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Computational Preliminaries

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Cybercryptography: Applicable Cryptography for Cyberspace Security

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Abstract

Computation has long been the deriving force in the development of both mathematics and cryptography, modern computation theory is however rooted in Turing’s 1936 paper on Computable Numbers, where a universal computing model, now called Turing machine is proposed.

It is possible to invent a single machine which can be used to compute any computable sequence.

Those who can imagine anything, can create the impossible.

Alan Turing (1912–1954)

Father of Modern Computer Science

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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 \(\sum _{i=1}^{\infty } |x_i|{ }^2\) 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, ⋯ ), the product ax as (ax 1, ax 2, ⋯ ), 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. Xingzhi College, Zhejiang Normal University, Jinhua, China

    Song Y. Yan

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Yan, S.Y. (2019). Computational Preliminaries. In: Cybercryptography: Applicable Cryptography for Cyberspace Security. Springer, Cham. https://doi.org/10.1007/978-3-319-72536-9_3

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  • DOI: https://doi.org/10.1007/978-3-319-72536-9_3

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