@techreport{TR-IC-00-10,
number = {IC-00-10},
author = {Julio López and Ricardo Dahab},
title = {An Overview of Elliptic Curve Cryptography},
month = {May},
year = {2000},
institution = {Institute of Computing, University of Campinas},
note = {In English, 34 pages.
\par\selectlanguage{english}\textbf{Abstract}
Elliptic curve cryptography (ECC) was introduced by Victor
Miller and Neal Koblitz in 1985. ECC, proposed as an alternative
to established public-key systems such as DSA and RSA, has
recently gained a lot attention in industry and academia. The
main reason for the attractiveness of ECC is the fact that there
is no sub-exponential algorithm known to solve the discrete
logarithm problem on a properly chosen elliptic curve. This
means that significantly smaller parameters can be used in ECC
than in other competitive systems such RSA and DSA, but with
equivalent levels of security. Some benefits of having smaller
key sizes include faster computations, and reductions in
processing power, storage space and bandwidth. This makes ECC
ideal for constrained environments such as pagers, PDAs,
cellular phones and smart cards. The implementation of ECC, on
the other hand, requires several choices such as the type of the
underlying finite field, algorithms for implementing the finite
field arithmetic, the type of elliptic curve, algorithms for
implementing the elliptic group operation, and elliptic curve
protocols. Many of these selections may have a major impact on
the overall performance. In this paper we present a selective
overview of the main methods and techniques used for
practical implementations of elliptic curve cryptosystems. We
also present a summary of the most recent reported software
implementations of ECC.
}
}