Sensitive Information Security Based on Elliptic Curves

The elliptic curve cryptography algorithm represents a major advancement in the field of computer security. This innovative algorithm uses elliptic curves to encrypt and secure data, providing an exceptional level of security while optimizing the efficiency of computer resources. This study focuses on how elliptic curves cryptography helps to protect sensitive data. Text is encrypted using the elliptic curve technique because it provides great security with a smaller key on devices with limited resources, such as mobile phones. The elliptic curves cryptography of this study is better than using a 256-bit RSA key. To achieve equivalent protection by using the elliptic curves cryptography, several Python libraries such as cryptography, pycryptodome, pyQt5, secp256k1, etc. were used. These technologies are used to develop a software based on elliptic curves. If built, the software helps to encrypt and decrypt data such as a text messages and it offers the authentication for the communication.

Remote sensing image encryption algorithm based on novel hyperchaos and an elliptic curve cryptosystem

Remote sensing images carry crucial ground information,often involving the spatial distribution and spatiotemporal changes of surface elements.To safeguard this sensitive data,image encryption technology is essential.In this paper,a novel Fibonacci sine exponential map is designed,the hyperchaotic performance of which is particularly suitable for image encryption algorithms.An encryption algorithm tailored for handling the multi-band attributes of remote sensing images is proposed.The algorithm combines a three-dimensional synchronized scrambled diffusion operation with chaos to efficiently encrypt multiple images.Moreover,the keys are processed using an elliptic curve cryptosystem,eliminating the need for an additional channel to transmit the keys,thus enhancing security.Experimental results and algorithm analysis demonstrate that the algorithm offers strong security and high efficiency,making it suitable for remote sensing image encryption tasks.

Data Mining with Privacy Protection Using Precise Elliptical Curve Cryptography

Protecting the privacy of data in the multi-cloud is a crucial task.Data mining is a technique that protects the privacy of individual data while mining those data.The most significant task entails obtaining data from numerous remote databases.Mining algorithms can obtain sensitive information once the data is in the data warehouse.Many traditional algorithms/techniques promise to provide safe data transfer,storing,and retrieving over the cloud platform.These strategies are primarily concerned with protecting the privacy of user data.This study aims to present data mining with privacy protection(DMPP)using precise elliptic curve cryptography(PECC),which builds upon that algebraic elliptic curve infinitefields.This approach enables safe data exchange by utilizing a reliable data consolidation approach entirely reliant on rewritable data concealing techniques.Also,it outperforms data mining in terms of solid privacy procedures while maintaining the quality of the data.Average approximation error,computational cost,anonymizing time,and data loss are considered performance measures.The suggested approach is practical and applicable in real-world situations according to the experimentalfindings.

Logistic Regression with Elliptical Curve Cryptography to Establish Secure IoT

Nowadays,Wireless Sensor Network(WSN)is a modern technology with a wide range of applications and greatly attractive benefits,for example,self-governing,low expenditure on execution and data communication,long-term function,and unsupervised access to the network.The Internet of Things(IoT)is an attractive,exciting paradigm.By applying communication technologies in sensors and supervising features,WSNs have initiated communication between the IoT devices.Though IoT offers access to the highest amount of information collected through WSNs,it leads to privacy management problems.Hence,this paper provides a Logistic Regression machine learning with the Elliptical Curve Cryptography technique(LRECC)to establish a secure IoT structure for preventing,detecting,and mitigating threats.This approach uses the Elliptical Curve Cryptography(ECC)algorithm to generate and distribute security keys.ECC algorithm is a light weight key;thus,it minimizes the routing overhead.Furthermore,the Logistic Regression machine learning technique selects the transmitter based on intelligent results.The main application of this approach is smart cities.This approach provides continuing reliable routing paths with small overheads.In addition,route nodes cooperate with IoT,and it handles the resources proficiently and minimizes the 29.95%delay.

A Secure Hardware Implementation for Elliptic Curve Digital Signature Algorithm

Since the end of the 1990s,cryptosystems implemented on smart cards have had to deal with two main categories of attacks:side-channel attacks and fault injection attacks.Countermeasures have been developed and validated against these two types of attacks,taking into account a well-defined attacker model.This work focuses on small vulnerabilities and countermeasures related to the Elliptic Curve Digital Signature Algorithm(ECDSA)algorithm.The work done in this paper focuses on protecting the ECDSA algorithm against fault-injection attacks.More precisely,we are interested in the countermeasures of scalar multiplication in the body of the elliptic curves to protect against attacks concerning only a few bits of secret may be sufficient to recover the private key.ECDSA can be implemented in different ways,in software or via dedicated hardware or a mix of both.Many different architectures are therefore possible to implement an ECDSA-based system.For this reason,this work focuses mainly on the hardware implementation of the digital signature ECDSA.In addition,the proposed ECDSA architecture with and without fault detection for the scalar multiplication have been implemented on Xilinxfield programmable gate arrays(FPGA)platform(Virtex-5).Our implementation results have been compared and discussed.Our area,frequency,area overhead and frequency degradation have been compared and it is shown that the proposed architecture of ECDSA with fault detection for the scalar multiplication allows a trade-off between the hardware overhead and the security of the ECDSA.

Text Encryption Using Pell Sequence and Elliptic Curves with Provable Security

The demand for data security schemes has increased with the significant advancement in the field of computation and communication networks.We propose a novel three-step text encryption scheme that has provable security against computation attacks such as key attack and statistical attack.The proposed scheme is based on the Pell sequence and elliptic curves,where at the first step the plain text is diffused to get a meaningless plain text by applying a cyclic shift on the symbol set.In the second step,we hide the elements of the diffused plain text from the attackers.For this purpose,we use the Pell sequence,a weight function,and a binary sequence to encode each element of the diffused plain text into real numbers.The encoded diffused plain text is then confused by generating permutations over elliptic curves in the third step.We show that the proposed scheme has provable security against key sensitivity attack and statistical attacks.Furthermore,the proposed scheme is secure against key spacing attack,ciphertext only attack,and known-plaintext attack.Compared to some of the existing text encryption schemes,the proposed scheme is highly secure against modern cryptanalysis.

Asymmetric Key Cryptosystem for Image Encryption by Elliptic Curve over Galois Field GF(2^(n))

Protecting the integrity and secrecy of digital data transmitted through the internet is a growing problem.In this paper,we introduce an asymmetric key algorithm for specifically processing images with larger bit values.To overcome the separate flaws of elliptic curve cryptography(ECC)and the Hill cipher(HC),we present an approach to picture encryption by combining these two encryption approaches.In addition,to strengthen our scheme,the group laws are defined over the rational points of a given elliptic curve(EC)over a Galois field(GF).The exclusive-or(XOR)function is used instead of matrix multiplication to encrypt and decrypt the data which also refutes the need for the inverse of the key matrix.By integrating the inverse function on the pixels of the image,we have improved system security and have a wider key space.Furthermore,through comprehensive analysis of the proposed scheme with different available analyses and standard attacks,it is confirmed that our proposed scheme provides improved speed,security,and efficiency.

A Low-Cost and High-Performance Cryptosystem Using Tripling-Oriented Elliptic Curve

Developing a high-performance public key cryptosystem is crucial for numerous modern security applications.The Elliptic Curve Cryptosystem(ECC)has performance and resource-saving advantages compared to other types of asymmetric ciphers.However,the sequential design implementation for ECC does not satisfy the current applications’performance requirements.Therefore,several factors should be considered to boost the cryptosystem performance,including the coordinate system,the scalar multiplication algo-rithm,and the elliptic curve form.The tripling-oriented(3DIK)form is imple-mented in this work due to its minimal computational complexity compared to other elliptic curves forms.This experimental study explores the factors playing an important role in ECC performance to determine the best combi-nation that leads to developing high-speed ECC.The proposed cryptosystem uses parallel software implementation to speed up ECC performance.To our knowledge,previous studies have no similar software implementation for 3DIK ECC.Supported by using parallel design,projective coordinates,and a fast scalar multiplication algorithm,the proposed 3DIK ECC improved the speed of the encryption process compared with other counterparts and the usual sequential implementation.The highest performance level for 3DIK ECC was achieved when it was implemented using the Non-Adjacent Form algorithm and homogenous projection.Compared to the costly hardware implementations,the proposed software implementation is cost effective and can be easily adapted to other environments.In addition,the power con-sumption of the proposed ECC is analyzed and compared with other known cryptosystems.thus,the current study presents a detailed overview of the design and implementation of 3DIK ECC.

Smart Grid Communication Under Elliptic Curve Cryptography

Smart Grids(SGs)are introduced as a solution for standard power dis-tribution.The significant capabilities of smart grids help to monitor consumer behaviors and power systems.However,the delay-sensitive network faces numer-ous challenges in which security and privacy gain more attention.Threats to trans-mitted messages,control over smart grid information and user privacy are the major concerns in smart grid security.Providing secure communication between the service provider and the user is the only possible solution for these security issues.So,this research work presents an efficient mutual authentication and key agreement protocol for smart grid communication using elliptic curve crypto-graphy which is robust against security threats.A trust authority module is intro-duced in the security model apart from the user and service provider for authentication.The proposed approach performance is verified based on different security features,communication costs,and computation costs.The comparative analysis of experimental results demonstrates that the proposed authentication model attains better performance than existing state of art of techniques.

Secure and efficient elliptic curve cryptography resists side-channel attacks

An embedded cryptosystem needs higher reconfiguration capability and security. After analyzing the newly emerging side-channel attacks on elliptic curve cryptosystem （ECC）, an efficient fractional width-w NAF （FWNAF） algorithm is proposed to secure ECC scalar multiplication from these attacks. This algorithm adopts the fractional window method and probabilistic SPA scheme to reconfigure the pre-computed table, and it allows designers to make a dynamic configuration on pre-computed table. And then, it is enhanced to resist SPA, DPA, RPA and ZPA attacks by using the random masking method. Compared with the WBRIP and EBRIP methods, our proposals has the lowest total computation cost and reduce the shake phenomenon due to sharp fluctuation on computation performance.

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.

A Novel Approach towards Cost Effective Region-Based Group Key Agreement Protocol for Ad Hoc Networks Using Elliptic Curve Cryptography

This paper addresses an interesting security problem in wireless ad hoc networks: the dynamic group key agreement key establishment. For secure group communication in an ad hoc network, a group key shared by all group members is required. This group key should be updated when there are membership changes (when the new member joins or current member leaves) in the group. In this paper, we propose a novel, secure, scalable and efficient region-based group key agreement protocol for ad hoc networks. This is implemented by a two-level structure and a new scheme of group key update. The idea is to divide the group into subgroups, each maintaining its subgroup keys using group elliptic curve diffie-hellman (GECDH) Protocol and links with other subgroups in a tree structure using tree-based group elliptic curve diffie-hellman (TGECDH) protocol. By introducing region-based approach, messages and key updates will be limited within subgroup and outer group;hence computation load is distributed to many hosts. Both theoretical analysis and experimental results show that this Region-based key agreement protocol performs well for the key establishment problem in ad hoc network in terms of memory cost, computation cost and communication cost.

Cryptanalysis and Improvement of Signcryption Schemes on Elliptic Curves

In this paper, we analyze two signcryption schemes on elliptic curves proposed by Zheng Yu-liang and Hideki Imai. We point out a serious problem with the schemes that the elliptic curve based signcryption schemes lose confidentiality to gain non-repudiation. We also propose two improvement versions that not only overcome the security leak inherent in the schemes but also provide public verifiability or forward security. Our improvement versions require smaller computing cost than that required by signature-then-encryption methods.

Secured Data Storage Using Deduplication in Cloud Computing Based on Elliptic Curve Cryptography

The tremendous development of cloud computing with related technol-ogies is an unexpected one.However,centralized cloud storage faces few chal-lenges such as latency,storage,and packet drop in the network.Cloud storage gets more attention due to its huge data storage and ensures the security of secret information.Most of the developments in cloud storage have been positive except better cost model and effectiveness,but still data leakage in security are billion-dollar questions to consumers.Traditional data security techniques are usually based on cryptographic methods,but these approaches may not be able to with-stand an attack from the cloud server's interior.So,we suggest a model called multi-layer storage(MLS)based on security using elliptical curve cryptography(ECC).The suggested model focuses on the significance of cloud storage along with data protection and removing duplicates at the initial level.Based on divide and combine methodologies,the data are divided into three parts.Here,thefirst two portions of data are stored in the local system and fog nodes to secure the data using the encoding and decoding technique.The other part of the encrypted data is saved in the cloud.The viability of our model has been tested by research in terms of safety measures and test evaluation,and it is truly a powerful comple-ment to existing methods in cloud storage.

Comparative Evaluation of Elliptic Curve Cryptography Based Homomorphic Encryption Schemes for a Novel Secure Multiparty Computation

In this paper, we focus on Elliptic Curve Cryptography based approach for Secure Multiparty Computation (SMC) problem. Widespread proliferation of data and the growth of communication technologies have enabled collaborative computations among parties in distributed scenario. Preserving privacy of data owned by parties is crucial in such scenarios. Classical approach to SMC is to perform computation using Trusted Third Party (TTP). However, in practical scenario, TTPs are hard to achieve and it is imperative to eliminate TTP in SMC. In addition, existing solutions proposed for SMC use classical homomorphic encryption schemes such as RSA and Paillier. Due to the higher cost incurred by such cryptosystems, the resultant SMC protocols are not scalable. We propose Elliptic Curve Cryptography (ECC) based approach for SMC that is scalable in terms of computational and communication cost and avoids TTP. In literature, there do exist various ECC based homomorphic schemes and it is imperative to investigate and analyze these schemes in order to select the suitable for a given application. In this paper, we empirically analyze various ECC based homomorphic encryption schemes based on performance metrics such as computational cost and communication cost. We recommend an efficient algorithm amongst several selected ones, that offers security with lesser overheads and can be applied in any application demanding privacy.

Secure Authentication of WLAN Based on Elliptic Curve Cryptosystem

The security of wireless local area network (WLAN) becomes a bottleneck for its further applications. At present, many standard organizations and manufacturers of WLAN try to solve this problem. However, owing to the serious secure leak in IEEE802.11 standards, it is impossible to utterly solve the problem by simply adding some remedies. Based on the analysis on the security mechanism of WLAN and the latest techniques of WLAN security, a solution to WLAN security was presented. The solution makes preparation for the further combination of WLAN and Internet.

ASIP for Elliptic Curve Cryptography Based on VLIW Architecture

The requirement of the flexible and effective implementation of the Elliptic Curve Cryptography (ECC) has become more and more exigent since its dominant position in the public-key cryptography application.Based on analyzing the basic structure features of Elliptic Curve Cryptography (ECC) algorithms,the parallel schedule algorithm of point addition and doubling is presented.And based on parallel schedule algorithm,the Application Specific Instruction-Set Co-Processor of ECC that adopting VLIW architecture is also proposed in this paper.The coprocessor for ECC is implemented and validated using Altera’s FPGA.The experimental result shows that our proposed coprocessor has advantage in high performance and flexibility.

Binary Sequences from a Pair of Elliptic Curves

A family of binary sequences were constructed by using an elliptic curve and its twisted curves over finite fields. It was shown that these sequences possess ＂good＂ cryptographie properties of 0-1 distribution, long period and large linear complexity. The results indicate that such se quences provide strong potential applications in cryptography.

Computation of Complex Primes Using Elliptic Curves: Application for Cryptosystem Design

This paper provides several generalizations of Gauss theorem that counts points on special elliptic curves. It is demonstrated how to implement these generalizations for computation of complex primes, which are applicable in several protocols providing security in communication networks. Numerical examples illustrate the ideas discussed in this paper.