A comparison of different finite fields for elliptic curve cryptosystems

We examine the relative efficiency of four methods for finite field representation in the context of elliptic curve cryptography (ECC). We conclude that a set of fields called the optimized extension fields (OEFs) give greater performance, even when used with affine coordinates, when compared against the type of fields recommended in the emerging ECC standards. Although this performance advantage is only marginal, and hence, there is probably no need to change the current standards to allow OEF fields in standards compliant implementations.