Harald Niederreiter

Niederreiter's initial research interests were in the abstract algebra of abelian groups and finite fields, subjects also represented by his later book Finite Fields (with Rudolf Lidl, 1983).^[1] From his doctoral thesis onwards, he also incorporated discrepancy theory and the theory of uniformly distributed sets in metric spaces into his study of these subjects.^[2]

In 1970, Niederreiter began to work on numerical analysis and random number generation, and in 1974 he published the book Uniform Distribution of Sequences. Combining his work on pseudorandom numbers with the Monte Carlo method, he did pioneering research in the quasi-Monte Carlo method in the late 1970s, and again later published a book on the topic, Random Number Generation and Quasi-Monte Carlo Methods (1995).^[1][2]

Niederreiter's interests in pseudorandom numbers also led him to study stream ciphers in the 1980s, and this interest branched out into other areas of cryptography such as public key cryptography. The Niederreiter cryptosystem, an encryption system based on error-correcting codes that can also be used for digital signatures, was developed by him in 1986.^[1] His work in cryptography is represented by his book Algebraic Geometry in Coding Theory and Cryptography (with C. P. Xing, 2009).^[2]

Returning to pure mathematics, Niederreiter has also made contributions to algebraic geometry with the discovery of many dense curves over finite fields,^[1] and published the book Rational Points on Curves over Finite Fields: Theory and Applications (with C. P. Xing, 2001).^[2]

Niederreiter is a member of the Austrian Academy of Sciences and the German Academy of Sciences Leopoldina. In 1998 he was an invited speaker at the International Congress of Mathematicians,^[4] and won the Kardinal Innitzer Prize.^[1][2] He became a fellow of the American Mathematical Society in 2013.^[2]

Niederreiter's book Random Number Generation and Quasi-Monte Carlo Methods won the Outstanding Simulation Publication Award.^[1]

In 2014, a workshop in honor of Niederreiter's 70th birthday was held at the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences,^[5] and a Festschrift was published in his honor.^[6]