Speeding up elliptic cryptosystems using a new signed binary representation for integers

Abstract

Two new signed binary representations are presented that simplify hardware or software necessary in elliptic curve cryptosystems. Simplified algorithms are presented for computing the new binary representations. This speeds up elliptic cryptosystems. The algorithms are useful for smart card and digital signature verification applications. The first algorithm computes a new representation for an integer d and speeds up the computation of d/spl times/P, where P is a point on an elliptic curve. The second algorithm computes a new representation for two integers g and h and speeds up the computation of (g/spl times/P)+(h/spl times/Q), where P and Q are points on an elliptic curve.