Optimal extension fields for fast arithmetic in public-key algorithms [chapter]

Daniel V. Bailey, Christof Paar
1998 Lecture Notes in Computer Science  
This contribution introduces a class of Galois eld used to achieve fast nite eld arithmetic which we call an Optimal Extension Field (OEF). This approach is well suited for implementation of publickey cryptosystems based on elliptic and hyperelliptic curves. Whereas previous reported optimizations focus on nite elds of the form GF(p) and GF(2 m ), an OEF is the class of elds GF(p m ), for p a prime of special form and m a positive integer. Modern RISC workstation processors are optimized to
more » ... orm integer arithmetic on integers of size up to the word size of the processor. Our construction employs well-known techniques for fast nite eld arithmetic which fully exploit the fast integer arithmetic found on these processors. In this paper, we describe our methods to perform the arithmetic in an OEF and the methods to construct OEFs. We provide a list of OEFs tailored for processors with 8, 16, 32, and 64 bit word sizes. We report on our application of this approach to construction of elliptic curve cryptosystems and demonstrate a substantial performance improvement over all previous reported software implementations of Galois eld arithmetic for elliptic curves.
doi:10.1007/bfb0055748 fatcat:7fclfpqsyrej3jqy4h6excogdi