scholarly journals A Novel Algebraic Technique for Design of Computational Substitution-Boxes Using Action of Matrices on Galois Field

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 197630-197643 ◽  
Author(s):  
Nasir Siddiqui ◽  
Hira Khalid ◽  
Fiza Murtaza ◽  
Muhammad Ehatisham-Ul-Haq ◽  
Muhammad Awais Azam
Keyword(s):  
Galois Field ◽  
Substitution Boxes ◽  
Algebraic Technique

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 A review of cryptographic properties of S-boxes with generation and analysis of crypto secure S-boxes.

2018 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Detailed Analysis ◽  
Boolean Functions ◽  
Public Key Cryptography ◽  
Galois Field ◽  
Data Encryption ◽  
Public Key ◽  
Data Encryption Standard ◽  
Detailed Review ◽  
Substitution Boxes ◽  
Modern Cryptography

In modern as well as ancient ciphers of public key cryptography, substitution boxes find a permanent seat. Generation and cryptanalysis of 4-bit as well as 8-bit crypto S-boxes is of utmost importance in modern cryptography. In this paper, a detailed review of cryptographic properties of S-boxes has been illustrated. The generation of crypto S-boxes with 4-bit as well as 8-bit Boolean functions (BFs) and Polynomials over Galois field GF(p q ) has also been of keen interest of this paper. The detailed analysis and comparisonof generated 4-bit and 8-bit S-boxes with 4-bit as well as 8-bit S-boxes of Data Encryption Standard (DES) and Advance Encryption Standard (AES) respectively, has incorporated with example. Detailed analysis of generated S-boxes claims a better result than DES and AES in view of security of crypto S-boxes.

scholarly journals An Efficient Information Hiding Mechanism Based on Confusion Component over Local Ring and Moore-Penrose Pseudo Inverse

2021 ◽  
Vol 20 ◽  
pp. 24-36
Author(s):  
Nabilah Abughazalah ◽  
Majid Khan
Keyword(s):  
Present Article ◽  
Local Ring ◽  
Information Hiding ◽  
Galois Field ◽  
Ring Structure ◽  
Basic Requirement ◽  
Secret Information ◽  
Substitution Boxes ◽  
Efficient Information ◽  
Pseudo Inverse

The basic requirement by adding confusion is to ensure the confidentiality of the secret information. In the present article, we have suggested new methodology for the construction of nonlinear confusion component. This confusion component is used for enciphering the secret information and hiding it in a cover medium by proposed scheme. The proposed scheme is based on ring structure instead of Galois field mechanism. To provide multi-layer security, secret information is first encrypted by using confusion component and then utilized three different substitution boxes (S-boxes) to hide into the cover medium

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.

Mathematical Method to Search for Monic Irreducible Polynomials with Decimal Equivalents of Polynomials over Galois Field GF(pq)

2017 ◽  
Vol 2 (11) ◽  
pp. 17-22
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Mathematical Method ◽  
Execution Time ◽  
Galois Field ◽  
Polynomial Multiplication ◽  
Irreducible Polynomials ◽  
Multiplicative Inverse ◽  
Advance Encryption Standard ◽  
Cipher Text ◽  
Substitution Boxes ◽  
Encryption And Decryption

Substitution boxes or S-boxes play a significant role in encryption and decryption of bit level plaintext and cipher-text respectively. Irreducible Polynomials (IPs) have been used to construct 4-bit or 8-bit substitution boxes in many cryptographic block ciphers. In Advance Encryption Standard the 8-bit the elements S-box have been obtained from the Multiplicative Inverse (MI) of elemental polynomials (EPs) of the 1st IP over Galois field GF(28) by adding an additive element. In this paper a mathematical method and the algorithm of the said method with the discussion of the execution time of the algorithm, to obtain monic IPs over Galois field GF(pq) have been illustrated with example. The method is very similar to polynomial multiplication of two polynomials over Galois field GF(pq) but has a difference in execution. The decimal equivalents of polynomials have been used to identify Basic Polynomials (BPs), EPs, IPs and Reducible polynomials (RPs). The monic RPs have been determined by this method and have been cancelled out to produce monic IPs. The non-monic IPs have been obtained with multiplication of α where α GF(pq) and assume values from 2 to (p-1) to monic IPs.

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 S-Box on Subgroup of Galois Field

Cryptography ◽  
2019 ◽  
Vol 3 (2) ◽  
pp. 13
Author(s):  
Tariq Shah ◽  
Ayesha Qureshi
Keyword(s):  
Galois Field ◽  
Cryptographic Primitives ◽  
Small Unit ◽  
Nonlinear Part ◽  
Substitution Boxes ◽  
Strict Avalanche Criterion ◽  
Multiplicative Subgroup ◽  
Cryptographic Techniques ◽  
Majority Logic Criterion

In substitution–permutation network as a cryptosystem, substitution boxes play the role of the only nonlinear part. It would be easy for adversaries to compromise the security of the system without them. 8-bit S-boxes are the most used cryptographic components. So far, cryptographers were constructing 8-bit S-boxes used in cryptographic primitives by exhaustive search of permutations of order 256. However, now for cryptographic techniques with 8-bit S-boxes as confusion layers, researchers are trying to reduce the size of S-box by working with a small unit of data. The aim is to make the techniques compact, fast and elegant. The novelty of this research is the construction of S-box on the elements of the multiplicative subgroup of the Galois field instead of the entire Galois field. The sturdiness of the proposed S-box against algebraic attacks was hashed out by employing the renowned analyses, including balance, nonlinearity, strict avalanche criterion, and approximation probabilities. Furthermore, the statistical strength of the S-box was tested by the majority logic criterion. The fallouts show that the S-box is appropriate for applications for secure data communications. The S-box was also used for watermarking of grayscale images with good outcomes.

scholarly journals Multiplication and Division over Extended Galois Field GF(p^q): A new Approach to find Monic Irreducible Polynomials over any Galois Field GF(p^q).

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Efficient Algorithm ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Galois Field ◽  
Division Algorithm ◽  
Irreducible Polynomials ◽  
New Approach ◽  
Multiplication Algorithm ◽  
Research Article ◽  
Substitution Boxes

Irreducible Polynomials (IPs) have been of utmost importance in generation of substitution boxes in modern cryptographic ciphers. In this paper an algorithm entitled Composite Algorithm using both multiplication and division over Galois fields have been demonstrated to generate all monic IPs over extended Galois Field GF(p^q) for large value of both p and q. A little more efficient Algorithm entitled Multiplication Algorithm and more too Division Algorithm have been illustrated in this Paper with Algorithms to find all Monic IPs over extended Galois Field GF(p^q) for large value of both p and q. Time Complexity Analysis of three algorithms with comparison to Rabin’s Algorithms has also been exonerated in this Research Article.

scholarly journals A review of cryptographic properties of S-boxes with generation and analysis of crypto secure S-boxes.

2018 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Detailed Analysis ◽  
Boolean Functions ◽  
Public Key Cryptography ◽  
Galois Field ◽  
Data Encryption ◽  
Public Key ◽  
Data Encryption Standard ◽  
Detailed Review ◽  
Substitution Boxes ◽  
Modern Cryptography

In modern as well as ancient ciphers of public key cryptography, substitution boxes find a permanent seat. Generation and cryptanalysis of 4-bit as well as 8-bit crypto S-boxes is of utmost importance in modern cryptography. In this paper, a detailed review of cryptographic properties of S-boxes has been illustrated. The generation of crypto S-boxes with 4-bit as well as 8-bit Boolean functions (BFs) and Polynomials over Galois field GF(p q ) has also been of keen interest of this paper. The detailed analysis and comparisonof generated 4-bit and 8-bit S-boxes with 4-bit as well as 8-bit S-boxes of Data Encryption Standard (DES) and Advance Encryption Standard (AES) respectively, has incorporated with example. Detailed analysis of generated S-boxes claims a better result than DES and AES in view of security of crypto S-boxes.

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