Formulas for arithmetic are explicitly given. The security of the system is based on the discrete logarithm problem in these fields. Therefore we also describe a DL algorithm based on the ideas of Pohlig and Hellman, especially adopted to quadratic function fields of characteristic two. Efficient Algorithms for Multiplication on Elliptic Curves. In this paper we examine four different algorithms for this problem.
All algorithms read the bits of the multiplier from the high order to the low order bit.
Block versions are also derived. Fast Multiplication on Elliptic Curves over Small Fields of Characteristic Two. The Frobenius expansion algorithm is analyzed in theory and practice and can gain significant improvements in practical applications. These curves are therefore especially interesting for implementations of elliptic curve cryptosystems. On the Generation of Cryptographically Strong Elliptic Curves.