Architectures for Unified Field Inversion with Applications in Elliptic Curve Cryptography

E. Savas and C. K. Koc

The 9th IEEE International Conference on Electronics, Circuits and Systems - ICECS 2002, to appear, Dubrovnik, Croatia, September 15-18, 2002.

Abstract

We present two new inversion algorithms for binary extension and prime fields, which are slightly modified versions of the Montgomery inverse algorithm. An hardware architecture implementing these algorithms is also introduced. In our proposed architecture, the field elements are represented using a multi-word format which allows a scalable and unified architecture to operate in a broad range of precision. This hardware architecture can be used to obtain efficient implementations of elliptic curve cryptography primitives.