scholarly journals Construction of an S-Box Based on Chaotic and Bent Functions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 671
Author(s):  
Zijing Jiang ◽  
Qun Ding
Keyword(s):  
Chaos Theory ◽  
Boolean Functions ◽  
Security Analysis ◽  
Bent Function ◽  
Bent Functions ◽  
Encryption Algorithm ◽  
Symmetric Encryption ◽  
Differential Uniformity ◽  
Strict Avalanche Criterion ◽  
Independence Criterion

An S-box is the most important part of a symmetric encryption algorithm. Various schemes are put forward by using chaos theory. In this paper, a construction method of S-boxes with good cryptographic properties is proposed. The output of an S-box can be regarded as a group of Boolean functions. Therefore, we can use the different properties of chaos and Bent functions to generate a random Bent function with a high nonlinearity. By constructing a set of Bent functions as the output of an S-box, we can create an S-box with good cryptological properties. The nonlinearity, differential uniformity, strict avalanche criterion and the independence criterion of output bits are then analyzed and tested. A security analysis shows that the proposed S-box has excellent cryptographic properties.

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 Evolving Dynamic S-Boxes Using Fractional-Order Hopfield Neural Network Based Scheme

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 717 ◽  
Author(s):  
Musheer Ahmad ◽  
Eesa Al-Solami
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Hopfield Neural Network ◽  
Performance Assessments ◽  
Comparison Analysis ◽  
Differential Uniformity ◽  
High Nonlinearity ◽  
Substitution Boxes ◽  
Strict Avalanche Criterion ◽  
Independence Criterion

Static substitution-boxes in fixed structured block ciphers may make the system vulnerable to cryptanalysis. However, key-dependent dynamic substitution-boxes (S-boxes) assume to improve the security and robustness of the whole cryptosystem. This paper proposes to present the construction of key-dependent dynamic S-boxes having high nonlinearity. The proposed scheme involves the evolution of initially generated S-box for improved nonlinearity based on the fractional-order time-delayed Hopfield neural network. The cryptographic performance of the evolved S-box is assessed by using standard security parameters, including nonlinearity, strict avalanche criterion, bits independence criterion, differential uniformity, linear approximation probability, etc. The proposed scheme is able to evolve an S-box having mean nonlinearity of 111.25, strict avalanche criteria value of 0.5007, and differential uniformity of 10. The performance assessments demonstrate that the proposed scheme and S-box have excellent features, and are thus capable of offering high nonlinearity in the cryptosystem. The comparison analysis further confirms the improved security features of anticipated scheme and S-box, as compared to many existing chaos-based and other S-boxes.

scholarly journals Generation Of Numerous S-Box for Advanced Encryption Standard

2019 ◽  
Vol 8 (2S4) ◽  
pp. 125-127
Keyword(s):  
Linear Part ◽  
Encryption Algorithm ◽  
Advanced Encryption Standard ◽  
Symmetric Encryption ◽  
Substitution Box ◽  
Text And Image ◽  
Differential Approximation ◽  
Strength Differential ◽  
Non Linear ◽  
Independence Criterion

Substitution box is the non-linear part in Symmetric Encryption Algorithm. It gives the various alternate methods for the construction of S-Box by taking AES Substitution Box as base or modified version of AES S-Box. Hence it is proving that either AES S-box or modified version such as Gray S-Box, S8 S-Box is also satisfying the important parameters of S-Box such as nonlinearity, SAC, Bit Independence Criterion, Diffusion Strength, Differential Approximation probability while we are encrypting both the text and image

scholarly journals Construction of S-Box Based on Chaotic Map and Algebraic Structures

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 351 ◽  
Author(s):  
Iqtadar Hussain ◽  
Amir Anees ◽  
Temadher Al-Maadeed ◽  
Muhammad Mustafa
Keyword(s):  
Chaotic Map ◽  
Logistic Map ◽  
Symmetric Encryption ◽  
Secret Key ◽  
Substitution Box ◽  
Differential Approximation ◽  
Security Applications ◽  
Strict Avalanche Criterion ◽  
Main Component ◽  
Independence Criterion

The Advanced Encryption Standard (AES) is widely used in different kinds of security applications. The substitution box (S-box) is the main component of many modern symmetric encryption ciphers that provides confusion between the secret key and ciphertext. The S-box component that is used in AES is fixed. If we construct this component dynamically, the encryption strength of AES would be greater than before. In this manuscript, we used chaotic logistic map, Mobius transformation and symmetric group S 256 to construct S-box for AES. The idea behind the proposed work is to make supplementary safe S-box. The presented S-box is analyzed for the following analyses: linear approximation probability (LP), nonlinearity (NL), differential approximation probability (DP), strict avalanche criterion (SAC), and bit independence criterion (BIC). The analyses show that the proposed technique is useful in generating high resistance S-box to known attacks.

Research on Design and Construction Method of Bent Functions

2014 ◽  
Vol 571-572 ◽  
pp. 114-117
Author(s):  
Guang Xue Meng ◽  
Yan Guang Shen ◽  
Tao Jiang
Keyword(s):  
Projective Geometry ◽  
Boolean Functions ◽  
Construction Method ◽  
Bent Function ◽  
Bent Functions ◽  
C Language ◽  
Walsh Spectra ◽  
Algebra Method ◽  
Design And Construction

Bent function is a class of the highest nonlinear Boolean functions. In this paper three methods of design and construction are discussed with examples, which are algebra method, the character function in projective geometry and random researching method. Also, the Bent function of class is implemented with C language. At last, the concatenate construction from m = 2n-k Bent functions of k variables to a Bent function of n variables is given and verified with Walsh spectra.

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.

A Note for Order-Preserving Encryption Based on Negative Hypergeometric Distribution

2014 ◽  
Vol 926-930 ◽  
pp. 2478-2481
Author(s):  
Dong Ping Hu ◽  
Yuan Ping Zhu ◽  
Ai Hua Yin
Keyword(s):  
Security Analysis ◽  
Hypergeometric Distribution ◽  
Encryption Algorithm ◽  
Encryption Scheme ◽  
Symmetric Encryption ◽  
Sampling Algorithm ◽  
Negative Hypergeometric Distribution ◽  
Proof Procedure

Order-preserving encryption (OPE) scheme is a deterministic symmetric encryption scheme whose encryption algorithm produces ciphertexts that preserves numerical ordering of the plaintexts. The cryptographic study of OPE was initiated by Boldyreva, Chenette, Lee, and ONeill [1]. They proposed an OPE scheme based on a sampling algorithm for the negative hypergeometric distribution (NHGD). In this paper, we present the security analysis of NHGD-based OPE and the proof procedure of efficiency.

scholarly journals State of the ART in Boolean Functions Cryptographic Assessment

2013 ◽  
Vol 1 (2013) ◽  
pp. 88-94
Keyword(s):  
Boolean Functions ◽  
State Of The Art ◽  
Encryption Algorithm ◽  
Symmetric Encryption

Boolean functions play important role in cryptography, since in convention a symmetric encryption algorithm can be designed by composing Boolean functions satisfying good cryptographic criteria. In this paper; state of the art in mathematical and practical study of the most important cryptographic criteria of Boolean functions and how to implement algorithms that fulfill these criteria are introduced. Also; the most known constructions for generating Boolean functions that satisfy good cryptographic criteria are summarized

On Walsh Spectrum of Cryptographic Boolean Function

2017 ◽  
Vol 67 (5) ◽  
pp. 536
Author(s):  
Shashi Kant Pandey ◽  
B. K. Dass
Keyword(s):  
Boolean Function ◽  
General Expression ◽  
Significant Role ◽  
Boolean Functions ◽  
Diophantine Equations ◽  
Bent Function ◽  
Bent Functions ◽  
Necessary Condition ◽  
Walsh Spectrum ◽  
Walsh Transformation

<p>Walsh transformation of a Boolean function ascertains a number of cryptographic properties of the Boolean function viz, non-linearity, bentness, regularity, correlation immunity and many more. The functions, for which the numerical value of Walsh spectrum is fixed, constitute a class of Boolean functions known as bent functions. Bent functions possess maximum possible non-linearity and therefore have a significant role in design of cryptographic systems. A number of generalisations of bent function in different domains have been proposed in the literature. General expression for Walsh transformation of generalised bent function (GBF) is derived. Using this condition, a set of Diophantine equations whose solvability is a necessary condition for the existence of GBF is also derived. Examples to demonstrate how these equations can be utilised to establish non-existence and regularity of GBFs is presented.</p>

A Novel Image Encryption Algorithm Using Multiple Encryption Techniques for Mobile Devices

2020 ◽  
Vol 10 (2) ◽  
pp. 123-142
Author(s):  
Showkat Ahmad Bhat ◽  
Amandeep Singh
Keyword(s):  
Wireless Communication ◽  
Communication Networks ◽  
Image Encryption ◽  
High Speed ◽  
Security Analysis ◽  
Encryption Algorithm ◽  
Multiple Encryption ◽  
Communication Devices ◽  
Cryptographic Attacks ◽  
Image Encryption Algorithm

Background & Objective: Digital multimedia exchange between different mobile communication devices has increased rapidly with the invention of the high-speed data services like LTE-A, LTE, and WiMAX. However, there are always certain security risks associated with the use of wireless communication technologies. Methods: To protect the digital images against cryptographic attacks different image encryption algorithms are being employed in the wireless communication networks. These algorithms use comparatively less key spaces and accordingly offer inadequate security. The proposed algorithm described in this paper based on Rubik’s cube principle because of its high confusion and diffusion properties, Arnold function having effective scrambling power, blocking cipher with block encryption and permutation powers. The main strength of the proposed algorithm lies in the large key spaces and the combination of different high power encryption techniques at each stage of algorithm. The different operations employed on the image are with four security keys of different key spaces at multiple stages of the algorithm. Results & Conclusion: Finally, the effectiveness and the security analysis results shows that the proposed image encryption algorithm attains high encryption and security capabilities along with high resistance against cryptanalytic attacks, differential attacks and statistical attacks.

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