Papers › Complete solving the quadratic equation mod 2ⁿ
Complete solving the quadratic equation mod 2ⁿ
S. M. Dehnavi, M. R. Mirzaee Shamsabad, A. Mahmoodi Rishakani
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Quadratic functions have applications in cryptography. In this paper, we investigate the modular quadratic equation ax²+bx+c=0 (mod 2ⁿ), 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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