An Improved Signed Digit Representation of Integers

Abstract

This research modifies the GNAF (Generalized NAF), which is one of the signed-digit representations that have been used to speed up point multiplication in pairing-based cryptosystems. The hamming weight of MGNAF (Modified Generalized Non-Adjacent Form), which is proposed in this paper, is less than GNAF for radixes higher than 2 (in cost of a bigger digit set). Moreover, in radix 2 the hamming weight of MGNAF is as low as GNAF and the well-known NAF (Non-Adjacent Form) with the same digit set. Keywords: Cryptography, Digit Set, Generalized NAF, Hamming Weight, Non-Adjacent Form, Radix-r Representation