Abstract
The status of the development and application of high-speed multiplier structures based on optimal normal bases is explored. These structures are significant in that they can be used to construct multipliers for fields large enough for cryptographic systems based on the discrete logarithm problem. Their characteristics also make them ideal candidates for implementing compact, high-speed elliptic curve cryptosystems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
W. Diffie, and M. Hellman, “New directions in cryptography”, IEEE Trans. on Info. Theory, vol. IT-22, pp.644–654, 1976.
R. L. Rivest, A. Shamir, and L. Adleman, “A method of obtaining digital signatures and public key cryptosystems”, Comm. ACM, Vol.21, pp. 120–126, 1978.
P.K.S. Wah and M.Z. Wang, “Realization and application of the Massey-Omura lock”, Proceeding of 1984 International Zurich Seminar of Digital Communication, pp. j2.1–2.8.
T. ElGamal, “A public key cryptosystem and a signature scheme based on discrete logarithms”, IEEE Trans. on Info. Theory, Vol. IT-31, pp. 469–472, 1985.
R.C. Mullin, I.M. Onyszchuk, S.A. Vanstone, and R.M. Wilson, “Optimal normal bases inGF(p”)“Discrete Applied Mathematics, Vol. 22, pp. 149–161, 1988–89.
CA34C168 Data Encryption Processor Data Sheet, Newbridge Microsystems, Kanata, Ontario, Canada.
G. Agnew, T. Beth, R. Mullin, and S. Vanstone, “Arithmetic operations in GF 2n”, Journal of Cryptology.
G. Agnew, R. Mullin, and S. Vanstone, “An implementation of a fast public key cryptosystem”, Journal of Cryptology, Vol. 3 No. 2, Springer-Verlag, pp 63–80, 1991.
N. Koblitz, “Elliptic curve cryptosystems” Mathematics of computation - 48, pp. 203–209, 1987.
V. Miller, “Use of elliptic curves in cryptography”, Proceedings of CRYPTO’ 85, Springer-Verlag, pp. 417–426, Aug. 1985.
A. Menezes, S. Vanstone, and T. Okamoto, “Reducing elliptic curve logarithms to logarithms in a finite field”, STOC 1991, ACM Press, pp. 80–89, 1991.
G. Agnew, R. Mullin, and S. Vanstone, “A fast elliptic curve cryptosystem”, Lecture Notes in Computer Science #434, Proceedings of Eurocrypt’89, Springer-Verlag, pp. 706–708, Apr. 1989.
G. Agnew, R. Mullin, and S. Vanstone, “An implementation of elliptic curve cryptosystems over F2155”, IEEE Journal on Selected Areas in Communications Vol. 11, No. 5, pp. 804–811, 1993.
G. Agnew, R. Mullin, and S. Vanstone, “On the development of a fast elliptic curve cryptosystem”, Lecture Notes in Computer Science, Advances in Cryptography - EUROCRYPT’92, Springer-Verlag, pp. 482–487.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Agnew, G.B. (1994). Development of Fast Multiplier Structures with Cryptographic Applications. In: Blahut, R.E., Costello, D.J., Maurer, U., Mittelholzer, T. (eds) Communications and Cryptography. The Springer International Series in Engineering and Computer Science, vol 276. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2694-0_1
Download citation
DOI: https://doi.org/10.1007/978-1-4615-2694-0_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6159-6
Online ISBN: 978-1-4615-2694-0
eBook Packages: Springer Book Archive