Edit Profile Williams, Hugh Cowie Compute Distance To: Compute Author ID: williams.hugh-cowie Published as: Williams, H. C.; Williams, Hugh; Williams, Hugh C. Homepage: http://people.ucalgary.ca/~hwilliam/ External Links: MGP · Wikidata · dblp · GND Documents Indexed: 225 Publications since 1965, including 16 Books Biographic References: 2 Publications all top 5 Co-Authors 57 single-authored 29 Mollin, Richard Anthony 14 Buchmann, Johannes A. 13 Jacobson, Michael John jun. 11 Zarnke, C. R. 10 Scheidler, Renate 6 Guy, Richard Kenneth 6 Roettger, Eric L. 5 Fung, Gilbert W. 5 Lukes, Richard F. 5 Shanks, Daniel C. 5 Stanton, Ralph Gordon 5 van der Poorten, Alfred J. 4 Beach, B. D. 4 Cormack, Gordon V. 4 Dueck, Gerhard W. 4 Patterson, C. D. 4 Stein, Andreas 4 Stephens, Alisa J. 3 Hartnell, Bert L. 3 Judd, J. S. 3 Müller, Siguna 3 Seah, Eric 3 Shallit, Jeffrey O. 3 Teske, Edlyn 3 Thomas, Robert S. D. 3 Wooding, Kjell 2 Baillie, Robert 2 Barrucand, Pierre-A. 2 Berrizbeitia, Pedro 2 Granville, Andrew James 2 Holte, Robert C. 2 Louboutin, Stéphane R. 2 McCarthy, David 2 Patterson, Roger D. 2 Sawilla, Reginald E. 2 Schmid, B. K. 2 Silvester, Alan K. 2 te Riele, Herman 2 Wunderlich, Marvin C. 2 Zimmer, Horst Günter 1 Alster, Kazimierz 1 Bach, Eric 1 Baniuk, L. 1 Broere, J. 1 Buell, Duncan A. 1 Buhr, P. A. 1 Cheng, K. H. F. 1 Cheng, Kell 1 de Haan, Ronald 1 Diaz y Diaz, Francisco 1 Dubner, Harvey 1 Düllmann, Stephan 1 German, R. A. 1 Gryte, D. G. 1 Hambleton, Samuel A. 1 Kingsley, Roger A. 1 Kurtz, G. C. 1 Lee, Yoonjin 1 Loxton, John H. 1 Matthew, Gary K. 1 Meek, Dereck S. 1 Morain, François 1 Newman, Morris 1 Pethő, Attila 1 Pohst, Michael E. 1 Purdy, George B. 1 Ramachandran, Shantha 1 Sands, Jonathan W. 1 Sellers, James Allen 1 Ströher, Harald 1 Sudler, Culbreth jun. 1 Tennenhouse, M. 1 Terras, Audrey Anne 1 Terras, Riho 1 Thiel, Christoph 1 Urbanowicz, Jerzy 1 van Rees, G. H. John 1 Washington, Lawrence C. 1 Williams, Kenneth S. all top 5 Serials 62 Mathematics of Computation 9 Acta Arithmetica 7 The Fibonacci Quarterly 6 Canadian Mathematical Bulletin 6 Pacific Journal of Mathematics 6 Proceedings of the Japan Academy. Series A 6 Utilitas Mathematica 5 Experimental Mathematics 4 Designs, Codes and Cryptography 3 Canadian Journal of Mathematics 3 Journal of Cryptology 2 The Mathematical Intelligencer 2 Ars Combinatoria 2 Journal of Number Theory 2 Journal für die Reine und Angewandte Mathematik 2 Journal of Integer Sequences 2 Integers 2 International Journal of Number Theory 2 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 1 Computers & Mathematics with Applications 1 Discrete Mathematics 1 IEEE Transactions on Information Theory 1 Rocky Mountain Journal of Mathematics 1 Annales des Sciences Mathématiques du Québec 1 Colloquium Mathematicum 1 Functiones et Approximatio. Commentarii Mathematici 1 Kiberneticheskiĭ Sbornik. Novaya Seriya 1 The Mathematics Student 1 Nagoya Mathematical Journal 1 Proceedings of the American Mathematical Society 1 Publicationes Mathematicae 1 Cryptologia 1 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Journal of Symbolic Computation 1 Journal of Complexity 1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 1 The Journal of Supercomputing 1 Elemente der Mathematik 1 Notices of the American Mathematical Society 1 Nieuw Archief voor Wiskunde. Vierde Serie 1 Journal de Théorie des Nombres de Bordeaux 1 Fundamenta Informaticae 1 Journal of the Australian Mathematical Society 1 BIT. Nordisk Tidskrift for Informationsbehandling 1 International Journal of Mathematics and Computer Science 1 Contributions to Discrete Mathematics 1 Lecture Notes in Computer Science 1 Canadian Mathematical Society Series of Monographs and Advanced Texts all top 5 Fields 202 Number theory (11-XX) 20 Field theory and polynomials (12-XX) 19 Information and communication theory, circuits (94-XX) 13 General and overarching topics; collections (00-XX) 13 Computer science (68-XX) 11 Numerical analysis (65-XX) 8 History and biography (01-XX) 4 Combinatorics (05-XX) 4 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 159 Publications have been cited 687 times in 422 Documents Cited by ▼ Year ▼ A modification of the RSA public-key encryption procedure. Zbl 0466.94018Williams, H. C. 25 1980 On the parallel generation of the residues for the continued fraction factoring algorithm. Zbl 0617.10005Williams, H. C.; Wunderlich, M. C. 21 1987 A \(p+1\) method of factoring. Zbl 0492.10004Williams, H. C. 19 1982 Solving the Pell equation. Zbl 1177.11027Jacobson, Michael J. jun.; Williams, Hugh C. 18 2009 Édouard Lucas and primality testing. Zbl 1155.11363Williams, Hugh C. 14 1998 Key-exchange in real quadratic congruence function fields. Zbl 0851.94021Scheidler, R.; Stein, A.; Williams, Hugh C. 14 1996 On numbers analogous to the Carmichael numbers. Zbl 0368.10011Williams, H. C. 14 1977 Computer verification of the Ankeny-Artin-Chowla Conjecture for all primes less than \(100 000 000 000\). Zbl 0987.11065van der Poorten, A. J.; te Riele, H. J. J.; Williams, H. C. 11 2001 A key-exchange system based on imaginary quadratic fields. Zbl 0659.94004Buchmann, Johannes; Williams, H. C. 11 1988 On prime valued polynomials and class numbers of real quadratic fields. Zbl 0629.12004Mollin, R. A.; Williams, H. C. 11 1988 A computational technique for evaluating \(L(1,\chi)\) and the class number of a real quadratic field. Zbl 0345.12004Williams, H. C.; Broere, J. 11 1976 Some algorithms for prime testing using generalized Lehmer functions. Zbl 0342.10007Williams, H. C.; Judd, J. S. 11 1976 Numerical results on class groups of imaginary quadratic fields. Zbl 1143.11370Jacobson, Michael J.; Ramachandran, Shantha; Williams, Hugh C. 10 2006 A conjecture of S. Chowla via the generalized Riemann hypothesis. Zbl 0649.12005Mollin, R. A.; Williams, H. C. 10 1988 Continued fractions and number-theoretic computations. Zbl 0594.12003Williams, Hugh C. 10 1985 Primality testing on a computer. Zbl 0406.10008Williams, H. C. 10 1978 Some methods for evaluating the regulator of a real quadratic function field. Zbl 0987.11071Stein, Andreas; Williams, Hugh C. 9 1999 Class numbers of real quadratic fields, continued fractions, reduced ideals, prime-producing quadratic polynomials and quadratic residue covers. Zbl 0771.11039Louboutin, S.; Mollin, R. A.; Williams, H. C. 9 1992 Calculation of the regulator of \(Q(\sqrt D)\) by use of the nearest integer continued fraction algorithm. Zbl 0401.10011Williams, H. C.; Buhr, P. A. 9 1979 A computational technique for determining the class number of a pure cubic field. Zbl 0324.12005Barrucand, Pierre; Williams, H. C.; Baniuk, L. 9 1976 Some computer results on units in quadratic and cubic fields. Zbl 0348.12003Beach, B. D.; Williams, H. C.; Zarnke, C. R. 9 1971 A key-exchange protocol using real quadratic fields. Zbl 0816.94018Scheidler, Renate; Buchmann, Johannes A.; Williams, Hugh C. 8 1994 Computation of the class number of a real quadratic field. Zbl 0757.11036Mollin, R. A.; Williams, H. C. 8 1992 Solution of the class number one problem for real quadratic fields of extended Richaud-Degert type (with one possible exception). Zbl 0696.12004Mollin, R. A.; Williams, H. C. 8 1990 Prime producing quadratic polynomials and real quadratic fields of class number one. Zbl 0695.12002Mollin, R. A.; Williams, H. C. 8 1989 Calculation of the regulator of a pure cubic field. Zbl 0431.12006Williams, H. C.; Cormack, G.; Seah, E. 8 1980 Some primes of the form \((a^n-1)/(a-1)\). Zbl 0417.10004Williams, H. C.; Seah, E. 8 1979 An investigation of bounds for the regulator of quadratic fields. Zbl 0859.11057Jacobson, Michael J. jun.; Lukes, Richard F.; Williams, Hugh C. 7 1995 On the computation of a table of complex cubic fields with discriminant \(D>-10^ 6\). Zbl 0705.11063Fung, Gilbert W.; Williams, H. C. 7 1990 Some computational results on a problem concerning powerful numbers. Zbl 0642.12001Stephens, A. J.; Williams, H. C. 7 1988 A note on the Fibonacci quotient \(F_{p-\varepsilon}/p\). Zbl 0491.10009Williams, H. C. 7 1982 New quadratic polynomials with high densities of prime values. Zbl 1009.11060Jacobson, Michael J. jun.; Williams, Hugh C. 6 2003 Results and estimates on pseudopowers. Zbl 0853.11103Bach, Eric; Lukes, Richard; Shallit, Jeffrey; Williams, H. C. 6 1996 Some results on pseudosquares. Zbl 0852.11072Lukes, R. F.; Patterson, C. D.; Williams, H. C. 6 1996 Numerical sieving devices: Their history and some applications. Zbl 0856.11048Lukes, R. F.; Patterson, C. D.; Williams, H. C. 6 1995 Short representation of quadratic integers. Zbl 0833.11060Buchmann, Johannes; Thiel, Christoph; Williams, Hugh 6 1995 Computation of the first factor of the class number of cyclotomic fields. Zbl 0762.11039Fung, Gilbert; Granville, Andrew; Williams, Hugh C. 6 1992 On a determination of real quadratic fields of class number one and related continued fraction period length less than 25. Zbl 0743.11062Mollin, R. A.; Williams, H. C. 6 1991 Torsion groups of elliptic curves with integral j-invariant over pure cubic fields. Zbl 0734.14014Fung, G. W.; Ströher, H.; Williams, H. C.; Zimmer, H. G. 6 1990 On principal ideal testing in algebraic number fields. Zbl 0624.12007Buchmann, Johannes; Williams, H. C. 6 1987 Effective primality tests for some integers of the forms \(A5^ n-1\) and \(A7^ n-1\). Zbl 0608.10003Williams, H. C. 6 1987 A rapid method of evaluating the regulator and class number of a pure cubic field. Zbl 0528.12004Williams, H. C.; Dueck, G. W.; Schmid, B. K. 6 1983 The calculation of a large cubic class number with an application to real cyclotomic fields. Zbl 0527.12004Seah, Eric; Washington, Lawrence C.; Williams, Hugh C. 6 1983 Some remarks concerning the M.I.T. public-key cryptosystem. Zbl 0418.94010Williams, H. C.; Schmid, B. 6 1979 On the imaginary bicyclic biquadratic fields with class-number 2. Zbl 0379.12002Buell, D. A.; Williams, H. C.; Williams, K. S. 6 1977 An upper bound for the period of the simple continued fraction for \(\sqrt D\). Zbl 0346.10005Stanton, R. G.; Sudler, C. jun.; Williams, H. C. 6 1976 Determination of the primality of \(N\) by using factors of \(N^2\pm 1\). Zbl 0322.10007Williams, H. C.; Judd, J. S. 6 1976 Some prime numbers of the forms \(2A3^n+1\) and \(2A3^n-1\). Zbl 0259.10005Williams, H. C.; Zarnke, C. R. 6 1972 New computations concerning the Cohen-Lenstra heuristics. Zbl 1050.11096te Riele, Herman; Williams, Hugh 5 2003 Solving the Pell equation. Zbl 1043.11027Williams, H. C. 5 2002 Class number one for real quadratic fields, continued fractions and reduced ideals. Zbl 0714.11067Mollin, R. A.; Williams, H. C. 5 1989 Computation of real quadratic fields with class number one. Zbl 0699.12006Stephens, A. J.; Williams, H. C. 5 1988 On the infrastructure of the principal ideal class of an algebraic number field of unit rank one. Zbl 0653.12005Buchmann, Johannes; Williams, H. C. 5 1988 On principal ideal testing in totally complex quartic fields and the determination of certain cyclotomic constants. Zbl 0626.12006Buchmann, Johannes; Williams, H. C. 5 1987 Simple groups of square order and an interesting sequence of primes. Zbl 0365.20025Newman, Morris; Shanks, Daniel; Williams, H. C. 5 1980 The primality of \(N = 2A3^n-1\). Zbl 0251.10009Williams, H. C. 5 1972 An upper bound on the least inert prime in a real quadratic field. Zbl 1053.11092Granville, Andrew; Mollin, R. A.; Williams, H. C. 4 2000 A public-key cryptosystem utilizing cyclotomic fields. Zbl 0829.94005Scheidler, Renate; Williams, Hugh C. 4 1995 On a solution of a class number two problem for a family of real quadratic fields. Zbl 0734.11058Mollin, R. A.; Williams, H. C. 4 1991 Quadratic fields and cryptography. Zbl 0711.11038Buchmann, Johannes; Williams, H. C. 4 1990 Quadratic polynomials which have a high density of prime values. Zbl 0701.11035Fung, G. W.; Williams, H. C. 4 1990 On the computation of the class number of an algebraic number field. Zbl 0677.12003Buchmann, Johannes; Williams, H. C. 4 1989 Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant. Zbl 0649.12003Barrucand, Pierre; Loxton, John; Williams, H. C. 4 1987 A note on class-number one in pure cubic fields. Zbl 0439.12005Williams, H. C.; Shanks, Daniel 4 1979 Quadratic fields with 3-rank equal to 4. Zbl 0409.12009Diaz y Diaz, Francisco; Shanks, Daniel; Williams, H. C. 4 1979 Some observations on primality testing. Zbl 0382.10005Williams, H. C.; Holte, R. 4 1978 Some primality tests that eluded Lucas. Zbl 1364.11161Roettger, E. L.; Williams, H. C.; Guy, R. K. 3 2015 Construction of all cubic function fields of a given square-free discriminant. Zbl 1390.11134Jacobson, M. J. jun.; Lee, Y.; Scheidler, R.; Williams, H. C. 3 2015 Some fourth-order linear divisibility sequences. Zbl 1237.11006Williams, H. C.; Guy, R. K. 3 2011 Modular arithmetic on elements of small norm in quadratic fields. Zbl 1028.11080Jacobson, M. J. jun.; Williams, H. C. 3 2002 The efficiency and security of a real quadratic field based key exchange protocol. Zbl 0986.94024Jacobson, Michael J. jun.; Scheidler, Renate; Williams, Hugh C. 3 2001 A note on Shanks’s chains of primes. Zbl 1032.11065Teske, Edlyn; Williams, Hugh C. 3 2000 An improved method of computing the regulator of a real quadratic function field. Zbl 0935.11048Stein, Andreas; Williams, Hugh C. 3 1998 An open architecture number sieve. Zbl 0711.11051Stephens, A. J.; Williams, H. C. 3 1990 Solution of a problem of Yokoi. Zbl 0705.11060Mollin, R. A.; Williams, H. C. 3 1990 On the existence of a short proof for the value of the class number and regulator of a real quadratic field. Zbl 0701.11048Buchmann, Johannes; Williams, H. C. 3 1989 Some computational results on a problem of Eisenstein. Zbl 0689.10024Stephens, A. J.; Williams, H. C. 3 1989 A note on the primality of \(6^{2^ n}+1\) and \(10^{2^ n}+1\). Zbl 0661.10009Williams, H. C. 3 1988 An \(M^ 3\) public-key encryption scheme. Zbl 0612.94010Williams, H. C. 3 1986 The primality of R1031. Zbl 0602.10001Williams, H. C.; Dubner, Harvey 3 1986 A note on class-number one in certain real quadratic and pure cubic fields. Zbl 0589.12003Tennenhouse, M.; Williams, H. C. 3 1986 Some public-key crypto-functions as intractable as factorization. Zbl 0652.94012Williams, H. C. 3 1985 Graphing L-functions of Kronecker symbols in the real part of the critical strip. Zbl 0592.10038Purdy, G.; Terras, R.; Terras, A.; Williams, H. C. 3 1985 Computation of the class number and class group of a complex cubic field. Zbl 0576.12006Dueck, G.; Williams, H. C. 3 1985 The influence of computers in the development of number theory. Zbl 0486.10001Williams, H. C. 3 1982 A class of primality tests for trinomials which includes the Lucas-Lehmer test. Zbl 0482.10007Williams, H. C. 3 1982 A numerical investigation into the length of the period of the continued fraction expansion of sqrt(D). Zbl 0476.10008Williams, H. C. 3 1981 Some results concerning the nearest integer continued fraction expansion of \(\sqrt D\). Zbl 0425.10037Williams, H. C. 3 1980 Certain pure cubic fields with class-number one. Zbl 0356.12004Williams, H. C. 3 1977 Some algorithms for solving a cubic congruence modulo \(p\). Zbl 0294.10001Williams, H. C.; Zarnke, C. R. 3 1974 A report on prime numbers of the forms \(M =(6a+1) 2^{2n-1}-1\) and \(M' =(6a-1) 2^{2n} -1\). Zbl 0157.08701Williams, H. C.; Zarnke, C. R. 3 1968 Doubly-focused enumeration of pseudosquares and pseudocubes. Zbl 1143.11360Wooding, Kjell; Williams, Hugh C. 2 2006 An improved real-quadratic-field-based key exchange procedure. Zbl 1101.68551Jacobson, Michael J. jun.; Scheidler, Renate; Williams, Hugh C. 2 2006 Explicit primality criteria for \((p-1) p^n-1\). Zbl 1018.11062Stein, Andreas; Williams, H. C. 2 2000 On certain continued fraction expansions of fixed period length. Zbl 0926.11005van der Poorten, A. J.; Williams, H. C. 2 1999 Halfway to a solution of \(x^ 2 - Dy^ 2 = -3\). Zbl 0820.11015Mollin, R. A.; van der Poorten, A. J.; Williams, H. C. 2 1994 How was \(F_ 6\) factored? Zbl 0779.11002Williams, H. C. 2 1993 On real quadratic fields of class number two. Zbl 0774.11061Mollin, R. A.; Williams, H. C. 2 1992 A complete generalization of Yokoi’s \(p\)-invariants. Zbl 0762.11035Mollin, R. A.; Williams, H. C. 2 1992 A method of tabulating the number-theoretic function \(g(k)\). Zbl 0761.11037Scheidler, Renate; Williams, Hugh C. 2 1992 Cubic fields with geometry. Zbl 1451.11001Hambleton, Samuel A.; Williams, Hugh C. 1 2018 Some primality tests that eluded Lucas. Zbl 1364.11161Roettger, E. L.; Williams, H. C.; Guy, R. K. 3 2015 Construction of all cubic function fields of a given square-free discriminant. Zbl 1390.11134Jacobson, M. J. jun.; Lee, Y.; Scheidler, R.; Williams, H. C. 3 2015 Some arithmetic properties of certain sequences. Zbl 1378.11022Roettger, E. L.; Williams, H. C. 1 2015 Some extensions of the Lucas functions. Zbl 1332.11023Roettger, E. L.; Williams, H. C.; Guy, R. K. 1 2013 Some monoapparitic fourth order linear divisibility sequences. Zbl 1278.11014Williams, Hugh C.; Guy, Richard K. 1 2012 Public-key cryptography based on a cubic extension of the Lucas functions. Zbl 1237.94092Roettger, Eric; Williams, Hugh C. 1 2012 Some fourth-order linear divisibility sequences. Zbl 1237.11006Williams, H. C.; Guy, R. K. 3 2011 Solving the Pell equation. Zbl 1177.11027Jacobson, Michael J. jun.; Williams, Hugh C. 18 2009 A cubic extension of the Lucas functions. Zbl 1215.11010Müller, Siguna; Roettger, Eric; Williams, Hugh C. 1 2009 Sequences of Jacobian varieties with torsion divisors of quadratic order. Zbl 1188.11034Patterson, Roger D.; van der Poorten, Alfred J.; Williams, Hugh C. 1 2008 A new look at an old equation. Zbl 1206.11152Sawilla, R. E.; Silvester, A. K.; Williams, H. C. 1 2008 Characterization of a generalized Shanks sequence. Zbl 1221.11211Patterson, Roger D.; van der Poorten, Alfred J.; Williams, Hugh C. 1 2007 Numerical results on class groups of imaginary quadratic fields. Zbl 1143.11370Jacobson, Michael J.; Ramachandran, Shantha; Williams, Hugh C. 10 2006 Doubly-focused enumeration of pseudosquares and pseudocubes. Zbl 1143.11360Wooding, Kjell; Williams, Hugh C. 2 2006 An improved real-quadratic-field-based key exchange procedure. Zbl 1101.68551Jacobson, Michael J. jun.; Scheidler, Renate; Williams, Hugh C. 2 2006 Some results concerning certain periodic continued fractions. Zbl 1080.11008Cheng, Kell; Williams, Hugh 1 2005 Imaginary cyclic quartic fields with large minus class numbers. Zbl 1125.11350Jacobson, M. J. jun.; Williams, H. C.; Wooding, K. 1 2004 New quadratic polynomials with high densities of prime values. Zbl 1009.11060Jacobson, Michael J. jun.; Williams, Hugh C. 6 2003 New computations concerning the Cohen-Lenstra heuristics. Zbl 1050.11096te Riele, Herman; Williams, Hugh 5 2003 Solving the Pell equation. Zbl 1043.11027Williams, H. C. 5 2002 Modular arithmetic on elements of small norm in quadratic fields. Zbl 1028.11080Jacobson, M. J. jun.; Williams, H. C. 3 2002 Computer verification of the Ankeny-Artin-Chowla Conjecture for all primes less than \(100 000 000 000\). Zbl 0987.11065van der Poorten, A. J.; te Riele, H. J. J.; Williams, H. C. 11 2001 The efficiency and security of a real quadratic field based key exchange protocol. Zbl 0986.94024Jacobson, Michael J. jun.; Scheidler, Renate; Williams, Hugh C. 3 2001 An upper bound on the least inert prime in a real quadratic field. Zbl 1053.11092Granville, Andrew; Mollin, R. A.; Williams, H. C. 4 2000 A note on Shanks’s chains of primes. Zbl 1032.11065Teske, Edlyn; Williams, Hugh C. 3 2000 Explicit primality criteria for \((p-1) p^n-1\). Zbl 1018.11062Stein, Andreas; Williams, H. C. 2 2000 The size of the fundamental solutions of consecutive Pell equations. Zbl 0961.11007Jacobson, Michael J. jun.; Williams, Hugh C. 1 2000 Some methods for evaluating the regulator of a real quadratic function field. Zbl 0987.11071Stein, Andreas; Williams, Hugh C. 9 1999 On certain continued fraction expansions of fixed period length. Zbl 0926.11005van der Poorten, A. J.; Williams, H. C. 2 1999 A problem concerning a character sum. Zbl 0938.11061Teske, Edlyn; Williams, Hugh C. 1 1999 Édouard Lucas and primality testing. Zbl 1155.11363Williams, Hugh C. 14 1998 An improved method of computing the regulator of a real quadratic function field. Zbl 0935.11048Stein, Andreas; Williams, Hugh C. 3 1998 Daniel Shanks (1917-1996). Zbl 0908.01035Williams, H. C. 1 1997 Daniel Shanks (1917-1996). Zbl 0867.01016Williams, H. C. 1 1997 Key-exchange in real quadratic congruence function fields. Zbl 0851.94021Scheidler, R.; Stein, A.; Williams, Hugh C. 14 1996 Results and estimates on pseudopowers. Zbl 0853.11103Bach, Eric; Lukes, Richard; Shallit, Jeffrey; Williams, H. C. 6 1996 Some results on pseudosquares. Zbl 0852.11072Lukes, R. F.; Patterson, C. D.; Williams, H. C. 6 1996 An investigation of bounds for the regulator of quadratic fields. Zbl 0859.11057Jacobson, Michael J. jun.; Lukes, Richard F.; Williams, Hugh C. 7 1995 Numerical sieving devices: Their history and some applications. Zbl 0856.11048Lukes, R. F.; Patterson, C. D.; Williams, H. C. 6 1995 Short representation of quadratic integers. Zbl 0833.11060Buchmann, Johannes; Thiel, Christoph; Williams, Hugh 6 1995 A public-key cryptosystem utilizing cyclotomic fields. Zbl 0829.94005Scheidler, Renate; Williams, Hugh C. 4 1995 A key-exchange protocol using real quadratic fields. Zbl 0816.94018Scheidler, Renate; Buchmann, Johannes A.; Williams, Hugh C. 8 1994 Halfway to a solution of \(x^ 2 - Dy^ 2 = -3\). Zbl 0820.11015Mollin, R. A.; van der Poorten, A. J.; Williams, H. C. 2 1994 Factoring integers before computers. Zbl 0847.11002Williams, H. C.; Shallit, J. O. 1 1994 Errata: On the computation of a table of complex cubic fields with discriminant \(D> -10^ 6\). Zbl 0835.11041Fung, G. W.; Williams, H. C. 1 1994 How was \(F_ 6\) factored? Zbl 0779.11002Williams, H. C. 2 1993 Classification and enumeration of real quadratic fields having exactly one non-inert prime less than a Minkowski bound. Zbl 0803.11054Mollin, R. A.; Williams, H. C. 1 1993 Class groups of exponent two in real quadratic fields. Zbl 0795.11057Louboutin, S.; Mollin, R. A.; Williams, H. C. 1 1993 Class numbers of real quadratic fields, continued fractions, reduced ideals, prime-producing quadratic polynomials and quadratic residue covers. Zbl 0771.11039Louboutin, S.; Mollin, R. A.; Williams, H. C. 9 1992 Computation of the class number of a real quadratic field. Zbl 0757.11036Mollin, R. A.; Williams, H. C. 8 1992 Computation of the first factor of the class number of cyclotomic fields. Zbl 0762.11039Fung, Gilbert; Granville, Andrew; Williams, Hugh C. 6 1992 On real quadratic fields of class number two. Zbl 0774.11061Mollin, R. A.; Williams, H. C. 2 1992 A complete generalization of Yokoi’s \(p\)-invariants. Zbl 0762.11035Mollin, R. A.; Williams, H. C. 2 1992 A method of tabulating the number-theoretic function \(g(k)\). Zbl 0761.11037Scheidler, Renate; Williams, Hugh C. 2 1992 Consecutive powers in continued fractions. Zbl 0764.11010Mollin, R. A.; Williams, H. C. 1 1992 On a determination of real quadratic fields of class number one and related continued fraction period length less than 25. Zbl 0743.11062Mollin, R. A.; Williams, H. C. 6 1991 On a solution of a class number two problem for a family of real quadratic fields. Zbl 0734.11058Mollin, R. A.; Williams, H. C. 4 1991 Some formulas concerning the fundamental unit of a real quadratic field. Zbl 0745.11049Williams, H. C. 2 1991 Powers of 2, continued fractions, and the class number one problem for real quadratic fields \(\mathbb{Q}(\sqrt d)\), with \(d\equiv 1\pmod 8\). Zbl 0771.11006Mollin, R. A.; Williams, H. C. 1 1991 On the divisor function and class numbers of real quadratic fields. III. Zbl 0748.11053Mollin, R. A.; Williams, H. C. 1 1991 Affirmative solution of a conjecture related to a sequence of Shanks. Zbl 0743.11063Mollin, R. A.; Williams, H. C. 1 1991 Some remarks concerning the complexity of computing class groups of quadratic fields. Zbl 0744.11067Buchmann, Johannes A.; Williams, Hugh C. 1 1991 Solution of the class number one problem for real quadratic fields of extended Richaud-Degert type (with one possible exception). Zbl 0696.12004Mollin, R. A.; Williams, H. C. 8 1990 On the computation of a table of complex cubic fields with discriminant \(D>-10^ 6\). Zbl 0705.11063Fung, Gilbert W.; Williams, H. C. 7 1990 Torsion groups of elliptic curves with integral j-invariant over pure cubic fields. Zbl 0734.14014Fung, G. W.; Ströher, H.; Williams, H. C.; Zimmer, H. G. 6 1990 Quadratic fields and cryptography. Zbl 0711.11038Buchmann, Johannes; Williams, H. C. 4 1990 Quadratic polynomials which have a high density of prime values. Zbl 0701.11035Fung, G. W.; Williams, H. C. 4 1990 An open architecture number sieve. Zbl 0711.11051Stephens, A. J.; Williams, H. C. 3 1990 Solution of a problem of Yokoi. Zbl 0705.11060Mollin, R. A.; Williams, H. C. 3 1990 A key exchange system based on real quadratic fields. Extended abstract. Zbl 0722.68043Buchmann, Johannes A.; Williams, Hugh C. 2 1990 Class number problems for real quadratic fields. Zbl 0705.11057Mollin, R. A.; Williams, H. C. 2 1990 The period length of Voronoi’s algorithm for certain cubic orders. Zbl 0732.11055Williams, H. C. 1 1990 Continued fractions of period five and real quadratic fields of class number one. Zbl 0705.11059Mollin, R. A.; Williams, H. C. 1 1990 Prime producing quadratic polynomials and real quadratic fields of class number one. Zbl 0695.12002Mollin, R. A.; Williams, H. C. 8 1989 Class number one for real quadratic fields, continued fractions and reduced ideals. Zbl 0714.11067Mollin, R. A.; Williams, H. C. 5 1989 On the computation of the class number of an algebraic number field. Zbl 0677.12003Buchmann, Johannes; Williams, H. C. 4 1989 On the existence of a short proof for the value of the class number and regulator of a real quadratic field. Zbl 0701.11048Buchmann, Johannes; Williams, H. C. 3 1989 Some computational results on a problem of Eisenstein. Zbl 0689.10024Stephens, A. J.; Williams, H. C. 3 1989 Quadratic non-residues and prime-producing polynomials. Zbl 0714.11066Mollin, R. A.; Williams, H. C. 2 1989 Period four and real quadratic fields of class number one. Zbl 0705.11058Mollin, R. A.; Williams, H. C. 1 1989 A key-exchange system based on imaginary quadratic fields. Zbl 0659.94004Buchmann, Johannes; Williams, H. C. 11 1988 On prime valued polynomials and class numbers of real quadratic fields. Zbl 0629.12004Mollin, R. A.; Williams, H. C. 11 1988 A conjecture of S. Chowla via the generalized Riemann hypothesis. Zbl 0649.12005Mollin, R. A.; Williams, H. C. 10 1988 Some computational results on a problem concerning powerful numbers. Zbl 0642.12001Stephens, A. J.; Williams, H. C. 7 1988 Computation of real quadratic fields with class number one. Zbl 0699.12006Stephens, A. J.; Williams, H. C. 5 1988 On the infrastructure of the principal ideal class of an algebraic number field of unit rank one. Zbl 0653.12005Buchmann, Johannes; Williams, H. C. 5 1988 A note on the primality of \(6^{2^ n}+1\) and \(10^{2^ n}+1\). Zbl 0661.10009Williams, H. C. 3 1988 On the parallel generation of the residues for the continued fraction factoring algorithm. Zbl 0617.10005Williams, H. C.; Wunderlich, M. C. 21 1987 On principal ideal testing in algebraic number fields. Zbl 0624.12007Buchmann, Johannes; Williams, H. C. 6 1987 Effective primality tests for some integers of the forms \(A5^ n-1\) and \(A7^ n-1\). Zbl 0608.10003Williams, H. C. 6 1987 On principal ideal testing in totally complex quartic fields and the determination of certain cyclotomic constants. Zbl 0626.12006Buchmann, Johannes; Williams, H. C. 5 1987 Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant. Zbl 0649.12003Barrucand, Pierre; Loxton, John; Williams, H. C. 4 1987 An \(M^ 3\) public-key encryption scheme. Zbl 0612.94010Williams, H. C. 3 1986 The primality of R1031. Zbl 0602.10001Williams, H. C.; Dubner, Harvey 3 1986 A note on class-number one in certain real quadratic and pure cubic fields. Zbl 0589.12003Tennenhouse, M.; Williams, H. C. 3 1986 Fast primality tests for numbers less than 50 \(\cdot \,10^ 9\). Zbl 0594.10001Kurtz, G. C.; Shanks, Daniel; Williams, H. C. 2 1986 The spacing of the minima in certain cubic lattices. Zbl 0615.12003Williams, H. C. 1 1986 Primality testing on a computer. Zbl 0607.10004Williams, H. C. 1 1986 Advances in cryptology - CRYPTO ’85. Proceedings. (A Conference on the Theory and Application of Cryptographic techniques held at the University of California, Santa Barbara, August 18-22, 1985). Zbl 0583.00049Williams, Hugh C. (ed.) 1 1986 ...and 59 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 484 Authors 47 Williams, Hugh Cowie 23 Mollin, Richard Anthony 18 Scheidler, Renate 14 Louboutin, Stéphane R. 13 Jacobson, Michael John jun. 10 Buchmann, Johannes A. 10 Stein, Andreas 6 Shallit, Jeffrey O. 5 Berrizbeitia, Pedro 4 Grau, José María 4 Luca, Florian 4 Lukes, Richard F. 4 Morain, François 4 Moree, Pieter 4 Oller-Marcén, Antonio M. 4 Pomerance, Carl Bernard 4 Sun, Zhi-Wei 3 Bach, Eric 3 Brent, Richard Peirce 3 Byeon, Dongho 3 Cao, Zhenfu 3 Castagnos, Guilhem 3 Clark, Peter Louis 3 Fung, Gilbert W. 3 González-Jiménez, Enrique 3 Granville, Andrew James 3 Ichimura, Humio 3 Koblitz, Neal I. 3 Lee, Jungyun 3 Lee, Yoonjin 3 Nawata, Norio 3 Panario, Daniel 3 Pethő, Attila 3 Roettger, Eric L. 3 Sadornil, Daniel 3 Srinivasan, Anitha 3 Teske, Edlyn 3 Tomita, Koshi 2 Adam, David 2 Aouissi, Siham 2 Atkin, Arthur Oliver Lonsdale 2 Azizi, Abdelmalek 2 Bauer, Mark L. 2 Bernstein, Daniel Julius 2 Bhargava, Manjul 2 Biasse, Jean-François 2 Cahen, Paul-Jean 2 Chakraborty, Kalyan 2 Chen, Yonggao 2 Cohen, Henri 2 Crandall, Richard E. 2 Dahl, Alexander 2 Deng, Lih-Yuan 2 Dilcher, Karl 2 Dong, Xiaolei 2 Dubner, Harvey 2 Elia, Michele 2 Felix, Adam Tyler 2 Fontein, Felix 2 Fujita, Yasutsugu 2 Guy, Richard Kenneth 2 Hendy, Michael D. 2 Hofheinz, Dennis 2 Hoque, Azizul 2 İşcan, Hülya 2 Iskra, Boris 2 Ismaili, Moulay Chrif 2 Jeans, N. S. 2 Jiang, Zhengtao 2 Karaali, Fitnat 2 Karaatli, Olcay 2 Kawamoto, Fuminori 2 Keskin, Refik 2 Kiltz, Eike 2 Klaška, Jiří 2 Laguillaumie, Fabien 2 Lamzouri, Youness 2 Lange, Tanja 2 Lenstra, Hendrik W. jun. 2 Loxton, John H. 2 Lu, Henry Horng-Shing 2 Matthews, Keith R. 2 Mayer, Daniel C. 2 McIntosh, Richard J. 2 Micali, Silvio 2 Mishra, Mohit 2 Muñoz Masqué, Jaime 2 Murru, Nadir 2 Murty, Maruti Ram 2 Najman, Filip 2 Pan, Hao 2 Paulus, Sachar Manfred 2 Pohst, Michael E. 2 Pollack, Paul 2 Pollard, John M. 2 Rezai Rad, Monireh 2 Riesel, Hans 2 Robertson, John P. 2 Rozenhart, Pieter 2 Schipani, Davide ...and 384 more Authors all top 5 Cited in 111 Serials 98 Mathematics of Computation 47 Journal of Number Theory 21 Proceedings of the Japan Academy. Series A 14 Journal of Cryptology 11 International Journal of Number Theory 9 Journal de Théorie des Nombres de Bordeaux 8 Proceedings of the American Mathematical Society 7 Rocky Mountain Journal of Mathematics 7 Designs, Codes and Cryptography 7 Experimental Mathematics 5 Computers & Mathematics with Applications 5 Nagoya Mathematical Journal 5 Journal of Symbolic Computation 5 Applicable Algebra in Engineering, Communication and Computing 4 Bulletin of the Australian Mathematical Society 4 Discrete Mathematics 4 The Mathematical Intelligencer 4 Annales de l’Institut Fourier 4 Archiv der Mathematik 4 Czechoslovak Mathematical Journal 4 Journal of Soviet Mathematics 4 Theoretical Computer Science 3 Acta Arithmetica 3 Applied Mathematics and Computation 3 BIT 3 Journal of Computational and Applied Mathematics 3 Acta Mathematica Hungarica 3 Journal of Complexity 3 The Ramanujan Journal 3 Journal of Integer Sequences 3 Integers 2 Discrete Applied Mathematics 2 Information Processing Letters 2 Israel Journal of Mathematics 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Duke Mathematical Journal 2 Functiones et Approximatio. Commentarii Mathematici 2 Inventiones Mathematicae 2 Journal of Algebra 2 Journal of Pure and Applied Algebra 2 Mathematika 2 Pacific Journal of Mathematics 2 Results in Mathematics 2 Tokyo Journal of Mathematics 2 Transactions of the American Mathematical Society 2 Advances in Applied Mathematics 2 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 2 The Journal of Supercomputing 2 Kyushu Journal of Mathematics 2 Finite Fields and their Applications 2 Wuhan University Journal of Natural Sciences (WUJNS) 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Advances in Mathematics of Communications 2 Acta Mathematica Universitatis Ostraviensis 2 ISRN Combinatorics 2 Research in Number Theory 1 Archive for History of Exact Sciences 1 Indian Journal of Pure & Applied Mathematics 1 Linear and Multilinear Algebra 1 Mathematical Notes 1 Periodica Mathematica Hungarica 1 Advances in Mathematics 1 Computing 1 Indiana University Mathematics Journal 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of the Mathematical Society of Japan 1 The Journal of Symbolic Logic 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Mathematics and Computers in Simulation 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Osaka Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Tohoku Mathematical Journal. Second Series 1 Acta Applicandae Mathematicae 1 Discrete & Computational Geometry 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 International Journal of Electronics 1 Numerical Algorithms 1 Annals of Physics 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Indagationes Mathematicae. New Series 1 Cybernetics and Systems Analysis 1 Russian Mathematics 1 Tatra Mountains Mathematical Publications 1 Journal of Mathematical Sciences (New York) 1 Science in China. Series E 1 Abstract and Applied Analysis 1 Journal of Inequalities and Applications 1 Revista Matemática Complutense 1 Journal of Discrete Mathematical Sciences & Cryptography 1 LMS Journal of Computation and Mathematics 1 Acta Mathematica Sinica. English Series 1 Journal of the Australian Mathematical Society 1 Iranian Journal of Science and Technology. Transaction A: Science 1 Missouri Journal of Mathematical Sciences 1 Journal of Discrete Algorithms ...and 11 more Serials all top 5 Cited in 26 Fields 371 Number theory (11-XX) 63 Information and communication theory, circuits (94-XX) 34 Algebraic geometry (14-XX) 26 Computer science (68-XX) 14 Field theory and polynomials (12-XX) 10 Combinatorics (05-XX) 9 Commutative algebra (13-XX) 9 Numerical analysis (65-XX) 6 Group theory and generalizations (20-XX) 3 History and biography (01-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Functional analysis (46-XX) 2 Associative rings and algebras (16-XX) 2 Special functions (33-XX) 2 Convex and discrete geometry (52-XX) 2 Quantum theory (81-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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