Darrel Hankerson

221 Parker Hall
Auburn University
Auburn, AL 36849-5307

E-mail: hankedr. Auburn addresses are generally auburn.edu
Voice: 334 844-5111

Sample chapter available. Illustration by Helen D'Souza.

Areas of interest

Cryptography and differential equations

Recent work

I am currently a Research Associate with Certicom Corp., near Toronto, Canada. Certicom is especially interested in wireless security and elliptic curve cryptography.

The Springer-Verlag Guide to Elliptic Curve Cryptography, with A. Menezes and S. Vanstone, appeared January 2004.

I am indebted to the Department of Combinatorics and Optimization at the University of Waterloo and the Centre for Applied Cryptographic Research for visiting professor appointments during the six summers 2000--2005. Much of my work there involved elliptic curve cryptography, in particular, efficient implementation.

Along with Çetin K. Koç, Julio López, and Mads Rasmussen, I gave a series of talks as part of the Workshop in Implementation of Cryptographic Methods, University of Campinas, Brazil, April 2005.

I was a speaker at the Certicom Elliptic Curve Conference, Toronto, November 2004.

I gave a series of talks as part of a short course in elliptic curve cryptography, VI Coloquio Nacional de Codigos, Criptograpfia y Areas Relacionadas, Mexico, 2004.

I gave a series of talks at the Workshop on Cryptographic Algorithms and Protocols (WCAP'03), Institute of Computing -- UNICAMP, Campinas, Brazil, July 21--23, 2003. The main themes of this workshop were voting protocols (David Chaum and Jeroen van de Graaf) and topics in elliptic curve cryptography (DH and Alfred Menezes).

Neal Koblitz (University of Washington), Alfred Menezes (University of Waterloo, Canada), and I gave an invited minitutorial on elliptic curve cryptography at the SIAM 50th Anniversary Meeting, July 2002. Prof Koblitz discussed ``hard'' number theory problems, introduced elliptic curves and various cryptosystems, along with curve selection and ``magic curves'' (commonly known as Koblitz curves). Prof Menezes discussed the elliptic curve discrete log problem and attacks. I spoke on elliptic curves with efficient endomorphisms.

I gave a talk at the 5th Workshop on Elliptic Curve Cryptography (ECC 2001). October 29-31, 2001. Slides from some of the ECC 2001 talks are available in the conferences section of http://cacr.math.uwaterloo.ca.

Selected publications

1. Several sections on elliptic curve cryptography (with A. Menezes) in Encyclopedia of Cryptography and Security, edited by Henk van Tilborg, Springer-Verlag, 2005.

2. Software multiplication using Gaussian normal bases (PS, PDF), with R. Dahab, F. Hu, M. Long, J. López, and A. Menezes. IEEE Transactions on Computers, to appear. A version appears as Technical Report CACR 2004-12, University of Waterloo, 2004.

3. Guide to Elliptic Curve Cryptography, with A. Menezes and S. Vanstone, Springer-Verlag, 2004.

4. Field inversion and point halving revisited (PS, PDF), with K. Fong, J. López, and A. Menezes. IEEE Transactions on Computers 53(8):1047-1059, 2004. An extended version including material on use of single-instruction multiple-data (SIMD) registers for field arithmetic appears as Technical Report CORR 2003-18, University of Waterloo.

5. Introduction to Information Theory and Data Compression, second edition, with Greg Harris and Peter D. Johnson Jr., CRC Press, 2003 (first edition 1997).

6. Software Implementation of the NIST Elliptic Curves Over Prime Fields, with M. Brown, J. Lopez, and A. Menezes. Cryptographers' Track at the San Francisco RSA Conference 2001, Lecture Notes in Computer Science (Topics in Cryptology -- CT-RSA 2001), Springer-Verlag, 2020:250--265, 2001. An extended version (Postscript, PDF) appears in the technical reports area of the Centre for Applied Cryptographic Research as CORR 2000-56.

7. Software Implementation of Elliptic Curve Cryptography Over Binary Fields, with J. Lopez and A. Menezes. Cryptographic Hardware and Embedded Systems (CHES), Lecture Notes in Computer Science, Springer-Verlag, 1965:1--24, 2000. A version is available from the technical reports area of the Centre for Applied Cryptographic Research as CORR 2000-42.

8. Coding Theory and Cryptography: The Essentials, second edition, with D.R. Hoffman, D.A. Leonard, C.C. Lindner, K.T. Phelps, C.A. Rodger, and J.R. Wall, Marcel Dekker, 2000.

9. PGP in Constrained Wireless Devices, with M. Brown, D. Cheung, J. Lopez, M. Kirkup, and A. Menezes, 9th USENIX Security Symposium, Denver 2000.

10. Oscillation of first and second order delay difference equations, with G. Harris, Dynamic Systems and Applications, 4(2):251-261, 1995.

11. Existence of solutions for right focal boundary value problems, with J. Ehme, Journal of Nonlinear Analysis, 18:191--197, 1992.

12. Wavefronts for a cooperative tridiagonal system of differential equations, with B. Zinner, Journal of Dynamics and Differential Equations, 5(2):359-373, 1993.

13. A focal boundary value problem for difference equations (with C. Denny), Internat. J. Math. Math. Sci., 16(1):169-176, 1993.

14. An existence and uniqueness theorem for difference equations, SIAM Journal on Mathematical Analysis, 20(5):1208-1217, 1989.

15. Optimality for boundary value problems for Lipschitz equations, with Johnny Henderson, Journal of Differential Equations, 77(2):392-404, 1989.

16. A classification of the solutions of a difference equation according to their behavior at infinity, with Allan Peterson. Journal of Mathematical Analysis and Applications, 136(1):249-266, 1988.

Graduate students

• Doris Low, MAM, 2000. Currently with TRW, Colorado.
• Rachel Wallace (co-directed with Johnny Henderson), MAM June 1993.
• Cathryn Denny, MS August 1991. Employed by the Air Force as an Information Systems Management Specialist, and later as a Senior Systems Analyst with the Santa Rosa School Board.

Departmental service

I currently serve as the system administrator for the departmental network of Sun and HP machines. Some of these machines are part of a computer laboratory, which was funded by the National Science Foundation from a grant proposal where I served as co-PI with Alfred Menezes. I am also involved in systems support for the Drop-in Center, which is directed by Professor Overtoun Jenda.

Other areas of interest

• I am a contributing programmer in support of GNU awk (gawk), part of the GNU Project.
• In 2001-02, I ran the Network and Operating System Administration course (6520) in the Department of Computer Science and Software Engineering.
• Member: TeX Users Group.