Hugh C. Williams
Hugh Cowie Williams (born July 23, 1943 in London , Ontario ) is a Canadian mathematician who deals with algorithmic number theory and cryptography .
Williams studied mathematics at the University of Waterloo (bachelor's degree in 1966, master's degree in 1967), where he received his doctorate in computer science under Ronald C. Mullin in 1969 ( A generalization of the Lucas functions ). As a postdoctoral student he was at York University and from 1970 Assistant Professor at the University of Manitoba , where he became Associate Professor in 1972 and Professor in 1979. From 2001 he was a professor at the University of Calgary , where he has been Professor Emeritus since 2004. Since 2001 he has held the “iCore Chair” in algorithmic number theory and cryptography. Together with Rei SafaviNaini , he heads the Institute for Security, Privacy and Information Assurance (ISPIA)  formerly the Center for Information Security and Cryptography (CISaC)  at the University of Calgary. From 1998 to 2001 he was also an adjunct professor at the University of Waterloo. Among other things, he was visiting scholar at the University of Bordeaux , Macquarie University and Leiden University . From 1978 to January 2007 he was Associate Editor of the journal Mathematics of Computation with and as successor to Daniel Shanks .
Williams dealt, among other things, with primality tests. He also developed special hardware for number theoretic calculations ("number sieves"), for example the MSSU 1995. In cryptography, he and Renate Scheidler and Johannes Buchmann developed a public key cryptography process in 1994 that is based on real square number fields. Williams also developed algorithms for calculating invariants of algebraic number fields such as class numbers and regulators.
He is also into the history of mathematics and wrote a book on the history of the primality tests. In it he showed, among other things, that shortly before his untimely death, Édouard Lucas was already working on a test similar to today's elliptical curve method. He also reconstructed the method that Fortuné Landry used in 1880 (at the age of 82 ) to factor the sixth Fermat number (a 20digit number).
Together with Jeffrey Shallit and François Morain , he discovered a forgotten mechanical number sieve by Eugène Olivier Carissan, the first such device from the beginning of the 20th century, and described it in detail.
The Williams number is named after him.
Fonts
 The influence of computers in the development of number theory. In: Computational Mathematics with Applications. Volume 8, 1982, pp. 7593.
 Factoring on a computer. Mathematical Intelligencer, 1984, No. 3.
 with Attila Pethö , HorstGünter Zimmer , Michael Pohst (Eds.): Computational Number Theory. de Gruyter 1991.
 with JO Shallit: Factoring integers before computers. In: W. Gautschi (Ed.): Mathematics of computation  50 years of computational mathematics 1943–1993. Proc. Symposium Applied Math., Volume 48. American Mathematical Society, 1994, pp. 481531.
 Édouard Lucas and primality testing. Wiley 1998. (Canadian Mathematical Society Series of Monographs and Advanced Texts. Volume 22.)
 with MJ Jacobson: Solving the Pell Equation . Springer 2008.
Web links
 Literature by and about Hugh C. Williams in the catalog of the German National Library
 Hugh C. Williams on the University of Calgary website
 Profile of Hugh C. Williams on the faculty with links to publications
Individual evidence
 ^ Hugh C. Williams in the Mathematics Genealogy Project (English)
 ↑ ISPIA website

↑ In the 1970s he wrote the overview Primality testing on a computer. in Ars Combinatoria. Volume 5, 1978, pp. 127185, and developed new methods for this in the 1970s.
Williams, JS Judd: Determination of the primality of N by using prime factors of ± 1. In: Mathematics of Computation. Volume 30, 1976, pp. 157172
Some algorithms for prime testing using generalized Lehmer functions. In: Mathematics of Computation. Volume 30, 1976, pp. 867886  ↑ Hardware sieves: function and applications, further projects
 ^ Buchmann, Williams: Quadratic fields and cryptography. In: Loxton (Ed.): Number theory and cryptography. 1989
 ↑ Williams: How was factored? In: Mathematics of Computation. Volume 61, 1993, p. 463. Landry did not publish his method, but there were references in the estate.
 ^ J. Shallit, HC Williams, F. Morain: Discovery of a lost factoring machine. In: Mathematical Intelligencer. 17, No. 3, 1995, pp. 4147; Ivars Peterson: Cranking out primes: tracking down a longlost factoring machine  Carissan's factoring machine  Cover Story. ( Memento of July 8, 2012 in the web archive archive.today ) The brothers E. and Pierre Carissan set up the machine in the Bordeaux observatory and demonstrated it to the public in 1920.
personal data  

SURNAME  Williams, Hugh C. 
ALTERNATIVE NAMES  Williams, Hugh Cowie 
BRIEF DESCRIPTION  Canadian mathematician 
DATE OF BIRTH  July 23, 1943 
PLACE OF BIRTH  London , Ontario 