KSII Transactions on Internet and Information Systems (TIIS)

Korean Society for Internet Information (한국인터넷정보학회)
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w-Bit Shifting Non-Adjacent Form Conversion

  • Hwang, Doo-Hee (School of Computer Science and Engineering, Pusan National University) ;
  • Choi, Yoon-Ho (School of Computer Science and Engineering, Pusan National University)
  • Received : 2017.10.11
  • Accepted : 2018.03.09
  • Published : 2018.07.31
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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 $NAF_w$ algorithm, we propose a new NAF conversion algorithm, called w-bit Shifting Non-Adjacent Form($SNAF_w$), where w is width of scanning window. By skipping some unnecessary bit comparisons, the proposed algorithm improves the NAF conversion speed of the $NAF_w$ algorithm. To verify the excellence of the $SNAF_w$ algorithm, the $NAF_w$ algorithm and the $SNAF_w$ 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 $SNAF_2$ 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 $NAF_2$ algorithm. In addition, we show that $SNAF_w$ algorithm is always faster than $NAF_w$ algorithm, regardless of the size of w.

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References

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