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On the distribution of quadratic residues and non-residues modulo composite integers and applications to cryptography

Author

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  • Ţiplea, Ferucio Laurenţiu
  • Iftene, Sorin
  • Teşeleanu, George
  • Nica, Anca-Maria

Abstract

We develop exact formulas for the distribution of quadratic residues and non-residues in sets of the form a+X={(a+x)modn∣x∈X}, where n is a prime or the product of two primes and X is a subset of integers with given Jacobi symbols modulo prime factors of n. We then present applications of these formulas to Cocks’ identity-based encryption scheme and statistical indistinguishability.

Suggested Citation

  • Ţiplea, Ferucio Laurenţiu & Iftene, Sorin & Teşeleanu, George & Nica, Anca-Maria, 2020. "On the distribution of quadratic residues and non-residues modulo composite integers and applications to cryptography," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    • Handle: RePEc:eee:apmaco:v:372:y:2020:i:c:s0096300319309853
    DOI: 10.1016/j.amc.2019.124993
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    Cited by:

    1. Ferucio Laurenţiu Ţiplea, 2022. "Efficient Generation of Roots of Power Residues Modulo Powers of Two," Mathematics, MDPI, vol. 10(6), pages 1-9, March.
    2. Xiaodan Yuan & Wenpeng Zhang, 2023. "On cubic residues and related problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(3), pages 806-815, September.

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