@techreport{TR-IC-98-39,
  number = {IC-98-39},
  author = {Julio López and R. Dahab},
  title = {Improved Algorithms for Elliptic Curve Arithmetic in {$GF(2^n)$}},
  month = {October},
  year = {1998}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 12 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      This paper describes three contributions for the efficient
      implementation of elliptic curve cryptosystems in $GF(2^n)$. The
      first is a new method for doubling an elliptic curve point,
      which is simpler to implement than the fastest known method, due
      to Schroeppel, and which favors sparse elliptic curve
      coefficients. The second is a generalized and improved version
      of the Guajardo and Paar's formulas for computing repeated
      doubling points. The third contribution consists of a new kind
      of projective coordinates that provides the fastest known
      arithmetic on elliptic curves. The algorithms resulting from
      this new formulation lead to a running time improvement for
      computing a scalar multiplication of about $17\%$ over previous
      projective coordinate methods.
  }
}