Harald G. Niederreiter (born June 7, 1944) is an Austrian mathematician known for his work in discrepancy theory,

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

quasi-Monte Carlo method In numerical analysis, the quasi-Monte Carlo method is a method for numerical integration and solving some other problems using low-discrepancy sequences (also called quasi-random sequences or sub-random sequences) to achieve variance reduction. ...

s, and

cryptography Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...

Education and career

Niederreiter was born on June 7, 1944, in

Vienna Vienna ( ; ; ) is the capital city, capital, List of largest cities in Austria, most populous city, and one of Federal states of Austria, nine federal states of Austria. It is Austria's primate city, with just over two million inhabitants. ...

, and grew up in

Salzburg Salzburg is the List of cities and towns in Austria, fourth-largest city in Austria. In 2020 its population was 156,852. The city lies on the Salzach, Salzach River, near the border with Germany and at the foot of the Austrian Alps, Alps moun ...

... He began studying mathematics at the

University of Vienna The University of Vienna (, ) is a public university, public research university in Vienna, Austria. Founded by Rudolf IV, Duke of Austria, Duke Rudolph IV in 1365, it is the oldest university in the German-speaking world and among the largest ...

in 1963, and finished his doctorate there in 1969, with a thesis on discrepancy in

compact Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to: * Interstate compact, a type of agreement used by U.S. states * Blood compact, an ancient ritual of the Philippines * Compact government, a t ...

abelian group In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commu ...

s supervised by Edmund Hlawka. He began his academic career as an assistant professor at the University of Vienna, but soon moved to

Southern Illinois University Southern Illinois University is a system of public universities in the southern region of the U.S. state of Illinois. Its headquarters is in Carbondale, Illinois. Board of trustees The university is governed by the nine member SIU Board of T ...

. During this period he also visited the University of Illinois at Urbana-Champaign,

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

, and

University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public university, public Land-grant university, land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school the ...

. In 1978 he moved again, becoming the head of a new mathematics department at the

University of the West Indies The University of the West Indies (UWI), originally University College of the West Indies, is a public university system established to serve the higher education needs of the residents of 18 English-speaking countries and territories in t ...

Jamaica Jamaica is an island country in the Caribbean Sea and the West Indies. At , it is the third-largest island—after Cuba and Hispaniola—of the Greater Antilles and the Caribbean. Jamaica lies about south of Cuba, west of Hispaniola (the is ...

. In 1981 he returned to Austria for a post at the

Austrian Academy of Sciences The Austrian Academy of Sciences (; ÖAW) is a legal entity under the special protection of the Republic of Austria. According to the statutes of the Academy its mission is to promote the sciences and humanities in every respect and in every fi ...

, where from 1989 to 2000 he served as director of the Institutes of Information Processing and Discrete Mathematics. In 2001 he became a professor at the

National University of Singapore The National University of Singapore (NUS) is a national university, national Public university, public research university in Singapore. It was officially established in 1980 by the merging of the University of Singapore and Nanyang University ...

. In 2009 he returned to Austria again, to the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences. He also worked from 2010 to 2011 as a professor at the King Fahd University of Petroleum and Minerals in

Saudi Arabia Saudi Arabia, officially the Kingdom of Saudi Arabia (KSA), is a country in West Asia. Located in the centre of the Middle East, it covers the bulk of the Arabian Peninsula and has a land area of about , making it the List of Asian countries ...

Research

Niederreiter's initial research interests were in the

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...

s and

finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field (mathematics), field that contains a finite number of Element (mathematics), elements. As with any field, a finite field is a Set (mathematics), s ...

s, 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 space In mathematics, a metric space is a Set (mathematics), set together with a notion of ''distance'' between its Element (mathematics), elements, usually called point (geometry), points. The distance is measured by a function (mathematics), functi ...

s into his study of these subjects. In 1970, Niederreiter began to work on

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

and

random number generation Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that cannot be reasonably predicted better than by random chance. This means that the particular ou ...

, and in 1974 he published the book ''Uniform Distribution of Sequences''. Combining his work on pseudorandom numbers with the

Monte Carlo method Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be ...

, he did pioneering research in the

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

such as

public key cryptography Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic al ...

. The Niederreiter cryptosystem, an encryption system based on

error-correcting code In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The centra ...

s 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

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

Niederreiter is a member of the

and the

German Academy of Sciences Leopoldina The German National Academy of Sciences Leopoldina (), in short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded on 1 January 1652, based on academic models in Italy, it was originally named the ''Academi ...

. In 1998 he was an

invited speaker at the International Congress of Mathematicians An invitation system is a method of encouraging people to join an organization, such as a Club (organization), club or a website. In regular society, it refers to any system whereby new members are chosen; they cannot simply apply. In relation to w ...

, and won the Kardinal Innitzer Prize. He became a

fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

in 2013. Niederreiter's book ''Random Number Generation and Quasi-Monte Carlo Methods'' won the Outstanding Simulation Publication Award. 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

, and a

Festschrift In academia, a ''Festschrift'' (; plural, ''Festschriften'' ) is a book honoring a respected person, especially an academic, and presented during their lifetime. It generally takes the form of an edited volume, containing contributions from the h ...

was published in his honor..

References

{{DEFAULTSORT:Niederreiter, Harald 1944 births Living people Austrian mathematicians University of Vienna alumni Academic staff of the University of Vienna Southern Illinois University faculty Academic staff of the University of the West Indies Academic staff of the National University of Singapore Academic staff of King Fahd University of Petroleum and Minerals Members of the Austrian Academy of Sciences Fellows of the American Mathematical Society