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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Authors

  • P. Anuradha Kameswari Department of Mathematics, Andhra University, Visakhapatnam, Andhra Pradesh, India
  • S. B. T. Sundari Katakam Department of Mathematics, Andhra University, Visakhapatnam, Andhra Pradesh, India

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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Published

15-03-2019

How to Cite

P. Anuradha Kameswari, & S. B. T. Sundari Katakam. (2019). 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. 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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Section

Research Article