An approach of encryption that combines ECC and the adjacency matrices of graphs using extended generalized Lucas matrix as key matrix

The most important approaches for safeguarding our communications and data nowadays are message encryption techniques. The use of the internet and network communications has increased the pace of message encryption technology development. Sharing sensitive, private messages through unsecured networks makes it possible for an attack, theft, or hacking of the messages. In order to reduce this term, cryptographic methods have been found essential. There are several symmetric enciphering methods; a few examples are the Caesar Cipher, Hill Cipher, and others. In order to generate a complex cipher text, the enciphering method described in this article encrypts and decrypts the messages given to it using a selfinvertible key matrix and an adjacency matrix of certain graphs like A graph, Centipede C2, Domino graph. Since we are using the self-invertible matrix as a key matrix, whose inverse always exists, thus we can decode the ciphertext without computing the inverse of the key matrix. The lessening in computational complexity facilitates our ability to determine the inverse of a key matrix.

This is a paper on Elliptic Curve Cryptography (ECC), which is a public-key cryptosystem for encoding data and forwarding over unsecure networks. The technical description and benefits of ECC are stated and contrasted with other cryptosystems. This is then followed by a proposal for a new image cryptosystem, which is based on the binary value of pixels and grouping bits. A simple application is executed to show how the ECC can be used to convert, group, map and encrypt an image. Finally, an analysis is carried out to ascertain the strength of the encrypted image to withstand statistical and brute force attacks.

This paper is concerned with the identification of important nodes in node-weighted graphs by applying matrix functions, in particular the matrix exponential. Many tools that use an adjacency matrix for a graph have been developed to study the importance of the nodes in unweighted or edge-weighted networks. However, adjacency matrices for node-weighted graphs have not received much attention. The present paper proposes using a line graph associated with a node-weighted graph to construct an edge-weighted graph that can be analyzed with available methods. Both undirected and directed graphs with positive node weights are considered. We show that when the weight of a node increases, the importance of this node in the graph increases as well, provided that the adjacency matrix is suitably scaled. Applications to real-life problems are presented.

Elliptic curve cryptography includes symmetric key cryptography systems that base their security on mathematical problems of elliptic curves. There are several ways that can be used to define the elliptic curve equation that depends on the infinite field used, one of which is the infinite field prima ( where ). Elliptic curve cryptography can be used for multiple protocol purposes, digital signatures, and encryption schemes.The purpose of this study is to determine the process of hiding encrypted messages using the Noiseless Steganography method as well as the generation of private keys and public keys and the process of verifying the validity of the Elliptic Curves Cryptography Digital Signature Algorithm (ECDSA). The result of this thesis is that a line graph is obtained that store or hides a message using the steganography method and a message authenticity from the process of key generation and verification of validity using the ECDSA method. By selecting three samples consisting of one test sample and two differentiating samples, a line graph, an MD5 hash value, and a value at the point are obtained different. Successively obtained values to message “Matematika 2018”, “MATEMATIKA 2018”, and “2018 matematika” are and . The discussion in this thesis only covers the elliptic curves on prime finite field. So, for the next thesis, the next researcher can do a discussion about the elliptic curve on the finite field or the application of elliptic curve cryptography and other steganographic methods

Various applications use asymmetric cryptography to secure communications between both parties, and it raises the main issue of generating vast amounts of computation and storage. Thus, elliptic curve cryptography (ECC) is a methodology that emerged to overcome this issue using its low computation and generation of small keys with its strong encryption strategy. ECC is becoming mandatory and used mostly for public key encryption protocols. ECC has expanded cumulative acceptance in practice due to the reduced bit magnitude of operands compared to RSA for safety level. Previously, protocols designed for ECC suggested calculation of scalar development and it was accomplished in finite fields as projective, affine, and Jacobian simulations of coordinates. Arithmetic operations in a limited area establish the core benefits of the ECC algorithm. Even though ECC generated an issue of complex key generation using its curve formation, to overcome this issue a hyperelliptic curve cryptosystems (HECC) is proposed in this study. HECC perform ECC in the Public Key Cryptography (PKC) domain. This study presented an optimization-based key generation and made a random selection of integers for encrypting the message. Selecting a prime number as the private key and multiplying it to the encrypted message to generate a public key is done. This encrypted message is mapped to the curve to check whether it satisfies the curve equation or not. Once an encrypted message is obtained, it is then sent to a second party for pursuing the message. On the side of the second party, a reverse process called decryption takes place. Thus, a secured transmission of data communication takes place. Implementing this algorithm in MATLAB resulted in 94% accuracy and an error of 6%, which was a higher performance ratio than previous methods.

In this paper, a modified of Jena remote user authentication scheme using smart cards based on Elliptic Curve Discrete Logarithm Problem (ECDLP) has been proposed. A remote user authentication scheme is a two-party protocol whereby an authentication server confirms the identity of a remote individual logging on to the server over an untrusted, unsecured network. The password based authentication schemes are commonly used for authenticating remote users. Many passwords based schemes both with and without smart card have been proposed; each scheme has its merits and demerits. However, the scheme proposed by Jena is vulnerable to the masquerade attack. In this paper, we shall discuss the masquerade attack on their scheme. Furthermore, we shall present an enhanced scheme for preventing the above attack.

Many computing systems have recently suffered significantly from hacking and preventing hacking is important in protecting business, sensitive information and every day network communications. Many efforts have been made to provide security assurance by proposing security solutions. However, the gap between hacking incidents and current security solutions is significant. Fortunately, hacking attempts can be addressed if the pre-hacking step, called scanning, is properly investigated and good counter measures are in place. The importance of scanning appears is in providing sophisticated hackers with the necessary information about nominated victims systems which eventually forms their hacking strategies. Therefore, this article proposes a security solution that aims to make scanning difficult by addressing its properties, which makes developing hacking strategies against protected computer networks unpractical. The proposed security solution protects computer networks by dynamically generating a unique protocol to replace the expected standard protocols and changing network paths periodically in order to confuse scanning attempts, as well as to prevent unauthorized scanning and hacking traffic. Key Words: hacking,sensitive information, unauthorized scanning, hacking traffic, network communications

Elliptic Curve Cryptography (ECC) is a promising public key cryptography, probably takes the place of RSA. Not only ECC uses less memory, key pair generation and signing are considerably faster, but also ECC's key size is less than that of RSA while it achieves the same level of security. However, the magic behind RSA and its friends can be easily explained, is also widely understood, the foundations of ECC are still a mystery to most of us. This paper's aims are to provide detailed mathematical foundations of ECC, especially, the subgroup and its generator (also called base point) formed by one elliptic curve are researched as highlights, because they are very important for practical ECC implementation. The related algorithms and their implementation details are demonstrated, which is useful for the computing devices with restricted resource, such as embedded systems, mobile devices and IoT devices.

In this study, elliptic curve cryptography (ECC) is elected for tenant authentication, data encryption, and data decryption due to its minimum key size. The proposed ECC‐based authentication approach allows the authorised person to access private data; it protects different related attacks effectively. To develop more secure data encryption, the authors have combined a nature‐inspired optimisation, such as a moth search algorithm (MSA) with ECC, to select the correct and optimal value of the elliptic curve. The proposed encryption and decryption approach combines DNA encoding with the ECC encryption algorithm. The mechanism of DNA encoded ECC provided multi‐level security with less computational power. The security analysis of the proposed method has been provided to prove its effectiveness against certain attacks, such as denial‐of‐service attack, impersonation attack, reply attack, plaintext attack and chosen‐ciphertext attack. The experimental result is evaluated based on encryption time, decryption time, throughput and key size of the security model. The average execution time of the proposed encryption and decryption is only 83.153 and 86.076 s, respectively. From the evaluation, it is clearly determined that the proposed technique provides two‐layer security with minimum key size and less storage space.

This paper aims to provide a comprehensive review on Elliptic Curve Cryptography (ECC), a public key cryptographic system and its applications. The paper discusses important mathematical properties and operations of elliptic curves, like point addition and multiplication operations and its implementation in cryptographic methods such as encryption and decryption. This paper provides a detailed workout on important mathematical problems on elliptic curves and ECC which provides insight into working of essential cryptographic techniques in ECC. And the paper also provides a literature review of research works based on ECC in various fields such as Internet of Things (IoT), Cloud computing, Blockchain and Image Security. And the paper further provides insight into the recent applications of ECC in fields like IoT and Blockchain by comprehensively discussing the proposed mechanism for each of the recent applications and also briefly discussing the security of the proposed mechanism.

A systematic review on elliptic curve cryptography algorithm for internet of things: Categorization, application areas, and security

Elliptic curve cryptography (ECC) provides a secure means of exchanging keys among communicating hosts using the Diffie Hellman key exchange algorithm. Encryption and decryption of texts and messages have also been attempted. This paper presents the ECC implementation for digital signature authentication and then applying the knapsack algorithm on ECC signing message. In this paper, we attempt to provide more secure digital signature scheme by using knapsack based ECC. We compare our proposed algorithm with RSA based digital signature authentication algorithm and show that our algorithm is better due to the high degree of sophistication and complexity involved. It is almost infeasible to attempt a brute force attack. Moreover, only one parameter namely the knapsack vector a i needs to be kept secret. On the contrary in RSA, three parameters such as the modulus n, its factors p and q need to be kept secret.

Internet of Things (IoT) is a network paradigm in which data aggregation and data security plays a vital role. Data aggregation in IoT describes collection of information from different users and data security means encryption of collected data using cryptography method. The proposed work comprises of devices and gateway to perform data aggregation and data encryption. Data aggregation is performed using clustering in which data are clustered and secured by Particle Swarm Optimization (PSO) algorithm which finds the cluster head. After finding cluster head, nodes requests to join as cluster member. PSO computes fitness function using metrics i.e. energy, end-to-end delay, scoring factor, packet drops and successful packet transformation. After completion of clustering process, data encryption process is held in which, cluster head collects data from the cluster members and encrypts it using Elliptic Curve Cryptography (ECC) method. Finally, encrypted data are dispatched to gateway device. Experimental result shows, the proposed work on Secure Particle Swarm Optimization (SPSO)prompts better performance in following metrics i.e. delay, throughput and energy consumption.

Healthcare centre is the most susceptible sctor. Cyber-attack on medical institutions, such as hospitals and health care centre have increased year after year. Autism health care centre is one of the victims. Autism MRI scan images include sensitive and confidential information about a patient's health and other personal information. Therefore, image encryption is a fundamental aspect of information security, especially in today's digital era where the proliferation of images and the need to protect sensitive visual content are of paramount importance. In order to protect the confidentiality and integrity of images, image encryption techniques work to make sure that only authorised users can view and understand the visual data while prohibiting unauthorised access and modification. The pixel values and spatial properties of the image are hidden using a variety of cryptographic methods and key-based actions. Symmetric encryption algorithm, like Advanced Encryption Standard (AES), which use the same key for encryption and decryption operations, are among the famous image encryption techniques. After that, asymmetric encryption algorithm like Rivest-Shamir-Adleman (RSA), which employ two distinct keys for both encryption and decryption. Next, the research includes a hybridization method of Elliptic Curve Cryptography (ECC) with the Hill Cypher (HC) for image encryption and decryption. There are five different Autism MRI Scan images selected to be used as the input image for encryption process. Then, each image will have two different file format which is PNG and BMP and two different file size which is 256*256px and 512*512px. This research's goal is to compare how well symmetric encryption, asymmetric encryption and hybrid encryption work as three separate image encryption techniques. This can help users rapidly and efficiently speed up the encryption and decryption of images and enhance the security of MRI scan images. By applying differential analysis parameters like Number of Pixel Change Rate (NPCR), Unified Average Changing Intensity (UACI) and statistical analysis parameters like Histogram Analysis (HA), the characteristics of the image encryption approach are examined. At the end of the experiment, AES encryption proves to be the best among the three types of encryption with better performance in terms of security with NPCR percentage of 99.72%, UACI percentage of 32.68% and has a higher speed of encryption which only takes 0.0238s but has the second-best distribution in HA of pixel value to frequency compares to ECC with HC.

In today’s world, the progress of communication technology plays a role in our everyday lives. The internet and the conversion of data into forms have significantly expanded the sharing of information leading to fast-paced growth. Despite having secure methods available, safeguarding data remains a top priority. This study aims to improve the security and durability of data transmission by combining steganography and cryptography techniques. Steganography, which involves hiding messages within another medium, and cryptography which entails encrypting messages using keys are both effective ways to ensure data security. The research delves into combinations of algorithms that integrate steganography and cryptography examining their impact on enhancing security. It categorizes methods based on technical and non-technical aspects as well as their domains. Moreover, it underscores the importance of data security in media formats such as images, videos, and audio. In analyzing message lengths noticeable character patterns were observed in both Vigenère Cipher and Elliptic Curve Cryptography. In short messages "s" was prominent in the Vigenère Cipher accounting for 26.3% of occurrences while Elliptic Curve Cryptography showed a prevalence of "t" at 3.9%. Medium-length messages continued to show the dominance of "s" in the Vigenère Cipher at 22.5% while Elliptic Curve Cryptography highlighted "p" as a character at 4.3%. Lastly, longer messages maintained the prevalence of "s" in the Vigenère Cipher at 24.3% with "v" emerging as dominant in Elliptic Curve Cryptography at 3.9%. These findings show that combining steganography and cryptography methods can greatly enhance the protection of multimedia data.