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). 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. 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). 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. His work in cryptography is represented by his book
Algebraic Geometry in Coding Theory and Cryptography (with C. P. Xing, 2009). Returning to pure mathematics, Niederreiter has also made contributions to
algebraic geometry with the discovery of many dense curves over finite fields, and published the book
Rational Points on Curves over Finite Fields: Theory and Applications (with C. P. Xing, 2001). ==Awards and honors==