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.

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.

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.

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.

Constructing quasi-random subsets of Z_N by using elliptic curves

Let ε ： y^2 = x3 ＋ Ax ＋ B be an elliptic curve defined over the finite field Zp（p 〉 3） and G be a rational point of prime order N on ε. Define a subset of ZN, the residue class ring modulo N, asS：={n：n∈ZN,n≠0,（X（nG）/p）=1} where X（nG） denotes the x-axis of the rational points nC and （＊/P） is the Legendre symbol. Some explicit results on quasi-randomness of S are investigated. The construction depends on the intrinsic group structures of elliptic curves and character sums along elliptic curves play an important role in the proofs.

An Algebraic Proof of the Associative Law of Elliptic Curves

In this paper we revisit the addition of elliptic curves and give an algebraic proof to the associative law by use of MATHEMATICA. The existing proofs of the associative law are rather complicated and hard to understand for beginners. An ‘‘elementary” proof to it based on algebra has not been given as far as we know. Undergraduates or non-experts can master the addition of elliptic curves through this paper. After mastering it they should challenge the elliptic curve cryptography.

On the Torsion Subgroups of Certain Elliptic Curves over Q

Let E be an elliptic curve over a given number field . By Mordell’s Theorem, the torsion subgroup of E defined over Q is a finite group. Using Lutz-Nagell Theorem, we explicitly calculate the torsion subgroup E(Q)tors for certain elliptic curves depending on their coefficients.

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.

On Two Problems About Isogenies of Elliptic Curves Over Finite Fields

Isogenies occur throughout the theory of elliptic curves.Recently,the cryptographic protocols based on isogenies are considered as candidates of quantum-resistant cryptographic protocols.Given two elliptic curves E1,E2 defined over a finite field k with the same trace,there is a nonconstant isogeny b from E2 to E1 defined over k.This study gives out the index of Homk(E1,E2)b as a nonzero left ideal in Endk(E2)and figures out the correspondence between isogenies and kernel ideals.In addition,some results about the non-trivial minimal degree of isogenies between two elliptic curves are also provided.

Cryptographic Schemes Based on Elliptic Curves over the Ring Zp[i]

Elliptic Curve Cryptography recently gained a lot of attention in industry. The principal attraction of ECC compared to RSA is that it offers equal security for a smaller key size. The present paper includes the study of two elliptic curve and defined over the ring where . After showing isomorphism between and , we define a composition operation (in the form of a mapping) on their union set. Then we have discussed our proposed cryptographic schemes based on the elliptic curve . We also illustrate the coding of points over E, secret key exchange and encryption/decryption methods based on above said elliptic curve. Since our proposed schemes are based on elliptic curve of the particular type, therefore the proposed schemes provides a highest strength-per-bit of any cryptosystem known today with smaller key size resulting in faster computations, lower power assumption and memory. Another advantage is that authentication protocols based on ECC are secure enough even if a small key size is used.

SPEED UP RATIONAL POINT SCALAR MULTIPLICATIONS ON ELLIPTIC CURVES BY FROBENIUS EQUATIONS

Let q be a power of a prime and φ be the Frobenius endomorphism on E（Fqk）, then q = tφ - φ^2. Applying this equation, a new algorithm to compute rational point scalar multiplications on elliptic curves by finding a suitable small positive integer s such that q^s can be represented as some very sparse φ-polynomial is proposed. If a Normal Basis （NB） or Optimal Normal Basis （ONB） is applied and the precomputations are considered free, our algorithm will cost, on average, about 55% to 80% less than binary method, and about 42% to 74% less than φ-ary method. For some elliptic curves, our algorithm is also taster than Mǖller＇s algorithm. In addition, an effective algorithm is provided for finding such integer s.

On Elliptic Curves with Everywhere Good Reduction over Certain Number Fields

We prove the existence and nonexistence of elliptic curves having good reduction everywhere over certain real quadratic fields Q(m) for m≤200. These results of computations give best-possible data including structures of Mordell-Weil groups over some real quadratic fields via two-descent. We also prove similar results for the case of certain cubic fields. Especially, we give the first example of elliptic curve having everywhere good reduction over a pure cubic field using our method.