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Since the advent of networked systems, fuzzy graph theory has surfaced as a fertile paradigm for handling uncertainties and ambiguities. Among the different modes of handling challenges created by the uncertainties and ambiguities of current networked systems, integrating fuzzy graph theory with cryptography has emerged as the most promising approach. In this regard, this review paper elaborates on potentially studying fuzzy graph-based cryptographic techniques, application perspectives, and future research directions. Since the expressive power of fuzzy graphs allows the cryptographic schemes to handle imprecise information and to enhance security in many domains, several domains have benefited, such as image encryption, key management, and attribute-based encryption. The paper analyzes in depth the research landscape, mainly by focusing on the varied techniques used, such as fuzzy logic for key generation and fuzzy attribute representation for access control policies. A comparison with performance metrics unveils the trade-offs and advantages of different fuzzy graph-based approaches in efficiency, security strength, and computational overhead. Additionally, the survey explores the security applications of fuzzy graph-based cryptography and underpins potential development for secure communication in wireless sensor networks, privacy-preserving data mining, fine-grained access control in cloud computing, and blockchain security. Some challenges and research directions, such as the standardization of fuzzy logic operators, algorithmic optimization, integration with emerging technologies, and exploitation of post-quantum cryptography applications, are also brought out. This review will thus bring insight into this interdisciplinary domain and stimulate further research for the design of more robust, adaptive, and secure cryptographic systems in the wake of rising complexities and uncertainties.

We propose a verifiable $(t,n)$-threshold secret sharing scheme using Lagrange interpolation and secure cryptographic hash functions. This scheme is an improvement of Shao’s scheme [Inform. Sci.278 (2014) 104–109]. In our variant, verification of shares is achieved through computation of their multiplicative inverses in conjunction with a secure hash function such as SHA-3. This idea results in a significant size reduction, in comparison with Shao’s scheme, to the shares assigned to each participant. Applications of the proposed scheme include sharing of cryptographic keys, access codes, etc. Furthermore, we improve our construction to present a method for secret sharing with adjustable access structure. This can further be extended to a secret sharing scheme with essential participants, where any authorized set of participants must meet a threshold in the number of essential participants it contains. While our proposal has smaller share sizes compared to Shao’s scheme, it also adds the capabilities of changeable parameters and essential participants.

A secret sharing scheme is a system designed to share a piece of information or the secret among a group of people such that only authorized people can reconstruct the secret from their shares. Since Blakley and Shamir proposed threshold secret sharing schemes in 1979 independently, many secret sharing schemes have been constructed. In this paper, we present several threshold schemes that are generalizations of Shamir's secret sharing scheme.

A convertible authenticated encryption scheme allows a designated receiver to retrieve an authenticated ciphertext and convert the authenticated ciphertext into an ordinary signature. The receiver can prove the dishonesty of the sender to anyone if the sender repudiates his/her signature. Recently, many researchers have proposed convertible authenticated encryption schemes based on cryptological algorithms. In this paper, the authors shall present a new convertible authenticated encryption scheme based on the ElGamal cryptosystem. The proposed scheme is more efficient than Wu-Hsu's scheme in terms of computational complexity.

It is a difficult task to compute the r-th order nonlinearity of a given function with algebraic degree strictly greater than r > 1. Though lower bounds on the second order nonlinearity are known only for a few particular functions, the majority of which are cubic. We investigate lower bounds on the second order nonlinearity of cubic Boolean functions , where , d_l = 2^il + 2^jl + 1, m, i_l and j_l are positive integers, n > i_l > j_l. Furthermore, for a class of Boolean functions we deduce a tighter lower bound on the second order nonlinearity of the functions, where , d_l = 2^i_lγ + 2^j_lγ + 1, i_l > j_l and γ ≠ 1 is a positive integer such that gcd(n,γ) = 1.

Lower bounds on the second order nonlinearity of cubic monomial Boolean functions, represented by f_μ(x) = Tr(μx^2i+2j+1), , i and j are positive integers such that i > j, were obtained by Gode and Gangopadhvay in 2009. In this paper, we first extend the results of Gode and Gangopadhvay from monomial Boolean functions to Boolean functions with more trace terms. We further generalize and improve the results to a wider range of n. Our bounds are better than those of Gode and Gangopadhvay for monomial functions f_μ(x). Especially, our lower bounds on the second order nonlinearity of some Boolean functions F(x) are better than the existing ones.

Rational secret sharing was first introduced by Halpern and Teague (STOC, 2004). Since then, a series of works have focused on designing rational secret sharing protocols. However, most existing solutions can share only one secret at one secret sharing process. To share multiple secrets such as m secrets, the dealer must redistribute shares for m times. In addition, previous works assume existence of broadcast channel which is not realistic. Motivated by those problems, this paper proposes a rational multi-secret sharing scheme, which combines the secret sharing scheme with game theory. In the protocol, the problem of sharing multiple secrets is addressed, and there are multiple secrets to be shared during one secret sharing process. Furthermore, this work starts off by constructing a protocol in simultaneous broadcast networks, and then we emulate the broadcast channel over point-to-point networks. Based on a computational assumption, we show that rational players have no incentive to deviate from the protocol and every player can obtain multi-secret fairly.

In this paper, firstly we extend the polynomial quotient modulo an odd prime $p$ to its general case with modulo $p^r$ and $r\ge 1$. From the new quotient proposed, we define a class of $p^{r+1}$-periodic binary threshold sequences. Then combining the Legendre symbol and Euler quotient modulo $p^r$ together, with the condition of $2^{p-1}\not\equiv 1(mod{p}^2)$, we present exact values of the linear complexity for $p\equiv \pm 3(mod8)$, and all the possible values of the linear complexity for $p\equiv \pm 1(mod8)$. The linear complexity is very close to the period and is of desired value for cryptographic purpose. Our results extend the linear complexity results of the corresponding $p^2$-periodic binary sequences in earlier work.

The Cramer-Shoup (CS) like cryptosystem based on index exchangeable family (IEF) construction is a novel scheme introduced in Asiaccs 2016 by Li et al. Its versatility was illustrated by building two public key encryption (PKE) schemes, a cramer-shoup encryption scheme based on IEFs, as well as an outsourcing technique based on non-abelian analog. However, the two schemes are not secure over the recommended linear group of Li et al. For them, we provide a new key-recovery attack by solving a linear equation respectively. Furthermore, we peel off complex encryption and decryption processes and propose more than three different attack methods. Finally, we give a corresponding example to illustrate the correctness of our attack methods. Our attack methods break an instance of claiming 80 bit security less than one minute under a personal computer.

Synchronization of neural networks by mutual learning has been demonstrated to be possible for constructing key exchange protocol over public channel. However, the neural cryptography schemes presented so far are not the securest under regular flipping attack (RFA) and are completely insecure under majority flipping attack (MFA). We propose a scheme by splitting the mutual information and the training process to improve the security of neural cryptosystem against flipping attacks. Both analytical and simulation results show that the success probability of RFA on the proposed scheme can be decreased to the level of brute force attack (BFA) and the success probability of MFA still decays exponentially with the weights' level L. The synchronization time of the parties also remains polynomial with L. Moreover, we analyze the security under an advanced flipping attack.

Virus machines are computational devices inspired by the movement of viruses between hosts and their capacity to replicate using the resources of the hosts. This behavior is controlled by an external graph of instructions that opens different channels of the system to make viruses capable of moving. This model of computation has been demonstrated to be as powerful as turing machines by different methods: by generating Diophantine sets, by computing partial recursive functions and by simulating register machines. It is interesting to investigate the practical use cases of this model in terms of possibilities and efficiency. In this work, we give the basic modules to create an arithmetic calculator. As a practical application, two pairing functions are calculated by means of two different virus machines. Pairing functions are important resources in the field of cryptography. The functions calculated are the Cantor pairing function and the Gödel pairing function.

Although deep learning models have shown promising results in solving problems related to image recognition or natural language processing, they do not match how the biological brain works. Some of the differences include the amount of energy consumed, the way neurons communicate, or the way they learn. To close the gap between artificial neural networks and biological ones, researchers proposed the spiking neural network. Layered Spiking Neural P systems (LSN P systems) are networks of spiking neurons used to solve various classification problems. In this paper, we study the LSN P systems in the context of a federated learning client–server architecture over horizontally partitioned data. We analyze the privacy implications of pre-trained LSN P systems through membership inference attacks. We also perform experiments to assess the performance of an LSN P system trained in the federated learning setup. Our findings suggest that LSN P systems demonstrate higher accuracy and faster convergence compared to federated algorithms based on either perceptron or spiking neural networks.

Cellular automata (CA) are discrete dynamical systems that can be employed as cryptography algorithms. Irreversible CA with toggle rules — either to the right or to the left — were already proposed for encrypting. However, the similarity between ciphertexts when the plaintext is submitted to a small perturbation was identified as a flaw in this model. Here, such a model is altered by using bi-directional toggle CA rules instead of one-directional ones. Numerical experiments showed that the similarity flaw was eliminated by considering this modification, obtaining protection against differential cryptanalysis.

In this paper, a new cryptographic protocol to securely share a secret among a set of participants is presented. It is based on the use of non-reversible elementary cellular automata with rule numbers 90 and 150. The protocol is shown to be perfect and ideal.

An algorithm to share a secret among a set of users is introduced in this work. It is based on the use of linear cellular automata over the finite set 𝔽₂ and it is considered as a generalization of a previous work due to the authors dealing with an elementary cellular automata-based secret sharing scheme. The algorithm is shown to be secure, ideal, and perfect.

In this paper we propose a high performance searching-based chaotic cipher. Experiments shows that its efficiency is comparable to the efficiencies of some widely used and known ciphers, namely, AES, RC4 and Sosemanuk. Also, its performance is better than some recently proposed chaotic ciphers of the same kind. The proposed cryptosystem shows independence with respect to the statistical characteristics of the plain texts, which prevents statistical attacks. The results of the tests suggest that this chaotic cipher can be competitive for practical usage.

Pseudo-random bit sequence have a wide range of applications in the field of cryptography and communications. For the good chaotic dynamical properties of chaotic systems sequence such as randomness and initial sensitivity, chaotic systems have a strong advantage in generating the pseudo-random bit sequence. However, in practical use, the dynamical properties of chaotic systems will be degraded because of the limited calculation accuracy and it even could cause a variety of security issues. To improve the security, in full analyses of the pseudo-random bit generator proposed in our former paper, we point out some problems in our former design and redesign a better pseudo-random bit generator base on it. At the same time, we make some relevant theoretical and experimental analyses on it. The experiments show that the design proposed in this paper has good statistical properties and security features.

In this paper, we study in detail the multifractal features of the main matrices of an encryption system based on a rule-90 cellular automaton. For this purpose, we consider the scaling method known as the wavelet transform multifractal detrended fluctuation analysis (WT-MFDFA). In addition, we analyze the multifractal structure of the matrices of different dimensions, and find that there are minimal differences in all the examined multifractal quantities such as the multifractal support, the most frequent singularity exponent, and the generalized Hurst exponent.

Cellular automaton (CA) has a lot of inherent features, such as simple regular structure, local interaction, random-like behavior and massive parallelism, which make it a good candidate to design cryptosystems. Therefore, a number of CA-based image encryption systems have been proposed, though the drawbacks of small key space and weak security in one-dimensional (1D) CA cryptosystems are obvious. In this paper, a novel image encryption scheme is presented using a two-dimensional (2D) CA with nonlinear balanced rules. During the whole process of encryption, the confusion operation is performed by the nonlinear rule of CA, while the diffusion operation is achieved by the local interactions among cells. So confusion and diffusion are well integrated in our proposed scheme. The corresponding simulations and analyses illustrate that the scheme has quite prominent cryptographic properties as well as high security.

The increasing risk along with the drastic development of multimedia data transmission has raised a big concern on data security. A good pseudo-random number generator is an essential tool in cryptography. In this paper, we propose a novel pseudo-random number generator based on the controlled combination of the outputs of several digitized chaotic Rényi maps. The generated pseudo-random sequences have passed both the NIST 800-22 Revision 1a and the DIEHARD tests. Moreover, simulation results show that the proposed pseudo-random number generator requires less operation time than existing generators and is highly sensitive to the seed.

Reservoir Computing (RC) refers to a Recurrent Neural Network (RNNs) framework, frequently used for sequence learning and time series prediction. The RC system consists of a random fixed-weight RNN (the input-hidden reservoir layer) and a classifier (the hidden-output readout layer). Here, we focus on the sequence learning problem, and we explore a different approach to RC. More specifically, we remove the nonlinear neural activation function, and we consider an orthogonal reservoir acting on normalized states on the unit hypersphere. Surprisingly, our numerical results show that the system’s memory capacity exceeds the dimensionality of the reservoir, which is the upper bound for the typical RC approach based on Echo State Networks (ESNs). We also show how the proposed system can be applied to symmetric cryptography problems, and we include a numerical implementation.