w-Bit Shifting Non-Adjacent Form Conversion

Abstract

As a unique form of signed-digit representation, non-adjacent form (NAF) minimizes Hamming weight by removing a stream of non-zero bits from the binary representation of positive integer. Thanks to this strong point, NAF has been used in various applications such as cryptography, packet filtering and so on. In this paper, to improve the NAF conversion speed of the algorithm, we propose a new NAF conversion algorithm, called-bit Shifting Non-Adjacent Form(), where is width of scanning window. By skipping some unnecessary bit comparisons, the proposed algorithm improves the NAF conversion speed of the algorithm. To verify the excellence of the algorithm, the algorithm and the algorithm are implemented in the 8-bit microprocessor ATmega128. By measuring CPU cycle counter for the NAF conversion under various input patterns, we show that the 2 algorithm not only increases the NAF conversion speed by 24% on average but also reduces deviation in the NAF conversion time for each input pattern by 36%, compared to the 2 algorithm. In addition, we show that algorithm is always faster than algorithm, regardless of the size of .