Quadratic residues and the representation of a number as a sum of four squares

1968 ◽  
pp. 26-33
Author(s):  
K. Chandrasekharan
Keyword(s):  
Quadratic Residues

Identity oriented signature scheme based on quadratic residues

2005 ◽  
Vol 168 (1) ◽  
pp. 235-242 ◽  
Author(s):  
Weidong Qiu ◽  
Kefei Chen
Keyword(s):  
Signature Scheme ◽  
Quadratic Residues

Quadratic Residues

1986 ◽  
pp. 109-156
Author(s):  
Nikolaos Kritikos
Keyword(s):  
Quadratic Residues

scholarly journals A New Symmetric Key Cryptographic Algorithm using Paley Graphs and ASCII Values

2021 ◽  
Vol 297 ◽  
pp. 01046
Author(s):  
Zhour Oumazouz ◽  
Driss Karim
Keyword(s):  
Brute Force ◽  
Strong Regularity ◽  
Quadratic Residues ◽  
Cryptographic Algorithm ◽  
Paley Graph ◽  
Encryption And Decryption ◽  
Symmetric Key ◽  
Brute Force Attack ◽  
The Moment ◽  
Paley Graphs

The main objective of the study conducted in this article is to introduce a new algorithm of encryption and decryption of a sensitive message after transforming it into a binary message. Our proposed encryption algorithm is based on the study of a particular graph constructed algebraically from the quadratic residues. We have exploited the Paley graph to introduce an abstract way of encryption of such message bit according to the other message bits by the intermidiate study of the neighborhood of a graph vertex. The strong regularity of the Paley graphs and the unknown behavior of the quadratic residues will play a very important role in the cryptanalysis part which allows to say that the brute force attack remains for the moment the only way to obtain the set of possible messages.

scholarly journals Combinatorics on Finite Fields: the Sign Repartition for the Quadratic Residues

2014 ◽  
Vol 22 (1) ◽  
pp. 41-44
Author(s):  
Şerban Bărcănescu
Keyword(s):  
Finite Fields ◽  
Class Number ◽  
Quadratic Extensions ◽  
Quadratic Residues

AbstractIn the present paper we present the equivalence between the combinatorial determination of the sign repartition for the quadratic residues and non-residues to the computation of the class number of certain quadratic extensions of the field of rationals.

A Property of Twin Primes

Integers ◽  
2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Christian Aebi ◽  
Grant Cairns
Keyword(s):  
Twin Primes ◽  
Quadratic Residues

Abstract.We determine the product of the invertible quadratic residues in

scholarly journals On finite differences, permutations, and Quadratic residues

1977 ◽  
Vol 9 (4) ◽  
pp. 413-419
Author(s):  
Arnošt J.J Heidrich
Keyword(s):  
Finite Differences ◽  
Quadratic Residues
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