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Mathematical Preliminaries

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Cybercryptography: Applicable Cryptography for Cyberspace Security

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Abstract

Cryptography is intimately connected to mathematics, in fact, the construction and the security of many cryptographic schemes and protocols depend heavily on some deep ideas and sophisticated techniques in mathematics, particularly in the theory of numbers.

All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA).

Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.

Vladimir Arnold (1937–2010)

Eminent Russian Mathematician and 2001 Wolf Prize Recipient

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Notes

  1. 1.

    The order of an element a modulo n is the smallest integer r such that a r ≡ 1 ( mod n); we shall discuss this later in Sect. 2.5.

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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). Mathematical Preliminaries. In: Cybercryptography: Applicable Cryptography for Cyberspace Security. Springer, Cham. https://doi.org/10.1007/978-3-319-72536-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-72536-9_2

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