• Journal of KIISE:Computer Systems and Theory
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• v.31 no.10
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• pp.588-592
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• 2004

Scalar multiplication is to compute $textsc{k}$P when an integer $textsc{k}$ and an elliptic curve point f are given. As a general method to accelerate scalar multiplication, Agnew, Mullin and Vanstone proposed to use $textsc{k}$'s with fixed Hamming weights. We suggest a new method that uses $textsc{k}$'s with fixed signed Hamming weights and show that this method is more secure.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.7
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• pp.3455-3474
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• 2018

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.

• Journal of KIISE
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• v.44 no.5
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• pp.537-544
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• 2017

As a special form of the signed-digit representation, the NAF(non-adjacent form) minimizes the hamming weight by reducing the average density of the non-zero bits from the binary representation of the positive integer k. Due to this advantage, the NAF is used in various fields; in particular, it is actively used in cryptology. The existing NAF-conversion algorithm, however, is problematic because the conversion speed decreases when the LSB(least significant bit) frequently becomes "1" during the binary positive integer conversion process. This paper suggests a method for the improvement of the NAF-conversion speed for which the problems that occur in the existing NAF-conversion process are solved. To verify the performance improvement of the algorithm, the CPU cycle for the various inputs were measured on the ATmega128, a low-performance 8-bit microprocessor. The results of this study show that, compared with the existing algorithm, the suggested algorithm not only improved the processing speed of the major patterns by 20% or more on average, but it also reduced the NAF-conversion time by 13% or more.