Storage-eecient Finite Field Basis Conversion

The problem of nite eld basis conversion is to convert from the representation of a eld 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 nite eld GF(2 m), for example, the storage requirement of the new algorithms is only O(m) bits, compared to O(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.