scholarly journals Cryptosystems using an improving hiding technique based on latin square and magic square

2020 ◽  
Vol 20 (1) ◽  
pp. 510
Author(s):  
Sahab Dheyaa Mohammed ◽  
Taha Mohammed Hasan
Keyword(s):  
Finite Field ◽  
Latin Square ◽  
Sensitive Data ◽  
Avalanche Effect ◽  
Magic Squares ◽  
P Values ◽  
Encrypted Data ◽  
Magic Square ◽  
Encryption Method ◽  
Randomness Tests

<p>Hackers should be prevented from disclosing sensitive data when sent from one device to another over the network. Therefore, the proposed method was established to prevent the attackers from exploiting the vulnerabilities of the redundancy in the ciphertext and enhances the substitution and permutation operations of the encryption process .the solution was performed by eliminates these duplicates by hiding the ciphertext into a submatrix 4 x4 that chooses randomly from magic square 16x16 in each ciphering process. Two techniques of encrypted and hiding were executed in the encryption stage by using a magic square size 3 × 3   and Latin square size 3 × 3 to providing more permutation and also to ensure an inverse matrix of decryption operation be available. In the hiding stage, the ciphertext was hidden into a 16×16 matrix that includes 16 sub-magic squares to eliminate the duplicates in the ciphertext. Where all elements that uses were polynomial numbers of a finite field of degree Galois Fields GF ( ).  The proposed technique is robust against disclosing the repetition encrypted data based on the result of Avalanche Effect in an accepted ratio (62%) and the results of the output of the proposed encryption method have acceptable randomness based on the results of the p-values (0.629515) of the National Institute of Standards and Technology (NIST) randomness tests. The work can be considered significant in the field of encrypting databases because the repetition of encrypted data inside databases is considered an important vulnerability that helps to guess the plaintext from the encrypted text.</p>

Magic squares of squares over a finite field

2021 ◽  
pp. 111-122
Author(s):  
Stewart Hengeveld ◽  
Giancarlo Labruna ◽  
Aihua Li
Keyword(s):  
Finite Field ◽  
Prime Numbers ◽  
Similar Question ◽  
Magic Squares ◽  
Content Type ◽  
Magic Square ◽  
Twin Primes ◽  
Quadratic Residues ◽  
Perfect Squares ◽  
Open Question

A magic square M M over an integral domain D D is a 3 × 3 3\times 3 matrix with entries from D D such that the elements from each row, column, and diagonal add to the same sum. If all the entries in M M are perfect squares in D D , we call M M a magic square of squares over D D . In 1984, Martin LaBar raised an open question: “Is there a magic square of squares over the ring Z \mathbb {Z} of the integers which has all the nine entries distinct?” We approach to answering a similar question when D D is a finite field. We claim that for any odd prime p p , a magic square over Z p \mathbb Z_p can only hold an odd number of distinct entries. Corresponding to LaBar’s question, we show that there are infinitely many prime numbers p p such that, over Z p \mathbb Z_p , magic squares of squares with nine distinct elements exist. In addition, if p ≡ 1 ( mod 120 ) p\equiv 1\pmod {120} , there exist magic squares of squares over Z p \mathbb Z_p that have exactly 3, 5, 7, or 9 distinct entries respectively. We construct magic squares of squares using triples of consecutive quadratic residues derived from twin primes.

7. Square arrays

2016 ◽  
pp. 109-122
Author(s):  
Robin Wilson
Keyword(s):  
Latin Square ◽  
Latin Squares ◽  
Magic Squares ◽  
Magic Square ◽  
Orthogonal Latin Squares ◽  
Square Array

‘Square arrays’ is concerned with magic squares and latin squares. An n × n magic square, or a magic square of order n, is a square array of numbers (usually the numbers from 1 to n 2) arranged so that the sum of the numbers in each of the n rows, each of the n columns, or each of the two main diagonals is the same. A latin square of order n, is a square array with n symbols arranged so that each symbol appears just once in each row and each column. Orthogonal latin squares are also discussed along with Euler’s 36 officers problem.

Latin square matrices and their inverses

2019 ◽  
Vol 103 (557) ◽  
pp. 265-276
Author(s):  
K. Robin McLean
Keyword(s):  
Linear Algebra ◽  
Computer Algebra ◽  
Latin Square ◽  
Magic Squares ◽  
Magic Square

Magic squares have long been popular in recreational mathematics. Their potential for introducing students to ideas in linear algebra was recognised over forty years ago in [1] and later in [2]. More recently they have proved to be a fascinating topic for undergraduate exploration, especially when students have access to a computer algebra package [3]. Some results on powers of magic square matrices can be found in [4], [5] and [6]. (Readers who google the title ‘Odd magic powers’ of Thompson’s paper [5] will be treated to a wide variety of non-mathematical exotica!)

A New Algorithm Based on Magic Square and a Novel Chaotic System for Image Encryption

2019 ◽  
Vol 29 (1) ◽  
pp. 1202-1215 ◽  
Author(s):  
Rageed Hussein AL-Hashemy ◽  
Sadiq A. Mehdi
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Color Image ◽  
Security Analysis ◽  
Correlation Coefficients ◽  
Magic Squares ◽  
Magic Square ◽  
Key Space ◽  
Encryption Method ◽  
Differential Attacks

Abstract This article introduces a simple and effective new algorithm for image encryption using a chaotic system which is based on the magic squares. This novel 3D chaotic system is invoked to generate a random key to encrypt any color image. A number of chaotic keys equal to the size of the image are generated by this chaotic system and arranged into a matrix then divided into non-overlapped submatrices. The image to be encrypted is also divided into sub-images, and each sub-image is multiplied by a magic matrix to produce another set of matrices. The XOR operation is then used on the resultant two sets of matrices to produce the encrypted image. The strength of the encryption method is tested in two folds. The first fold is the security analysis which includes key space analysis and sensitivity analysis. In the second fold, statistical analysis was performed, which includes the correlation coefficients, information entropy, the histogram, and analysis of differential attacks. Finally, the time of encryption and decryption was computed and show very good results.

scholarly journals Maintaining the Integrity of Encrypted Data by Using the Improving Hash Function Based on GF 28

TEM Journal ◽  
2020 ◽  
pp. 1277-1284
Author(s):  
Sahab Dheyaa Mohammed ◽  
Abdul Monem S. Rahma ◽  
Taha Mohammed Hasan
Keyword(s):  
Equation System ◽  
Sensitive Information ◽  
Avalanche Effect ◽  
Magic Square ◽  
Linear Equation System ◽  
Encryption And Decryption ◽  
And Diffusion ◽  
Confusion And Diffusion ◽  
Effect Test ◽  
Randomness Tests

The issue of protecting the information from penetration has become an important issue. The system that depends on the encryption ensures the confidentiality of the information non-disclosure of sensitive information but does not ensure the integrity of data from destruction and change. In this paper, a proposed system is designed to protect the confidentiality and integrity of data from penetration, disclosure, and destruction. The proposed system based on the polynomial numbers of GF (𝟐𝟖) is achieved by improving the encryption approach using the idea of the magic square and the linear equation system also uses improving the digital signature method for ensuring that data is not changed or modified. The system has higher encryption and decryption throughput (548.924Kb /sec), (548.924 Kb /sec) and acceptable value 0.759294 of the randomness data according to the NIST randomness tests as well as a high confusion and diffusion in cipher text based on the ratio of Avalanche effect test.

scholarly journals Privacy-Preserving Deep Neural Network Methods: Computational and Perceptual Methods—An Overview

Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1367
Author(s):  
Raghida El El Saj ◽  
Ehsan Sedgh Sedgh Gooya ◽  
Ayman Alfalou ◽  
Mohamad Khalil
Keyword(s):  
Neural Networks ◽  
Classification Accuracy ◽  
Deep Neural Networks ◽  
Privacy Preserving ◽  
Sensitive Data ◽  
Encrypted Data ◽  
High Classification Accuracy ◽  
Hide Information ◽  
Network Methods ◽  
Cloud Environments

Privacy-preserving deep neural networks have become essential and have attracted the attention of many researchers due to the need to maintain the privacy and the confidentiality of personal and sensitive data. The importance of privacy-preserving networks has increased with the widespread use of neural networks as a service in unsecured cloud environments. Different methods have been proposed and developed to solve the privacy-preserving problem using deep neural networks on encrypted data. In this article, we reviewed some of the most relevant and well-known computational and perceptual image encryption methods. These methods as well as their results have been presented, compared, and the conditions of their use, the durability and robustness of some of them against attacks, have been discussed. Some of the mentioned methods have demonstrated an ability to hide information and make it difficult for adversaries to retrieve it while maintaining high classification accuracy. Based on the obtained results, it was suggested to develop and use some of the cited privacy-preserving methods in applications other than classification.

Computing Blindfolded on Data Homomorphically Encrypted under Multiple Keys: A Survey

2022 ◽  
Vol 54 (9) ◽  
pp. 1-37
Author(s):  
Asma Aloufi ◽  
Peizhao Hu ◽  
Yongsoo Song ◽  
Kristin Lauter
Keyword(s):  
Homomorphic Encryption ◽  
Lessons Learned ◽  
Secret Key ◽  
Sensitive Data ◽  
Encrypted Data ◽  
Outsourced Computation ◽  
Secret Keys ◽  
Comprehensive Survey ◽  
Multiple Keys ◽  
Cryptographic Techniques

With capability of performing computations on encrypted data without needing the secret key, homomorphic encryption (HE) is a promising cryptographic technique that makes outsourced computations secure and privacy-preserving. A decade after Gentry’s breakthrough discovery of how we might support arbitrary computations on encrypted data, many studies followed and improved various aspects of HE, such as faster bootstrapping and ciphertext packing. However, the topic of how to support secure computations on ciphertexts encrypted under multiple keys does not receive enough attention. This capability is crucial in many application scenarios where data owners want to engage in joint computations and are preferred to protect their sensitive data under their own secret keys. Enabling this capability is a non-trivial task. In this article, we present a comprehensive survey of the state-of-the-art multi-key techniques and schemes that target different systems and threat models. In particular, we review recent constructions based on Threshold Homomorphic Encryption (ThHE) and Multi-Key Homomorphic Encryption (MKHE). We analyze these cryptographic techniques and schemes based on a new secure outsourced computation model and examine their complexities. We share lessons learned and draw observations for designing better schemes with reduced overheads.

scholarly journals Privacy-Preserving Sorting Algorithms Based on Logistic Map for Clouds

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Hua Dai ◽  
Hui Ren ◽  
Zhiye Chen ◽  
Geng Yang ◽  
Xun Yi
Keyword(s):  
Data Privacy ◽  
Logistic Map ◽  
Security Analysis ◽  
Privacy Preserving ◽  
Service Recommendation ◽  
Sensitive Data ◽  
Encrypted Data ◽  
Sorting Algorithms ◽  
Common Operation ◽  
Cloud Servers

Outsourcing data in clouds is adopted by more and more companies and individuals due to the profits from data sharing and parallel, elastic, and on-demand computing. However, it forces data owners to lose control of their own data, which causes privacy-preserving problems on sensitive data. Sorting is a common operation in many areas, such as machine learning, service recommendation, and data query. It is a challenge to implement privacy-preserving sorting over encrypted data without leaking privacy of sensitive data. In this paper, we propose privacy-preserving sorting algorithms which are on the basis of the logistic map. Secure comparable codes are constructed by logistic map functions, which can be utilized to compare the corresponding encrypted data items even without knowing their plaintext values. Data owners firstly encrypt their data and generate the corresponding comparable codes and then outsource them to clouds. Cloud servers are capable of sorting the outsourced encrypted data in accordance with their corresponding comparable codes by the proposed privacy-preserving sorting algorithms. Security analysis and experimental results show that the proposed algorithms can protect data privacy, while providing efficient sorting on encrypted data.

scholarly journals A Secure Ciphertext Retrieval Scheme against Insider KGAs for Mobile Devices in Cloud Storage

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Run Xie ◽  
Chanlian He ◽  
Dongqing Xie ◽  
Chongzhi Gao ◽  
Xiaojun Zhang
Keyword(s):  
Cloud Computing ◽  
Mobile Devices ◽  
Data Privacy ◽  
Security Analysis ◽  
Data Retrieval ◽  
Sensitive Data ◽  
Encrypted Data ◽  
Security Issues ◽  
Efficiency Comparison ◽  
Cloud Servers

With the advent of cloud computing, data privacy has become one of critical security issues and attracted much attention as more and more mobile devices are relying on the services in cloud. To protect data privacy, users usually encrypt their sensitive data before uploading to cloud servers, which renders the data utilization to be difficult. The ciphertext retrieval is able to realize utilization over encrypted data and searchable public key encryption is an effective way in the construction of encrypted data retrieval. However, the previous related works have not paid much attention to the design of ciphertext retrieval schemes that are secure against inside keyword-guessing attacks (KGAs). In this paper, we first construct a new architecture to resist inside KGAs. Moreover we present an efficient ciphertext retrieval instance with a designated tester (dCRKS) based on the architecture. This instance is secure under the inside KGAs. Finally, security analysis and efficiency comparison show that the proposal is effective for the retrieval of encrypted data in cloud computing.

scholarly journals Text File Privacy on the Cloud Based on Diagonal Fragmentation and Encryption

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Tawfiq Barhoom ◽  
Mahmoud Abu Shawish
Keyword(s):  
Data Privacy ◽  
Cloud Services ◽  
Text File ◽  
Layer Model ◽  
Encrypted Data ◽  
Cloud Server ◽  
Cloud Environments ◽  
Encryption Algorithms ◽  
Well Data ◽  
Encryption Method

Despite the growing reliance on cloud services and software, privacy is somewhat difficult. We store our data on remote servers in cloud environments that are untrusted. If we do not handle the stored data well, data privacy can be violated with no awareness on our part. Although it requires expensive computation, encrypting the data before sending it appears to be a solution to this problem. So far, all known solutions to protect textual files using encryption algorithms fell short of privacy expectations. Thus is because encrypting cannot stand by itself. The encrypted data on the cloud server becomes full file in the hand causing the privacy of this data to be intrusion-prone, thus allowing intruders to access the file data once they can decrypt it. This study aimed to develop an effective cloud confidentiality model based on combining fragmentation and encryption of text files to compensate for reported deficiency in encryption methods. The fragmentation method used the strategy of dividing text files into two triangles through the axis. Whereas the encryption method used the Blowfish algorithm. The research concluded that high confidentiality is achieved by building a multi-layer model: encryption, chunk, and fragmentation of every chunk to prevent intruders from reaching the data even if they were able to decrypt the file. Using the privacy accuracy equation (developed for the purpose in this research), the model achieved accuracy levels of 96% and 90% when using 100 and 200 words in each chunk on small, medium, and large files respectively.

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