Quantum Algorithm for Polynomial Root Finding Problem

Quantum computation is a new computing model based on fundamental quantum mechanical principle. Grover's algorithm finds the solution for a searching problem in the square root time of exhaustive search. Brassard, Hoyer, Tapp's algorithm counts the number of solutions for a searching probl...

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Bibliographic Details
Published in2014 Tenth International Conference on Computational Intelligence and Security pp. 469 - 473
Main Authors Sun, Guodong, Su, Shenghui, Xu, Maozhi
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.11.2014
Subjects
Algorithm design and analysis
Cryptography
Polynomial root finding problem
Polynomials
Quantum computing
Quantum counting
Quantum mechanics
Quantum searching
Search problems
Signature algorithm
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DOI10.1109/CIS.2014.40

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Summary:Quantum computation is a new computing model based on fundamental quantum mechanical principle. Grover's algorithm finds the solution for a searching problem in the square root time of exhaustive search. Brassard, Hoyer, Tapp's algorithm counts the number of solutions for a searching problem. Through exploiting the two quantum algorithms, we propose a quantum algorithm for solving a new cryptography problem -- polynomial root finding problem, which could be used to design a cryptosystem. The algorithm will take O(rootM/t) steps for finding one of the t solutions to the problem, where M is the modular of the equation. The success rate of the algorithm is a constant and the cost of the algorithm depends on the calculations of modular exponentiation and the number of iterations.
DOI:10.1109/CIS.2014.40