Complete solving the quadratic equation mod $2^n$
Number Theory
2017-11-13 v1
Abstract
Quadratic functions have applications in cryptography. In this paper, we investigate the modular quadratic equation 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 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.
Keywords
Cite
@article{arxiv.1711.03621,
title = {Complete solving the quadratic equation mod $2^n$},
author = {S. M. Dehnavi and M. R. Mirzaee Shamsabad and A. Mahmoodi Rishakani},
journal= {arXiv preprint arXiv:1711.03621},
year = {2017}
}
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8 pages