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

discrepancy theory In mathematics, discrepancy theory describes the deviation of a situation from the state one would like it to be in. It is also called the theory of irregularities of distribution. This refers to the theme of ''classical'' discrepancy theory, name ...

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

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). This is in contrast to the regu ...

s, and

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

Education and career

Niederreiter was born on June 7, 1944, in

Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...

, and grew up in

Salzburg Salzburg (, ; literally "Salt-Castle"; bar, Soizbuag, label=Bavarian language, Austro-Bavarian) is the List of cities and towns in Austria, fourth-largest city in Austria. In 2020, it had a population of 156,872. The town is on the site of the ...

... He began studying mathematics at the

University of Vienna The University of Vienna (german: Universität Wien) is a public research university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich histor ...

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 * Blood compact, an ancient ritual of the Philippines * Compact government, a type of colonial rule utilized in British ...

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 commut ...

s supervised by

Edmund Hlawka Edmund Hlawka (November 5, 1916, Bruck an der Mur, Styria – February 19, 2009) was an Austrian mathematician. He was a leading number theorist. Hlawka did most of his work at the Vienna University of Technology. He was also a visiting professo ...

. 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 Tr ...

. During this period he also visited the

University of Illinois at Urbana-Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univ ...

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

, and

University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...

. 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 17 English-speaking countries and territories in th ...

Jamaica Jamaica (; ) is an island country situated in the Caribbean Sea. Spanning in area, it is the third-largest island of the Greater Antilles and the Caribbean (after Cuba and Hispaniola). Jamaica lies about south of Cuba, and west of His ...

. In 1981 he returned to Austria for a post at the Austrian Academy of Sciences, 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 public research university in Singapore. Founded in 1905 as the Straits Settlements and Federated Malay States Government Medical School, NUS is the oldest autonomous university in the c ...

. 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 King Fahd University of Petroleum and Minerals (KFUPM) ( ar, جامعة الملك فهد للبترول و المعادن, – short: ar, جامعة البترول ), after 1975 as the University of Petroleum and Minerals and initially as the ...

Saudi Arabia Saudi Arabia, officially the Kingdom of Saudi Arabia (KSA), is a country in Western Asia. It covers the bulk of the Arabian Peninsula, and has a land area of about , making it the fifth-largest country in Asia, the second-largest in the A ...

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. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''a ...

s and

finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...

s, subjects also represented by his later book ''Finite Fields'' (with Rudolf Lidl, 1983). From his doctoral thesis onwards, he also incorporated

and the theory of uniformly distributed sets in

metric space In mathematics, a metric space is a set together with a notion of ''distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general settin ...

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 that cannot be reasonably predicted better than by random chance is generated. This means that the particular outc ...

, 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 determi ...

, 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 cipher stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream (keystream). In a stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of the keystream ...

s 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 alg ...

. The

Niederreiter cryptosystem In cryptography, the Niederreiter cryptosystem is a variation of the McEliece cryptosystem developed in 1986 by Harald Niederreiter. It applies the same idea to the parity check matrix, H, of a linear code. Niederreiter is equivalent to McEliece fr ...

, an encryption system based on

error-correcting code In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is ...

s that can also be used for

digital signature A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature, where the prerequisites are satisfied, gives a recipient very high confidence that the message was created b ...

s, 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 Austrian Academy of Sciences and the

German Academy of Sciences Leopoldina The German National Academy of Sciences Leopoldina (german: Deutsche Akademie der Naturforscher Leopoldina – Nationale Akademie der Wissenschaften), short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded ...

. In 1998 he was an

invited speaker at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

, and won the Kardinal Innitzer Prize. He became a

fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...

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 Austrian Academy of Sciences, 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 Academics of the University of Vienna Southern Illinois University faculty University of the West Indies academics National University of Singapore faculty King Fahd University of Petroleum and Minerals faculty Members of the Austrian Academy of Sciences Fellows of the American Mathematical Society