Biblio

Pairings on elliptic curves which are carried out by the Miller loop and final exponentiation are used for innovative protocols such as ID-based encryption and group signature authentication. As the recent progress of attacks for finite fields in which pairings are defined, the importance of the use of the curves with prime embedding degrees \$k\$ has been increased. In this manuscript, the authors provide a method for providing efficient final exponentiation algorithms for a specific cyclotomic family of curves with arbitrary prime \$k\$ of \$k\textbackslashtextbackslashequiv 1(\textbackslashtextbackslashtextmod\textbackslashtextbackslash 6)\$. Applying the proposed method for several curves such as \$k=7\$, 13, and 19, it is found that the proposed method gives rise to the same algorithms as the previous state-of-the-art ones by the lattice-based method.

Cloud based cyber physical system (CPS) enables individuals to store and share data collected from both cyberspace and the physical world. This leads to the proliferation of massive data at a user's local site. Since local storage systems can't store and maintain huge data, it is a wise and practical way to outsource such huge data to the cloud. Cloud storage provides scalable storage space to manage data economically and flexibly. However, the integrity of outsourced data is a critical challenge because user's lose control of their data once it's transferred to cloud servers. Several auditing schemes have been put forward based on public key infrastructure (PKI) or identity-based cryptography to verify data integrity. However, “the PKI-based schemes suffer from certificate management problem and identity-based schemes face the key escrow” problem. Therefore, to address these problems, certificateless public auditing schemes have been introduced on the basis of bilinear pairing, which incur high computation overhead, and thus it is not suitable for CPS. To reduce the computation overhead, in this paper, Using elliptic curve cryptography, we propose an efficient pairing-free certificateless public auditing scheme for cloud-based CPS. The proposed scheme is more secure against type I/II/III adversaries and efficient compared to other certificateless based schemes.

IoT is still an emerging technology without a lot of standards around it, which makes it difficult to integrate it into existing businesses, what's more, with restricted assets and expanding gadgets that essentially work with touchy information. Thus, information safety has become urgent for coders and clients. Thus, painstakingly chosen and essentially tested encryption calculations should be utilized to grow the gadgets productively, to decrease the danger of leaking the delicate information. This investigation looks at the ECC calculation (Elliptic Curve Cryptography) and Rivest-Shamir-Adleman (RSA) calculation. Furthermore, adding the study of DNA encoding operation in DNA computing with ECC to avoid attackers from getting access to the valuable data.

IT world is migrating towards utilizing cloud computing as an essential data storing and exchanging platform. With the amelioration of technology, a colossal amount of data is generating with time. Cloud computing provides an enormous data storage capacity with the flexibility of accessing it without the time and place restrictions with virtualized resources. Healthcare industries spawn intense amounts of data from various medical instruments and digital records of patients. To access data remotely from any geographical location, the healthcare industry is moving towards cloud computing. EHR and PHR are patient's digital records, which include sensitive information of patients. Apart from all the proficient service provided by cloud computing, security is a primary concern for various organizations. To address the security issue, several cryptographic techniques implemented by researchers worldwide. In this paper, a vigorous cryptographic method discussed which is implemented by combining DNA cryptography and Elliptic Curve Cryptography to protect sensitive data in the cloud.

The advantage of cryptographic systems based on elliptical curves over traditional systems is that they provide equivalent protection even when the key length used is small. This reduces the load time of the processors of the receiving and transmitting devices. But the development of computer technology leads to an increase in the stability of the cryptosystem, that is, the length of the keys. This article presents a method for converting elliptic curve equations to hidden parameter elliptic curve equations to increase stability without increasing key length.

Elliptic curve is a major area of research due to its application in elliptic curve cryptography. Due to their small key sizes, they offer the twofold advantage of reduced storage and transmission requirements. This also results in faster execution times. The authors propose an architecture to automatically generate test cases, for verification of elliptic curve operational circuits, based on user-defined prime field and the parameters used in the circuit to be tested. The ECC test case generations are based on the Galois field arithmetic operations which were the subject of previous work by the authors. One of the strengths of elliptic curve mathematics is its simplicity, which involves just three points (P, Q, and R), which pass through a line on the curve. The test cases generate points for a user-defined prime field which sequentially selects the input vector points (P and/or Q), to calculate the resultant output vector (R) easily. The testbench proposed here targets field programmable gate array (FPGAs) platforms and experimental results for ECC test case generation on different prime fields are presented, while ModelSim is used to validate the correctness of the ECC operations.

Digital signatures are increasingly used today. It replaces wet signature with the development of technology. Elliptic curve digital signature algorithm (ECDSA) is used in many applications thanks to its security and efficiency. However, some mathematical operations such as inversion operation in modulation slow down the speed of this algorithm. In this study, we propose a more efficient and secure ECDSA. In the proposed method, the inversion operation in modulation of signature generation and signature verification phases is removed. Thus, the efficiency and speed of the ECDSA have been increased without reducing its security. The proposed method is implemented in Python programming language using P-521 elliptic curve and SHA-512 algorithm.

The advantage of elliptic curve (EC) cryptographic systems is that they provide equivalent security even with small key lengths. However, the development of modern computing technologies leads to an increase in the length of keys. In this case, it is recommended to use a secret parameter to ensure sufficient access without increasing the key length. To achieve this result, the initiation of an additional secret parameter R into the EC equation is used to develop an EC-based key distribution algorithm. The article describes the algebraic structure of an elliptic curve with a secret parameter.

Homomorphic Encryption (HE) comes as a sophisticated and powerful cryptography system that can preserve the privacy of data in all cases when the data is at rest or even when data is in processing and computing. All the computations needed by the user or the provider can be done on the encrypted data without any need to decrypt it. However, HE has overheads such as big key sizes and long ciphertexts and as a result long execution time. This paper proposes a novel solution for big data analytic based on clustering and the Elliptical Curve Cryptography (ECC). The Extremely Distributed Clustering technique (EDC) has been used to divide big data into several subsets of cloud computing nodes. Different clustering techniques had been investigated, and it was found that using hybrid techniques can improve the performance and efficiency of big data analytic while at the same time data is protected and privacy is preserved using ECC.

The transmission of various facilities and services via the network is known as cloud computing. They involve data storage, data centers, networks, internet, and software applications, among other systems and features. Cryptography is a technique in which plain text is converted into cipher-text to preserve information security. It basically consists of encryption and decryption. The level of safety is determined by the category of encryption and decryption technique employed. The key plays an important part in the encryption method. If the key is leaked, anyone can intrude into the data and there is no use of this encryption. When the data is lost and the server fails to deliver it to the user, then it is to be recovered from any of the backup server using a recovery technique. The main objective is to develop an advanced method to increase the scope for data protection in cloud. Elliptic Curve Cryptography is a relatively new approach in the area of cryptography. The degree of security provides higher as compared to other Cryptographic techniques. The raw data and it’s accompanying as CII characters are combined and sent into the Elliptic Curve Cryptography as a source. This method eliminates the need for the transmitter and recipient to have a similar search database. Finally, a plain text is converted into cipher-text using Elliptic Curve Cryptography. The results are oat aimed by implementing a C program for Elliptic Curve Cryptography. Encryption, decryption and recovery using suitable algorithms are done.

In recent times, security and privacy concerns associated with IoT devices have caught the attention of research community. The problem of securing IoT devices is immensely aggravating due to advancement in technology. These IoT devices are resource-constraint i.e. in terms of power, memory, computation, etc., so they are less capable to secure themselves. So we need a better approach to secure IoT devices within the limited resources. Several studies state that for these lightweight IoT devices Elliptic Curve Cryptography (ECC) suits perfectly. But there are several elliptic curve domain parameter standards, which may be used for different security levels. When any ECC based product is deployed then the selection of a suitable elliptic curve standard according to usability is become very important. So we have to choose one suitable standard domain parameter for the required security level. In this paper, two different elliptic curve standard domain parameters named secp256k1 and secp192k1 proposed by an industry consortium named Standards for Efficient Cryptography Group (SECG) [1] are implemented and then analyzed their performances metrics. The performance of each domain parameter is measured in computation time.

Binary Edwards curves (BEC) over finite fields can be used as an additive cyclic elliptic curve group to enable elliptic curve cryptography (ECC), where the most time consuming is scalar multiplication. This operation is computed by means of the group operation, either point addition or point doubling. The most notorious property of these curves is that their group operation is complete, which mitigates the need to verify for special cases. Different formulae for the group operation in BECs have been reported in the literature. Of particular interest are those designed to work with the differential properties of the Montgomery ladder, which offer constant time computation of the scalar multiplication as well as reduced field operations count. In this work, we review and compare the complexity of BEC differential addition and doubling in terms of field operations. We also provide software implementations of scalar multiplications which employ these formulae under a fair scenario. Our work provides insights on the advantages of using BECs in ECC. Our study of the different formulae for group addition in BEC also showcases the advantages and limitations of the different design strategies employed in each case.

Cryptography is the science or process used for the encryption and decryption of data that helps the users to store important information or share it across networks where it can be read only by the intended user. In this paper, Elliptic Curve Cryptography (ECC) has been proposed because of its small key size, less memory space and high speed. Elliptic curve scalar multiplication is an important part of elliptic curve systems. Here, the scalar multiplication is performed with the help of hybrid Karatsuba multiplier as the area utilization of Karatsuba multiplier is less. An alternative of digital signature algorithm, that is, Elliptic Curve Digital Signature Algorithm (ECDSA) along with the primary operations of elliptic curves have also been discussed in this paper.

Ciphertext Policy Attribute-Based Encryption (CPABE) has gained popularity in the research area among the many proposed security models for providing fine-grained access control of data. Lightweight ECC-based CP-ABE schemes can provide feasible selective sharing from resource-constrained devices. However, the existing schemes lack support for a complete revocation mechanism at the user and attribute levels. We propose a novel scheme called Ecc Proxy based Scalable Attribute Revocation (EPSAR-CP-ABE) scheme. It extends an existing ECC-based CP-ABE scheme for lightweight IoT and smart-card devices to implement scalable attribute revocation. The scheme does not require re-distribution of secret keys and re-encryption of ciphertext. It uses a proxy server to furnish a proxy component for decryption. The dependency of the proposed scheme is minimal on the proxy server compared to the other related schemes. The storage and computational overhead due to the attribute revocation feature are negligible. Hence, the proposed EPSAR-CP-ABE scheme can be deployed practically for resource-constrained devices.

In this study, a novel decentralized authentication model is proposed for establishing a secure communications structure in VoIP applications. The proposed scheme considers a distributed architecture called the blockchain. With this scheme, we highlight the multimedia data is more resistant to some of the potential attacks according to the centralized architecture. Our scheme presents the overall system authentication architecture, and it is suitable for mutual authentication in terms of privacy and anonymity. We construct an ECC-based model in the encryption infrastructure because our structure is time-constrained during communications. This study differs from prior work in that blockchain platforms with ECC-Based Biometric Signature. We generate a biometric key for creating a unique ID value with ECC to verify the caller and device authentication together in blockchain. We validated the proposed model by comparing with the existing method in VoIP application used centralized architecture.

With the advancement in the growth of Internet-of-Things (IoT), its number of applications has also increased such as in healthcare, smart cities, vehicles, industries, household appliances, and Smart Grids (SG). One of the major applications of IoT is the SG and smart meter which consists of a large number of internet-connected sensors and can communicate bi-directionally in real-time. The SG network involves smart meters, data collectors, generators, and sensors connected with the internet. SG networks involve the generation, distribution, transmission, and consumption of electrical power supplies. It consists of Household Area Network (HAN), and Neighborhood Area Network (NAN) for communication. Smart meters can communicate bidirectionally with consumers and provide real-time information to utility offices. But this communication channel is a wide-open network for data transmission. Therefore, it makes the SG network and smart meter vulnerable to outside hacker and various Cyber-Physical System (CPS) attacks such as False Data Injection (FDI), inserting malicious data, erroneous data, manipulating the sensor reading values. Here cryptography techniques can play a major role along with the private blockchain model for secure data transmission in smart meters. Hence, to overcome these existing issues and challenges in smart meter communication we have proposed a blockchain-based system model for secure communication along with a novel Advanced Elliptic Curve Cryptography Digital Signature (AECCDS) algorithm in Fog Computing (FC) environment. Here FC nodes will work as miners at the edge of smart meters for secure and real-time communication. The algorithm is implemented using iFogSim, Geth version 1.9.25, Ganache, Truffle for compiling smart contracts, Anaconda (Python editor), and ATOM as language editor for the smart contracts.

Security is the main concern for wireless sensor nodes and exposed against malicious attacks. To secure the communication between sensor nodes several key managing arrangements are already implemented. The key managing method for any protected application must minimally deliver safety facilities such as truthfulness. Diffie–Hellman key exchange in the absence of authentication is exposed to MITM (man-in-the-middle) attacks due to which the attacker node can easily interrupt the communication, by appearing as a valid node in the network. In wireless sensor networks, single path routing is very common but it suffers with the two problems i:e link failure which results in data loss and if any node in single path is compromised, there is no alternative to send the data to the destination securely. To overcome this problem, multipath routing protocol is used which provides both availability and consistency of data. AOMDV (Ad-hoc On-demand Multipath Distance Vector Routing Protocol) is used in a proposed algorithm which provides alternative paths to reach the data packets to the destination. This paper presents an algorithm DH-SAM (Diffie-Hellman- Sybil Attack Mitigation) to spot and mitigate Sybil nodes and make the network trusted with the objective of solving the issue of MITM attack in the network. After node authentication, secure keys are established between two communicating nodes for data transmission using the Diffie-Hellman algorithm. Performance evaluation of DH-SAM is done by using different metrics such as detection rate, PDR, throughput, and average end to end (AE2E) delay.

Smart energy management system in smart grid carries a large number of sensitive data, which needs encryption algorithm to ensure the security of system communication. At present, most of the terminal devices of smart grid are embedded devices with limited computing resources, and their communication encryption mostly relies on AES encryption algorithm. It is difficult in key management and key distribution. Therefore, this paper proposes an improved ECC-AES hybrid encryption algorithm. Firstly, ECC algorithm is improved to improve the speed of encryption and decryption, and then the improved ECC algorithm is used as a supplement to AES algorithm. ECC is used to encrypt the AES key, which improves the security of the algorithm. At the same time, the experimental simulation also proves that the improved ECC algorithm has obvious performance improvement in computing time, CPU occupancy and memory usage.

In the past few years, the blockchain emerged as peer-to-peer distributed ledger technology for recording transactions, maintained by many peers without any central trusted regulatory authority through distributed public-key cryptography and consensus mechanism. It has not only given the birth of cryptocurrencies, but it also resolved various security, privacy and transparency issues of decentralized systems. This article discussed the blockchain basics overview, architecture, and blockchain security components such as hash function, Merkle tree, digital signature, and Elliptic curve cryptography (ECC). In addition to the core idea of blockchain, we focus on ECC's significance in the blockchain. We also discussed why RSA and other key generation mechanisms are not suitable for blockchain-based IoT applications. We also analyze many possible blockchain-based applications where ECC algorithm is better than other algorithms concerning security and privacy assurance. At the end of the article, we will explain the comparative analysis of ECC and RSA.

The development of technologies makes it possible to increase the power of information processing systems, but the modernization of processors brings not only an increase in performance but also an increase in the number of errors and vulnerabilities that can allow an attacker to attack the system and gain access to confidential information. White-Box cryptography allows (due to its structure) not only monitoring possible changes but also protects the processed data even with full access of the attacker to the environment. Elliptic Curve Cryptography (ECC) due to its properties, is becoming stronger and stronger in our lives, as it allows you to get strong encryption at a lower cost of processing your own algorithm. This allows you to reduce the load on the system and increase its performance.

Elliptic Curve Cryptography (ECC) is a revolution in asymmetric key cryptography which is based on the hardness of discrete logarithms. ECC offers lightweight encryption as it presents equal security for smaller keys, and reduces processing overhead. But asymmetric schemes are vulnerable to several cryptographic attacks such as plaintext attacks, known cipher text attacks etc. Frequency analysis is a type of cipher text attack which is a passive traffic analysis scenario, where an opponent studies the frequency or occurrence of single letter or groups of letters in a cipher text to predict the plain text part. Block cipher modes are not used in asymmetric key encryption because encrypting many blocks with an asymmetric scheme is literally slow and CBC propagates transmission errors. Therefore, in this research we present a new approach to defence against frequency analysis in ECC using K-Means clustering to defence against Frequency Analysis. In this proposed methodology, security of ECC against frequency analysis is achieved by clustering the points of the curve and selecting different cluster for encoding a text each time it is encrypted. This technique destroys the regularities in the cipher text and thereby guards against cipher text attacks.

In the current scenario, various forms of information are spread everywhere, especially through the Internet. A lot of valuable information is contained in the dissemination, so security issues have always attracted attention. With the emergence of cryptographic algorithms, information security has been further improved. Generally, cryptography encryption is divided into symmetric encryption and asymmetric encryption. Although symmetric encryption has a very fast computation speed and is beneficial to encrypt a large amount of data, the security is not as high as asymmetric encryption. The same pair of keys used in symmetric algorithms leads to security threats. Thus, if the key can be protected, the security could be improved. Using an asymmetric algorithm to protect the key and encrypting the message with a symmetric algorithm would be a good choice. This paper will review security issues in the information transmission and the method of hybrid encryption algorithms that will be widely used in the future. Also, the various characteristics of algorithms in different systems and some typical cases of hybrid encryption will be reviewed and analyzed to showcase the reinforcement by combining algorithms. Hybrid encryption algorithms will improve the security of the transmission without causing more other problems. Additionally, the way how the encryption algorithms combine to strength the security will be discussed with the aid of an example.

Satisfying security requirements for Mobile Ad-hoc Networks (MANETs) is a key challenge due to the limited power budget for the nodes composing those networks. Therefore, it is essential to exploit lightweight cryptographic algorithms to preserve the confidentiality of the messages being transmitted between different nodes in MANETs. At the heart of such algorithms lies the Elliptic Curve Cryptography (ECC). The importance of ECC lies in offering equivalent security with smaller key sizes, which results in faster computations, lower power consumption, as well as memory and bandwidth savings. However, when exploiting ECC in MANETs, it is essential to properly choose the parameters of ECC such that an acceptable level of confidentiality is achieved without entirely consuming the power budget of nodes. In addition, the delay of the communication should not abruptly increase. In this paper, we study the effect of changing the prime number use in ECC on power consumption, delay, and the security of the nodes in MANETs. Once a suitable prime number is chosen, a comparative analysis is conducted between two reactive routing protocols, namely, Ad-hoc on Demand Distance Vector (AODV) and Dynamic Source Routing (DSR) in terms of power consummation and delay. Experimental results show that a prime number value of 197 for ECC alongside with DSR for routing preserve an acceptable level of security for MANETs with low average power consumption and low average delay in the communication.

Blockchain is a decentralized technology that provides untampered and anonymous security service to users. Without relying on trusted third party, it can establish the value transfer between nodes and reduce the transaction costs. Mature public key cryptosystem and signature scheme are important basis of blockchain security. Currently, most of the public key cryptosystems are based on classic difficult problems such as RSA and ECC. However, the above asymmetric cryptosystems are no longer secure with the development of quantum computing technology. To resist quantum attacks, researchers have proposed encryption schemes based on lattice recently. Although existing schemes have theoretical significance in blockchain, they are not suitable for the practical application due to the large size of key and signature. To tackle the above issues, this paper proposes an anti-quantum signature scheme over ideal lattice in blockchain. First, we transfer the signature scheme from the standard lattice to the ideal lattice, which reduces the size of public key. Afterwards, a novel signature scheme is proposed to reduce both the size of the private and public key significantly. Finally, we theoretically prove the security of our ideal lattice-based signature scheme with a reduction to the hardness assumption of Ideal Small Integer Sulotion problem which can resist quantum attacks. The efficiency analysis demonstrates that our signature scheme can be practically used in blockchain.

Mobile Adhoc networks (MANETs) comprises of mobile devices or nodes that are connected wirelessly and have no infrastructure. Detecting malicious activities in MANETs is a challenging task as they are vulnerable to attacks where the performance of the entire network degrades. Hence it is necessary to provide security to the network so that the nodes are prone to attack. Selecting a good routing protocol in MANET is also important as frequent change of topology causes the route reply to not arrive at the source node. In this paper, R-AODV (Reverse Adhoc On-Demand Distance Vector) protocol along with ECC (Elliptic Key Cryptography) algorithm is designed and implemented to detect and to prevent the malicious node and to secure data transmission against blackhole attack. The main objective is to keep the data packets secure. ECC provides a smaller key size compared to other public-key encryption and eliminates the requirement of pre-distributed keys also makes the path more secure against blackhole attacks in a MANET. The performance of this proposed system is simulated by using the NS-2.35 network simulator. Simulation results show that the proposed protocol provides good experimental results on various metrics like throughput, end-to-end delay, and PDR. Analysis of the results points to an improvement in the overall network performance.