Arjen Klaas Lenstra (born 2 March 1956, in Groningen) 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, mathematical structure, structure, space, Mathematica ...

cryptographer Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More gen ...

and computational number theorist. He is a professor emeritus from the

École Polytechnique Fédérale de Lausanne The École Polytechnique Fédérale de Lausanne (, EPFL) is a public university, public research university in Lausanne, Switzerland, founded in 1969 with the mission to "train talented engineers in Switzerland". Like its sister institution E ...

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

Career

He studied mathematics at the

University of Amsterdam The University of Amsterdam (abbreviated as UvA, ) is a public university, public research university located in Amsterdam, Netherlands. Established in 1632 by municipal authorities, it is the fourth-oldest academic institution in the Netherlan ...

. He is a former professor at the EPFL (

Lausanne Lausanne ( , ; ; ) is the capital and largest List of towns in Switzerland, city of the Swiss French-speaking Cantons of Switzerland, canton of Vaud, in Switzerland. It is a hilly city situated on the shores of Lake Geneva, about halfway bet ...

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

Citibank Citibank, N.A. ("N. A." stands for "National bank (United States), National Association"; stylized as citibank) is the primary U.S. banking subsidiary of Citigroup, a financial services multinational corporation, multinational corporation. Ci ...

and

Bell Labs Nokia Bell Labs, commonly referred to as ''Bell Labs'', is an American industrial research and development company owned by Finnish technology company Nokia. With headquarters located in Murray Hill, New Jersey, Murray Hill, New Jersey, the compa ...

Research

Lenstra is active in

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), ...

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 mathematics, integer factorization is the decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is a comp ...

. With Mark Manasse, 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 ...

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, Michael Graff and

Paul Leyland Paul Leyland is a British astronomer and 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 4 ...

. 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 ...

. 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 : \begin & ...

. 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 (1601–1665), the first known to have studied them, is a natural number, positive integer of the form:F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers ...

, 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 o ...

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 ...

. 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. ...

, and Benne de Weger of

Eindhoven University of Technology The Eindhoven University of Technology (), Abbreviation, abbr. TU/e, is a public university, public technical university in the Netherlands, situated in Eindhoven. In 2020–21, around 14,000 students were enrolled in its Bachelor of Science, BS ...

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 secure ...

certificates with different public keys and the same

MD5 The MD5 message-digest algorithm is a widely used hash function producing a 128-bit hash value. MD5 was designed by Ronald Rivest in 1991 to replace an earlier hash function MD4, and was specified in 1992 as Request for Comments, RFC 1321. MD5 ...

hash, a demonstrably practical

hash collision In computer science, a hash collision or hash clash is when two distinct 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 ...

. The construction included private keys for both public keys.

Distinctions

Lenstra is the recipient of the

RSA Award for Excellence in Mathematics Formally called since 2025 The RSAC Conference Award for Excellence in Mathematics, is an annual award. It is announced at the annual RSA Conference in recognition of innovations and contributions in the field of cryptography. An award committee o ...

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 o ...

is a professor in mathematics at

Leiden University Leiden University (abbreviated as ''LEI''; ) is a Public university, public research university in Leiden, Netherlands. Established in 1575 by William the Silent, William, Prince of Orange as a Protestantism, Protestant institution, it holds the d ...

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