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

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 form...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 372; p. 124993
Main Authors Ţiplea, Ferucio Laurenţiu, Iftene, Sorin, Teşeleanu, George, Nica, Anca-Maria
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.05.2020
Subjects
Identity-based encryption
Jacobi symbol
Probability distribution
Statistical distance
Jacobi symbol
Statistical distance
Identity-based encryption
Probability distribution
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2019.124993