Cryptology ePrint Archive: Report 2005/384

Some Explicit Formulae of NAF and its Left-to-Right Analogue

Dong-Guk Han and Tetsuya Izu and Tsuyoshi Takagi

Abstract: 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.

Category / Keywords: foundations / signed binary representation,non-adjacent form, Hamming weight, zero-run length

Date: received 23 Oct 2005, last revised 28 Oct 2005

Contact author: christa at fun ac jp

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Version: 20051028:084538 (All versions of this report)

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