A new S-box construction method meeting strict avalanche criterion

Ever since Baptista in 1998 introduced his cryptographic scheme utilizing the only in online version. ergodic property of chaotic maps which is able to produce different cipher values for the same plaintext within the same message, intense scrutiny has been given upon the design. The capability to do the above mentioned output is akin to the Vigenere cipher and thus has the capacity to render an attacker with infinitely many choices (theoretically speaking) or in cryptographic terms would render an attacker to have a set off possible ciphertexts that could all have the possibility to just be mapped to a unique plaintext. This makes it computationally infeasible for the attacker to re-construct the correct plaintext. The Baptista design has been attacked and repaired many times. Alvarez noticed the characteristic of the cryptosystem that generates a sequence which can be exploited by an attacker. The attack which is dubbed the one-time pad attack is akin to an attack upon a One-Time-Pad (OTP) cryptosystem that reuses its key. Since then, attempts were made to redefine the cryptosystem such that it would be resistant towards the attack. Most of the attempts failed due to either the repaired cryptosystem still generates an exploitable sequence or it is not invertible. In this work we pair the Baptista design with a concept taken from the Iterated Function Systems (IFS). Although we did not encompass the whole concept of iterating the IFS, it could be seen that this could be easily done with the same desirable results. Four main outcomes are discussed. Beginning with the discussion on the infeasibility of Alvarez’s one-time pad attack on the design, we then discuss the quantitative properties of the design in discussing its cryptographic properties namely the Maximum Deviation Factor (MDF), Correlation Coefficient Factor (CCF) and the Strict Avalanche Criterion (SAC). Each experimental result shows promising results for this new design.KeywordsCryptosystemStrict Avalanche Criterion (SAC)Iterated Function Systems (IFS)Chaotic MapsOne-time Pad (OTP)These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Cryptography deals with designing practical mathematical algorithms having the two primitive elements of confusion and diffusion. The security of encrypted data is highly dependent on these two primitive elements and a key. S-box is the nonlinear component present in a symmetric encryption algorithm that provides confusion. A cryptographically strong bijective S-box structure in cryptosystem ensures near-optimal resistance against cryptanalytic attacks. It provides uncertainty and nonlinearity that ensures high confidentiality and security against cryptanalysis attacks. The nonlinearity of an S-box is highly dependent on the dispersal of input data using an S-box. Cryptographic performance criteria of chaos-based S-boxes are worse than algebraic S-box design methods, especially differential probability. This article reports a novel approach to design an 8 × 8 S-box using chaos and randomization using dispersion property to S-box cryptographic properties, especially differential probability. The randomization using dispersion property is introduced within the design loop to achieve low differential uniformity possibly. Two steps are involved in generating the proposed S-box. In the first step, a piecewise linear chaotic map (PWLCM) is utilized to generate initial S-box positions. Generally, the dispersion property is a post-processing technique that measures maximum nonlinearity in a given random sequence. However, in the second step, the concept is carefully reverse engineered, and the dispersion property is used within the design loop for systematic dispersal of input substituting sequence. The proposed controlled randomization changes the probability distribution statistics of S-box’s differentials. The proposed methodology systematically substitutes the S-box positions that cause output differences to recur for a given input difference. The proposed S-box is analyzed using well-established and well-known statistical cryptographic criteria of nonlinearity, strict avalanche criteria (SAC), bit independence criteria (BIC), differential probability, and linear probability. Further, the S-box’s boomerang connectivity table (BCT) is generated to analyze its strength against boomerang attack. Boomerang is a relatively new attacking framework for cryptosystem. The proposed S-box is compared with the state-of-the-art latest related publications. Results show that the proposed S-box achieves an upper bound of cryptographic properties, especially differential probability. This work hypothesizes that highly dispersive hamming distances at output difference, generated a systematic S-box. The mixing property of chaos generated trajectories utilized for decimal mapping. To test the randomness of generated chaotic trajectories, a cryptographically secure pseudo-random sequence was generated using a chaotic map that was tested using the National Institute of Standards and Technology (NIST) NIST-800-22 test suit.

The strict avalanche criterion (SAC) was introduced by Webster and Tavares [10] in a study of cryptographic design criteria. This is an indicator for local property. In order to improve the global analysis of cryptographically strong functions, Zhang and Zheng [11] introduced the global avalanche characteristics (GAC). The sum-of-squares indicator related to the GAC is defined as σfe∑vΔf2(v), where Δf(v)e∑x (−1)f(x)⊕f(x}⊕ v). In this paper, we give a few methods to construct Boolean functions controlling five good cryptographic properties, namely balancedness, good local and GAC, high nonlinearity and high algebraic degree. We improve upon the results of Stanica [8] and Zhang and Zheng [11].

The Strict Avalanche Criterion (SAC) is a measure of both confusion and diffusion, which are key properties of a cryptographic hash function. This work provides a working definition of the SAC, describes an experimental methodology that can be used to statistically evaluate whether a cryptographic hash meets the SAC, and uses this to investigate the degree to which compression function of the SHA-1 hash meets the SAC. The results (P < 0.01) are heartening: SHA-1 closely tracks the SAC after the first 24 rounds, and demonstrates excellent properties of confusion and diffusion throughout.

The strict avalanche criterion was introduced by Webster and Tavares [] in order to combine the ideas of completeness and the avalanche effect. A cryptographic transformation is complete if each output bit depends on all the input bits, and it exhibits the avalanche effect if an average of one half of the output bits change whenever a single input bit is complemented. To fulfil the strict avalanche criterion, each output bit should change with probability one half whenever a single input bit is complemented. This means, in particular, that there is no good lower order (fewer bits) approximation to the function. This is clearly a desirable cryptographic property since such an approximation would enable a corresponding reduction in the amount of work needed for an exhaustive search.

In this paper, we presented a low-power, less area architecture of S-Box used in advanced encryption standard (AES) using programmable cellular automata (PCA). The proposed architecture performance in terms of security is evaluated using cryptographic properties such as nonlinearity, input/output entropy, correlation immunity bias, balancedness property, strict avalanche criterion, and it is found that the proposed method is secure enough for cryptography applications. The proposed architecture of AES with PCA-based S-Box is implemented on ASIC using TSMC 0.18-\({\upmu }\)m and UMC 0.13-\({\upmu }\)m CMOS technology libraries. Simulation studies show that the proposed architecture has average energy consumption of 58.702 nJ, power dissipation of 3.259 mW, area of 0.184 mm\(^2\), for TSMC 0.18-\({\upmu }\)m at 13.69 MHz and energy consumption of 18.275 nJ, power dissipation of 1.026 mW, area of 0.069 \({\upmu m}^{2}\) for UMC 0.13-\({\upmu }\)m at 13.69 MHz. The proposed architecture shows reduction in power dissipation by 83% and in energy consumption by 10% compared to the best classical S-Box and composite field arithmetic-based S-Box for AES algorithm. The S-Box using PCA is more flexible and dynamic in nature with low power, lesser energy consumption area and hence suitable for wireless body area network applications.

To further enhance the nonlinear and cryptographic properties of chaotic S-boxes, a novel S-box design is proposed based on the discrete chaotic map and improved artificial bee colony algorithm. Firstly, the S-box generated by chaotic sequence is initialized by the opposition-based optimization. Then, the dual transposition artificial bee colony algorithm is used to optimize the population, where the Gaussian swap is engaged to strengthen the optimum efficiency, and make the population acquire a better quality with each other. With the Gaussian mutation operator, the opposition-based optimization performs self-learning to obtain better population. Comparing with some recent S-boxes based on chaos. The S-boxes generated by the proposed scheme can achieve better performance in bijection, nonlinearity, strict avalanche criterion(SAC), bit independence criterion(BIC), I / O XOR distribution and linear approximation probability(LP). It provides a new and effective method for designing S-boxes with good cryptographic properties.

Data encryption algorithms play a vital part in the security for data in communication. In this paper, we present an efficient hybrid linear cellular automata (HLCA) based encryption algorithm architecture. This paper aims on the analysis of utilization of hardware for standard AES algorithm and proposed hybrid linear cellular automata (HLCA) based encryption algorithm with respect to device utilization, power consumption and frequency of operation. The performance of the proposed hybrid linear cellular automata encryption algorithm with respect to security is analyzed using cryptographic properties like non-linearity, strict avalanche criteria, correlation immunity bias and entropy. The attained results show that the hybrid linear cellular automata (HLCA) based encryption algorithm architecture gives better performance compared to AES algorithm with respect to security, device utilization, power consumption and throughput. The proposed hybrid linear cellular automata encryption algorithm achieved a throughput of 1.60 Gbps with an operating frequency of 498 MHz.

In today's digital world, the most inevitable challenge is the protection of digital information. Due to the weak confidentiality preserving techniques, the existing world is facing several digital information breaches. To make our digital data indecipherable to the unauthorized person, a technique for finding a cryptographically strong Substitution box (S-box) have presented. An S-box with sound cryptographic assets such as nonlinearity (NL), strict avalanche criterion (SAC), bit independence criteria (BIC), bit independence criteria of nonlinearity (BIC-NL), Bit independence criteria of Strict avalanche criteria (BIC-SAC), and Input/output XOR is considered as the robust S-box. The Decision-Making Trial and Evaluation Laboratory (DEMATEL) approach of multi-criteria decision making (MCDM) is proposed for finding the interrelation among cryptographic properties. A combination of two MCDM methods namely Entropy and multi-objective optimization based on ratio analysis (MOORA) is applied for the best S-box selection. A robust substitution box is selected for secure communications in cryptography by using the combination of DEMETAL selection criteria, entropy weight assigning, and MOORA ranking scheme. The combination of these three methods provides a fast selection procedure for the secure confusion component. The offered selection method can also be utilized for the choice of the best cryptosystem with highly secure properties and resistive against all possible linear and differential attacks in the cryptanalysis.

Cryptography play an most essential role in the field of data security. This paper, we proposed cryptographically secure encryption algorithm architecture using order one dimensional programmable linear cellular automata (1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> LCA). This paper also emphasizes on the comparative analysis of hardware utilization for conventional AES algorithm and encryption algorithm using 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> LCA in terms of power, area and throughput. Moreover, the cryptographic properties like correlation immunity bias, strict avalanche criteria, non linearity and entropy are used to evaluate the level of security provided by AES algorithm and encryption algorithm architecture using LCA. The synthesis results of FPGA shows that the encryption algorithm architecture using 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order one dimensional programmable linear cellular automata (1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> LCA) gives better level of security, low power consumption, high efficiency compared to that of standard AES algorithm. The proposed encryption algorithm attained a throughput of 1.33 Gbps and high operating frequency of 534 MHz compared with existing designs.

A necessary and sufficient condition on the Walsh-spectrum of a boolean function is given, which implies that this function fulfills the Strict Avalanche Criterion. This condition is shown to be fulfilled for a class of functions exhibiting simple spectral symmetries. Finally, an extended definition of the Strict Avalanche Criterion is proposed and the corresponding spectral characterization is derived.KeywordsBoolean FunctionExhaustive SearchTruth TableSpectral CharacterizationSymmetry ReasonThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The Substitution Box (S-box) is a fundamental nonlinear transformation utilized within cryptographic algorithms to map an input bit string into an output bit string. Due to the complexity and variability of cryptographic attacks, constructing S-boxes using traditional methods has proven challenging. However, recent advancements in optimization algorithms have provided new ideas for S-box construction. To address the difficulty of constructing high-performance S-boxes through traditional means, this paper proposes a design for an 8×8 S-box based on the improved sine-cosine algorithm. In this study, genetic algorithm's mutation and crossover operations are incorporated into the sine-cosine algorithm to optimize the initial S-box constructed using the improved Newton iterative method. The resulting S-box is then evaluated based on cryptographic criteria such as bijection, nonlinearity, strict avalanche criterion, bit-independent criterion, linear probability, and differential probability. Comparative analysis with several previous S-box generation methods demonstrates that the proposed S-box design exhibits superior cryptographic properties.

Substitution boxes with resilient cryptographic possessions are normally utilized in block ciphers to give the substantial property of nonlinearity. They are important to resist standard attacks such as linear and differential cryptanalysis. A cryptographically robust S-box must be sound with respect to cryptographic properties like nonlinearity, bit independent criteria, strict avalanche criteria, linear and differential approximation probability. In this paper, we have developed an innovative construction scheme of nonlinear component of block cipher based on the action of projective linear groups on the projective line, and the permutation triangle groups. This nonlinear component, namely S-box, is responsible for making the relation between plaintext and ciphertext intractable which is one of the most important requirements of any modern block ciphers. By widening the scope of the proposed S-boxes, we have applied these lightweight nonlinear components in watermarking scheme.

In this paper the authors present a statistical test for testing the strict avalanche criterion (SAC), a property that cryptographic primitives such as block ciphers and hash functions must have. Random permutations should also behave as good random number generators when, given any initial input, its output is considered part of a pseudorandom stream and then used as an input block to produce more output bits. Using these two ideal properties, we construct a test framework for cyptographic primitives that is shown at work on the block cipher TEA. In this way, we are able to distinguish reduced round versions of it from a random permutation.

The creation of S-boxes and the study of their cryptographic strength is one of the main activities in symmetric cryptography. It is known that one of the most important transformations responsible for the cryptographic strength of a symmetric block encryption algorithm is the S-box replacement table. In this regard, in this paper, we consider a new method for obtaining 4-bit S-boxes based on the exponentiation operation in the Galois field. Currently, there are a large number of methods for checking the cryptographic strength of S-boxes, one of which is the study of a strict avalanche criterion. Therefore, the study of cryptographic strength of the S-box obtained by the new method based of a strict avalanche criterion (SAC) of a Boolean function in comparison with the results of S-boxes of popular algorithms, showed very good results.