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A Public-Key System Based on Primes and Addition

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Telecommunications and Remote Sensing (ICTRS 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1990))

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Abstract

In this paper, we describe a public-key algorithm that uses random primes to construct a matrix that is made public. To encrypt an integer, say P, representing a given plaintext message, the integer P is used to select a unique set of integers S from this constructed matrix. To encrypt the message, the integers in the set S are added, and the resulting sum represents the encrypted message. To decrypt the message, three secret keys are used in a mathematical algorithm to determine the original message P from the sum.

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Notes

  1. 1.

    The sum of the elements in any row m of the rotated Pascal Triangle is the value of the element at position \([m+1,1]\) which is \(\left( {\begin{array}{c}2m-1\\ m-1\end{array}}\right) \), easily deduced by considering the entries in a Pascal Triangle.

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Author information

Authors and Affiliations

  1. University of New Brunswick, Fredericton, NB, Canada

    Rodney H. Cooper & Brent R. Petersen

  2. Employed in the private sector, Calgary, AB, Canada

    Jeff Retallick

Authors
  1. Rodney H. Cooper
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  2. Jeff Retallick
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  3. Brent R. Petersen
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Corresponding author

Correspondence to Rodney H. Cooper .

Editor information

Editors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Boris Shishkov

  2. Nikola Vaptsarov Naval Academy, Varna, Bulgaria

    Andon Lazarov

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Cooper, R.H., Retallick, J., Petersen, B.R. (2023). A Public-Key System Based on Primes and Addition. In: Shishkov, B., Lazarov, A. (eds) Telecommunications and Remote Sensing. ICTRS 2023. Communications in Computer and Information Science, vol 1990. Springer, Cham. https://doi.org/10.1007/978-3-031-49263-1_4

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  • DOI: https://doi.org/10.1007/978-3-031-49263-1_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49262-4

  • Online ISBN: 978-3-031-49263-1

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