On the signed-binary window method [cryptosystem applications]

We propose a left-to-right (i.e., from the most significant column to the least significant column) algorithm for computing a signed-binary (SB) representation of pairs of integers with minimum joint weight as well as maximum average length of zero-column runs. The proposed method speeds up the scalar multiplication of elliptic curve cryptosystems; (ECC) by all known strategies, while at the same time reduces the hardware overhead. Furthermore, we present the necessary and sufficient condition that an SB representation of n integers has minimum joint weight.