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The digital images are widely captured, transmitted, and stored by limited resource devices. Those devices need lightweight encryption (LWE) techniques to protect secret and personal images. Designing LWE algorithms for digital images is challenging due to the large size and high inter-pixel correlations of digital images. This paper presents an image encryption technique based on the Nonlinear feedback shift register (NLFSR) and DNA computation. The image is permuted first using pseudorandom sequence generated by a NLSFR based Key stream generator followed by a substitution of pixel values using DNA computations in cipher block chaining mode. Furthermore, security analysis tests, histograms, correlation, entropy, NPCR, and UACI are used to verify our scheme. The security and performance analysis of the proposed techniques analyses showed their efficacy and resistance to attacks. The analysis of the results certainly indicates the scheme is highly secure and lightweight. The proposed scheme can be used for secure image transmission and storage in medical IoT, smart surveillance, etc.

Nonlinear feedback shift registers (NFSRs) are used in many recent stream ciphers as their main building blocks. One security criterion for the design of a stream cipher is to assure its used NFSR has a long period. As the period of a Fibonacci NFSR is equal to its largest cycle length, a common way to get a maximum-period Fibonacci NFSR is to join the cycles of an original Fibonacci NFSR into a maximum cycle. Nevertheless, so far only the maximum-period Fibonacci NFSRs with stage numbers no greater than 33 have been found. Considering that Galois NFSRs may have higher implementation efficiency than Fibonacci NFSRs, this paper first generalizes the cycle joining method for Fibonacci NFSRs to Galois NFSRs and establishes some conditions for maximum-period Galois NFSRs. It then reveals the cycle structure of some cascade connections of two Fibonacci NFSRs. Based on both, the paper constructs some long-period Galois NFSRs including maximum-period Galois NFSRs with stage numbers up to 41. Finally, it analyzes their hardware implementation via the technology mapping obtained by synthesizing the NFSRs with Synopsys Design Compiler L - 2016.03-Sp1 using the TSMC 90nm CMOS library, and the results show that they have good hardware performance.

Plantlet is a new variant of Sprout lightweight stream cipher. It uses 61 bit LFSR and 40 bit NFSR. This paper presents a study of Plantlet stream cipher with probability based approach for making algebraic attack on Plantlet. In this paper, we have used low degree multiple of Boolean function to apply algebraic attack. The low degree multiple of Boolean function is multiplied to output keystream function in order to get output equation such that it consists of only LFSR state variables. These equations are further solved to find secret key and internal states. In this manner, the complexity of solving equations is reduced. In this paper, it takes 2 60.99 Plantlet encryptions to solve system of equations. Commonly, standard algebraic attack and fast algebraic attack have been applied on various stream ciphers. However, the probabilistic algebraic attack has been implemented on Grain family of stream ciphers but not on Plantlet. The probabilistic algebraic attack can be applied on other stream ciphers.

Nonlinear feedback shift registers (NFSRs) are the main components of stream ciphers and convolutional decoders. Recent years have seen an increase in the requirement for information security, which has sparked NFSR research. However, the NFSR study is very imperfect as a result of the lack of appropriate mathematical tools. Many scholars have discovered in recent years that the introduction of semi-tensor products (STP) of matrices can overcome this issue because STP can convert the NFSR into a quasi-linear form. As a result of STP, new NFSR research has emerged from a different angle. In view of this, in order to generalize the latest achievements of NFSRs based on STP and provide some directions for future development, the research results are summarized and sorted out, broadly including the modeling of NFSRs, the analysis of the structure of NFSRs, and the study of the properties of NFSRs.

De Bruijn sequence is an important kind of nonlinear shift register sequence, which has a very wide range of applications in the fields of communication and cryptography. From the perspective of the relationship between linear terms, quadratic terms and cubic terms in the feedback functions of de Bruijn sequences, some new necessary conditions for feedback functions of de Bruijn sequences are obtained. Some examples show that the known necessary conditions cannot deduce the proposed necessary conditions.

Herein, a true random number generator (TRNG) based on a CuxTe1−x diffusive memristor (DM) using its threshold switching (TS) behavior is reported. The intrinsic stochasticity of the TS behavior contributes to the randomness of the TRNG system. The switching behavior is discussed through field‐induced nucleation theory and surface diffusion dynamics. Demonstrating the performance of TRNG as a hardware security application, the DM‐based TRNG passes all 15 National Institute of Standards and Technology randomness tests without any post‐processing step, even in high‐temperature conditions. Moreover, a nonlinear‐feedback shift register is implemented for a high‐speed TRNG, producing the highest rate among the reported volatile‐memristor‐based TRNGs. A Cu0.1Te0.9/HfO2/Pt diffusive memristor has a stochastic delay and relaxation times, which can be used as random sources in a true random number generator (TRNG) system. The TRNG is implemented by a simple circuit configuration, that consists of a memristor, a nonlinear‐feedback shift register that includes an XNOR gate, an XOR gate, and shift registers with four D flip‐flops.

Observability ensures that any two distinct initial states can be uniquely determined by their outputs, so the stream ciphers can avoid unobservable nonlinear feedback shift registers (NFSRs) to prevent the occurrence of equivalent keys. This paper discusses the observability of Galois NFSRs over finite fields. Galois NFSRs are treated as logical networks using the semi-tensor product. The vector form of the state transition matrix is introduced, by which a necessary and sufficient condition is proposed, as well as an algorithm for determining the observability of general Galois NFSRs. Moreover, a new observability matrix is defined, which can derive a matrix method with lower computation complexity. Furthermore, the observability of two special types of Galois NFSRs, a full-length Galois NFSR and a nonsingular Galois NFSR, is investigated. Two methods are proposed to determine the observability of these two special types of NFSRs, and some numerical examples are provided to support these results.

Nonlinear feedback shift registers (NFSRs) have been widely used in hardware-oriented stream ciphers. Whether a family of NFSR sequences includes an affine sub-family of sequences is a fundamental problem for NFSRs. Let f be the characteristic function of an NFSR whose algebraic degree is d . The previous necessary condition on affine sub-families of NFSR sequences given by Zhang et al. [IEEE Trans. Inf. Theory, 65(2), 2019] provides a set of possible affine NFSRs defined by the variables appearing in the terms with the maximum degree d in f , which leads to the fastest algorithm so far for finding affine sub-families. In this paper, a new necessary condition for the existence of an affine sub-family in a family of NFSR sequences is proposed. The new necessary condition is further concerned with the algebraic relations between the terms with the maximum degree d in f , not only the variables involved in them, and so yields a smaller space of possible affine sub-families and less computation complexity for a large number of NFSRs.

Convolutional codes have been widely used in many applications such as digital video, radio, and mobile communication. Nonlinear feedback shift registers （NFSRs） are the main building blocks in convolutional decoders. A decoding error may result in a succession of further decoding errors. However, a stable NFSR can limit such an error-propagation. This paper studies the stability of NFSRs using a Boolean network approach. A Boolean network is an autonomous system that evolves as an automaton through Boolean functions. An NFSR can be viewed as a Boolean network. Based on its Boolean network representation, some sufficient and necessary conditions are provided for globally （locally） stable NFSRs. To determine the global stability of an NFSR with its stage greater than 1, the Boolean network approach requires lower time complexity of computations than the exhaustive search and the Lyapunov＇s direct method.

In this paper,we regard the nonlinear feedback shift register（NLFSR） as a special Boolean network,and use semi-tensor product of matrices and matrix expression of logic to convert the dynamic equations of NLFSR into an equivalent algebraic equation. Based on them,we propose some novel and generalized techniques to study NLFSR. First,a general method is presented to solve an open problem of how to obtain the properties（the number of fixed points and the cycles with different lengths） of the state sequences produced by a given NLFSR,i.e.,the analysis of a given NLFSR. We then show how to construct all 2^2^n-（l-n）/2^2^n-lshortest n-stage feedback shift registers（nFSR） and at least 2^2^n-（l-n）-1/2^2^n-l-1shortest n-stage nonlinear feedback shift registers（nNLFSR） which can output a given nonperiodic/periodic sequence with length l. Besides,we propose two novel cycles joining algorithms for the construction of full-length nNLFSR. Finally,two algorithms are presented to construct 2^2^n-2-1different full-length nNLFSRs,respectively.