Fast implementation of elliptic curve arithmetic in GF

$\left({p}^{n}\right)$.

*(English)* Zbl 0955.94002
Imai, Hideki (ed.) et al., Public key cryptography. 3rd international workshop on Practice and theory in public key cryptosystems, PKC 2000, Melbourne, Victoria, Australia, January 18-20, 2000. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1751, 405-421 (2000).

The authors describe efficient methods for speeding up field arithmetic in GF

$\left({p}^{n}\right)$, where

$p$ is an odd prime of length 32 or 64 bits. They provide several tables of results on distinct architectures (Pentium II, and Alpha 21164 microprocessors). Although the current versions of the standards on public-key cryptography (IEEE-P1363, ANSI X9.62, etc) do not recommend such fields as underlying fields, the results stated in this article are of interest from an academic point of view, and are suitable for practical implementations of elliptic curve cryptography.