*p-adic Numbers, p-adic Analysis, and Zeta-Functions*, Graduate Texts in Mathematics No. 58, Springer-Verlag, 1977. Second edition, 1984.*p-adic Analysis: A Short Course on Recent Work*, London Mathematical Society Lecture Note Series No. 46, Cambridge University Press, Cambridge, 1980.*Introduction to Elliptic Curves and Modular Forms*, Graduate Texts in Math. No. 97, Springer-Verlag, 1984. Second edition, 1993.*A Course in Number Theory and Cryptography*, Graduate Texts in Math. No. 114, Springer-Verlag, 1987. Second edition, 1994.*Algebraic Aspects of Cryptography*, Algorithms and Computation in Mathematics Vol. 3, Springer-Verlag, 1998.*Random Curves: Journeys of a Mathematician*, Springer-Verlag, 2007.

*Number Theory Related to Fermat's Last Theorem*, Progress in Math. No. 26, Birkhauser, Boston, 1982.*Advances in Cryptology - Crypto '96*, Lec. Notes in Computer Science No. 1109, Springer, 1996.*Towards a Quarter-Century of Public Key Cryptography*, Springer, 2000.

- Mathematics under hardship conditions in the Third
World,
*AMS-MAA Joint Lecture Series*, 1992. - The story of the proof of Fermat's Last Theorem,
*Undergraduate Mathematical Sciences Colloquium*, Univ. Washington, 1993.

*p*-adic variation of the zeta-function over families of varieties defined over finite fields,*Compositio Mathematica*, Vol. 31, 1975, 119-218.- Netselostnost periodov parabolicheskikh form vne
kriticheskoi polosy (Non-integrality of the periods of cusp forms outside
the critical strip),
*Funktsional'nyi Analiz i ego Prilozheniya*, Vol. 9, 1975, 52-55. - 2-adic and 3-adic ordinals of 1/
*j*-expansion coefficients for the weight 2 Eisenstein series,*Bulletin of the London Mathematical Society*, Vol. 9, 1977, 188-192. - Interpretation of the
*p*-adic log gamma function and Euler constants using the Bernoulli measure,*Transactions of the American Mathematical Society*, Vol. 242, 1978, 261-269. - Gamma function identities and elliptic differentials on
Fermat curves,
*Duke Mathematical Journal*, Vol. 45, 1978, 87-99. - (with D. Rohrlich) Simple factors in the Jacobian of a
Fermat curve,
*Canadian Journal of Mathematics*, Vol. 30, 1978, 1183-1205. - (with A. Ogus) Algebraicity of some products of values
of the gamma function, Appendix to: P. Deligne, Valeurs de fonctions L et
périodes d'intégrales,
*Proceedings of Symposia in Pure Mathematics*, Vol. 33 Part 2, 1979, 313-346. - (with B. H. Gross) Gauss sums and the
*p*-adic gamma-function,*Annals of Mathematics*, Vol. 109, 1979, 569-581. - A new proof of certain relations between
*p*-adic*L*-functions and log gamma-functions,*Duke Mathematical Journal*, Vol. 46, 1979, 455-468. *q*-extension of the*p*-adic gamma function,*Transactions of the American Mathematical Society*, Vol. 260, 1980, 449-457.- The hypergeometric function with
*p*-adic parameters,*Proceedings of the Queen's Number Theory Conference 1979*, Queen's University, Kingston, Ontario, 1980, 319-328. - On Carlitz's
*q*-Bernoulli numbers,*Journal of Number Theory*, Vol. 14, 1982, 332-339. *p*-adic analog of Heine's hypergeometric*q*-series,*Pacific Journal of Mathematics*, Vol. 102, 1982, 373-383.*q*-extension of the*p*-adic gamma function. II,*Transactions of the American Mathematical Society*, Vol. 273, 1982, 111-129.- The number of points on certain families of
hypersurfaces over finite fields,
*Compositio Mathematica*, Vol. 48, 1983, 3-23. *p*-adic eigen-functions for Kubert distributions,*Canadian Journal of Mathematics*, Vol. 35, 1983, 674-686.*p*-adic integral transforms on compact subgroups of*C*,_{p}*Pacific Journal of Mathematics*, Vol. 120, 1985.*p*-adic congruences and modular forms of half integer weight,*Mathematische Annalen*, Vol. 274, 1986, 199-220.- Elliptic curve cryptosystems,
*Mathematics of Computation*, Vol. 48, 1987, 203-209. - Congruences for periods of modular forms,
*Duke Mathematical Journal*, Vol. 54, 1987, 361-373. - Primality of the number of points on an elliptic curve
over a finite field,
*Pacific Journal of Mathematics*, Vol. 131, 1988, 157-165. - Hyperelliptic cryptosystems,
*Journal of Cryptology*, Vol. 1, 1989, 139-150. - A family of jacobians suitable for discrete log
cryptosystems,
*Advances in Cryptology - Crypto '88*, Springer-Verlag, 1990, 94-99. - Discrete logarithms and discreet curves, in:
*A Perspective in Theoretical Computer Science - Commemorative Volume for Gift Siromoney*, World Sci. Publ. Co. Ltd, 1989, 106-120. - Jacobi sums, irreducible zeta-polynomials, and
cryptography,
*Canadian Math. Bulletin*, Vol. 34 (2), 1991, 229-235. - Constructing elliptic curve cryptosystems in
characteristic 2,
*Advances in Cryptology - Crypto '90*, Springer-Verlag, 1991, 156-167. - Elliptic curve implementation of zero-knowledge blobs,
*Journal of Cryptology*, Vol. 4, 1991, 207-213. - CM-curves with good cryptographic properties,
*Advances in Cryptology - Crypto '91*, Springer-Verlag, 1992, 279-287. - (with M. R. Fellows) Self-witnessing polynomial-time
complexity and prime factorization,
*Designs, Codes and Cryptography*, Vol. 2, 1992, 231-235. - (with M. R. Fellows) Fixed-parameter complexity and
cryptography, in G. Cohen, Teo Mora, and O. Moreno Eds.,
*Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Proc. 10th Intern. Symp., San Juan, Puerto Rico, May 1993*, Springer-Verlag, 1993, 121-131. - (with M. R. Fellows) Combinatorially based cryptography
for children (and adults),
*Proc. 24th Southeastern Intern. Conf. Combinatorics, Graph Theory and Computing*(Boca Raton, Florida, February 1993),*Congressus Numerantium*, Vol. 99, 1994, 9-41. - (with M. R. Fellows) Combinatorial cryptosystems
galore!, in
*Finite Fields: Theory, Applications, and Algorithms, Second Intern. Conf. Finite Fields*(Las Vegas, August 1993),*Contemporary Math.*Vol. 168, 1994, 51-61. - Computational algebra problems arising from
combinatorial cryptography,
*Proceedings of Discussion Meeting on Cryptography and Computation*(31 August - 1 September, 1995, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore), 12 pages. - (with R. Balasubramanian) The improbability that an
elliptic curve has subexponential discrete logarithm problem under the
Menezes-Okamoto-Vanstone algorithm,
*Journal of Cryptology*, Vol. 11, 1998, 141-145. - (with J. P. Buhler) Lattice basis reduction, Jacobi
sums, and hyperelliptic cryptosystems,
*Bulletin of the Australian Mathematical Society*, Vol. 57, 1998, 147-154. - An elliptic curve implementation of the finite field
digital signature algorithm,
*Advances in Cryptology - Crypto '98*, Springer-Verlag, 1998, 327-337. - (with R. G. Downey and M. R. Fellows) Techniques for exponential
parameterized reductions in vertex set problems, unpublished but included
in R. G. Downey and M. R. Fellows,
*Parameterized Complexity*, Springer-Verlag, 1999, 220-222. - (with M. J. Jacobson, J. H. Silverman, A. Stein, and E.
Teske) Analysis of the xedni calculus attack,
*Designs, Codes and Cryptography*, Vol. 20, 2000, 41-64. - Almost primality of group orders of elliptic curves
defined over small finite fields,
*Experimental Mathematics*, Vol. 10, 2001, 553-558. - (with A. J. Menezes) Obstacles to the torsion-subgroup
attack on the Decision Diffie-Hellman problem,
*Mathematics of Computation*, Vol. 73, 2004, 2027-2041. - (with A. J. Menezes) Another look at `provable
security,'
*Journal of Cryptology*, Vol. 20, 2007, 3-37; available here. - (with A. J. Menezes) Pairing-based cryptography at high
security levels,
*Proceedings of the Tenth IMA International Conference on Cryptography and Coding*, Springer-Verlag, LNCS 3796, 2005, 13-36; available here. - (with A. J. Menezes) Another look at generic groups,
*Advances in Mathematics of Communications*, Vol. 1, 2007, 13-28; available here. - (with A. J. Menezes) Another look at `provable
security'. II,
*Advances in Cryptology - Indocrypt 2006*, Springer-Verlag, LNCS 4329, 2006, 148-175; available here. - Another look at automated theorem-proving,
*Journal of Mathematical Cryptology*, Vol. 1, 2007, 385-403; available here. - (with A. J. Menezes) Another look at non-standard
discrete log and Diffie-Hellman problems,
*Journal of Mathematical Cryptology*, Vol. 2, 2008, 311-326; available here. - (with A. H. Koblitz and A. J. Menezes) Elliptic curve
cryptography: The serpentine course of a paradigm shift,
*Journal of Number Theory*Vol. 131, 2011, 781-814; available here. Videoabstract available here. - (with A. J. Menezes) Intractable assumptions in
cryptography,
*Proc. 9th International Conf. Finite Fields and Their Applications*,*Contemporary Mathematics*, Vol. 518, 2010, 279-300. - A security weakness in composite-order pairing-based
protocols with imbedding degree k>2, available here.
- (with A. J. Menezes and I. E. Shparlinski) Discrete
logarithms, Diffie-Hellman, and reductions,
*Vietnam Journal of Mathematics*, Vol. 39, 2011, 267-285; available here. - Another look at automated theorem-proving. II,
*Journal of Mathematical Cryptology*, Vol. 5, 2011, 205-224; available here. - (with A. J. Menezes) Another look at security
definitions,
*Advances in Mathematics of Communications*, Vol. 7, 2013, 1-38; available here. - (with A. J. Menezes) Another look at HMAC,
*Journal of Mathematical Cryptology*, Vol. 7, 2013, 225-251; available here. - (with A. J. Menezes) Another look at non-uniformity,
*Groups, Complexity, Cryptology*, Vol. 5, No. 2, 2013, 117-139; available here. - (with A. J. Menezes) Another look at security theorems
for 1-key nested MACs,
*Open Problems in Mathematics and Computational Science*, Springer-Verlag, 2014, 69-89; available here. - (with A. J. Menezes) The random oracle model: A
twenty-year retrospective,
*Designs, Codes and Cryptography*, Vol. 77, 2015, 587-610; available here. - (with S. Chatterjee, A. J. Menezes, and P. Sarkar)
Another look at tightness. II: Practical issues in cryptography,
*Paradigms in Cryptology – Mycrypt 2016,*Springer-Verlag, 2017, 21-55, available here.

- Number theory and cryptography, in M. Artin, H. Kraft,
and R. Remmert, eds.,
*Duration and Change: Fifty Years at Oberwolfach*, Springer-Verlag, 1994, 211-236. - Elliptic curve cryptosystems: An overview,
*Proceedings of Discussion Meeting on Cryptography and Computation*(31 August - 1 September, 1995, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore), 8 pages. - (with A. Menezes and S. A. Vanstone) The state of
elliptic curve cryptography,
*Designs, Codes and Cryptography*, Vol. 19, 2000, 173-194. - A survey of number theory and cryptography, in R. P.
Bambah, V. C. Dumir, and R. J. Hans Gill, eds,
*Number Theory*, Indian National Science Academy, 2000, 217-239. - Cryptography, in B. Engquist and W. Schmid, eds.,
*Mathematics Unlimited - 2001 and Beyond*, Springer-Verlag, 2001, 749-769. - Some number-theoretic issues in modern cryptography,
*Newsletter of the Ramanujan Mathematical Society*(Madras), Vol. 11, No. 1-2, 2001, 1-14. - Good and bad uses of elliptic curves in cryptography,
*Moscow Math. Journal*, Vol. 2, 2002, 693-715. - (with A. J. Menezes) A survey of public-key
cryptosystems,
*SIAM Review*, Vol. 46, 2004, 599-634. - (with A. J. Menezes) Cryptocash, cryptocurrencies, and
cryptocontracts,
*Designs, Codes and Cryptography*, Vol. 78, 2016, 87-102. - (with A. J. Menezes) Cryptographers prepare for a
possible post-quantum future,
*Canadian Math. Soc. Notes*, Oct/Nov 2017, 16-17.

- A mathematical visit to Hanoi,
*The Mathematical Intelligencer*, Vol. 2, No. 1, 1979, 38-42. - The
*p*-adic approach to solutions of equations over finite fields,*The American Mathematical Monthly*, Vol. 87, 1980, 115-118. - Mathematics as propaganda, in L.A. Steen, ed.,
*Mathematics Tomorrow*, Springer-Verlag, New York, 1981. - Why study equations over finite fields?,
*Mathematics Magazine*, May 1982, 144-149. - (with Ann Hibner Koblitz) Mathematics and the external
world, an interview with A.T. Fomenko,
*The Mathematical Intelligencer*, Vol. 8, No. 2, 1986, 8-17, 25. - Book review of
*Ultrametric Calculus: An Introduction to p-adic Analysis*by W. H. Schikhof,*American Scientist*, Vol. 74, 1986, 681-682. - Vietnam after the agony,
*Frontline*(Madras, India), Vol. 4, No. 14 (July 11-24, 1987), 48-56; Triumphs and problems of science in Vietnam,*Frontline*, Vol. 4, No. 15 (July 25-August 7, 1987), 52-55. - Problems that teach the obvious but difficult,
*The American Mathematical Monthly*, Vol. 95, 1988, 254-257. - A tale of three equations; or the emperors have no
clothes,
*The Mathematical Intelligencer*, Vol. 10, No. 1, 1988, 4-11; and: Reply to unclad emperors,*ibid*., 14-16. - Book review of
*A Course in Number Theory*by H. E. Rose,*American Scientist*, March 1990. - Three practical applications of algebraic curves,
*Journal of Sichuan University Natural Science Edition*, Vol. 26, Special Issue, December 1989, 28-35. - Book review of
*Primes of the Form x²+ny²: Fermat, Class Field Theory, and Complex Multiplication*by D. A. Cox,*Mathematics of Computation*, Vol. 56, 1991, 401-403. - Recollections of mathematics in a country under siege,
Interview with Professor Hoang Tuy, Director of the Hanoi Mathematical
Institute,
*The Mathematical Intelligencer*, Vol. 12, No. 3, 1990, 16-34. - Are student ratings unfair to women?,
*Association for Women in Mathematics Newsletter*, Vol. 20, No. 5, 1990, 17-19. - Mathematics under hardship conditions in the Third
World,
*Notices of the Amer. Math. Soc.*, Vol. 38, 1991, 1123-1128. - The profit motive: the bane of mathematics education,
*Humanistic Mathematics Network Journal*, No. 7, 1992, 89-92. - (with M. R. Fellows) Kid Krypto,
*Advances in Cryptology - Crypto '92*, Springer-Verlag, 1993, 378-396. - Foreword to Alfred J. Menezes' book
*Elliptic Curve Public Key Cryptosystems*, Kluwer Publishers, 1993. - (with M. R. Fellows and Ann Hibner Koblitz) Cultural
aspects of math education reform,
*Notices of the Amer. Math. Society*, Vol. 41, 1994, 5-9. - Math majors learn from sixth grade experience,
*Paideia*, U.W. Office of Undergraduate Education, Spring 1994. - Book review of
*Multicultural Mathematics*by David Nelson*et al.*,*American Scientist*, Vol. 83 (March-April 1995), 194-195. - The case against computers in K-13 math education
(kindergarten through calculus),
*The Mathematical Intelligencer*, Vol. 18, No. 1, 1996, 9-16. - Cryptography as a teaching tool,
*Cryptologia*, Vol. 21, 1997, 317-326. - Book review of
*Discrete Mathematics in the Schools*, edited by J. G. Rosenstein, D. S. Franzblau, and F. S. Roberts,*SIGACT News*(publication of the ACM Special Interest Group on Automata and Computability Theory), Vol. 29, No. 1, 1998, 8-12. - (with Tim Bell, Michael Fellows, Matthew Powell, Harold
Thimbleby, and Ian Witten) Explaining cryptographic systems to the general
public,
*IFIP First World Conference on Information Security Education*, 1999, 221-233. Also in:*Computers and Education*, Vol. 40, 2003, 199-215. - (with Ann Hibner Koblitz) The Kovalevskaia Fund,
*The Mathematical Intelligencer*, Vol. 22, No. 2, 2000, 62-65. - (with Ann Hibner Koblitz) Book review of
*In Code: A Voyage of Mathematical Discovery*by Sarah and David Flannery,*London Times Higher Education Supplement*, Nov. 10, 2000. - Essay-review of three books on cryptography,
*Amer. Math. Monthly*, Vol. 108, 2001, 983-988. - Book review of
*Radical Equations: Math Literacy and Civil Rights*by Robert P. Moses and Charles E. Cobb Jr. (Beacon Press, 2001),*Notices of the Amer. Math. Society*, Vol. 49, 2002, 328-332. - Book review of
*El Ultimo Secreto de Colonia Dignidad*by Carlos Basso,*Notices of the Amer. Math. Society*, Vol. 51, 2004, 32-33. - The uneasy relationship between mathematics and
cryptography,
*Notices of the Amer. Math. Society*, Vol. 54, 2007, 972-979; available here. - Book review of
*Elliptic Curves: Number Theory and Cryptography*, 2nd Edition, by L. C. Washington,*SIAM Review*, Vol. 51, 2009, 230-231. - (with A. J. Menezes) The brave new world of bodacious
assumptions in cryptography,
*Notices of the Amer. Math. Society*, Vol. 57, 2010, 357-365; available here. - Secret codes and online security: A seminar for
entering students,
*Cryptologia*, Vol. 34, 2010, 145-154. - Book review of
*Decrypted Secrets: Methods and Maxims of Cryptology*, 4th Edition, by F. L. Bauer,*SIAM Review*, Vol. 52, 2010, 777-778. - Interview with Professor Ngo Bao Chau,
*The Mathematical Intelligencer*, Vol. 33, No. 1, 2011, 46-50; available here. - "The Word for World is Forest": A long-range
funding source for women in math in developing countries,
*The Mathematical Intelligencer*, Vol. 33, No. 4, 2011, 21-24; available here. - Crypto galore!, in H. L. Bodlaender, R. Downey, F. V.
Fomin, and D. Marx (eds.),
*The Multivariate Algorithmic Revolution and Beyond: Essays Dedicated to Michael R. Fellows on the Occasion of His 60th Birthday*, LNCS 7370, Springer-Verlag, 2012, 39-50. - Grothendieck's 1967 lectures in the forest in Vietnam,
*The Mathematical Intelligencer*, Vol. 35, No. 2, 2013, 32-34; available here. - (with F. Verhulst and S. Krantz) Hype! An exchange of
views,
*The Mathematical Intelligencer*, Vol. 36, No. 3, 2014, 8-13; available here. - (with A. J. Menezes) A riddle wrapped in an enigma,
*IEEE Security & Privacy,*Vol. 14, No. 6, 2016, 34-42; available here. - Why STEM majors
need the humanities,
*The Chronicle of Higher Education,*6 January 2017; available here. - An American mathematician’s perspective on
multiple-choice tests, edited version appeared in Vietnamese translation
in the magazine
*Tia Sáng,*20 Nov. 2016; available here. - Time for a paradigm shift in our disciplinary culture?
(write-up of keynote talk),
*Paradigms in Cryptology – Mycrypt 2016,*Springer-Verlag, 2017, 11-18; available here. - (with P.D. Hiêu) Cryptology during the French and
American wars in Vietnam,
*Cryptologia*, Vol. 41, No 6 (Dec. 2017), 491-511; available here - El lado oscuro del papel norteamericano en la
educación superior en países en desarrollo (The dark side of
the American role in higher education in developing countries), to appear
in
*Anales de la Academia de Ciencias de Cuba*(*Annals of the Cuban Academy of Sciences*). - Bitcoin: The good and the bad news about
cryptocurrency, appeared in Vietnamese translation in
*Tia Sáng,*20 Nov. 2017. - Provincial universities can be key to economic
development and social equality, appeared in Vietnamese translation in
*Tia Sáng,*5 Dec. 2017.

Return
to my home page.

Return to Math Department home page.