[Resource Topic] 2019/638: On the Distribution of Quadratic Residues and Non-residues Modulo Composite Integers and Applications to Cryptography

Resource Public-key cryptography
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Welcome to the resource topic for 2019/638

Title:
On the Distribution of Quadratic Residues and Non-residues Modulo Composite Integers and Applications to Cryptography

Authors: Ferucio Laurentiu Tiplea, Sorin Iftene, George Teseleanu, Anca-Maria Nica

Abstract:

We develop exact formulas for the distribution of quadratic residues and non-residues in sets of the form a+X=\{(a+x)\bmod n\mid x\in 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.

ePrint: https://eprint.iacr.org/2019/638

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