta Arithmetica, Bd. 188, S. 401--411.
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L. Merai, A. Winterhof (2018) On the pseudorandomness of some automatic sequences. Cryptography and Communications, Bd. 10 (6), S. 1013--1022.
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Mérai, L. (2018) On the elliptic curve endomorphism generator. Des. Codes Cryptogr., Bd. 86 (5), S. 1113–1129.
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L. Mérai, J. Rivat, A. Sárközy (2018) The measures of pseudorandomness and the NIST tests. Lecture Notes in Comput. Sci., Bd. 10737, S. 197--216.
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L. Merai, A. Winterhof (2018) On the Nth linear complexity of automatic sequences. Journal of Number Theory, Bd. 187, S. 415-429.
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M. Karpinski, L. Mérai, I. E. Shparlinski (2018) Identity Testing and Interpolation from High Powers of Polynomials of Large Degree over Finite Fields. J. Complexity, Bd. 49, S. 74--84.
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D. Gómez-Pérez, L. Mérai, H. Niederreiter (2018) On the expansion complexity of sequences over finite fields. IEEE Trans. Inform. Theory, Bd. 64 (6), S. 4228--4232.
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Mérai, L. (2017) Predicting the elliptic curve congruential generator. Appl. Algebra Eng. Commun. Comput., Bd. 28 (3), S. 193-203.
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Mérai, L. (2017) On pseudorandom properties of certain sequences of points on elliptic curve. Lecture Notes Computer Science, Bd. 10064, S. 54-63.
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L. Merai, H. Niederreiter, A. Winterhof (2017) Expansion complexity and linear complexity of sequences over finite fields. Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences, Bd. 9 (4), S. 501-509.
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Merai, Laszlo (2016) The cross-correlation measure of families of finite binary sequences: Limiting distributions and minimal values. Discret Appl. Math., Bd. 214, S. 153-168.
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L. Merai, A. Winterhof (2016) On the linear complexity profile of some sequences derived from elliptic curves. Designs, Codes, and Cryptography, Bd. 81, S. 259-267.
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L. Merai, A. Winterhof (2016) On the pseudorandomness of the Liouville function of polynomials over a finite field. Uniform Distribution Theory, Bd. 11 (1), S. 47-58.
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Mérai, L. (2016) On the typical values of the cross-correlation measure. Monatshefte für Mathematik, Bd. 180, S. 83-99.
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Merai, Laszlo; Yayla, Oguz (2015) Improving results on the pseudorandomness of sequences generated via the additive order of a finite field. Discret. Math., Bd. 338 (11), S. 2020-2025.
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Mérai, L. (2015) Pseudorandomness of binary sequences derived from linear recursions. Periodica Math. Hungar, Bd. 71, S. 64-77.
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Mérai, L. (2014) The higher dimensional analogue of certain estimates of Roth and Sárközy, Periodica Math. Hungar. 68 (2014) 77--91. Periodica Math. Hungar., Bd. 68, S. 77-91.
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Mérai, L. (2014) On the elliptic curve power generator. Unif. Distrib. Theory, Bd. 9 (2), S. 59-65.
Contribution in Collection (1)
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R. Hofer, L. Merai, A. Winterhof (2017) Measures of pseudorandomness: Arithmetic autocorrelation and correlation measure. In: C. Elsholtz, P. Grabner (Hrsg.), Number Theory - Diophantine problems, uniform distribution and applications, Festschrift in honour of Robert F. Tichy's 60th birthday.: Springer, S. 303-312.
Workingpaper (3)
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Merai, L.; Winterhof, A. (2021) Pseudorandom sequences derived from automatic sequences.
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Anbar, N.; Kalaycı, T.; Meidl, W.; Mérai, L. (2020) On functions with the maximal number of bent components.
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B. Kerr, L. Mérai, I. E. Shparlinski (2020) On digits of Mersenne numbers.