# Implementing Wiener's Extensions in the Range $N^\frac{1}{4}\leq d <N^{\frac{3}{4}-\beta}$ and $N^{\frac{1}{4}}\leq d<N^{(\frac{1-\gamma}{2})}$, $\gamma\leq\frac{1}{2}$ with Lattice Reduction

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## Keywords:

Lattice reduction, LLL algorithm, quadratic form, Wiener Attack extensions## Abstract

In this paper, Wiener Attack extensions on RSA are implemented with approximation via lattice reduction. The continued fraction based arguments of Wiener Attack extensions in the range $N^\frac{1}{4}\leq d <N^{\frac{3}{4}-\beta}$, $p-q=N^{\beta}$ and $N^{\frac{1}{4}}\leq d<N^{(\frac{1-\gamma}{2})}$, $|\rho q - p|\leq \frac{N^{\gamma}}{16}$, $1 \leq \rho \leq 2$, $\gamma\leq\frac{1}{2}$, are implemented with the Lattice based arguments and the LLL algorithm is used for reducing a basis of a lattice.

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*International Journal of Mathematics And Its Applications*,

*7*(1), 137–148. Retrieved from https://ijmaa.in/index.php/ijmaa/article/view/275

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.