Hugh C. Williams

Q: What Schools Are Affiliated With Hugh C. Williams

Hugh C. Williams is affiliated with the following schools: University of Calgary, University of Waterloo, University of British Columbia, University of Manitoba, Case Western Reserve University

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Hugh C. Williams

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According to Wikipedia, Hugh Cowie Williams is a Canadian mathematician. He deals with number theory and cryptography. Early life Williams studied mathematics at the University of Waterloo , where he received his doctorate in 1969 in computer science under Ronald C. Mullin . He was a post-doctoral student at York University.

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Hugh C. Williams's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Aggrecan degradation in human cartilage. Evidence for both matrix metalloproteinase and aggrecanase activity in normal, osteoarthritic, and rheumatoid joints. (1997) (469)
A modification of the RSA public-key encryption procedure (Corresp.) (1980) (271)
Cell-mediated Catabolism of Aggrecan (1995) (192)
Structure of human neutrophil elastase in complex with a peptide chloromethyl ketone inhibitor at 1.84-A resolution. (1989) (190)
A $p+1$ method of factoring (1982) (164)
CCR5, CXCR4, and CD4 Are Clustered and Closely Apposed on Microvilli of Human Macrophages and T Cells (2001) (155)
VDIPEN, a metalloproteinase-generated neoepitope, is induced and immunolocalized in articular cartilage during inflammatory arthritis. (1995) (136)
Édouard Lucas and primality testing (1999) (92)
Symmetries of culture (1990) (91)
A key-exchange system based on imaginary quadratic fields (1988) (91)
Advances in Cryptology — CRYPTO ’85 Proceedings (2000) (89)
A Key Exchange System Based on Real Quadratic Fields (1989) (69)
Solving the Pell Equation (2008) (68)
Crystallographie study of a β-lactam inhibitor complex with elastase at 1.84 Å resolution (1987) (67)
Quantification of a matrix metalloproteinase-generated aggrecan G1 fragment using monospecific anti-peptide serum. (1995) (60)
Short Representation of Quadratic Integers (1995) (52)
Key-Exchange in Real Quadratic Congruence Function Fields (1996) (50)
On the parallel generation of the residues for the continued fraction factoring algorithm (1987) (50)
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85 (1986) (46)
Aggrecanase and metalloproteinase-specific aggrecan neo-epitopes are induced in the articular cartilage of mice with collagen II-induced arthritis. (1997) (46)
Methyl- 14 C-glycinated hemoglobin as a substrate for proteases. (1971) (43)
An M³ Public-Key Encryption Scheme (1985) (42)
On Numbers Analogous to the Carmichael Numbers (1977) (41)
Some remarks concerning the M.I.T. public-key cryptosystem (1979) (39)
Some Public Key Crypto-Functions as Intractable as Factorization (1985) (39)
Computer verification of the Ankeny-Artin-Chowla Conjecture for all primes less than 100 000 000 000 (2001) (36)
Some Methods for Evaluating the Regulator of a Real Quadratic Function Field (1999) (36)
A computational technique for evaluating (1,) and the class number of a real quadratic field (1976) (35)
Continued fractions and number-theoretic computations (1985) (34)
Calculation of the regulator of a pure cubic field (1980) (32)
Some results on pseudosquares (1996) (32)
Solution of the Class Number One Problem For Real Quadratic Fields of Extended Richaud-Degert Type (With One Possible Exception) (1990) (32)
A Note on the Fibonacci Quotient F p-ε/p (1982) (31)
Some algorithms for prime testing using generalized Lehmer functions (1976) (31)
Numerical Results on Class Groups of Imaginary Quadratic Fields (2006) (30)
A public-key cryptosystem utilizing cyclotomic fields (1995) (29)
An Investigation of Bounds for the Regulator of Quadratic Fields (1995) (28)
A Computational Technique for Determining the Class Number of a Pure Cubic Field (1976) (28)
New quadratic polynomials with high densities of prime values (2003) (27)
A key-exchange protocol using real quadratic fields (1994) (27)
Quadratic polynomials which have a high density of prime values (1990) (26)
On the computation of the class number of an algebraic number field (1989) (26)
Some computational results on a problem concerning powerful numbers (1988) (25)
On certain continued fraction expansions of fixed period length (1999) (25)
On the imaginary bicyclic biquadratic fields with class-number 2 (1977) (25)
Conversion of specifically 14 C-labeled lactate and pyruvate to glucose in man. (1969) (25)
On the infrastructure of the principal ideal class of an algebraic number field of unit rank one (1988) (23)
Substituted 2-aminopyridines as inhibitors of nitric oxide synthases. (2000) (23)
Key-exchange in real quadratic congruence function fields (1996) (23)
Corrigenda for "A Conjecture of S. Chowla via the Generalized Riemann Hypothesis" (1988) (23)
Halfway to a solution of $X^2 - DY^2 = -3$ (1994) (22)
An Improved Real-Quadratic-Field-Based Key Exchange Procedure (2006) (22)
The primality of R1031 (1986) (22)
Effects of VLA-4 antagonists in rat whole embryo culture. (2002) (22)
A Rapid Method of Evaluating the Regulator and Class Number of a Pure Cubic Field (1983) (22)
Estimation of the glucuronic acid pathway contribution to glucose metabolism in adipose tissue and the effect of growth hormone. (1966) (21)
Simple groups of square order and interesting sequence of primes (1980) (21)
Inhibition of cathepsin D by synthetic oligopeptides. (1979) (20)
Torsion groups of elliptic curves with integral j-invariant over pure cubic fields (1990) (19)
On the Complexity and Efficiency of a New Key Exchange System (1989) (19)
Quadratic fields and cryptography (1991) (19)
Results and estimates on pseudopowers (1996) (18)
New Computations Concerning the Cohen-Lenstra Heuristics (2003) (18)
On prime valued polynomials and class numbers of real quadratic fields (1988) (18)
Human polymorphonuclear leukocyte collagenase and gelatinase. Comparison of certain enzymatic properties. (1984) (17)
On a determination of real quadratic fields of class number one and related continued fractionperiod length less than $25$ (1991) (17)
On a generalization of the Lucas functions (1972) (17)
Some primes of the form (ⁿ-1)/(-1) (1979) (17)
Class Numbers of Real Quadratic Fields, Continued Fractions, Reduced Ideals, Prime-Producing Quadratic Polynomials and Quadratic Residue Covers (1992) (17)
An upper bound for the period of the simple continued fraction for $\sqrtD$. (1976) (16)
Some formulas concerning the fundamental unit of a real quadratic field (1991) (16)
Studies on the existence of a pathway in liver and muscle for the conversion of glucose into glycogen without glucose 6-phosphate as an intermediate. (1969) (16)
Some very large primes of the form ⋅2^{}+1 (1980) (15)
A very fast electronic number sieve (1995) (15)
Decreased phosphofructokinase activity in preserved blood. (1955) (15)
The influence of computers in the development of number theory (1982) (15)
A note on class-number one in pure cubic fields (1979) (15)
Computation of the first factor of the class number of cyclotomic fields (1992) (15)
The calculation of a large cubic class number with an application to real cyclotomic fields (1983) (15)
Crystallization of human neutrophil elastase. (1987) (15)
On real quadratic fields of class number two (1992) (14)
Computation of real quadratic fields with class number one (1988) (14)
Prime producing quadratic polynomials and real quadratic fields of class number one (1989) (14)
Metabolism of pyruvate by rat adipose tissue in vitro. (1968) (14)
Some Prime Numbers of the Forms 2A3 n + 1 and 2A3 n - 1 (1972) (13)
Some observations on primality testing (1978) (13)
Factoring on a Computer (1984) (13)
Effective primality tests for some integers of the forms 5ⁿ-1 and 7ⁿ-1 (1987) (13)
The problem of Sierpiński concerning ⋅2ⁿ+1 (1981) (13)
An analogue of the nearest integer continued fraction for certain cubic irrationalities (1984) (12)
Expression and Immunoaffinity Purification of Human Inducible Nitric-oxide Synthase (1996) (12)
On the computation of a table of complex cubic fields with discriminant D>-10^6 (1990) (12)
Some generalizations of the Sₙ sequence of Shanks (1995) (12)
SOME FOURTH-ORDER LINEAR DIVISIBILITY SEQUENCES (2011) (12)
Calculation of the regulator of (√) by use of the nearest integer continued fraction algorithm (1979) (12)
Solution of the Cattle Problem of Archimedes (1965) (12)
Determination of the primality of by using factors of ²±1 (1976) (11)
An open architecture number sieve (1991) (11)
An Overview of Factoring (1983) (11)
Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant. (1987) (11)
An Improved Method of Computing the Regulator of a Real Quadratic Function Field (1998) (11)
Implementation of a key exchange protocol using real quadratic fields (extended abstract) (1991) (11)
On Principal Ideal Testing in Algebraic Number Fields (1987) (11)
An Upper Bound on the Least Inert Prime in a Real Quadratic Field (2000) (10)
Some Public-Key Crypto-Functions as Intractable as Factorization (1985) (10)
Some primes with interesting digit patterns (1978) (10)
Fast primality tests for numbers less than 50 · 10 9 (1986) (10)
A fast, rigorous technique for computing the regulator of a real quadratic field (2007) (10)
Direct Assay of Aα(1–21), a PMN Elastase‐Specific Cleavage Product of Fibrinogen, in the Chimpanzee (1991) (10)
The Primality of N=2A3n-1 (1972) (10)
Doubly-Focused Enumeration of Pseudosquares and Pseudocubes (2006) (10)
Improving the Speed of Calculating the Regulator of Certain Pure Cubic Fields (1980) (10)
Gunderson’s function in Fermat’s last theorem (1981) (10)
Some Computer Results on Units of Quadratic and Cubic Fields (1975) (10)
Modular Arithmetic on Elements of Small Norm in Quadratic Fields (2002) (9)
Presence of the glycolytic enzymes D-glyceraldehyde-3-phosphate dehydrogenase, phosphoglycerate kinase and triosephosphate isomerase in hemolysates of preserved blood. (1955) (9)
Computational number theory : proceedings of the Colloquium on Computational Number Theory held at Kossuth Lajos University, Debrecen (Hungary), September 4-9, 1989 (1991) (9)
A note on class-number one in certain real quadratic and pure cubic fields (1986) (9)
Determination of Principal Factors in (√D) and (√[3]D) (1982) (9)
Explicit primality criteria for (p-1)pn - 1 (2000) (9)
Pseudocubes and Primality Testing (2004) (9)
A generalization of Lehmer's functions (1976) (8)
Public-Key Cryptography Based on a Cubic Extension of the Lucas Functions (2012) (8)
A numerical investigation into the length of the period of the continued fraction expansion of (1981) (8)
Cubic Fields with Geometry (2018) (8)
Consecutive powers in continued fractions (1992) (8)
A Report on Prime Numbers of the Forms M = (6a + 1)22m-1- 1 and M' = (6a - 1)22m 1 (1968) (8)
Some new primes of the form ⋅2ⁿ+1 (1977) (8)
Effect of pH and CO2 concentration on glucose metabolism by rat adipose tissue in vitro. (1968) (8)
Quadratic fields with 3-rank equal to 4 (1979) (8)
A New Look at an Old Equation (2008) (8)
A class of primality tests for trinomials which includes the Lucas-Lehmer test (1982) (8)
Computation of the class number and class group of a complex cubic field (1985) (7)
HORMONAL REGULATION OF GLUCOSE METABOLISM IN ADIPOSE TISSUE IN VITRO * (1965) (7)
Effects of human polymorphonuclear leukocyte collagenase on sub-component C1q of the first component of human complement. (1978) (7)
A Packing Problem (1967) (7)
How was F6 Factored (1993) (7)
Some prime numbers of the forms 23ⁿ+1 and 23ⁿ-1 (1972) (7)
A report on prime numbers of the forms =(6+1)2^{2-1}-1 and ^{’}=(6-1)2^{2}-1 (1968) (7)
The Size of the Fundamental Solutions of Consecutive Pell Equations (2000) (7)
On principal ideal testing in totally complex quartic fields and the determination of certain cyclotomic constants (1987) (7)
Some remarks concerning the complexity of computing class groups of quadratic fields (1991) (7)
Some results concerning the nearest integer continued fraction expansion of D. (1980) (6)
Baby Step Giant Step in Real Quadratic Function Fields (1995) (6)
Proteoglycan-degrading activity of human stromelysin-1 and leukocyte elastase in rabbit joints. Quantitation of proteoglycan and a stromelysin-induced HABR fragment of aggrecan in synovial fluid and cartilage. (1996) (6)
Some results concerning certain periodic continued fractions (2005) (6)
Effects of Hyperglycemia, Tolbutamide and Glucagon on the Pathways of Glucose Oxidation in the Goosefish Islet in Vitro (1970) (6)
Efficient Ideal Reduction in Quadratic Fields (2006) (6)
A Note on Shanks's Chains of Primes (2000) (6)
Corrigenda: “The problem of Sierpiński concerning ⋅2ⁿ+1” [Math. Comp. 37 (1981), no. 155, 229–231] (1982) (6)
Characterization of a generalized Shanks sequence (2007) (6)
Computation of the Solution of x 3 + Dy 3 = 1 (1977) (6)
On a solution of a class number two problem for a family of real quadratic fields (1991) (6)
Some Extensions of the Lucas Functions (2013) (6)
Discovery of a lost factoring machine (1995) (5)
Construction of all cubic function fields of a given square-free discriminant (2015) (5)
A method of tabulating the number-theoretic function g(k) (1992) (5)
Certain pure cubic fields with class-number one (1977) (5)
Pathways of fructose conversion to glucose and glycogen in liver. (1972) (5)
Some computational results on a problem of Einsenstein (1989) (5)
Implementation of a Key Exchange Protocol Using Some Real Quadratic Fields (1990) (5)
Some primality tests that eluded Lucas (2015) (5)
A Problem Concerning a Character Sum (1999) (5)
Computation of the solution of ³+³=1 (1977) (5)
Some Results Concerning Voronoi's Continued Fraction Over (√[3]D) (1981) (5)
On the period length of some special continued fractions (1992) (5)
Some periodic continued fractions with long periods (1985) (4)
The spacing of the minima in certain cubic lattices. (1986) (4)
The Ideal Class Group (2009) (4)
Determination of principal factors in (√) and (\root3\of) (1982) (4)
How was F_6 factored (1993) (4)
Some results concerning Voronoĭ’s continued fraction over (\root3\of{}) (1981) (4)
The primality of certain integers of the form $2A r^n - 1$ (1981) (4)
Class number problems for real quadratic fields (1991) (4)
Classification and Enumeration of Real Quadratic Fields Having Exactly One Non-Inert Prime Less Than a Minkowski Bound (1993) (4)
Sequences of Jacobian Varieties with Torsion Divisors of Quadratic Order (2008) (3)
Errata: “On the computation of a table of complex cubic fields with discriminant >-10⁶” [Math. Comp. 55 (1990), no. 191, 313–325; MR1023760 (90m:11155)] (1994) (3)
Quadratic residue covers for certain real quadratic fields (1994) (3)
Affirmative solution of a conjecture related to a sequence of shanks (1991) (3)
Daniel Shanks (1917-1996) (1997) (3)
Number Theory and Finite Fields (2006) (3)
A comparison of dextran, polyvinylpyrrolidone, and isotonic saline infusion in the human. (1954) (3)
Period four and real quadratic fields of class number one (1989) (3)
Purification and characterization by fast-atom-bombardment mass spectrometry of the polymorphonuclear-leucocyte-elastase-generated Aα(1-21) fragment of fibrinogen from human blood after incubation with calcium ionophore A23187 (1992) (3)
Some properties of a special set of recurring sequences (1978) (3)
Two Related Quadratic Surds Having Continued Fractions with Exceptionally Long Periods (1974) (3)
Odd and Even Linear Divisibility Sequences of Order 4 (2015) (3)
How was ₆ factored? (1993) (3)
Computation of some number-theoretic coverings (1981) (3)
Continued fractions of period five and real quadratic fields of class number one (1990) (3)
Pig pancreatic anhydro-elastase. Role of the serine-195 hydroxy group in the binding of inhibitors and substrate. (1987) (3)
Crystallographic study of a beta-lactam inhibitor complex with elastase at 1.84 A resolution. (1987) (2)
A complete generalization of Yokoi's p-invariants (1992) (2)
Tilings and patterns , by B. Grunbaum and G. C. Shephard. Pp 700. £54·95. ISBN 0-7167-1193-1 (hardback) (Freeman) (1987) (2)
Solution of a problem of Yokoi (1990) (2)
How was $F\sb 6$ factored? (1993) (2)
Leukotrienes and Asthma (1992) (2)
Unconditional Verification of the Regulator and the Class Number (2009) (2)
Quadratic Non-Residues and Prime-Producing Polynomials (1989) (2)
Inhibition of immune aggregate-induced activation of the first complement component by cationic polypeptides. (1983) (2)
Some Monoapparitic Fourth Order Linear Divisibility Sequences (2012) (2)
Improved Primality Proving with Eisenstein Pseudocubes (2010) (2)
A CRT-Based Montgomery Multiplication for Finite Fields of Small Characteristic (2005) (2)
Imaginary Cyclic Quartic Fields with Large Minus Class Numbers (2004) (1)
Unique Rabin-Williams Signature Scheme Decryption (2019) (1)
$p$-adic computation of real quadratic class numbers (1990) (1)
Some Prime Numbers of the Forms (1972) (1)
Advances in Cryptology - CRYPTO '85, Santa Barbara, California, USA, August 18-22, 1985, Proceedings (1986) (1)
CLASSIFICATION AND SYMMETRIES OF A FAMILY OF CONTINUED FRACTIONS WITH BOUNDED PERIOD LENGTH (2012) (1)
POWERS OF 2, CONTINUED FRACTIONS, AND THE CLASS NUMBER ONE PROBLEM FOR REAL QUADRATIC FIELDS $Q(\sqrt{d})$, WITH d ≡ 1 (mod 8) (1991) (1)
Further tabulation of the Erdös-Selfridge function (1997) (1)
Corrigendum: “Some primes with interesting digit patterns” [Math. Comp. 32 (1978), no. 144, 1306–1310; MR 58 #484] (1982) (1)
Some Arithmetic Properties of Certain Sequences (2015) (1)
A Problem Concerning a Character Sum - Extended Abstract (1998) (1)
Public-Key Cryptography and Computational Number Theory: Proceedings of the International Conference organized by the Stefan Banach International Mathematical Center Warsaw, Poland, September 11-15, 2000 (2001) (1)
A Table of Fundamental Units for Cubic Fields (1975) (1)
Metabolism of myo-inositol in rabbit kidney and in man. (1970) (1)
Proof, Disproof and Advances Concerning Certain Conjectures on Real Quadratic Fields (1995) (1)
Purification and characterization by fast-atom-bombardment mass spectrometry of the polymorphonuclear-leucocyte-elastase-generated A alpha (1-21) fragment of fibrinogen from human blood after incubation with calcium ionophore A23187. (1992) (1)
A parallel version of the continued fraction integer factoring algorithm (1987) (1)
Inhibition of the local hemorrhagic Shwartzman reaction by an acid proteinase inhibitor, pepstatin (1975) (1)
FURTHER TABULATION OF THE ERD¨OS-SELFRIDGE FUNCTION (1997) (0)
(f, p) Representations of $\mathcal{O}$-ideals (2009) (0)
The Analytic Class Number Formula (2009) (0)
The influence of computing and informatics on mathematics and its teaching , edited by A. G. Howson and J. P. Kahane. Pp 155. £20 (hardback), £6·50 (paperback). 1986. ISBN 0-521-32402-5, 31189-6 (Cambridge University Press) (1987) (0)
Construction of All Cubic Fields of a Fixed Fundamental Discriminant (Renate Scheidler) (2018) (0)
Ideals and Continued Fractions (2009) (0)
Cubic Pell Equations (2018) (0)
Principal Ideal Testing in $\mathcal{O}$ (2009) (0)
and Security of a Real Quadratic Field Based-Key Exchange Protocol (2001) (0)
Advances in Cryptology (1985) (0)
Angle Sum of a Triangle (1987) (0)
Proceedings of the Fourth Manitoba Conference on Numerical Mathematics, October 2-5, 1974 (1975) (0)
Quadratic Number Fields (2009) (0)
Errata: “Certain pure cubic fields with class-number one” [Math. Comp. 31 (1977), no. 138, 578–580; MR 55 #5578] (1979) (0)
Public-key cryptography and computational number theory : proceedings of the international conference (2001) (0)
One Way Functions –Conjecture, Status, Applications and Future Research Scope (2017) (0)
More on software for CD-ROMs. (1989) (0)
Staff development project — First steps (2001) (0)
Shorter Compact Representations in Real Quadratic Fields (2013) (0)
Computation of the solution of $x\sp{3}+Dy\sp{3}=1$ (1977) (0)
Corrigenda for solution of a problem of Yokoi (1991) (0)
Purification and characterization by fast-atom-bombardment mass spectrometry of the polymorphonuclear-leucocyte-elastase-generated Am(1-21) fragment of fibrinogen from human blood after incubation with calcium ionophore A23187 (2005) (0)
Binary Cubic Forms (2018) (0)
The Subexponential Method (2009) (0)
Pseudopowers and primality proving (2007) (0)
Note on a Diophantine Equation. (1970) (0)
Voronoi’s Theory of Continued Fractions (2018) (0)
Some Additional Analytic Results (2009) (0)
Corrigenda: “Computation of the class number and class group of a complex cubic field” [Math. Comp. 45 (1985), no. 171, 223–231; MR0790655 (86m:11078)] by G. W. Dueck and Williams (1988) (0)
Chemical , biochemical , pharmacokinetic , and biological properties of L-680 , 833 : A potent , orally active monocyclic fi-lactam inhibitor of human polymorphonuclear leukocyte elastase ( sntetic hibItors / lung ijury / fb cleavae ) (2005) (0)
Report of the development testing of ESB model 264 batteries (1964) (0)
Mechanism of activation of human complement c 1 complex by immuno globulin g aggregates activation of complement c 1r in a complex of activated complement c 1r and dfp inactivated complement c 1s (1982) (0)
Improving the understanding of Basic programs using profiling techniques (1979) (0)
Novel reaction of elastase with cephalosporin. beta. -lactams (1987) (0)
Beneficial Use of Watersheds; Joint Discussion (PDF) (1970) (0)
Doubly-Focused Enumeration of Pseudosquares and Pseudocubes ( DRAFT ) (2006) (0)
From affine to Euclidean geometry; an axiomatic approach, by Wanda Szmielew. Pp 194. $34·95. 1983. ISBN 90-277-1243-3 (D. Reidel) (1984) (0)
Parametrization of Norm 1 Elements of $\mathbb{K}$ (2018) (0)
Early History of the Pell Equation (2009) (0)
The Minima of Forms and Units by Approximation (2018) (0)
Laudatio in Honour of Professor Dr. Johannes Buchmann on the Occasion of His 60th Birthday (2013) (0)
Applications to Cryptography (2009) (0)
Some Special Pell Equations (2009) (0)
[P.B. Curry, Sr. Residence] (0)
Relative Minima Adjacent to 1 in a Reduced Lattice (2018) (0)
Some Computational Techniques (2009) (0)
Reviews. Symmetry and the monster: one of the greatest quests of mathematics , by Mark Ronan. Pp.272. £8-99. 2006. ISBN: 978-0192807229 (Oxford University Press). (2010) (0)
Cubic Ideals and Lattices (2018) (0)
Abstracts The Édouard Lucas Memorial Lecture (2018) (0)
The Influence of Public-Key Cryptography on Mathematics (2022) (0)
Table of Pure Cubic Fields Q( [3 ]D) for D < 10 4 (1976) (0)
Determination of principal factors in $\mathcal{Q}(\sqrt{D})$ and $\mathcal{Q}(\root 3\of D)$ (1982) (0)
Staff development project - update (2002) (0)

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