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.

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.

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.

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.

Generalized synchronization between different chaotic maps via dead-beat control

This paper presents a new scheme to achieve generalized synchronization（GS） between different discrete-time chaotic（hyperchaotic） systems.The approach is based on a theorem,which assures that GS is achieved when a structural condition on the considered class of response systems is satisfied.The method presents some useful features：it enables exact GS to be achieved in finite time（i.e.,dead-beat synchronization）;it is rigorous,systematic,and straightforward in checking GS;it can be applied to a wide class of chaotic maps.Some examples of GS,including the Grassi-Miller map and a recently introduced minimal 2-D quadratic map,are illustrated.

A Novel Robust Watermarking Algorithm for Encrypted Medical Image Based on DTCWT-DCT and Chaotic Map

In order to solve the problem of patient information security protection in medical images,whilst also taking into consideration the unchangeable particularity of medical images to the lesion area and the need for medical images themselves to be protected,a novel robust watermarking algorithm for encrypted medical images based on dual-tree complex wavelet transform and discrete cosine transform(DTCWT-DCT)and chaotic map is proposed in this paper.First,DTCWT-DCT transformation was performed on medical images,and dot product was per-formed in relation to the transformation matrix and logistic map.Inverse transformation was undertaken to obtain encrypted medical images.Then,in the low-frequency part of the DTCWT-DCT transformation coefficient of the encrypted medical image,a set of 32 bits visual feature vectors that can effectively resist geometric attacks are found to be the feature vector of the encrypted medical image by using perceptual hashing.After that,different logistic initial values and growth parameters were set to encrypt the watermark,and zero-watermark technology was used to embed and extract the encrypted medical images by combining cryptography and third-party concepts.The proposed watermarking algorithm does not change the region of interest of medical images thus it does not affect the judgment of doctors.Additionally,the security of the algorithm is enhanced by using chaotic mapping,which is sensitive to the initial value in order to encrypt the medical image and the watermark.The simulation results show that the pro-posed algorithm has good homomorphism,which can not only protect the original medical image and the watermark information,but can also embed and extract the watermark directly in the encrypted image,eliminating the potential risk of decrypting the embedded watermark and extracting watermark.Compared with the recent related research,the proposed algorithm solves the contradiction between robustness and invisibility of the watermarking algorithm for encrypted medical images,and it has good results against both conventional attacks and geometric attacks.Under geometric attacks in particular,the proposed algorithm performs much better than existing algorithms.

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.

A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors

We study a novel class of two-dimensional maps with infinitely many coexisting attractors.Firstly,the mathematical model of these maps is formulated by introducing a sinusoidal function.The existence and the stability of the fixed points in the model are studied indicating that they are infinitely many and all unstable.In particular,a computer searching program is employed to explore the chaotic attractors in these maps,and a simple map is exemplified to show their complex dynamics.Interestingly,this map contains infinitely many coexisting attractors which has been rarely reported in the literature.Further studies on these coexisting attractors are carried out by investigating their time histories,phase trajectories,basins of attraction,Lyapunov exponents spectrum,and Lyapunov(Kaplan–Yorke)dimension.Bifurcation analysis reveals that the map has periodic and chaotic solutions,and more importantly,exhibits extreme multi-stability.

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features：（i） it enables synchronization to be achieved for both cases of n 〈 m and n 〉 m;（ii） it is rigorous,being based on theorems;（iii） it can be readily applied to any chaotic（hyperchaotic） maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map（as the drive system） and the three-dimensional hyperchaotic Wang map（as the response system）,and the three-dimensional H′enon-like map（as the drive system） and the two-dimensional Lorenz discrete-time system（as the response system）.

Double Encryption Using Trigonometric Chaotic Map and XOR of an Image

In the most recent decades,a major number of image encryption plans have been proposed.The vast majority of these plans reached a highsecurity level;however,their moderate speeds because of their complicated processes made them of no use in real-time applications.Inspired by this,we propose another efficient and rapid image encryption plan dependent on the Trigonometric chaotic guide.In contrast to the most of current plans,we utilize this basic map to create just a couple of arbitrary rows and columns.Moreover,to additionally speed up,we raise the processing unit from the pixel level to the row/column level.The security of the new plot is accomplished through a substitution permutation network,where we apply a circular shift of rows and columns to break the solid connection of neighboring pixels.At that point,we join the XOR operation with modulo function to cover the pixels values and forestall any leaking of data.High-security tests and simulation analyses are carried out to exhibit that the scheme is very secure and exceptionally quick for real-time image processing at 80 fps(frames per second).

无线基带信道模型Chaotic-Map误码特性分析

介绍了一种新的基于混沌映射的基带信道模型,即Chaotic-Map模型。对此模型的意义和用法进行了详细描述,研究了该模型中参数取值与信道特性的对应关系,并且通过仿真验证了该模型对具有突发误码特性的无线信道的适应性。

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.

High Security Nested PWLCM Chaotic Map Bit-Level Permutation Based Image Encryption

Chaotic systems produce pseudo-random sequences with good randomness;therefore, these systems are suitable to efficient image encryption. In this paper, a low complexity image encryption based on Nested Piece Wise Linear Chaotic Map (NPWLCM) is proposed. Bit planes of the grey or color levels are shuffled to increase the encryption complexity. A security analysis of the proposed system is performed and presented. The proposed method combine pixel shuffling, bit shuffling, and diffusion, which is highly disorder the original image. The initial values and the chaos control parameters of NPWLCM maps are derived from external secret key. The cipher image generated by this method is the same size as the original image and is suitable for practical use in the secure transmission of confidential information over the Internet. The experimental results of the proposed method show advantages of low complexity, and high-level security.

Permutation-substitution image encryption scheme based on a modified chaotic map in transform domain

A new chaotic image encryption scheme based on permutation and substitution in the Fourier domain is presented.Fractional Fourier Transform(FRFT)is used before the encryption scheme to get a large degree of randomization.The permutation is achieved by Baker map and the substitution by a key-related-to-plain-image algorithm based on the modified Logistic map.Modification of the Logistic map is developed to increase the space of the encryption key,and hence increase the security.The key of the encryption algorithm dependents on the plain image,and thus,the cipher image is sensitive to both the initial key and the plain image to resist known-plaintext and chosen plaintext attacks.The key space is large and hence the algorithm can effectively resist brute-force attacks.The proposed scheme is examined using different performance evaluation metrics and the results prove that the proposed scheme is highly secure,and it can effectively resist different attacks.

Optical Image Encryption Based on Mixed Chaotic Maps and Single-Shot Digital Holography

Random phase masks play a key role in optical image encryption schemes based on double random phase technique. In this paper, a mixed chaotic method is proposed, which can efficiently solve some weaknesses that one-dimensional (1-D) single chaotic maps encounter to generate random phase masks. Based on the chaotic random phase masks, optical image encryption and decryption are realized with a single-shot digital holographic technique. In the proposed encryption scheme, the initial value and parameters of mixed chaotic maps serve as secret keys, which is convenient for the key management and transmission. Moreover, it also possesses high resistance against statistical attack, brute-force attack, noise attack and shear attack. Simulation results and security analysis verify the validity and security of the proposed encryption scheme. © 2017, Tianjin University and Springer-Verlag Berlin Heidelberg.

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.

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.

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem

We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM)with the discrete fractional difference.Moreover,the chaos behaviors of the proposed map are observed and the bifurcation diagrams,the largest Lyapunov exponent plot,and the phase portraits are derived,respectively.Finally,with the secret keys generated by Menezes-Vanstone elliptic curve cryptosystem,we apply the discrete fractional map into color image encryption.After that,the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms.

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.