MGSDNAF - A Modified Signed Digit Generalized Non-Adjacent Form for Integers Representation

Abstract

This paper describes a new radix r integer representation, which is an improved version over of an existing integer representation, namely “Modified Generalized Non-Adjacent Form” (MGNAF). Similar to MGNAF, MGSDNAF reduces the integer’s Hamming Weight better than the GNAF, a well-known integer representation method. With a reduced Hamming Weight, exponentiations can be quickly calculated. Moreover, contrary to MGNAF, the digit set size in the proposed method is smaller; and therefore improved the memory usage in point multiplication -an operation that is highly used in the calculation of pairing-based cryptosystems.