## IACR paper details

Title | Polynomials for Ate Pairing and $\mathbf{Ate}_{i}$ Pairing |
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Booktitle | IACR Eprint archive |
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Pages | |
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Year | 2008 |
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URL | http://eprint.iacr.org/2008/202 |
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Author | Zhitu Su |
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Author | Hui Li |
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Author | JianFeng Ma |
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Abstract |
The irreducible factor $r(x)$ of $\mathrm{\Phi}_{k}(u(x))$ and $u(x)
$ are often used in constructing pairing-friendly curves. $u(x)$ and
$u_{c} \equiv u(x)^{c} \pmod{r(x)}$ are selected to be the Miller
loop control polynomial in Ate pairing and $\mathrm{Ate}_{i}$
pairing. In this paper we show that when $4|k$ or the minimal prime
which divides $k$ is larger than $2$, some $u(x)$ and $r(x)$ can not
be used as curve generation parameters if we want $\mathrm{Ate}_{i}$
pairing to be efficient. We also show that the Miller loop length
can not reach the bound $\frac{\mathrm{log_{2}r}}{\varphi(k)}$ when
we use the factorization of $\mathrm{\Phi}_{k}(u(x))$ to generate
elliptic curves. |
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Search for the paper

@misc{eprint-2008-17879,
title={Polynomials for Ate Pairing and $\mathbf{Ate}_{i}$ Pairing},
booktitle={IACR Eprint archive},
keywords={public-key cryptography /},
url={http://eprint.iacr.org/2008/202},
note={ ztsu@mail.xidian.edu.cn 14007 received 8 May 2008},
author={Zhitu Su and Hui Li and JianFeng Ma},
year=2008
}

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