Titlebook: Quantum Computational Number Theory; Song Y. Yan Book 2015 Springer International Publishing Switzerland 2015 Quantum computational number

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Quantum Algorithms for Integer Factorization,Problem (IFP), for which the inventor of RSA received the year 2002 Turing award, consider as the equivalent Nobel Prize in Computer Science. If IFP can be solved in polynomial-time, then RSA and many other cryptographic systems can be broken completely and efficiently.

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Quantum Computing for Elliptic Curve Discrete Logarithms,In this chapter we shall first discuss the Elliptic Curve Discrete Logarithm Problem (ECDLP) and the classical solutions to ECDLP, then we shall present some quantum algorithms for solving the ECDLP problem and for attacking the ECDLP-based cryptography.

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Song Y. YanIntroduces the basic concepts and results in number theory and quantum computing.Discusses three major intractable number-theoretic problems related to the construction of modern public-key cryptograp

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