New Point Compression Algorithms for Binary Curves

This paper presents two new algorithms for point compression for elliptic curves defined over F2m, m odd. The first algorithm works for curves with Tr(a) = 1 and offers computational advantages over previous methods. The second algorithm is based on the λ representation of an elliptic point. The proposed algorithms require m bits to compress an elliptic point and can be used for all random binary curves recommended by NIST.