## IACR paper details

Title | On the Decomposition of an Element of Jacobian of a Hyperelliptic Curve |
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Booktitle | IACR Eprint archive |
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Pages | |
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Year | 2007 |
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URL | http://eprint.iacr.org/2007/112 |
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Author | Koh-ichi Nagao |
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Abstract |
In this manuscript, if a reduced divisor $D_0$ of hyperelliptic curve of genus
$g$ over an extension field $F_{q^n}$ is written by a linear sum of $ng$
lements of $F_{q^n}$-rational points of the hyperelliptic curve whose
$x$-coordinates are in the base field $F_q$, $D_0$ is noted by a decomposed
divisor and the set of such $F_{q^n}$-rational points is noted by the
decomposed factor of $D_0$.
We propose an algorithm which checks whether a reduced divisor is decomposed
or not, and compute the decomposed factor, if it is decomposed. This
algorithm needs a process for solving equations system of degree $2$,
$(n^2-n)g$ variables, and $(n^2-n)g$ equations over $F_q$.
Further, for the cases $(g,n)=(1,3),(2,2),$ and $(3,2)$, the concrete
computations of decomposed factors are done by computer experiments. |
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Search for the paper

@misc{eprint-2007-13394,
title={On the Decomposition of an Element of Jacobian of a Hyperelliptic Curve},
booktitle={IACR Eprint archive},
keywords={ndex calculus attack, Jacobian, Hyperelliptic curve, DLP, Weil descent attack},
url={http://eprint.iacr.org/2007/112},
note={ nagao@kanto-gakuin.ac.jp 13662 received 28 Mar 2007, last revised 29 May 2007},
author={Koh-ichi Nagao},
year=2007
}

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