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.

https://www.mdpi.com/2073-8994/12/5/826/pdf

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

The cryptanalytic resistance of modern block and stream encryption systems mainly depends on the substitution box (S-box). In this context, the problem is thus to create an S-box with higher value of nonlinearity because this property can provide some degree of protection against linear and differential cryptanalysis attacks. In this paper, we design a scheme built on a human behavior-based optimization algorithm, supported with Self-Organizing Maps to prevent premature convergence and improve the nonlinearity property in order to obtain strong $8 \times 8$ substitution boxes. The experiments are compared with S-boxes obtained using other metaheuristic algorithms such as Ant Colony Optimization, Genetic Algorithm and an approach based on chaotic functions and show that the obtained S-boxes have good cryptographic properties. The obtained S-box is investigated against standard tests such as bijectivity, nonlinearity, strict avalanche criterion, bit independence criterion, linear probability and differential probability, proving that the proposed scheme is proficient to discover a strong nonlinear component of encryption systems.

/pdf/human-behaviour-based-optimization-supported-with-self-4p786j2hji.pdf

Human Behaviour Based Optimization Supported With Self-Organizing Maps for Solving the S-Box Design Problem

In this paper, we propose new models for directly evaluating DPA leakage from logic information in CMOS circuits These models are based on the transition probability for each gate, and are naturally applicable to various actual devices for simulating power analysis We also report the effectiveness of the previously known enhanced DPA on our model Furthermore, we demonstrate the weakness of previously known hardware countermeasures for both our model and FPGA and suggest secure conditions for the hardware countermeasure

DPA leakage models for CMOS logic circuits

Correlation power analysis of modes of encryption in AES and its countermeasures

Affine equivalence classification of Boolean functions has significant applications in logic synthesis and cryptography. Previous studies for classification have been limited by the large set of Boolean functions and the complex operations on the affine group. Although there are many research on affine equivalence classification for parts of Boolean functions in recent years, there are very few results for the entire set of Boolean functions. The best existing result has been achieved by Harrison with 15768919 affine equivalence classes for 6-variable Boolean functions. This paper presents a concise formula for affine equivalence classification of the entire set of Boolean functions as well as a formula for affine classification of Boolean functions with distinct ON-set size respectively. The method outlined in this paper greatly simplifies the affine group's action by constructing an isomorphism mapping from the affine group to a permutation group. By this method, we can compute the affine equivalence classes for up to 10 variables. Experiment results indicate that our scheme for calculating the affine equivalence classes for more than 6 variables is a significant advancement over previous published methods.

Computing Affine Equivalence Classes of Boolean Functions by Group Isomorphism

By some basic transforms and invariant theory, we give two results: 1) an algorithm, which can be used to judge if two Boolean functions are affinely equivalent and to obtain the equivalence relationship if they are equivalent. This is useful in studying Boolean functions and in engineering. For example, we classify all 8-variable homogeneous bent functions of degree 3 into two classes; 2) Reed-Muller codes R(4,6)/R(1,6), R(3,7)/R(1,7) are classified efficiently.

Analysis of affinely equivalent Boolean functions

Based on a theorem on the construction of a permutation, we propose an evolutionary algorithm that can efficiently design S-boxes with good cryptographic properties like high nonlinearity, low autocorrelation, low difference and high algebraic immunity. Furthermore, we observe that the polynomial representing a concrete designed S-box over a small field can be generalized to that over a large field. That is, we not only can design many concrete S-boxes, but also may find many types of affinely in equivalent S-boxes.

Evolutionary Design of S-Box with Cryptographic Properties

Side channel analysis(SCA) focuses on attacking cryptographic algorithm implementations by collecting leaked information and analyzing the correlation between the leaked and key information in the cryptographic system. Currently, SCA is the main threat to cryptographic implementations, with DPA (differential power analysis) and DFA (differential fault analysis) being two of the most threatening types of SCA. However, the existing countermeasures against DPA and DFA have shortcomings and can hardly protect cipher designs perfectly. Based on a comprehensive analysis of DPA and DFA, this paper proposes a new idea of using an evolutionary cipher (EVOC) against DPAs based on the model proposed by Kocher, and several different new types of DFAs. In fact, an EVOC is a kind of dynamic cipher designing method. Moreover, combined with intelligent searching algorithms and cryptography design policies, EVOCs utilize the dynamic and unpredictable properties of TRNG (a truly random number generator) to ensure cipher design at a high level of security. Therefore, with an EVOC we could design cryptography algorithms with high security to resist mathematical analysis as well as DPAs and DFAs. This paper analyzes and proves the security, efficiency, cost, and original features of EVOCs against DPA and DFA both theoretically and experimentally. Compared with existing countermeasures against SCAs, EVOCs use dynamic non-linear operations to destroy the bases of DPA and DFA. At the algorithm level, EVOCs are more efficient than other resistance methods. Based on the theory and experiments, this paper proposes certain modifications to the EVOC in the AES (advanced encryption standard) algorithm, which can be referenced by other dynamic designs of cryptographic algorithms.

Evolutionary ciphers against differential power analysis and differential fault analysis

Based on the trace representation of Boolean functions, we devise an evolutionary algorithm to design bent functions. Using this algorithm, we then construct many bent functions and perform some analyses. First, we observe that each of the four affinely inequivalent bent functions in six variables can be written as the linear sum of two or three monomial trace functions. We draw the conclusion that the affine transformation can be used to change the linear span of the Boolean functions and thereby change the trace representation of our obtained bent functions. Second, we find that certain exponents are more suitable for constructing bent functions than others. From this observation, we assign each exponent a cost function, which makes our algorithm more efficient than an exhaustive search algorithm or a random algorithm. Third, we classify the obtained bent functions into affinely inequivalent classes, and the number of classes is presented.

The evolutionary design of trace form bent functions in cryptography

In the field of information security, one of the most important topic is how to construct cryptosystem. In this paper, firstly we propose definition of cryptosystem with low-power consumption. Then, methods to construct symmetric and asymmetric cryptosystem with low-power consumption are given. Finally, we discuss how to design component element of cryptosystem with low-power consumption.

Research on cryptosystem with low-power consumption

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