scholarly journals A Novel Construction of Efficient Substitution-Boxes Using Cubic Fractional Transformation

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 245 ◽  
Author(s):  
Amjad Zahid ◽  
Muhammad Arshad ◽  
Musheer Ahmad
Keyword(s):  
Block Cipher ◽  
Block Ciphers ◽  
Performance Criteria ◽  
Differential Approximation ◽  
Effective Technique ◽  
Avalanche Effect ◽  
Substitution Boxes ◽  
Performance Results ◽  
Symmetric Block ◽  
Independence Criterion

A symmetric block cipher employing a substitution–permutation duo is an effective technique for the provision of information security. For substitution, modern block ciphers use one or more substitution boxes (S-Boxes). Certain criteria and design principles are fulfilled and followed for the construction of a good S-Box. In this paper, an innovative technique to construct substitution-boxes using our cubic fractional transformation (CFT) is presented. The cryptographic strength of the proposed S-box is critically evaluated against the state of the art performance criteria of strong S-boxes, including bijection, nonlinearity, bit independence criterion, strict avalanche effect, and linear and differential approximation probabilities. The performance results of the proposed S-Box are compared with recently investigated S-Boxes to prove its cryptographic strength. The simulation and comparison analyses validate that the proposed S-Box construction method has adequate efficacy to generate efficient candidate S-Boxes for usage in block ciphers.

scholarly journals An Innovative Design of Substitution-Boxes Using Cubic Polynomial Mapping

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 437 ◽  
Author(s):  
Amjad Zahid ◽  
Muhammad Arshad
Keyword(s):  
Input Sequence ◽  
Performance Criteria ◽  
Polynomial Mapping ◽  
Differential Uniformity ◽  
Construction Technique ◽  
Avalanche Effect ◽  
Innovative Design ◽  
Substitution Boxes ◽  
Cubic Polynomial ◽  
Performance Results

In this paper, we propose to present a novel technique for designing cryptographically strong substitution-boxes using cubic polynomial mapping. The proposed cubic polynomial mapping is proficient to map the input sequence to a strong 8 × 8 S-box meeting the requirements of a bijective function. The use of cubic polynomial maintains the simplicity of S-box construction method and found consistent when compared with other existing S-box techniques used to construct S-boxes. An example proposed S-box is obtained which is analytically evaluated using standard performance criteria including nonlinearity, bijection, bit independence, strict avalanche effect, linear approximation probability, and differential uniformity. The performance results are equated with some recently scrutinized S-boxes to ascertain its cryptographic forte. The critical analyses endorse that the proposed S-box construction technique is considerably innovative and effective to generate cryptographic strong substitution-boxes.

scholarly journals Crypto-Archaeology: unearthing design methodology of DES s-boxes

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Design Methodology ◽  
Block Cipher ◽  
Block Ciphers ◽  
Public Domain ◽  
Differential Cryptanalysis ◽  
Linear Cryptanalysis ◽  
Strict Avalanche Criterion ◽  
Independence Criterion

US defence sponsored the DES program in 1974 and released it in 1977. It remained as a well-known and well accepted block cipher until 1998. Thirty-two 4-bit DES S-Boxes are grouped in eight each with four and are put in public domain without any mention of their design methodology. S-Boxes, 4-bit, 8-bit or 32-bit, find a permanent seat in all future block ciphers. In this paper, while looking into the design methodology of DES S-Boxes, we find that S-Boxes have 128 balanced and non-linear Boolean Functions, of which 102 used once, while 13 used twice and 92 of 102 satisfy the Boolean Function-level Strict Avalanche Criterion. All the S-Boxes satisfy the Bit Independence Criterion. Their Differential Cryptanalysis exhibits better results than the Linear Cryptanalysis. However, no S-Boxes satisfy the S-Box-level SAC analyses. It seems that the designer emphasized satisfaction of Boolean-Function-level SAC and S-Box-level BIC and DC, not the S-Box-level LC and SAC.

scholarly journals On the semantic security of cellular automata based pseudo-random permutation using results from the Luby-Rackoff construction

2015 ◽  
Vol 15 (1) ◽  
pp. 21
Author(s):  
Kamel Mohammed Faraoun
Keyword(s):  
Cellular Automata ◽  
Block Cipher ◽  
Random Permutation ◽  
Block Ciphers ◽  
Random Permutations ◽  
Semantic Security ◽  
Transition Rules ◽  
Reversible Cellular Automata ◽  
Symmetric Block ◽  
Number Of Iterations

This paper proposes a semantically secure construction of pseudo-random permutations using second-order reversible cellular automata. We show that the proposed construction is equivalent to the Luby-Rackoff model if it is built using non-uniform transition rules, and we prove that the construction is strongly secure if an adequate number of iterations is performed. Moreover, a corresponding symmetric block cipher is constructed and analysed experimentally in comparison with popular ciphers. Obtained results approve robustness and efficacy of the construction, while achieved performances overcome those of some existing block ciphers.

A Novel Approach for Designing Dynamical S-Boxes Using Hyperchaotic System

2012 ◽  
Vol 6 (1) ◽  
pp. 100-119 ◽  
Author(s):  
Jun Peng ◽  
Du Zhang ◽  
Xiaofeng Liao
Keyword(s):  
Lorenz System ◽  
Initial Conditions ◽  
Hyperchaotic System ◽  
Differential Approximation ◽  
Novel Approach ◽  
Substitution Boxes ◽  
Hyperchaotic Lorenz System ◽  
Digital Image Encryption ◽  
Image Encryption Algorithm ◽  
Independence Criterion

In the information security field, the substitution boxes (S-boxes) have been extensively used in many cryptographic systems. This paper presents a novel approach for generating dynamically cryptographically S-boxes using a four-dimensional hyperchaotic Lorenz system. Within the algorithm, the initial condition is employed to drive the hyper-chaotic system to generate a chaotic sequence which is used to construct a chaotic key-dependent S-box. With different system initial conditions, many of distinct S-boxes can be obtained dynamically. Some cryptographic properties for a good S-box such as bijection, nonlinearity, SAC (Strict Avalanche Criterion), BIC (Bit Independence Criterion), and differential approximation probability are found to hold in the obtained S-boxes. The analytic results indicated that all the criteria for designing strong S-boxes can be achieved. The comparison of the proposed method for generating S-boxes with other chaos-based schemes indicates that our S-boxes have a better performance with respect to some properties. Finally, the authors give an example of a digital image encryption algorithm using their S-box and the results of image statistical analysis show that the algorithm has the desirable cryptographic properties.

scholarly journals Computing Symmetric Block Cipher Using Linear Algebraic Equation

2011 ◽  
pp. 7-11
Author(s):  
Pradeep Kumar Mallick ◽  
N.K. kamila ◽  
S. Patnaik
Keyword(s):  
Algebraic Equation ◽  
Linear Algebraic Equation ◽  
Block Cipher ◽  
Block Ciphers ◽  
Algebraic Equations ◽  
Text File ◽  
Linear Algebraic Equations ◽  
Encryption And Decryption ◽  
Current Algorithm ◽  
Symmetric Block

In this paper, a pair of symmetric block ciphers has been developed for encryption and decryption of text file. The characters in the file are represented by the ASCII codes. A substitution table and a reverse substitution table are formed by using a key. The process of encryption and decryption is carried by using linear algebraic equations. However, the cryptanalysis has been discussed for establishing the strength of the algorithm. Result and analysis exhibits that the current algorithm works well and more secured to break the cipher.

scholarly journals SITM: See-In-The-Middle Side-Channel Assisted Middle Round Differential Cryptanalysis on SPN Block Ciphers

2019 ◽  
pp. 95-122
Author(s):  
Shivam Bhasin ◽  
Jakub Breier ◽  
Xiaolu Hou ◽  
Dirmanto Jap ◽  
Romain Poussier ◽  
...  
Keyword(s):  
Block Cipher ◽  
State Of The Art ◽  
Block Ciphers ◽  
Differential Cryptanalysis ◽  
Side Channel ◽  
Secret Key ◽  
Side Channel Analysis ◽  
Cryptographic Algorithms ◽  
Channel Analysis ◽  
Symmetric Block

Side-channel analysis constitutes a powerful attack vector against cryptographic implementations. Techniques such as power and electromagnetic side-channel analysis have been extensively studied to provide an efficient way to recover the secret key used in cryptographic algorithms. To protect against such attacks, countermeasure designers have developed protection methods, such as masking and hiding, to make the attacks harder. However, due to significant overheads, these protections are sometimes deployed only at the beginning and the end of encryption, which are the main targets for side-channel attacks.In this paper, we present a methodology for side-channel assisted differential cryptanalysis attack to target middle rounds of block cipher implementations. Such method presents a powerful attack vector against designs that normally only protect the beginning and end rounds of ciphers. We generalize the attack to SPN based ciphers and calculate the effort the attacker needs to recover the secret key. We provide experimental results on 8-bit and 32-bit microcontrollers. We provide case studies on state-of-the-art symmetric block ciphers, such as AES, SKINNY, and PRESENT. Furthermore, we show how to attack shuffling-protected implementations.

A Method for Security Estimation of the Spn-Based Block Cipher Against Related-Key Attacks

2014 ◽  
Vol 60 (1) ◽  
pp. 25-45 ◽  
Author(s):  
Dmytro Kaidalov ◽  
Roman Oliynykov ◽  
Oleksandr Kazymyrov
Keyword(s):  
Block Cipher ◽  
Block Ciphers ◽  
Message Authentication ◽  
Brute Force ◽  
Symmetric Encryption ◽  
Authentication Codes ◽  
Cryptographic Primitives ◽  
Encryption Algorithms ◽  
Brute Force Attack ◽  
Symmetric Block

Abstract Symmetric block ciphers are the most widely used cryptographic primitives. In addition to providing privacy, block ciphers are used as basic components in the construction of hash functions, message authentication codes, pseudorandom number generators, as a part of various cryptographic protocols, etc. Nowadays the most popular block cipher is AES (Advanced Encryption Standard). It is used as a standard of symmetric encryption in many countries. Several years ago it was found a theoretical attack exploiting the AES key expansion algorithm that allows reducing significantly the complexity comparing to the brute force attack. This article presents an advanced method of finding the number of active substitutions that helps to estimate the security of encryption algorithms against related-key attacks. The method was applied to a prospective block cipher, which is a candidate for the Ukrainian standard

scholarly journals Crypto-Archaeology: unearthing design methodology of DES s-boxes

2017 ◽  
Author(s):  
Sankhanil Dey ◽  
Ranjan Ghosh
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Design Methodology ◽  
Block Cipher ◽  
Block Ciphers ◽  
Public Domain ◽  
Differential Cryptanalysis ◽  
Linear Cryptanalysis ◽  
Strict Avalanche Criterion ◽  
Independence Criterion

US defence sponsored the DES program in 1974 and released it in 1977. It remained as a well-known and well accepted block cipher until 1998. Thirty-two 4-bit DES S-Boxes are grouped in eight each with four and are put in public domain without any mention of their design methodology. S-Boxes, 4-bit, 8-bit or 32-bit, find a permanent seat in all future block ciphers. In this paper, while looking into the design methodology of DES S-Boxes, we find that S-Boxes have 128 balanced and non-linear Boolean Functions, of which 102 used once, while 13 used twice and 92 of 102 satisfy the Boolean Function-level Strict Avalanche Criterion. All the S-Boxes satisfy the Bit Independence Criterion. Their Differential Cryptanalysis exhibits better results than the Linear Cryptanalysis. However, no S-Boxes satisfy the S-Box-level SAC analyses. It seems that the designer emphasized satisfaction of Boolean-Function-level SAC and S-Box-level BIC and DC, not the S-Box-level LC and SAC.

scholarly journals S-box Construction Based on Linear Fractional Transformation and Permutation Function

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 826 ◽  
Author(s):  
Liyana Chew Nizam Chew ◽  
Eddie Shahril Ismail
Keyword(s):  
Irreducible Polynomial ◽  
Galois Field ◽  
Block Ciphers ◽  
Linear Fractional Transformation ◽  
Construction Technique ◽  
Avalanche Effect ◽  
Substitution Boxes ◽  
Before And After ◽  
Nonlinearity Test ◽  
Security Properties

Substitution boxes (S-box) with strong and secure cryptographic properties are widely used for providing the key property of nonlinearity in block ciphers. This is critical to be resistant to a standard attack including linear and differential cryptanalysis. The ability to create a cryptographically strong S-box depends on its construction technique. This work aims to design and develop a cryptographically strong 8 × 8 S-box for block ciphers. In this work, the construction of the S-box is based on the linear fractional transformation and permutation function. Three steps involved in producing the S-box. In step one, an irreducible polynomial of degree eight is chosen, and all roots of the primitive irreducible polynomial are calculated. In step two, algebraic properties of linear fractional transformation are applied in Galois Field GF (28). Finally, the produced matrix is permuted to add randomness to the S-box. The strength of the S-box is measured by calculating its potency to create confusion. To analyze the security properties of the S-box, some well-known and commonly used algebraic attacks are used. The proposed S-box is analyzed by nonlinearity test, algebraic degree, differential uniformity, and strict avalanche criterion which are the avalanche effect test, completeness test, and strong S-box test. S-box analysis is done before and after the application of the permutation function and the analysis result shows that the S-box with permutation function has reached the optimal properties as a secure S-box.

scholarly journals The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Sajjad Shaukat Jamal ◽  
Dawood Shah ◽  
Abdulaziz Deajim ◽  
Tariq Shah
Keyword(s):  
Secure Communication ◽  
Irreducible Polynomial ◽  
Galois Field ◽  
Block Ciphers ◽  
Affine Transformations ◽  
Differential Approximation ◽  
Irreducible Polynomials ◽  
Substitution Boxes ◽  
Nonlinearity Test ◽  
Galois Field Extensions

Substitution boxes are the only nonlinear component of the symmetric key cryptography and play a key role in the cryptosystem. In block ciphers, the S-boxes create confusion and add valuable strength. The majority of the substitution boxes algorithms focus on bijective Boolean functions and primitive irreducible polynomial that generates the Galois field. For binary field F2, there are exactly 16 primitive irreducible polynomials of degree 8 and it prompts us to construct 16 Galois field extensions of order 256. Conventionally, construction of affine power affine S-box is based on Galois field of order 256, depending on a single degree 8 primitive irreducible polynomial over ℤ2. In this manuscript, we study affine power affine S-boxes for all the 16 distinct degree 8 primitive irreducible polynomials over ℤ2 to propose 16 different 8×8 substitution boxes. To perform this idea, we introduce 16 affine power affine transformations and, for fixed parameters, we obtained 16 distinct S-boxes. Here, we thoroughly study S-boxes with all possible primitive irreducible polynomials and their algebraic properties. All of these boxes are evaluated with the help of nonlinearity test, strict avalanche criterion, bit independent criterion, and linear and differential approximation probability analyses to measure the algebraic and statistical strength of the proposed substitution boxes. Majority logic criterion results indicate that the proposed substitution boxes are well suited for the techniques of secure communication.

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