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arXiv · 1711.03621

Complete solving the quadratic equation mod $2^n$

S. M. Dehnavi·M. R. Mirzaee Shamsabad·A. Mahmoodi Rishakani
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Abstract

Quadratic functions have applications in cryptography. In this paper, we investigate the modular quadratic equation $$ ax^2+bx+c=0 \quad (mod \,\, 2^n), $$ and provide a complete analysis of it. More precisely, we determine when this equation has a solution and in the case that it has a solution, we not only determine the number of solutions, but also give the set of solutions in $O(n)$ time. One of the interesting results of our research is that, when this equation has a solution, then the number of solutions is a power of two.

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S. M. Dehnavi, M. R. Mirzaee Shamsabad, A. Mahmoodi Rishakani. 2017-11-09. Complete solving the quadratic equation mod $2^n$. https://arxiv.org/abs/1711.03621

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