Prof.
Harald Niederreiter
Senior Scientist Applied Discrete Mathematics and Cryptography
Contact
Email: Harald.Niederreiter(at)oeaw.ac.at
Telephone:
FORMER AND CURRENT POSITIONS
Previous Positions (excerpt):
- Director, Institute of Discrete Mathematics, Austrian Academy of Sciences
- Director, Institute of Information Processing, Austrian Academy of Sciences
- Professor of Mathematics, University of Illinois at Urbana-Champaign
- Professor of Mathematics and Computer Science, National University of Singapore
Visiting Positions (excerpt):
- The Institute for Advanced Study (Princeton, NJ, USA)
- University of California at San Diego (La Jolla, CA, USA)
- University of New South Wales (Sydney, Australia)
- Pennsylvania State University (University Park, PA, USA)
- Academia Sinica (Taipei, Taiwan)
- ETH (Zurich, Switzerland)
- Université de la Méditerranée (Marseille-Luminy, France)
Academic Honors and Awards
- Full member, Austrian Academy of Sciences
- Full member and former member of the presidium, German Academy of Natural Sciences Leopoldina
- Cardinal Innitzer Prize for Natural Sciences in Austria
- Invited speaker at ICM 1998 (Berlin) and ICIAM 2003 (Sydney)
- Singapore National Science Award 2003
- 2013 Fellow of the American Mathematical Society
Research interests
- Numerical Analysis
- Pseudorandom Numbers
- Quasi-Monte Carlo Methods
- Cryptology
- Finite Fields
- Applied Algebra
- Algorithms
- Number Theory
- Coding Theory
Publications
Journal Publication (30)
- Allouche, J.P.; Han, G.-N.; Niederreiter, H. (2020) Perfect linear complexity profile and Apwenian sequences. Finite Fields and Their Applications, Bd. 68, S. 101761.
- 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.
- Niederreiter, H. (2017) Recent constructions of low-discrepancy sequences. Math. Comput. Simulation, Bd. 135, S. 18-27.
- Meidl, Wilfried; Niederreiter, Harald (2016) Multisequences with high joint nonlinear complexity. Designs Codes Cryptogr., Bd. 81 (2), S. 337-346.
- Kritzer, P.; Niederreiter, H. (2016) Mixed orthogonal arrays, (u,m,e,s)-nets, and (u,e,s)-sequences. Discrete Mathematics, Bd. 339, S. 2199-2208.
- Niederreiter, H. (2016) A survey of some applications of finite fields. Designs, Codes and Cryptography, Bd. 78, S. 129-139.
- M. Gnewuch, F.Y. Kuo, H. Niederreiter, H. Wozniakowski (2015) Guest editors' preface Oberwolfach Workshop 1340 "Uniform Distribution Theory and Applications''. J. Complexity, Bd. 31 (3), S. vi.
- P. Kritzer, H. Niederreiter (2015) Propagation rules for (u,m,e,s)-nets and (u,e,s)-sequences. Journal of Complexity, Bd. 31 (3), S. 457-473.
- R. Hofer, H. Niederreiter (2014) Vandermonde nets. Acta Arith., Bd. 163 (2), S. 145-160.
- H. Niederreiter, C. Xing (2014) Sequences with high nonlinear complexity. IEEE Trans. Inform. Theory, Bd. 60 (10), S. 6696-6701.
- D. Gomez, R. Hofer, H. Niederreiter (2013) A general discrepancy bound for hybrid sequences involving Halton sequences. Uniform Distribution Theory, Bd. 8 (1), S. 31-45.
- C. Schretter, H. Niederreiter (2013) A direct inversion method for non-uniform quasi-random point sequences. Monte Carlo Methods and Applications, Bd. 19 (1), S. 1-9.
- H. Niederreiter, A. Yeo (2013) Halton-type sequences from global function fields. Science in China Series A - Mathematics, Bd. 56 (7), S. 1467-1476.
- R. Hofer, H. Niederreiter (2013) A construction of (t,s)-sequences with finite-row generating matrices using global function fields. Finite fields and their applications, Bd. 21, S. 97-110.
- Niederreiter, H. (2012) Improved discrepancy bounds for hybrid sequences involving Halton sequences. Acta Arithmetica, Bd. 155, S. 71-84.
- Niederreiter, H.; Shahverdian, A.Yu. (2012) Discrepancy estimates for rotation sequences and oscillation sequences. Asian-European Journal of Mathematics, Bd. 5 (2 Art. 1250020), S. 12.
- Niederreiter, H.; Vielhaber, M.; Wang, L. (2012) Improved results on the probabilistic theory of the joint linear complexity of multisequences. Science in China Series F, Bd. 55, S. 165-170.
- Niederreiter, H. (2012) The independence of two randomness properties of sequences over finite fields. Journal of Complexity, Bd. 28, S. 154-161.
- Niederreiter, H. (2011) Discrepancy bounds for hybrid sequences involving matrix-method pseudorandom vectors. Publ. Math. Debrecen, Bd. 79 (3-4), S. 589-603.
- P. Hellekalek, H. Niederreiter (2011) Construction of uniformly distributed sequences using the b-adic method. Uniform Distribution Theory, Bd. 6 (1), S. 185-200.
- H. Niederreiter, A. Winterhof (2011) Discrepancy bounds for hybrid sequences involving digital explicit inversive pseudorandom numbers. Uniform Distribution Theory, Bd. 6 (1), S. 33-56.
- A. Venkateswarlu, H. Niederreiter (2010) Improved results on periodic multisequences with large error linear complexity. Finite Fields and Their Applications, Bd. 16, S. 463-476.
- Niederreiter, H. (2010) Further discrepancy bounds and an Erdös-Turan-Koksma inequality for hybrid sequences. Monatshefte für Mathematik, Bd. 161, S. 193-222.
- Niederreiter, H. (2010) A discrepancy bound for hybrid sequences involving digital explicit inversive pseudorandom numbers. Uniform Distribution Theory, Bd. 5, S. 53-63.
- F.W. Fu, H. Niederreiter, F. Özbudak (2009) Joint linear complexity of arbitrary multisequences consisting of linear recurring sequences. Finite Fields and Their Applications, Bd. 15 (4), S. 475--496.
- Niederreiter, H. (2009) On the discrepancy of some hybrid sequences. Acta Arithmetica, Bd. 138 (4), S. 373--398.
- J. Dick, H. Niederreiter (2009) Duality for digital sequences. Journal of Complexity, Bd. 25 (5), S. 406-414.
- F.-W. Fu, H. Niederreiter, F. Özbudak (2009) Joint linear complexity of multisequences consisting of linear recurring sequences. Cryptography and Communications, Bd. 1 (1), S. 3-29.
- H. Niederreiter, J. Rivat (2009) On the Gowers norm of pseudorandom binary sequences. Bull. Aust. Math. Soc., Bd. 79, S. 259-271.
- H. Niederreiter, F. Pillichshammer (2009) Construction algorithms for good extensible lattice rules. Constr. Approx., Bd. 30 (3).
Book/Monograph (8)
- H. Niederreiter, A. Winterhof (2015) Applied number theory.; Berlin: Springer.
- H. Niederreiter, A. Ostafe, D. Panario, A. Winterhof (Eds.) (2014) Algebraic Curves and Finite Fields: Cryptography and Other Applications. In Reihe: Radon Series on Computational and Applied Mathematics, 16. Aufl.; Berlin: de Gruyter.
- P. Kritzer, H. Niederreiter, F. Pillichshammer, A. Winterhof (Eds.) (2014) Uniform Distribution and Quasi-Monte Carlo Methods: Discrepancy, Integration and Applications. In Reihe: Radon Series on Computational and Applied Mathematics, 15. Aufl.; Berlin: de Gruyter.
- H. Niederreiter, C. Xing (2009) Algebraic geometry in coding theory and cryptography.; Princeton: Princeton University Press.
- Niederreiter, Harald; Xing, C. P. (2001) Rational Points on Curves over Finite Fields: Theory and Applications. In Reihe: London Mathematical Society lecture note series, 285; Cambridge u. a.: Cambridge Univ. Press (245 Seiten).
- Lidl, Rudolf; Niederreiter, Harald (1997) Finite fields. In Reihe: Encyclopedia of mathematics and its applications, 20; Cambridge u. a.: Cambridge Univ. Press (755 Seiten).
- Lidl, Rudolf; Niederreiter, Harald (1994) Introduction to Finite Fields and Their Applications., überarb. Aufl.; Cambridge u. a.: Cambridge Univ. Press (416 Seiten).
- Niederreiter, Harald (1992) Random Number Generation and Quasi-Monte Carlo Methods. In Reihe: CBMS-NSF regional conference series in applied mathematics, 63; Philadelphia: Society for Industrial and Applied Mathematics (241 Seiten).
Conference Contribution: Publication in Proceedings (1)
Contribution in Collection (10)
- C. Schretter, Z. He, M. Gerber, N. Chopin, H. Niederreiter (2016) Van der Corput and golden ratio sequences along the Hilbert space-filling curve., Monte Carlo and quasi-Monte Carlo methods, 163. Aufl.: Springer, S. 531-544.
- R. Hofer, H. Niederreiter (2016) Vandermonde nets and Vandermonde sequences., Monte Carlo and quasi-Monte Carlo methods, 163. Aufl.; Cham: Springer, S. 87-105.
- Niederreiter, H. (2016) Finite fields., Encyclopedia of Applied and Computational Mathematics; Berlin: Springer, S. 541--545.
- Niederreiter, H. (2015) Random number generation., Princeton Companion to Applied Mathematics: Princeton University Press, S. 761-762.
- Niederreiter, H. (2013) Finite fields and quasirandom points. In: P. Charpin, A. Pott, A. Winterhof (Hrsg.), Finite fields and Applications: Character sums and polynomials, 11. Aufl.: de Gruyter, S. 169-196.
- Niederreiter, H. (2013) (t,m,s)-nets and (t,s)-sequences. In: G. Mullen, D. Panario (Hrsg.), Handbook of Finite Fields: Chapman & Hall, S. 619-630.
- Niederreiter, H. (2013) Algebraic geometry codes. In: G. Mullen, D. Panario (Hrsg.), Handbook of finite fields: Chapman & Hall, S. 703-712.
- Niederreiter, H. (2013) LFSR sequences and maximal period sequences. In: G. Mullen, D. Panario (Hrsg.), Handbook of Finite Fields: Chapman & Hall, S. 311-317.
- Niederreiter, H. (2012) Low-discrepancy simulation. In: J.-C. Duan, W.k. Härdle, J.E. Gentle (Hrsg.), Handbook of Computational Finance; Berlin: Springer, S. 703–729.
- Niederreiter, H. (2010) Quasi-Monte Carlo methods. In: Cont, R. (Hrsg.), Encyclopedia of Quantitative Finance: Wiley, S. 1460-1472.