Abstract

A method is described to represent points on elliptic curves over F 2 n , in the context of elliptic curve cryptosystems, using n bits. The method allows for full recovery of the x and y components of the point. This improves on the naive representation using 2n bits, and on a previously known compressed representation using n+ 1 bits. Since n bits are necessary to represent a point in the general case of a cryptosystem over F 2 n , the representation described in this note is minimal. Keywords: finite fields, elliptic curves, cryptography. 1 Background Elliptic curve (EC) cryptography is gaining favor as an efficient and attractive alternative to the more conventional public key schemes, e.g., RSA. EC cryptosystems are based on operations involving points on an elliptic curve over a finite field. Popular choices for the underlying finite field are F p , the integers modulo p for a (large) prime number p, and F 2 n , a finite field of characteristic two and dimension n. Thi...

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