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Classic and Quantum Computation

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Quantum Attacks on Public-Key Cryptosystems

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Abstract

In this chapter, we shall first give an account of the basic concepts and results in classical computability and complexity and then, the quantum computability and complexity, which will be used throughout the book.

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Notes

  1. 1.

    Hilbert space is defined to be a complete inner-product space. The set of all sequences x = (x 1, x 2, ⋯ ) of complex numbers (where \(\sum _{i=1}^{\infty }\vert x_{i}{\vert }^{2}\) is finite) is a good example of a Hilbert space, where the sum x + y is defined as \((x_{1} + y_{1},x_{2} + y_{2},\cdots \,)\), the product ax as \((ax_{1},ax_{2},\cdots \,)\), and the inner product as \((x,y) =\sum _{ i=1}^{\infty }\overline{x}_{i}y_{i}\), where \(\overline{x}_{i}\) is the complex conjugate of x i , x = (x 1, x 2, ⋯ ) and y = (y 1, y 2, ⋯ ). In modern quantum mechanics all possible physical states of a system are considered to correspond to space vectors in a Hilbert space.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, Cambridge, MA, USA

    Song Y. Yan

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Yan, S.Y. (2013). Classic and Quantum Computation. In: Quantum Attacks on Public-Key Cryptosystems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-7722-9_1

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  • DOI: https://doi.org/10.1007/978-1-4419-7722-9_1

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