Puzzle Type Examples of Linear Congruence

2018 ◽  
Vol 9 (9) ◽  
pp. 1252-1256
Author(s):  
Yogesh J. Bagul ◽  
Sham B. Garud
Keyword(s):  
Linear Congruence

A Linear Congruence with Side Conditions

1963 ◽  
Vol 70 (8) ◽  
pp. 837-840 ◽  
Author(s):  
David Rearick
Keyword(s):  
Linear Congruence

Number of small solutions of a homogeneous linear congruence

1991 ◽  
Vol 50 (4) ◽  
pp. 1055-1058 ◽  
Author(s):  
I. A. Semaev
Keyword(s):  
Linear Congruence ◽  
Homogeneous Linear

Linear congruence equations for the solutions of the N-Queens problem

1992 ◽  
Vol 41 (6) ◽  
pp. 301-306 ◽  
Author(s):  
Cengiz Erbas ◽  
Murat M. Tanik ◽  
Zekeriya Aliyazicioglu
Keyword(s):  
Linear Congruence

Algorithms for enumeration problem of linear congruence modulo m as sum of restricted partition numbers

2014 ◽  
Vol 10 (1) ◽  
pp. 69-89
Author(s):  
Tian-Xiao He ◽  
Peter J. -S. Shiue
Keyword(s):  
Linear Congruence ◽  
Restricted Partition ◽  
Congruence Modulo ◽  
Enumeration Problem

On finite algebras having a linear congruence class geometry

1984 ◽  
Vol 19 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Thomas Ihringer
Keyword(s):  
Congruence Class ◽  
Linear Congruence ◽  
Finite Algebras ◽  
Class Geometry

scholarly journals On Generalized Solutions of Linear Congruence ax ≡ b (mod n) for Large Modulus n

2018 ◽  
Vol 31 (1) ◽  
Author(s):  
Polemer M. Cuarto
Keyword(s):  
Number Theory ◽  
Research Method ◽  
Generalized Solution ◽  
Generalized Solutions ◽  
Linear Congruence ◽  
Public Key Cryptosystems ◽  
Alternative Method ◽  
Pure Mathematics ◽  
Cryptographic Algorithms ◽  
The Given

Number Theory, a branch of Pure Mathematics, is crucial in cryptographic algorithms. Many cryptographic systems depend heavily on some topics of Number Theory. One of these topics is the linear congruence. In cryptography, the concept of linear congruence is used to directly underpin public key cryptosystems during the process of ciphering and deciphering codes. Thus, linear congruence plays a very important role in cryptography. This paper aims to develop an alternative method and generalized solutions for solving linear congruence ax ≡ b (mod n). This study utilized expository-developmental research method. As a result, the alternative method considered two cases: (1) when (a,n) = 1 and  (2) when (a,n) > 1. The basic idea of the method is to convert the given congruence ax ≡ b (mod n) to ax = b + kn for some k, reduce modulus n by interchanging a and n, simplify the new congruence and perform the process recursively until obtaining a congruence that is trivial to solve. The advantage of this method over the existing approaches is that it can solve congruence even for large modulus n with much more efficiency. Generalized solution of linear congruence ax ≡ b (mod n) considering both cases was obtained in this study.

scholarly journals Solving System of Linear Congruence Equations over some Rings by Decompositions of Modules

2019 ◽  
Vol 4 (2) ◽  
pp. 133-152
Author(s):  
Mahmood Behboodi1 ◽  
Shadi Asgari ◽  
Ali Moradzadeh-Dehkordi ◽  
Amir Hashemi1 ◽  
◽  
...  
Keyword(s):  
Linear Congruence

scholarly journals Adaptive Partial Image Secret Sharing

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 703
Author(s):  
Xuehu Yan ◽  
Lei Sun ◽  
Yuliang Lu ◽  
Guozheng Yang
Keyword(s):  
Secret Sharing ◽  
Image Inpainting ◽  
Batch Processing ◽  
Linear Congruence ◽  
Secret Image ◽  
Meaningful Shares ◽  
Image Secret Sharing

In contrast to encrypting the full secret image in classic image secret sharing (ISS), partial image secret sharing (PISS) only encrypts part of the secret image due to the situation that, in general, only part of the secret image is sensitive or secretive. However, the target part needs to be selected manually in traditional PISS, which is human-exhausted and not suitable for batch processing. In this paper, we introduce an adaptive PISS (APISS) scheme based on salience detection, linear congruence, and image inpainting. First, the salient part is automatically and adaptively detected as the secret target part. Then, the target part is encrypted into n meaningful shares by using linear congruence in the processing of inpainting the target part. The target part is decrypted progressively by only addition operation when more shares are collected. It is losslessly decrypted when all the n shares are collected. Experiments are performed to verify the efficiency of the introduced scheme.

Inferring a sequence generated by a linear congruence

1982 ◽  
Author(s):  
Joan B. Plumstead
Keyword(s):  
Linear Congruence
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