@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.
  }
}