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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
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, 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 ...
in
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 ...
in
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 ...
of
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 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
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 ...
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
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 ...
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
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 ...
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
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 ...
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