scholarly journals A Novel Technique for the Construction of Safe Substitution Boxes Based on Cyclic and Symmetric Groups

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Abdul Razaq ◽  
Hanan A. Al-Olayan ◽  
Atta Ullah ◽  
Arshad Riaz ◽  
Adil Waheed
Keyword(s):  
Symmetric Group ◽  
Cyclic Group ◽  
Symmetric Groups ◽  
Galois Field ◽  
Substitution Box ◽  
Novel Technique ◽  
Initial Sequence ◽  
Substitution Boxes ◽  
The Matrix ◽  
Better Than

In the literature, different algebraic techniques have been applied on Galois field GF(28) to construct substitution boxes. In this paper, instead of Galois field GF(28), we use a cyclic group C255 in the formation of proposed substitution box. The construction proposed S-box involves three simple steps. In the first step, we introduce a special type of transformation T of order 255 to generate C255. Next, we adjoin 0 to C255 and write the elements of C255∪0 in 16×16 matrix to destroy the initial sequence 0,1,2,…,255. In the 2nd step, the randomness in the data is increased by applying certain permutations of the symmetric group S16 on rows and columns of the matrix. In the last step we consider the symmetric group S256, and positions of the elements of the matrix obtained in step 2 are changed by its certain permutations to construct the suggested S-box. The strength of our S-box to work against cryptanalysis is checked through various tests. The results are then compared with the famous S-boxes. The comparison shows that the ability of our S-box to create confusion is better than most of the famous S-boxes.

scholarly journals Generalized Pattern Avoidance Condition for the Wreath Product of Cyclic Groups with Symmetric Groups

2013 ◽  
Vol 2013 ◽  
pp. 1-17
Author(s):  
Sergey Kitaev ◽  
Jeffrey Remmel ◽  
Manda Riehl
Keyword(s):  
Symmetric Group ◽  
Wreath Product ◽  
Cyclic Group ◽  
Generating Functions ◽  
Symmetric Groups ◽  
Pattern Avoidance ◽  
Catalan Numbers ◽  
Cyclic Groups ◽  
Bijective Proof ◽  
Avoidance Condition

We continue the study of the generalized pattern avoidance condition for Ck≀Sn, the wreath product of the cyclic group Ck with the symmetric group Sn, initiated in the work by Kitaev et al., In press. Among our results, there are a number of (multivariable) generating functions both for consecutive and nonconsecutive patterns, as well as a bijective proof for a new sequence counted by the Catalan numbers.

scholarly journals 4, 8, 32, 64 bit Substitution Box generation using Irreducible or Reducible Polynomials over Galois Field GF(pq)

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Boolean Functions ◽  
Galois Field ◽  
Data Encryption ◽  
First Century ◽  
Additive Constant ◽  
Substitution Box ◽  
Data Encryption Standard ◽  
Substitution Boxes ◽  
Early Twenty ◽  
Encryption And Decryption

Substitution Box or S-Box had been generated using 4-bit Boolean Functions (BFs) for Encryption and Decryption Algorithm of Lucifer and Data Encryption Standard (DES) in late sixties and late seventies respectively. The S-Box of Advance Encryption Standard have also been generated using Irreducible Polynomials over Galois field GF(28) adding an additive constant in early twenty first century. In this paper Substitution Boxes have been generated from Irreducible or Reducible Polynomials over Galois field GF(pq). Binary Galois fields have been used to generate Substitution Boxes. Since the Galois Field Number or the Number generated from coefficients of a polynomial over a particular Binary Galois field (2q) is similar to log2q+1 bit BFs. So generation of log2q+1 bit S-Boxes is possible. Now if p = prime or non-prime number then generation of S-Boxes is possible using Galois field GF (pq ), where q = p-1.

scholarly journals 4, 8, 32, 64 bit Substitution Box generation using Irreducible or Reducible Polynomials over Galois Field GF(pq)

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Boolean Functions ◽  
Galois Field ◽  
Data Encryption ◽  
First Century ◽  
Additive Constant ◽  
Substitution Box ◽  
Data Encryption Standard ◽  
Substitution Boxes ◽  
Early Twenty ◽  
Encryption And Decryption

Substitution Box or S-Box had been generated using 4-bit Boolean Functions (BFs) for Encryption and Decryption Algorithm of Lucifer and Data Encryption Standard (DES) in late sixties and late seventies respectively. The S-Box of Advance Encryption Standard have also been generated using Irreducible Polynomials over Galois field GF(28) adding an additive constant in early twenty first century. In this paper Substitution Boxes have been generated from Irreducible or Reducible Polynomials over Galois field GF(pq). Binary Galois fields have been used to generate Substitution Boxes. Since the Galois Field Number or the Number generated from coefficients of a polynomial over a particular Binary Galois field (2q) is similar to log2q+1 bit BFs. So generation of log2q+1 bit S-Boxes is possible. Now if p = prime or non-prime number then generation of S-Boxes is possible using Galois field GF (pq ), where q = p-1.

Construction of New S-Boxes Over Finite Field and Their Application to Watermarking

2012 ◽  
Vol 67 (12) ◽  
pp. 705-710 ◽  
Author(s):  
Iqtadar Hussain ◽  
Tariq Shah ◽  
Muhammad Asif Gondal ◽  
Hasan Mahmood
Keyword(s):  
Correlation Energy ◽  
Signal To Noise Ratio ◽  
Structural Similarity ◽  
Galois Field ◽  
Substitution Box ◽  
Signal To Noise ◽  
Absolute Deviation ◽  
Copyright Information ◽  
Substitution Boxes ◽  
Paradigm Analysis

In this work, we develop an imperceptible watermarking technique for images that employ substitution boxes constructed over Galois field GF(24). The strength of the proposed substitution box (S-box) is analyzed and its suitability is investigated for watermarking applications by applying statistical methods, which include entropy, contrast, correlation, energy, homogeneity, mean of absolute deviation (MAD), mean square error (MSE), peak-to-peak signal to noise ratio (PSNR), and structural similarity (SSIM) paradigm analysis. The application of the proposed S-box is presented for embedding copyright information in images.

Unitary Representations of Generalized Symmetric Groups

1969 ◽  
Vol 21 ◽  
pp. 28-38 ◽  
Author(s):  
B. M. Puttaswamaiah
Keyword(s):  
Normal Subgroup ◽  
Symmetric Group ◽  
Permutation Group ◽  
Direct Product ◽  
Cyclic Group ◽  
Symmetric Groups ◽  
Unitary Representations ◽  
Complex Field ◽  
Permutation Matrices ◽  
Image Position

In this paper all representations are over the complex field K. The generalized symmetric group S(n, m) of order n!mn is isomorphic to the semi-direct product of the group of n × n diagonal matrices whose rath powers are the unit matrix by the group of all n × n permutation matrices over K. As a permutation group, S(n, m) consists of all permutations of the mn symbols {1, 2, …, mn} which commute withObviously, S (1, m) is a cyclic group of order m, while S(n, 1) is the symmetric group of order n!. If ci = (i, n+ i, …, (m – 1)n+ i) andthen {c1, c2, …, cn} generate a normal subgroup Q(n) of order mn and {s1, s2, …, sn…1} generate a subgroup S(n) isomorphic to S(n, 1).

Martin Shapiro: An Appreciation

The Forum ◽  
2016 ◽  
Vol 14 (2) ◽  
Author(s):  
R. Shep Melnick
Keyword(s):  
Institutional Environment ◽  
Empirical Studies ◽  
The Political ◽  
Public Officials ◽  
Thick Description ◽  
Past Half Century ◽  
The Us ◽  
The Matrix ◽  
The One ◽  
Better Than

AbstractOver the past half century no judicial politics scholar has been more respected or influential than Martin Shapiro. Yet it is hard to identify a school of thought one could call “Shapiroism.” Rather than offer convenient methodologies or grand theories, Shapiro provides rich empirical studies that show us how to think about the relationship between law and courts on the one hand and politics and governing on the other. Three key themes run through Shapiro’s impressive oevre. First, rather than study courts in isolation, political scientists should view them as “one government agency among many,” and seek to “integrate the judicial system in the matrix of government and politics in which it actually operates.” Law professors may understand legal doctrines better than political scientists, but we know (or should know) the rest of the political system better than they do. Second, although judges inevitably make political decisions, their institutional environment leads them to act differently from other public officials. Most importantly, their legitimacy rests on their perceived impartiality within the plaintiff-defendant-judge triad. The conflict between judges’ role as impartial arbiter and enforcer of the laws of the regime can never be completely resolved and places powerful constraints on their actions. Third, the best way to understand the complex relationship between courts and other elements of the regime is comparative analysis. Shapiro played a major role in resuscitating comparative law, especially in his work comparing the US and the EU. All this he did with a rare combination of thick description and crisp, jargon-free analysis, certainly a rarity the political science of our time.

scholarly journals Computing mu-values for Representations of Symmetric Groups in Engineering Systems

2018 ◽  
Vol 11 (3) ◽  
pp. 774-792
Author(s):  
Mutti-Ur Rehman ◽  
M. Fazeel Anwar
Keyword(s):  
Control Systems ◽  
Symmetric Groups ◽  
Singular Values ◽  
Linear Control ◽  
Linear Control Systems ◽  
Complex Numbers ◽  
Engineering Systems ◽  
Matrix Representations ◽  
The Matrix

In this article we consider the matrix representations of finite symmetric groups Sn over the filed of complex numbers. These groups and their representations also appear as symmetries of certain linear control systems [5]. We compute the structure singular values (SSV) of the matrices arising from these representations. The obtained results of SSV are compared with well-known MATLAB routine mussv.

scholarly journals ВДОСКОНАЛЕНА ПОЛІНОМІАЛЬНО-СКЛАДНА АТАКА ВІДНОВЛЕННЯ ВІДКРИТОГО ТЕКСТУ НА РАНЦЕВИЙ ШИФР НА ОСНОВІ МАТРИЦЬ

2020 ◽  
pp. 67-74
Author(s):  
Олексій Сергійович Вамболь
Keyword(s):  
Discrete Logarithm ◽  
Public Information ◽  
Galois Field ◽  
Secret Key ◽  
The Matrix ◽  
Encryption Schemes ◽  
Shared Secret ◽  
Symmetric Key ◽  
Asymmetric Encryption ◽  
The Given

Asymmetric ciphers are widely used to ensure the confidentiality of data transmission via insecure channels. These cryptosystems allow the interacting parties to create a shared secret key for a symmetric cipher in such a way that an eavesdropper gets no information useful for cryptanalysis. Network security protocols that use asymmetric ciphers include TLS, S/MIME, OpenPGP, Tor, and many others. Some of the asymmetric encryption schemes are homomorphic, that is, that they allow calculations on encrypted data to be performed without preliminary decryption. The aforesaid property makes possible using these cryptosystems not only for symmetric key establishment but also in several areas of application, in particular in secret voting protocols and cloud computing. The matrix-based knapsack cipher is a new additively homomorphic asymmetric encryption scheme, which is based on the properties of isomorphic transformations of the inner direct product of diagonal subgroups of a general linear group over a Galois field. Unlike classic knapsack encryption schemes, the cryptographic strength of this cipher depends on the computational complexity of the multidimensional discrete logarithm problem. Despite some useful properties, further research into the cryptographic strength of the matrix-based knapsack cipher has found serious drawbacks inherent in this cryptographic scheme. In the given paper an improved polynomial-time plaintext-recovery attack on the matrix-based knapsack cipher is proposed. Applying this cryptanalytic method requires only public information and has time complexity O(t1.34), where t denotes the decryption time of the attacked cryptosystem. The aforementioned attack is more productive and easier to implement in software in comparison with the original one. The advantages of the proposed method are due to using in its algorithm the simple and relatively fast matrix trace operation instead of more complex and slower transformations.

Machinability and Microstructure of SiC/h-BN Nano-Composites

2008 ◽  
Vol 569 ◽  
pp. 45-48
Author(s):  
Hai Yun Jin ◽  
Guan Jun Qiao ◽  
Zong Ren Peng ◽  
Ji Qiang Gao
Keyword(s):  
Fracture Strength ◽  
Nano Composites ◽  
Weak Interface ◽  
X Ray Diffraction ◽  
X Ray ◽  
Sic Particles ◽  
N2 Atmosphere ◽  
The Matrix ◽  
Better Than

SiC particles coated with nano-BN were synthesized and the machinable SiC/BN ceramic nano-composites were fabricated by Plasma Active Sintering (PAS) in N2 atmosphere. The existing and distribution of h-BN phase were revealed by X-ray diffraction (XRD), and SEM. For the existing of weak interface between h-BN and SiC grains, the machinability of both SiC/BN micro-composites and nano-composites were improved obviously. Because the nano-sized h-BN crystals were homogeneously dispersed around the SiC grains of the matrix, the fracture strength of the nano-composites was better than the SiC/h-BN micro-composite.

scholarly journals Certain unitary representations of the infinite symmetric group, II

1987 ◽  
Vol 106 ◽  
pp. 143-162 ◽  
Author(s):  
Nobuaki Obata
Keyword(s):  
Symmetric Group ◽  
Discrete Group ◽  
Inductive Limit ◽  
Symmetric Groups ◽  
Discrete Groups ◽  
Type I ◽  
Infinite Symmetric Group ◽  
Locally Finite ◽  
Distinctive Features ◽  
Infinite Dimensional

The infinite symmetric group is the discrete group of all finite permutations of the set X of all natural numbers. Among discrete groups, it has distinctive features from the viewpoint of representation theory and harmonic analysis. First, it is one of the most typical ICC-groups as well as free groups and known to be a group of non-type I. Secondly, it is a locally finite group, namely, the inductive limit of usual symmetric groups . Furthermore it is contained in infinite dimensional classical groups GL(ξ), O(ξ) and U(ξ) and their representation theories are related each other.

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