The first mechanical number sieve created by Eugène Olivier Carissan in 1912 was rediscovered and documented through the analytical research of Hugh C. Williams. This Canadian mathematician and historian has spent his career examining the intersection of number theory, cryptography, and the historical development of primality testing methods using both computational algorithms and archival investigation.
Academic Foundation
Hugh Cowie Williams was born in London in 1943. He pursued his higher education at the University of Waterloo, earning a bachelor's degree in 1966 and a master's degree in 1967. In 1969, he completed his doctorate in computer science under the supervision of Ralph Gordon Stanton and Ronald C. Mullin, focusing his dissertation on a generalization of the Lucas functions. He subsequently undertook post-doctoral studies at York University.
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The University of Manitoba served as the site of his initial faculty appointment in 1970, where he progressed to the rank of associate professor in 1972 and full professor in 1979. He returned to the University of Waterloo as an adjunct professor between 1998 and 2001. In 2001, he moved to the University of Calgary, assuming the iCore Chair in Algorithmic Number Theory and Cryptography. Since 2004, he has held the status of professor emeritus.
Contributions to Number Theory and Cryptography
His research portfolio includes the development of custom hardware for number-theoretical calculations, most notably the MSSU in 1995. In 1994, he collaborated with Johannes Buchmann and Renate Scheidler to create a public key cryptography method utilizing real quadratic number fields. His investigations into primality tests led to the naming of Williams primes in his honor. Additionally, he served as associate editor for the journal Mathematics of Computation from 1978 until early 2007.
Historical Research
Beyond contemporary algorithm design, Williams focuses on the history of mathematics. He authored a study on Édouard Lucas, demonstrating that Lucas had explored tests akin to the modern elliptic curve method. His work also reconstructed the 1880 factorization of the sixth Fermat number by Fortuné Landry. Furthermore, he has held visiting scholar positions at the University of Leiden, Macquarie University, and the University of Bordeaux.
Fast facts
- Born: 1943, London
- Citizenship: Canada
- Doctorate: University of Waterloo, 1969
- Field: Number theory and cryptography
- Academic Status: Professor emeritus, University of Calgary
- Key Publication: Édouard Lucas and primality testing, 1998
Questions readers ask
What specific area of cryptography did Hugh C. Williams develop?
He developed a public key cryptography method based on real quadratic number fields, working alongside Renate Scheidler and Johannes Buchmann in 1994.
What is the historical significance of the mechanical device he studied?
He worked with Jeffrey Shallit and François Morain to document a forgotten 1912 mechanical number sieve originally built by Eugène Olivier Carissan.
Achievements
- Held posts at University of Calgary, University of Waterloo and University of Manitoba
