My primary research interests are within the area of cryptography.
Specific interests include:
- Elliptic curve cryptography
- Key establishment protocols
- Practice-oriented provable security
- Algorithmic number theory
- "Reusing static keys in key agreement
protocols"
(with S. Chatterjee and B. Ustaoglu)
Indocrypt 2009, to appear.
- "On cryptographic protocols employing
asymmetric pairings - The role of Ψ revisited"
(with S. Chatterjee)
preprint, 2009.
- "Comparing two pairing-based
aggregate signature schemes"
(with S. Chatterjee, D. Hankerson and E. Knapp)
Designs, Codes and Cryptography, to appear.
- "Elliptic curve
cryptography: The serpentine course of a paradigm shift"
(with A. Hibner Koblitz and N. Koblitz)
Journal of Number Theory, to appear.
The eprint version is available
here.
The video abstract is
here.
- "On reusing ephemeral public
keys in Diffie-Hellman key agreement protocols"
(with B. Ustaoglu)
International Journal of Applied Cryptography,
to appear.
- "Analyzing
the Galbraith-Lin-Scott point multiplication method for elliptic curves
over binary fields"
(with K. Karabina and D. Hankerson)
IEEE Transactions on Computers, 58 (2009), 1411-1420.
- "An introduction to
pairing-based cryptography"
Recent Trends in Cryptography, edited by I. Luengo,
volume 477 of Contemporary Mathematics, AMS-RSME, 2009,
47-65.
- "Comparing the pre- and post-specified
peer models for key agreement"
(with B. Ustaoglu)
International Journal of Applied Cryptography,
1 (2009), 236-250.
An earlier version
appeared in Proceedings of ACISP 2008,
Lecture Notes in Computer Science, 5107 (2008), 53-68.
- "Software
implementation of pairings"
(with D. Hankerson and M. Scott)
Identity-Based Cryptography, edited by M. Joye
and G. Neven, IOS Press, 2008.
- "Another look at
non-standard discrete log and Diffie-Hellman problems"
(with N. Koblitz)
Journal of Mathematical Cryptology,
4 (2008), 311-326.
- "Security arguments for the UM key
agreement protocol in the NIST SP 800-56A standard"
(with B. Ustaoglu)
Proceedings of ASIACCS '08, ACM Press, 261-270.
- "Software
implementation of arithmetic in F3m"
(with O. Ahmadi and D. Hankerson)
Proceedings of WAIFI 2007,
Lecture Notes in Computer Science, 4547 (2007), 85-102.
- Advances
in Cryptology - CRYPTO 2007 (edited volume)
Lecture Notes in Computer Science, 4622, Springer-Verlag, 2007.
- "Formulas for
cube roots in F3m"
(with O. Ahmadi and D. Hankerson)
Discrete Applied Mathematics,
155 (2007), 260-270.
- "Irreducible polynomials of maximum
weight"
(with O. Ahmadi)
Utilitas Mathematica,
72 (2007), 111-123.
- "Another
look at HMQV"
Journal of Mathematical Cryptology,
1 (2007), 47-64.
- "Another look at generic groups"
(with N. Koblitz)
Advances in Mathematics of Communications,
1 (2007), 13-28.
- "Another look at
"provable security""
(with N. Koblitz)
Journal of Cryptology,
20 (2007), 3-37.
- "Another look at
"provable security". II"
(with N. Koblitz)
Progress in Cryptology - Indocrypt 2006,
Lecture Notes in Computer Science, 4329 (2006), 148-175.
- "On the importance of
public-key validation in the MQV and HMQV key agreement protocols"
(with B. Ustaoglu)
Progress in Cryptology - Indocrypt 2006,
Lecture Notes in Computer Science, 4329 (2006), 133-147.
- "Software
multiplication using Gaussian normal bases"
(with R. Dahab, D. Hankerson, F. Hu, M. Long and J. López)
IEEE Transactions on Computers,
55 (2006), 974-984.
- "Cryptographic
implications of Hess' generalized GHS attack"
(with E. Teske)
Applicable Algebra in Engineering, Communication and Computing,
16 (2006), 439-460.
- "On the number of
trace-one elements in polynomial bases for GF(2 n)"
(with O. Ahmadi)
Designs, Codes and Cryptography,
37 (2005), 493-507.
- "Pairing-based
cryptography at high security levels"
(with N. Koblitz)
Cryptography and Coding: 10th IMA International Conference,
Lecture Notes in Computer Science, 3796 (2005), 13-36.
- "Algebraic curves
and cryptography" (with S. Galbraith)
Finite Fields and Their Applications,
11 (2005), 544-577.
- Several sections on elliptic curve cryptography
(with D. Hankerson)
"Encyclopedia of Cryptography and Security",
edited by Henk van Tilborg,
Springer-Verlag, 2005.
-
Topics in Cryptology - CT-RSA 2005
(edited volume)
Lecture Notes in Computer Science, 3376, Springer-Verlag, 2005.
- "A survey of public-key
cryptosystems"
(with N. Koblitz)
SIAM Review,
46 (2004), 599-634.
- "Security
of signature schemes in a multi-user setting"
(with N. Smart)
Designs, Codes and Cryptography, 33 (2004), 261-274.
- "Hyperelliptic curves and cryptography"
(with M. Jacobson and A. Stein)
High Primes and Misdemeanours: Lectures in Honour of the 60th
Birthday of Hugh Cowie Williams,
Fields Institute Communications Series, 41 (2004), 255-282.
- "Obstacles to the torsion-subgroup attack on the decision
Diffie-Hellman problem" (with N. Koblitz)
Mathematics of Computation, 73 (2004), 2027-2041.
- "Field
inversion and point halving revisited"
(with K. Fong, D. Hankerson and J. López)
IEEE Transactions on Computers,
53 (2004), 1047-1059.
- "Weak fields for ECC"
(with E. Teske and A. Weng)
Topics in Cryptology - CT-RSA 2004,
Lecture Notes in Computer Science, 2964 (2004), 366-386.
-
Guide to Elliptic Curve Cryptography
(with D. Hankerson and S. Vanstone)
Springer, 2004.
- "An efficient
protocol for authenticated key agreement"
(with L. Law, M. Qu, J. Solinas and S. Vanstone)
Designs, Codes and Cryptography,
28 (2003), 119-134.
- "Validation of
elliptic curve public keys"
(with A. Antipa, D. Brown, R. Struik and S. Vanstone)
Proceedings of PKC 2003,
Lecture Notes in Computer Science, 2567 (2003), 211-223.
- "A small subgroup attack on a key
agreement protocol of Arazi"
(with D. Brown)
Bulletin of the ICA,
37 (2003), 45-50.
-
Progress in Cryptology - INDOCRYPT 2002
(edited with P. Sarkar)
Lecture Notes in Computer Science, 2551, Springer-Verlag, 2002.
- "Analysis of the
GHS Weil descent attack on the ECDLP over characteristic two finite
fields of composite degree" (with M. Maurer and E. Teske)
LMS Journal of Computation and Mathematics,
5 (2002), 127-174
An earlier version appeared in Proceedings of Indocrypt 2001,
Lecture Notes in Computer Science, 2247 (2001), 195-213.
- "Isomorphism classes
of genus-2 hyperelliptic curves over finite fields"
(with L. Encinas and J. Masque)
Applicable Algebra in Engineering, Communication and Computing,
13 (2002), 57-65.
- "Solving elliptic curve discrete
logarithm problems using Weil descent"
(with M. Jacobson and A. Stein)
Journal of the Ramanujan Mathematical Society,
16 (2001), 231-260.
- "The
elliptic curve digital signature algorithm (ECDSA)"
(with D. Johnson and S. Vanstone)
International Journal on Information Security,
1 (2001), 36-63.
- "Software
implementation of the NIST elliptic curves over prime fields"
(with M. Brown, D. Hankerson and J. Hernandez)
Topics in Cryptology - CT-RSA 2001,
Lecture Notes in Computer Science, 2020 (2001), 250-265.
- "Analysis of the
Weil descent attack of Gaudry, Hess and Smart"
(with M. Qu)
Topics in Cryptology - CT-RSA 2001,
Lecture Notes in Computer Science, 2020 (2001), 308-318.
- "Software
implementation of elliptic curve cryptography over binary fields"
(with D. Hankerson and J. Hernandez)
Proceedings of CHES 2000, Lecture Notes in Computer Science,
1965 (2000), 1-24.
- "PGP in constrained wireless devices"
(with M. Brown, D. Cheung, D. Hankerson, J. Hernandez and M. Kirkup)
Proceedings of the 9th USENIX Security Symposium, 2000,
247-261.
- "The
state of elliptic curve cryptography"
(with N. Koblitz and S. Vanstone)
Designs, Codes and Cryptography, 19 (2000), 173-193.
- "Coding Theory and Cryptology"
(with P. van Oorschot)
chapter in Handbook of Discrete and Combinatorial
Mathematics, CRC Press, 1999, pages 889-954.
- "Authenticated
Diffie-Hellman key agreement protocols"
(with S. Blake-Wilson)
Proceedings of the 5th Annual Workshop on Selected Areas
in Cryptography (SAC '98), Lecture Notes in Computer Science,
1556 (1999), 339-361.
- "Unknown key-share
attacks on the station-to-station (STS) protocol"
(with S. Blake-Wilson)
Proceedings of PKC '99, Lecture Notes in Computer Science,
1560 (1999), 154-170.
- "Entity authentication and
authenticated key transport protocols employing asymmetric techniques"
(with S. Blake-Wilson)
Proceedings of the 5th International Workshop on Security
Protocols,
Lecture Notes in Computer Science, 1361 (1998), 137-158.
- "The discrete logarithm problem
in GL(n,q)"
(with Yi-Hong Wu)
Ars Combinatoria, 47 (1998), 23-32.
- "An elementary introduction to hyperelliptic curves"
(with Yi-Hong Wu and R. Zuccherato)
appendix in
Algebraic Aspects of Cryptography by Neal Koblitz,
Springer-Verlag, 1998, pages 155-178.
- "Key agreement protocols
and their security analysis"
(with D. Johnson and S. Blake-Wilson)
Proceedings of the Sixth IMA International Conference
on Cryptography and Coding,
Lecture Notes in Computer Science, 1355 (1997), 30-45.
Full version.
- Handbook of Applied
Cryptography
(with P. van Oorschot and S. Vanstone)
CRC Press, 1997.
- "Elliptic curves and cryptography"
(with A. Jurisic)
Dr. Dobb's Journal,
April 1997, 23-36.
- "Some new key agreement protocols providing mutual implicit
authentication"
(with M. Qu and S. Vanstone)
Workshop on Selected Areas in Cryptography (SAC '95),
22-32, 1995.
- "Elliptic curve cryptosystems"
CryptoBytes - The Technical Newsletter of RSA Laboratories,
Volume 1, Number 2, Summer 1995, 1-4.
- Elliptic Curve Public Key Cryptosystems
Kluwer Academic Publishers, 1993.
- "Reducing elliptic curve
logarithms to logarithms in a finite field"
(with T. Okamoto and S. Vanstone)
IEEE Transactions on Information Theory, 39 (1993),
1639-1646.
- "Elliptic curve
cryptosystems and their implementation"
(with S. Vanstone)
Journal of Cryptology, 6 (1993), 209-224
- "Public-key
cryptosystems with very small key lengths"
(with G. Harper and S. Vanstone)
Advances in Cryptology - EUROCRYPT '92,
Lecture Notes in Computer Science, 658 (1993), 163-173.
- "Counting
points on elliptic curves over F2m"
(with S. Vanstone and R. Zuccherato)
Mathematics of Computation, 60 (1993), 407-420.
- Applications of Finite Fields
(with I. Blake, S. Gao, R. Mullin, S. Vanstone and T. Yaghoobian)
Kluwer Academic Publishers, 1992.
- "Subgroup refinement algorithms for root finding in GF(q)"
(with P. van Oorschot and S. Vanstone)
SIAM Journal on Computing, 21 (1992), 228-239.
- "A note on cyclic groups,
finite fields, and the discrete logarithm problem"
(with S. Vanstone)
Applicable Algebra in Engineering, Communication and Computing,
3 (1992), 67-74.
- Advances in
Cryptology - Proceedings of CRYPTO '90
(edited with S. Vanstone)
Lecture Notes in Computer Science, 537, Springer-Verlag, 1991.
- The implementation of
elliptic curve cryptosystems"
(with S. Vanstone)
Advances in Cryptology - AUSCRYPT '90,
Lecture Notes in Computer Science, 453 (1990), 2-13.
- "Isomorphism classes of elliptic curves over finite fields of
characteristic 2"
(with S. Vanstone)
Utilitas Mathematica, 38 (1990), 135-154.
- "On the number
of self-dual bases of GF(qm) over
GF(q)"
(with D. Jungnickel and S. Vanstone)
Proceedings of the American Mathematics Society,
109 (1990), 23-29.
- "Some computational
aspects of root finding in GF(qm)"
(with S. Vanstone and P. van Oorschot)
Symbolic and Algebraic Computation,
Lecture Notes in Computer Science, 358 (1989),
259-270.
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