Chaotic Map-Based Authentication and Key Agreement Protocol with Low-Latency for Metasystem

With the rapid advancement in exploring perceptual interactions and digital twins,metaverse technology has emerged to transcend the constraints of space-time and reality,facilitating remote AI-based collaboration.In this dynamic metasystem environment,frequent information exchanges necessitate robust security measures,with Authentication and Key Agreement(AKA)serving as the primary line of defense to ensure communication security.However,traditional AKA protocols fall short in meeting the low-latency requirements essential for synchronous interactions within the metaverse.To address this challenge and enable nearly latency-free interactions,a novel low-latency AKA protocol based on chaotic maps is proposed.This protocol not only ensures mutual authentication of entities within the metasystem but also generates secure session keys.The security of these session keys is rigorously validated through formal proofs,formal verification,and informal proofs.When confronted with the Dolev-Yao(DY)threat model,the session keys are formally demonstrated to be secure under the Real-or-Random(ROR)model.The proposed protocol is further validated through simulations conducted using VMware workstation compiled in HLPSL language and C language.The simulation results affirm the protocol’s effectiveness in resisting well-known attacks while achieving the desired low latency for optimal metaverse interactions.

Intrusion Detection Model Using Chaotic MAP for Network Coding Enabled Mobile Small Cells

Wireless Network security management is difficult because of the ever-increasing number of wireless network malfunctions,vulnerabilities,and assaults.Complex security systems,such as Intrusion Detection Systems(IDS),are essential due to the limitations of simpler security measures,such as cryptography and firewalls.Due to their compact nature and low energy reserves,wireless networks present a significant challenge for security procedures.The features of small cells can cause threats to the network.Network Coding(NC)enabled small cells are vulnerable to various types of attacks.Avoiding attacks and performing secure“peer”to“peer”data transmission is a challenging task in small cells.Due to the low power and memory requirements of the proposed model,it is well suited to use with constrained small cells.An attacker cannot change the contents of data and generate a new Hashed Homomorphic Message Authentication Code(HHMAC)hash between transmissions since the HMAC function is generated using the shared secret.In this research,a chaotic sequence mapping based low overhead 1D Improved Logistic Map is used to secure“peer”to“peer”data transmission model using lightweight H-MAC(1D-LM-P2P-LHHMAC)is proposed with accurate intrusion detection.The proposed model is evaluated with the traditional models by considering various evaluation metrics like Vector Set Generation Accuracy Levels,Key Pair Generation Time Levels,Chaotic Map Accuracy Levels,Intrusion Detection Accuracy Levels,and the results represent that the proposed model performance in chaotic map accuracy level is 98%and intrusion detection is 98.2%.The proposed model is compared with the traditional models and the results represent that the proposed model secure data transmission levels are high.

Securing 3D Point and Mesh Fog Data Using Novel Chaotic Cat Map

With the rapid evolution of Internet technology,fog computing has taken a major role in managing large amounts of data.The major concerns in this domain are security and privacy.Therefore,attaining a reliable level of confidentiality in the fog computing environment is a pivotal task.Among different types of data stored in the fog,the 3D point and mesh fog data are increasingly popular in recent days,due to the growth of 3D modelling and 3D printing technologies.Hence,in this research,we propose a novel scheme for preserving the privacy of 3D point and mesh fog data.Chaotic Cat mapbased data encryption is a recently trending research area due to its unique properties like pseudo-randomness,deterministic nature,sensitivity to initial conditions,ergodicity,etc.To boost encryption efficiency significantly,in this work,we propose a novel Chaotic Cat map.The sequence generated by this map is used to transform the coordinates of the fog data.The improved range of the proposed map is depicted using bifurcation analysis.The quality of the proposed Chaotic Cat map is also analyzed using metrics like Lyapunov exponent and approximate entropy.We also demonstrate the performance of the proposed encryption framework using attacks like brute-force attack and statistical attack.The experimental results clearly depict that the proposed framework produces the best results compared to the previous works in the literature.

Asymmetric image encryption algorithm based on a new three-dimensional improved logistic chaotic map

Based on some analyses of existing chaotic image encryption frameworks and a new designed three-dimensional improved logistic chaotic map(3D-ILM),an asymmetric image encryption algorithm using public-key Rivest–Shamir–Adleman(RSA)is presented in this paper.In the first stage,a new 3D-ILM is proposed to enhance the chaotic behavior considering analysis of time sequence,Lyapunov exponent,and Shannon entropy.In the second stage,combined with the public key RSA algorithm,a new key acquisition mathematical model(MKA)is constructed to obtain the initial keys for the 3D-ILM.Consequently,the key stream can be produced depending on the plain image for a higher security.Moreover,a novel process model(NPM)for the input of the 3D-ILM is built,which is built to improve the distribution uniformity of the chaotic sequence.In the third stage,to encrypt the plain image,a pre-process by exclusive OR(XOR)operation with a random matrix is applied.Then,the pre-processed image is performed by a permutation for rows,a downward modulo function for adjacent pixels,a permutation for columns,a forward direction XOR addition-modulo diffusion,and a backward direction XOR addition-modulo diffusion to achieve the final cipher image.Moreover,experiments show that the the proposed algorithm has a better performance.Especially,the number of pixels change rate(NPCR)is close to ideal case 99.6094%,with the unified average changing intensity(UACI)close to 33.4634%,and the information entropy(IE)close to 8.

New Family of Exact Solutions and Chaotic Soltions of Generalized Breor-Kaup System in （2＋1）-Dimensions via an Extended Mapping Approach

Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2+1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived solitary wave solution, we obtain some specific chaotic solitons to the (2+1)-dimensional GBK system.

Dynamic S-Box Generation Using Novel Chaotic Map with Nonlinearity Tweaking

A substitution box(S-Box)is a crucial component of contemporary cryptosystems that provide data protection in block ciphers.At the moment,chaotic maps are being created and extensively used to generate these SBoxes as a chaotic map assists in providing disorder and resistance to combat cryptanalytical attempts.In this paper,the construction of a dynamic S-Box using a cipher key is proposed using a novel chaotic map and an innovative tweaking approach.The projected chaotic map and the proposed tweak approach are presented for the first time and the use of parameters in their workingmakes both of these dynamic in nature.The tweak approach employs cubic polynomials while permuting the values of an initial S-Box to enhance its cryptographic fort.Values of the parameters are provided using the cipher key and a small variation in values of these parameters results in a completely different unique S-Box.Comparative analysis and exploration confirmed that the projected chaoticmap exhibits a significant amount of chaotic complexity.The security assessment in terms of bijectivity,nonlinearity,bits independence,strict avalanche,linear approximation probability,and differential probability criteria are utilized to critically investigate the effectiveness of the proposed S-Box against several assaults.The proposed S-Box’s cryptographic performance is comparable to those of recently projected S-Boxes for its adaption in real-world security applications.The comparative scrutiny pacifies the genuine potential of the proposed S-Box in terms of its applicability for data security.

A Chaotic Pulse Train Generator Based on Henon Map

The Henon map forms one of the most-studied two-dimensional discrete-time dynamical systems that exhibits chaotic behavior.The Henon map takes a point(Xn,Yn)in the plane and maps it to a new point(Xn+1,Yn+1).In this paper,a chaotic pulse generator based on the chaotic Henon map is proposed.It consists of a Henon map function subcircuit to realize the Henon map and another subcircuit to perform the iterative operation.The Henon map subcircuit comprises operational amplifiers,multipliers,delay elements and resistors,whereas,the iterative subcircuit is implemented with a simple design that comprises of an edge forming circuit followed by a monostable multivibrator and a voltage controlled switch without the use of any clock control.The proposed design can be used to realize the Henon map and also to generate a chaotic pulse train,with a controllable time interval and pulse position.The proposed circuit is implemented and simulated using Multisim 13.0 and MATLAB R2019b.The chaotic nature of the generated pulse train and also the time interval between the consecutive pulses is verified by the calculation of its Lyapunov exponents.

VLSI Implementation of Optimized 2D SIMM Chaotic Map for Image Encryption

The current research work proposed a novel optimization-based 2D-SIMM(Two-Dimensional Sine Iterative chaotic map with infinite collapse Mod-ulation Map)model for image encryption.The proposed 2D-SIMM model is derived out of sine map and Iterative Chaotic Map with Infinite Collapse(ICMIC).In this technique,scrambling effect is achieved with the help of Chaotic Shift Transform(CST).Chaotic Shift Transform is used to change the value of pixels in the input image while the substituted value is cyclically shifted according to the chaotic sequence generated by 2D-SIMM model.These chaotic sequences,generated using 2D-SIMM model,are sensitive to initial conditions.In the proposed algorithm,these initial conditions are optimized using JAYA optimization algorithm.Correlation coefficient and entropy are considered asfitness functions in this study to evaluate the best solution for initial conditions.The simulation results clearly shows that the proposed algorithm achieved a better performance over existing algorithms.In addition,the VLSI implementation of the proposed algorithm was also carried out using Xilinx system generator.With optimization,the correlation coefficient was-0.014096 and without optimization,it was 0.002585.

A Novel Internet of Medical Thing Cryptosystem Based on Jigsaw Transformation and Ikeda Chaotic Map

Image encryption has attracted much interest as a robust security solution for preventing unauthorized access to critical image data.Medical picture encryption is a crucial step in many cloud-based and healthcare applications.In this study,a strong cryptosystem based on a 2D chaotic map and Jigsaw transformation is presented for the encryption of medical photos in private Internet of Medical Things(IoMT)and cloud storage.A disorganized three-dimensional map is the foundation of the proposed cipher.The dispersion of pixel values and the permutation of their places in this map are accomplished using a nonlinear encoding process.The suggested cryptosystem enhances the security of the delivered medical images by performing many operations.To validate the efficiency of the recommended cryptosystem,various medical image kinds are used,each with its unique characteristics.Several measures are used to evaluate the proposed cryptosystem,which all support its robust security.The simulation results confirm the supplied cryptosystem’s secrecy.Furthermore,it provides strong robustness and suggested protection standards for cloud service applications,healthcare,and IoMT.It is seen that the proposed 3D chaotic cryptosystem obtains an average entropy of 7.9998,which is near its most excellent value of 8,and a typical NPCR value of 99.62%,which is also near its extreme value of 99.60%.Moreover,the recommended cryptosystem outperforms conventional security systems across the test assessment criteria.

An Efficient Three-Party Authenticated Key Exchange Procedure Using Chebyshev Chaotic Maps with Client Anonymity

Internet of Things(IoT)applications can be found in various industry areas,including critical infrastructure and healthcare,and IoT is one of several technological developments.As a result,tens of billions or possibly hundreds of billions of devices will be linked together.These smart devices will be able to gather data,process it,and even come to decisions on their own.Security is the most essential thing in these situations.In IoT infrastructure,authenticated key exchange systems are crucial for preserving client and data privacy and guaranteeing the security of data-in-transit(e.g.,via client identification and provision of secure communication).It is still challenging to create secure,authenticated key exchange techniques.The majority of the early authenticated key agreement procedure depended on computationally expensive and resource-intensive pairing,hashing,or modular exponentiation processes.The focus of this paper is to propose an efficient three-party authenticated key exchange procedure(AKEP)using Chebyshev chaotic maps with client anonymity that solves all the problems mentioned above.The proposed three-party AKEP is protected from several attacks.The proposed three-party AKEP can be used in practice for mobile communications and pervasive computing applications,according to statistical experiments and low processing costs.To protect client identification when transferring data over an insecure public network,our three-party AKEP may also offer client anonymity.Finally,the presented procedure offers better security features than the procedures currently available in the literature.

A Scheme of Fragile Watermarking Based on SVD and 2D Chaotic Mapping

This paper proposed a novel fragile watermarking scheme based on singular value decomposition (SVD) and 2D chaotic mapping. It obtains chaotic initial values from the image blocks singular value decomposition and the user’s key, then uses the chaotic mapping to get the chaotic sequence and inserts the sequence into the LSBs of the image blocks to get the watermarked image blocks. The paper reconstructed the watermarked image from all the embedded blocks. The analysis and experimental results show that the scheme is pretty fragile to tampering, and it can localize the tampering position accurately, reach 3×3 blocks.

Color image encryption algorithm based on chaotic mapping and DNA encoding

A color image encryption method combining deoxyribonucleic(DNA)encoding and hyperchaotic mapping is proposed to solve the problems of simple structure,low complexit and low security of the existing encryption system for low-dimensional chaotic mapping encoding system and a single DNA encoding system.Firstly,according to the information of the plaintext images,the initial values of all chaotic maps and the random matrices with the same size as the plaintext images are iteratively generated.Then,the generated initial values and random matrices are divided into the sub-blocks with the same size.The DNA encoding mode of each sub-block and the DNA operation rules between the sub-blocks are determined by the dynamic hyperchaotic sequence.Finally,the diffusion operation is adopted to achieve a better encryption effect.The simulation results indicate that the proposed encryption algorithm can resist a variety of attacks due to its high complexity,strong security and large key space.

Two-dimensional-lag complex logistic map with complex parameters and its encryption application

With the rapid development of internet technology,security protection of information has become more and more prominent,especially information encryption.Considering the great advantages of chaotic encryption,we propose a 2D-lag complex logistic map with complex parameters(2D-LCLMCP)and corresponding encryption schemes.Firstly,we present the model of the 2D-LCLMCP and analyze its chaotic properties and system stability through fixed points,Lyapunov exponent,bifurcation diagram,phase diagram,etc.Secondly,a block cipher algorithm based on the 2D-LCLMCP is proposed,the plaintext data is preprocessed using a pseudorandom sequence generated by the 2D-LCLMCP.Based on the generalized Feistel cipher structure,a round function F is constructed using dynamic S-box and DNA encoding rules as the core of the block cipher algorithm.The generalized Feistel cipher structure consists of two F functions,four XOR operations,and one permutation operation per round.The symmetric dynamic round keys that change with the plaintext are generated by the 2D-LCLMCP.Finally,experimental simulation and performance analysis tests are conducted.The results show that the block cipher algorithm has low complexit,good diffusion and a large key space.When the block length is 64 bits,only six rounds of encryption are required to provide sufficient security and robustness against cryptographic attacks.

On new chaotic mappings in symbol space

A well known chaotic mapping in symbol space is a shift mapping.However,other chaotic mappings in symbol space exist too.The basic change is to consider the process not only at a set of times which are equally spaced,say at unit time apart（a shift mapping）,but at a set of times which are not equally spaced,say if the unit time can not be fixed.The increasing mapping as a generalization of the shift mapping and the k-switch mapping are introduced.The increasing and k-switch mappings are chaotic.

A NOVEL RESEARCH OF CONFIDENTIAL COMMUNICATION BASED ON THE ELLIPTIC CURVE AND THE COMBINED CHAOTIC MAPPING

This letter presents a new type of chaotic encryption system based on combined chaotic mapping pseudo-random number generator, Hash table, and elliptic curve. In this program, the elliptic curve algorithm is used for the key distribution. After the linear transformation, the original chaotic sequence generated by drive system will be combined to chaotic mapping, converted to an encryption key sequence and constructed as Hash table for message authentication. The communication experiment used in the letter proves that the combination of combined chaotic encryption and conventional encryption is safe, feasible, and easy to implement by software.

Design and Implementation of Image Encryption Method by Using Chaotic Mapping Based on Multi-layer Parameter Disturbance

Bit-plane decomposition makes images obtain a number of layers. According to the amount of data information, images are encrypted, and the paper proposes image encryption method with Chaotic Mapping based on multi-layer parameter disturbance. The advantage of multi-layer parameter disturbance is that it not only scrambles pixel location of images, but also changes pixel values of images. Bit-plane decomposition can increase the space of key. And using chaotic sequence generated by chaotic system with different complexities to encrypt layers with different information content can save operation time. The simulation experiments show that using chaotic mapping in image encryption method based on multi-layer parameter disturbance can cover plaintext effectively and safely, which makes it achieve ideal encryption effect.

Digital image encryption with chaotic map lattices

This paper proposes a secure approach for encryption and decryption of digital images with chaotic map lattices. In the proposed encryption process, eight different types of operations are used to encrypt the pixels of an image and one of them will be used for particular pixels decided by the outcome of the chaotic map lattices. To make the cipher more robust against any attacks, the secret key is modified after encrypting each block of sixteen pixels of the image. The experimental results and security analysis show that the proposed image encryption scheme achieves high security and efficiency.

Artificial rabbit optimization algorithm based on chaotic mapping and Levy flight improvement

An artificial rabbit optimization(ARO)algorithm based on chaotic mapping and Levy flight improvement is proposed,which has the advantages of good initial population quality and fast convergence compared with the traditional ARO algorithm,called CLARO.CLARO is improved by applying three methods.Chaotic mapping is introduced,which can optimize the quality of the initial population of the algorithm.Add Levy flight in the exploration phase,which can avoid the algorithm from falling into a local optimum.The threshold of the energy factor is optimized,which can better balance exploration and exploitation.The efficiency of CLARO is tested on a set of 23 benchmark function sets by comparing it with ARO and different meta-heuristics algorithms.At last,the comparison experiments conclude that all three improvement strategies enhance the performance of ARO to some extent,with Levy flight providing the most significant improvement in ARO performance.The experimental results show that CLARO has better results and faster convergence compared to other algorithms,while successfully addressing the drawbacks of ARO and being able to face more challenging problems.

Dynamics analysis of chaotic maps: From perspective on parameter estimation by meta-heuristic algorithm

Chaotic encryption is one of hot topics in cryptography, which has received increasing attention. Among many encryption methods, chaotic map is employed as an important source of pseudo-random numbers(PRNS). Although the randomness and the butterfly effect of chaotic map make the generated sequence look very confused, its essence is still the deterministic behavior generated by a set of deterministic parameters. Therefore, the unceasing improved parameter estimation technology becomes one of potential threats for chaotic encryption, enhancing the attacking effect of the deciphering methods. In this paper, for better analyzing the cryptography, we focus on investigating the condition of chaotic maps to resist parameter estimation. An improved particle swarm optimization(IPSO) algorithm is introduced as the estimation method. Furthermore, a new piecewise principle is proposed for increasing estimation precision. Detailed experimental results demonstrate the effectiveness of the new estimation principle, and some new requirements are summarized for a secure chaotic encryption system.

Cryptanalysis and improvement of a digital image encryption method with chaotic map lattices

A digital image encryption scheme using chaotic map lattices has been proposed recently. In this paper, two fatal flaws of the cryptosystem are pointed out. According to these two drawbacks, cryptanalysts could recover the plaintext by applying the chosen plaintext attack. Therefore, the proposed cryptosystem is not secure enough to be used in the image transmission system. Experimental results show the feasibility of the attack. As a result, we make some improvements to the encryption scheme, which can completely resist our chosen plaintext attack.