## CryptoDB

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

Authors: Dong-Guk Han Tetsuya Izu Tsuyoshi Takagi URL: http://eprint.iacr.org/2005/384 Search ePrint Search Google 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.
##### BibTeX
@misc{eprint-2005-12718,
title={Some Explicit Formulae of NAF and its Left-to-Right Analogue},
booktitle={IACR Eprint archive},
keywords={foundations / signed binary representation,non-adjacent form, Hamming weight, zero-run length},
url={http://eprint.iacr.org/2005/384},
note={ christa@fun.ac.jp 13084 received 23 Oct 2005, last revised 28 Oct 2005},
author={Dong-Guk Han and Tetsuya Izu and Tsuyoshi Takagi},
year=2005
}