English

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 ax2+bx+c=0(mod2n), 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)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.

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}
}

Comments

8 pages

R2 v1 2026-06-22T22:41:36.319Z