The generalized Chinese remainder theorem for universal algebras; subdirect factorization

1956 ◽  
Vol 66 (1) ◽  
pp. 452-469 ◽  
Author(s):  
Alfred L. Foster
Keyword(s):  
Chinese Remainder Theorem ◽  
Universal Algebras ◽  
Subdirect Factorization

The identities of ? and unique subdirect factorization within ? classes of universal algebras

1955 ◽  
Vol 62 (1) ◽  
pp. 171-188 ◽  
Author(s):  
Alfred L. Foster
Keyword(s):  
Universal Algebras ◽  
Subdirect Factorization

scholarly journals Independence of algebras with edge term

2015 ◽  
Vol 25 (07) ◽  
pp. 1145-1157 ◽  
Author(s):  
Erhard Aichinger ◽  
Peter Mayr
Keyword(s):  
Polynomial Time ◽  
Sufficient Conditions ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Universal Algebras ◽  
Finite Algebras ◽  
Necessary And Sufficient ◽  
Independent Varieties ◽  
Subdirect Factorization ◽  
Independence Of Algebras

In [A. L. Foster, The identities of — and unique subdirect factorization within — classes of universal algebras, Math. Z. 62 (1955) 171–188], two varieties [Formula: see text] of the same type are defined to be independent if there is a binary term [Formula: see text] such that [Formula: see text] and [Formula: see text]. In this paper, we give necessary and sufficient conditions for two finite algebras with a Mal’cev term (or, more generally, with an edge term) to generate independent varieties. In particular we show that the independence of finitely generated varieties with edge term can be decided by a polynomial time algorithm.

scholarly journals Secure Video Surveillance Framework in Smart City

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4419
Author(s):  
Hao Li ◽  
Tianhao Xiezhang ◽  
Cheng Yang ◽  
Lianbing Deng ◽  
Peng Yi
Keyword(s):  
Video Surveillance ◽  
Smart City ◽  
Key Management ◽  
Surveillance System ◽  
Chinese Remainder Theorem ◽  
Smart Cities ◽  
Group Key Management ◽  
Video Surveillance System ◽  
Surveillance Systems ◽  
Key Update

In the construction process of smart cities, more and more video surveillance systems have been deployed for traffic, office buildings, shopping malls, and families. Thus, the security of video surveillance systems has attracted more attention. At present, many researchers focus on how to select the region of interest (RoI) accurately and then realize privacy protection in videos by selective encryption. However, relatively few researchers focus on building a security framework by analyzing the security of a video surveillance system from the system and data life cycle. By analyzing the surveillance video protection and the attack surface of a video surveillance system in a smart city, we constructed a secure surveillance framework in this manuscript. In the secure framework, a secure video surveillance model is proposed, and a secure authentication protocol that can resist man-in-the-middle attacks (MITM) and replay attacks is implemented. For the management of the video encryption key, we introduced the Chinese remainder theorem (CRT) on the basis of group key management to provide an efficient and secure key update. In addition, we built a decryption suite based on transparent encryption to ensure the security of the decryption environment. The security analysis proved that our system can guarantee the forward and backward security of the key update. In the experiment environment, the average decryption speed of our system can reach 91.47 Mb/s, which can meet the real-time requirement of practical applications.

scholarly journals Computationally Efficient Approach to Implementation of the Chinese Remainder Theorem Algorithm in Minimally Redundant Residue Number System

2021 ◽  
Author(s):  
Mikhail Selianinau
Keyword(s):  
Chinese Remainder Theorem ◽  
Number System ◽  
Residue Number System ◽  
Computer Applications ◽  
Efficient Approach ◽  
Residue Modulo ◽  
Modern Computer ◽  
New Variant ◽  
Residue Number ◽  
Residue Code

AbstractIn this paper, we deal with the critical problem of performing non-modular operations in the Residue Number System (RNS). The Chinese Remainder Theorem (CRT) is widely used in many modern computer applications. Throughout the article, an efficient approach for implementing the CRT algorithm is described. The structure of the rank of an RNS number, a principal positional characteristic of the residue code, is investigated. It is shown that the rank of a number can be represented by a sum of an inexact rank and a two-valued correction to it. We propose a new variant of minimally redundant RNS, which provides low computational complexity for the rank calculation, and its effectiveness analyzed concerning conventional non-redundant RNS. Owing to the extension of the residue code, by adding the excess residue modulo 2, the complexity of the rank calculation goes down from $O\left (k^{2}\right )$ O k 2 to $O\left (k\right )$ O k with respect to required modular addition operations and lookup tables, where k equals the number of non-redundant RNS moduli.

scholarly journals Multiparty weighted threshold quantum secret sharing based on the Chinese remainder theorem to share quantum information

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yao-Hsin Chou ◽  
Guo-Jyun Zeng ◽  
Xing-Yu Chen ◽  
Shu-Yu Kuo
Keyword(s):  
Quantum Information ◽  
Phase Shift ◽  
Quantum State ◽  
Secret Sharing ◽  
Chinese Remainder Theorem ◽  
Security Analysis ◽  
Quantum Secret Sharing ◽  
Security Protocol ◽  
Multiple Quantum ◽  
Cryptographic Primitive

AbstractSecret sharing is a widely-used security protocol and cryptographic primitive in which all people cooperate to restore encrypted information. The characteristics of a quantum field guarantee the security of information; therefore, many researchers are interested in quantum cryptography and quantum secret sharing (QSS) is an important research topic. However, most traditional QSS methods are complex and difficult to implement. In addition, most traditional QSS schemes share classical information, not quantum information which makes them inefficient to transfer and share information. In a weighted threshold QSS method, each participant has each own weight, but assigning weights usually costs multiple quantum states. Quantum state consumption will therefore increase with the weight. It is inefficient and difficult, and therefore not able to successfully build a suitable agreement. The proposed method is the first attempt to build multiparty weighted threshold QSS method using single quantum particles combine with the Chinese remainder theorem (CRT) and phase shift operation. The proposed scheme allows each participant has its own weight and the dealer can encode a quantum state with the phase shift operation. The dividing and recovery characteristics of CRT offer a simple approach to distribute partial keys. The reversibility of phase shift operation can encode and decode the secret. The proposed weighted threshold QSS scheme presents the security analysis of external attacks and internal attacks. Furthermore, the efficiency analysis shows that our method is more efficient, flexible, and simpler to implement than traditional methods.

scholarly journals Robust Secret Image Sharing Resistant to Noise in Shares

2021 ◽  
Vol 17 (1) ◽  
pp. 1-22
Author(s):  
Xuehu Yan ◽  
Lintao Liu ◽  
Longlong Li ◽  
Yuliang Lu
Keyword(s):  
Chinese Remainder Theorem ◽  
Recovery Phase ◽  
Error Correcting Codes ◽  
Secret Image Sharing ◽  
Data Loss ◽  
Least Significant Bit ◽  
Recovery Method ◽  
Secret Image ◽  
Image Sharing ◽  
Salt And Pepper

A secret image is split into   shares in the generation phase of secret image sharing (SIS) for a  threshold. In the recovery phase, the secret image is recovered when any   or more shares are collected, and each collected share is generally assumed to be lossless in conventional SIS during storage and transmission. However, noise will arise during real-world storage and transmission; thus, shares will experience data loss, which will also lead to data loss in the secret image being recovered. Secret image recovery in the case of lossy shares is an important issue that must be addressed in practice, which is the overall subject of this article. An SIS scheme that can recover the secret image from lossy shares is proposed in this article. First, robust SIS and its definition are introduced. Next, a robust SIS scheme for a  threshold without pixel expansion is proposed based on the Chinese remainder theorem (CRT) and error-correcting codes (ECC). By screening the random numbers, the share generation phase of the proposed robust SIS is designed to implement the error correction capability without increasing the share size. Particularly in the case of collecting noisy shares, our recovery method is to some degree robust to some noise types, such as least significant bit (LSB) noise, JPEG compression, and salt-and-pepper noise. A theoretical proof is presented, and experimental results are examined to evaluate the effectiveness of our proposed method.

Multilevel threshold secret sharing based on the Chinese Remainder Theorem

2014 ◽  
Vol 114 (9) ◽  
pp. 504-509 ◽  
Author(s):  
Lein Harn ◽  
Miao Fuyou
Keyword(s):  
Secret Sharing ◽  
Chinese Remainder Theorem ◽  
Threshold Secret Sharing
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