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From golden to unimodular cryptography

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  • Koshkin, Sergiy
  • Styers, Taylor

Abstract

We introduce a natural generalization of the golden cryptography, which uses general unimodular matrices in place of the traditional Q matrices, and prove that it preserves the original error correction properties of the encryption. Moreover, the additional parameters involved in generating the coding matrices make this unimodular cryptography resilient to the chosen plaintext attacks that worked against the golden cryptography. Finally, we show that even the golden cryptography is generally unable to correct double errors in the same row of the ciphertext matrix, and offer an additional check number which, if transmitted, allows for the correction.

Suggested Citation

  • Koshkin, Sergiy & Styers, Taylor, 2017. "From golden to unimodular cryptography," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 208-214.
    • Handle: RePEc:eee:chsofr:v:105:y:2017:i:c:p:208-214
    DOI: 10.1016/j.chaos.2017.10.015
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    References listed on IDEAS

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    1. Falcón, Sergio & Plaza, Ángel, 2008. "The k-Fibonacci hyperbolic functions," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 409-420.
    2. Stakhov, A.P., 2006. "Fibonacci matrices, a generalization of the “Cassini formula”, and a new coding theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 56-66.
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    Cited by:

    1. Nepomuceno, Erivelton G. & Lima, Arthur M. & Arias-García, Janier & Perc, Matjaž & Repnik, Robert, 2019. "Minimal digital chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 62-66.

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