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

被引：9

作者：

Tiplea, Ferucio Laurentiu ^{[1
,3
]}

Iftene, Sorin ^{[1
]}

Teseleanu, George ^{[2
,3
]}

Nica, Anca-Maria ^{[1
]}

机构：

[1] Alexandru Ioan Cuza Univ, Dept Comp Sci, Iasi 700506, Romania

[2] Adv Technol Inst, Bucharest 021101, Romania

[3] Romanian Acad, Simion Stoilow Inst Math, Bucharest 010702, Romania

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2020年 / 372卷

关键词：

Jacobi symbol; Probability distribution; Statistical distance; Identity-based encryption; IDENTITY-BASED ENCRYPTION; ANONYMOUS IBE; RESIDUOSITY;

D O I：

10.1016/j.amc.2019.124993

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop exact formulas for the distribution of quadratic residues and non-residues in sets of the form a + X = {(a + x) mod n vertical bar 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. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：18

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