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

被引：10
|
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.
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页数：18
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