Storage-efficient finite field basis conversion

Abstract

The problem of finite field basis conversion is to convert from the representation of a field element in one basis to the representation of the element in another basis. This paper presents new algorithms for the problem that require much less storage than previous solutions. For the finite field GF(2m), for example, the storage requirement of the new algorithms is only O(m) bits, compared toO(m 2) for previous solutions. With the new algorithms, it is possible to extend an implementation in one basis to support other bases with little additional cost, thereby providing the desired interoperability in many cryptographic applications.