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

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

Applied Mathematics and Computation, 2020, vol. 372, issue C

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.

Keywords: Jacobi symbol; Probability distribution; Statistical distance; Identity-based encryption (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:372:y:2020:i:c:s0096300319309853

DOI: 10.1016/j.amc.2019.124993

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