Arjen Klaas Lenstra (born 2 March 1956, in

Groningen Groningen (; gos, Grunn or ) is the capital city and main municipality of Groningen province in the Netherlands. The ''capital of the north'', Groningen is the largest place as well as the economic and cultural centre of the northern part of t ...

) is a Dutch

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

cryptographer 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 ...

and computational number theorist. He is currently a professor at the

École Polytechnique Fédérale de Lausanne École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

(EPFL) where he heads of the Laboratory for Cryptologic Algorithms.

Career

He studied mathematics at the

University of Amsterdam The University of Amsterdam (abbreviated as UvA, nl, Universiteit van Amsterdam) is a public research university located in Amsterdam, Netherlands. The UvA is one of two large, publicly funded research universities in the city, the other being ...

. He is currently a professor at the EPFL (

Lausanne , neighboring_municipalities= Bottens, Bretigny-sur-Morrens, Chavannes-près-Renens, Cheseaux-sur-Lausanne, Crissier, Cugy, Écublens, Épalinges, Évian-les-Bains (FR-74), Froideville, Jouxtens-Mézery, Le Mont-sur-Lausanne, Lugrin (FR-74), ...

), in the Laboratory for Cryptologic Algorithms, and previously worked for

Citibank Citibank, N. A. (N. A. stands for " National Association") is the primary U.S. banking subsidiary of financial services multinational Citigroup. Citibank was founded in 1812 as the City Bank of New York, and later became First National City ...

and

Bell Labs Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mult ...

Research

Lenstra is active in

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 ...

and

computational number theory In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithm ...

, especially in areas such as

integer factorization In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization. When the numbers are suf ...

. With

Mark Manasse Mark may refer to: Currency * Bosnia and Herzegovina convertible mark, the currency of Bosnia and Herzegovina * East German mark, the currency of the German Democratic Republic * Estonian mark, the currency of Estonia between 1918 and 1927 * Fi ...

, he was the first to seek volunteers over the internet for a large scale

volunteer computing Volunteer computing is a type of distributed computing in which people donate their computers' unused resources to a research-oriented project, and sometimes in exchange for credit points. The fundamental idea behind it is that a modern desktop co ...

project. Such projects became more common after the Factorization of RSA-129 which was a high publicity distributed factoring success led by Lenstra along with

Derek Atkins Derek A Atkins is a computer scientist specializing in computer security. He studied electrical engineering and computer science at the Massachusetts Institute of Technology. In June 2014, he became the chief technology officer of SecureRF. At ...

, Michael Graff and

Paul Leyland Paul Leyland is a British number theorist who has studied integer factorization and primality testing. He has contributed to the factorization of RSA-129, RSA-140, and RSA-155, as well as potential factorial primes as large as 400! + 1. He ...

. He was also a leader in the successful factorizations of several other

RSA numbers In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The challenge was to find the prime factors of each number. It was created by RSA Laboratories i ...

. Lenstra was also involved in the development of the

number field sieve In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than . Heuristically, its complexity for factoring an integer (consisting of bits) is of the form :\exp\left( ...

. With coauthors, he showed the great potential of the algorithm early on by using it to factor the ninth

Fermat number In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form :F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: : 3, 5, 17, 257, 65537, 4294967 ...

, which was far out of reach by other factoring algorithms of the time. He has since been involved with several other number field sieve factorizations including the current record,

RSA-768 In mathematics, the RSA numbers are a set of large semiprimes (numbers with exactly two prime factors) that were part of the RSA Factoring Challenge. The challenge was to find the prime factors of each number. It was created by RSA Laboratories ...

. Lenstra's most widely cited scientific result is the first polynomial time algorithm to factor polynomials with rational coefficients in the seminal paper that introduced the LLL lattice reduction algorithm with

Hendrik Willem Lenstra Hendrik Willem Lenstra Jr. (born 16 April 1949, Zaandam) is a Dutch mathematician. Biography Lenstra received his doctorate from the University of Amsterdam in 1977 and became a professor there in 1978. In 1987 he was appointed to the faculty of ...

and

László Lovász László Lovász (; born March 9, 1948) is a Hungarian mathematician and professor emeritus at Eötvös Loránd University, best known for his work in combinatorics, for which he was awarded the 2021 Abel Prize jointly with Avi Wigderson. He ...

. Lenstra is also co-inventor of the XTR

cryptosystem In cryptography, a cryptosystem is a suite of cryptographic algorithms needed to implement a particular security service, such as confidentiality (encryption). Typically, a cryptosystem consists of three algorithms: one for key generation, one for ...

. On 1 March 2005, Arjen Lenstra,

Xiaoyun Wang Wang Xiaoyun (; born 1966) is a Chinese cryptographer, mathematician, and computer scientist. She is a professor in the Department of Mathematics and System Science of Shandong University and an academician of the Chinese Academy of Sciences. Ear ...

, and Benne de Weger of

Eindhoven University of Technology The Eindhoven University of Technology ( nl, Technische Universiteit Eindhoven), abbr. TU/e, is a public technical university in the Netherlands, located in the city of Eindhoven. In 2020–21, around 14,000 students were enrolled in its BSc a ...

demonstrated construction of two

X.509 In cryptography, X.509 is an International Telecommunication Union (ITU) standard defining the format of public key certificates. X.509 certificates are used in many Internet protocols, including TLS/SSL, which is the basis for HTTPS, the secu ...

certificates with different public keys and the same MD5 hash, a demonstrably practical

hash collision In computer science, a hash collision or hash clash is when two pieces of data in a hash table share the same hash value. The hash value in this case is derived from a hash function which takes a data input and returns a fixed length of bits. Al ...

. The construction included private keys for both public keys.

Distinctions

Lenstra is the recipient of the

RSA Award for Excellence in Mathematics RSA may refer to: Organizations Academia and education * Rabbinical Seminary of America, a yeshiva in New York City *Regional Science Association International (formerly the Regional Science Association), a US-based learned society *Renaissance S ...

2008 Award.RSA Conference Awards

Private life

Lenstra's brother and co-author

Hendrik Lenstra Hendrik Willem Lenstra Jr. (born 16 April 1949, Zaandam) is a Dutch mathematician. Biography Lenstra received his doctorate from the University of Amsterdam in 1977 and became a professor there in 1978. In 1987 he was appointed to the faculty of ...

is a professor in mathematics at

Leiden University Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a Public university, public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William the Silent, William, Prince o ...

and his brother

Jan Karel Lenstra Jan Karel Lenstra (born 19 December 1947, in Zaandam) is a Dutch mathematician and operations researcher, known for his work on scheduling algorithms, local search, and the travelling salesman problem. Lenstra received his Ph.D. from the Univers ...

is a former director of

Centrum Wiskunde & Informatica The (abbr. CWI; English: "National Research Institute for Mathematics and Computer Science") is a research centre in the field of mathematics and theoretical computer science. It is part of the institutes organization of the Dutch Research Cou ...

(CWI).

References

External links