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Some Explicit Formulae of NAF and its Left-to-Right Analogue
Authors: Dong-Guk Han, Tetsuya Izu, Tsuyoshi TakagiAbstract:
Non-Adjacent Form (NAF) is a canonical form of signed binary representation of integers. We present some explicit formulae of NAF and its left-to-right analogue (FAN) for randomly chosen n-bit integers. Interestingly, we prove that the zero-run length appeared in FAN is asymptotically 16/7, which is longer than that of the standard NAF. We also apply the proposed formulae to the speed estimation of elliptic curve cryptosystems.
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