Message Verification Protocol Based on Bilinear Pairings and Elliptic Curves for Enhanced Security in Vehicular Ad Hoc Networks

Vehicular ad hoc networks(VANETs)provide intelligent navigation and efficient route management,resulting in time savings and cost reductions in the transportation sector.However,the exchange of beacons and messages over public channels among vehicles and roadside units renders these networks vulnerable to numerous attacks and privacy violations.To address these challenges,several privacy and security preservation protocols based on blockchain and public key cryptography have been proposed recently.However,most of these schemes are limited by a long execution time and massive communication costs,which make them inefficient for on-board units(OBUs).Additionally,some of them are still susceptible to many attacks.As such,this study presents a novel protocol based on the fusion of elliptic curve cryptography(ECC)and bilinear pairing(BP)operations.The formal security analysis is accomplished using the Burrows–Abadi–Needham(BAN)logic,demonstrating that our scheme is verifiably secure.The proposed scheme’s informal security assessment also shows that it provides salient security features,such as non-repudiation,anonymity,and unlinkability.Moreover,the scheme is shown to be resilient against attacks,such as packet replays,forgeries,message falsifications,and impersonations.From the performance perspective,this protocol yields a 37.88%reduction in communication overheads and a 44.44%improvement in the supported security features.Therefore,the proposed scheme can be deployed in VANETs to provide robust security at low overheads.

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.

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.

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.

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.

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.

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.

Curve25519点乘算法的高效FPGA实现

为了提高X25519密钥交换算法的运算效率,文章基于现场可编程门阵列(field programmable gate array,FPGA)提出一种高效的曲线Curve25519的点乘设计方案。首先在底层的有限域计算上,针对模约减计算次数多的问题,提出一种基于冗余数的模运算单元,减少了约减次数;同时,所提出的结构可以减少点乘中常系数乘法的运算周期,从而优化了点乘运算通路,提高了并行度,最终减少了运算时间。该文在Xilinx XC7Z020 FPGA上实现了该点乘设计方案,完成一次点乘需要125μs。研究结果表明,与现有的设计相比,所提出的方案具有较低的面积时间积,达到了面积和性能的平衡。

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.

Addition Sequence Method of Scalar Multiplication of Elliptic Curve over OEF

A new elliptic curve scalar multiplication algorithm is proposed. Thealgorithm uses the Frobenius map on optimal extension field (OEF) and addition sequence We introducea new algorithm on generating addition sequence efficiently and also give some analysis about it.Based on this algorithm, a new method of computing scalar multiplication of elliptic curve over anOEF is presented. The new method is more efficient than the traditional scalar multiplicationalgorithms of elliptic curve over OEF. Thecomparisons of traditional method and the new method arealso given.

Integral Points on a Class of Elliptic Curve

We prove all integral points of the elliptic curve y^2=x^2-30x＋133 are （x,y） = （-7,0）,（-3,±14）,（2, ±9）,（6,±13）, （5143326,±11664498677）, by using the method of algebraic number theory and p-adic analysis. Furthermore, we develop a computation method to find all integral points on a class of elliptic curve y^2= （x＋α）（x^2-α）（x^2-αx＋b） ,α ,b∈Z,α^2〈4b and find all integer solutions of hyperelliptic Diophantine equation Dy^2=Ax^4 ＋ Bx^2 ＋C,B^2〈4AC.

Verifiable (t, n) Threshold Signature Scheme Based on Elliptic Curve

Based on tht difficulty of solving the ECDLP (elliptic curve discretelogarithm problem) on the finite field, we present a (t, n) threshold signature scheme and averifiable key agreement scheme without trusted party. Applying a modified elliptic curve signatureequation, we gel a more efficient signature scheme than the existing ECDSA (elliptic curve digitalsignature algorithm) from the computability and security view. Our scheme has a shorter key, fastercomputation, and better security.

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.

RGB Based Multiple Share Creation in Visual Cryptography with Aid of Elliptic Curve Cryptography

In visual cryptography, many shares are generated which are illogical containing certain message within themselves. When all shares are piled jointly, they tend to expose the secret of the image. The notion of visual secret sharing scheme is to encrypt a secret image into n illogical share images. It is unable to reveal any data on the original image if at least one of the shares is not achieved. The original image, in fact, is realized by overlapping the entire shares directly, in order that the human visual system is competent to identify the collective secret image without employing any complicated computational tools. Therefore, they are communicated steadily as number of shares. The elliptic curve cryptography approach, in turn, is employed to augment the privacy and safety of the image. The new.fangled technique is utilized to generate the multiple shares which are subjected to encryption and decryption by means of the elliptic curve cryptography technique. The test outcomes have revealed the fact that the peak signal to noise ratio is 58.0025, Mean square error value is 0.1164 and the correlation coefficient is 1 for the decrypted image without any sort of distortion of the original image.

Elliptic Curve Scalar Multiplication with x-Coordinate

This paper gives a comprehensive method to do Elliptic Curve Scalar Multiplication with only x-coordinate. Explicit point operation formulae for all types of defining equations of the curves are derived. For each type of curve, the performance is analyzed. The formulae are applied in Montgomery Ladder to get scalar multiplication algorithm operated with only x-coordinate. The new scalar multiplication has the same security level and computation amount with protected binary scalar multiplication （PBSM） against side channel attack, and has the advantages of higher security and little memory needed.

An FPGA Implementation of GF(p) Elliptic Curve Cryptographic Coprocessor

A GF(p) elliptic curve cryptographic coprocessor is proposed and implemented on Field Programmable Gate Array (FPGA). The focus of the coprocessor is on the most critical, complicated and time-consuming point multiplications. The technique of coordinates conversion and fast multiplication algorithm of two large integers are utilized to avoid frequent inversions and to accelerate the field multiplications used in point multiplications. The characteristic of hardware parallelism is considered in the implementation of point multiplications. The coprocessor implemented on XILINX XC2V3000 computes a point multiplication for an arbitrary point on a curve defined over GF(2192?264?1) with the frequency of 10 MHz in 4.40 ms in the average case and 5.74 ms in the worst case. At the same circumstance, the coprocessor implemented on XILINX XC2V4000 takes 2.2 ms in the average case and 2.88 ms in the worst case.

Efficient Dynamic Threshold Group Signature Scheme Based on Elliptic Curve Cryptosystem

The short secret key characteristic of elliptic curve cryptosystem （ECC） are integrated with the （ t, n ） threshold method to create a practical threshold group signature scheme characterized by simultaneous signing. The scheme not only meets the requirements of anonymity and traceability of group signature but also can withstand Tseng and Wang＇s conspiracy attack. It allows the group manager to add new members and delete old members according to actual application, while the system parameters have a little change. Cryptanalysis result shows that the scheme is efficient and secure.