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Gotowa bibliografia na temat „Elliptic curve elgamal cryptosystem”

Autor: Grafiati

Data publikacji: 2 czerwca 2025

Data aktualizacji: 22 czerwca 2025

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Artykuły w czasopismach na temat "Elliptic curve elgamal cryptosystem"

Kamthawee, Krissanee, and Bhichate Chiewthanakul. "The Construction of ElGamal over Koblitz Curve." Advanced Materials Research 931-932 (May 2014): 1441–46. http://dx.doi.org/10.4028/www.scientific.net/amr.931-932.1441.

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Recently elliptic curve cryptosystems are widely accepted for security applications key generation, signature and verification. Cryptographic mechanisms based on elliptic curves depend on arithmetic involving the points of the curve. it is possible to use smaller primes, or smaller finite fields, with elliptic curves and achieve a level of security comparable to that for much larger integers. Koblitz curves, also known as anomalous binary curves, are elliptic curves defined over F2. The primary advantage of these curves is that point multiplication algorithms can be devised that do not use any point doublings. The ElGamal cryptosystem, which is based on the Discrete Logarithm problem can be implemented in any group. In this paper, we propose the ElGamal over Koblitz Curve Scheme by applying the arithmetic on Koblitz curve to the ElGamal cryptosystem. The advantage of this scheme is that point multiplication algorithms can be speeded up the scalar multiplication in the affine coodinate of the curves using Frobenius map. It has characteristic two, therefore it’s arithmetic can be designed in any computer hardware. Moreover, it has more efficient to employ the TNAF method for scalar multiplication on Koblitz curves to decrease the number of nonzero digits. It’s security relies on the inability of a forger, who does not know a private key, to compute elliptic curve discrete logarithm.

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Ismail, N. H. M., and M. Y. Misro. "Bézier Coefficients Matrix for ElGamal Elliptic Curve Cryptosystem." Malaysian Journal of Mathematical Sciences 16, no. 3 (2022): 483–99. http://dx.doi.org/10.47836/mjms.16.3.06.

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It is well-known that cryptography is a branch of secrecy in science and mathematics, which usually preserves the confidentiality and authenticity of the information, where its growth is parallel with the rapid evolution of the internet and communication. As one of the prominent public key cryptosystems, the Elliptic Curve Cryptosystem (ECC) offers efficiency and complex mathematical operations with a smaller bit compared to other types of public key schemes. Throughout the evolution of cryptography, ElGamal Elliptic Curve Cryptosystem (ElGamal ECC) revolved from ElGamal public key scheme for user efficiency and privacy. In this study, an improved method will be introduced using ElGamal ECC as the foundation with the incorporation of the Bézier curve coefficient matrix, where the ElGamal ECC value is considered as the control point of the Bézier curve during the encryption and decryption processes. The proposed method is designed to develop a robust ciphertext system algorithm for better efficiency and to increase the level of protection in ElGamal ECC. In this paper, the performance of the proposed method is compared with the normal ElGamal ECC. The results of this study show that the proposed method offers no significant difference in terms of the implementation time during the encryption and decryption process. However, it does offer extra layers of protection when operated with complex mathematical operations.

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Luhaib, Qasim Mohsin, and Ruma Kareem K. Ajeena. "Elliptic curve matrices over group ring to improve elliptic curve–discrete logarithm cryptosystems." Journal of Discrete Mathematical Sciences and Cryptography 26, no. 6 (2023): 1699–704. http://dx.doi.org/10.47974/jdmsc-1616.

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An elliptic curve matrix (ECM) is created randomly based on an elliptic curve group to modify the elliptic curve-discrete logarithm (EC-DL) cryptosystems, which are elliptic Diffie-Hellman key exchange (DHKE) and elliptic ElGamal public key cryptosystem (EEPKC), and to increase the security level in comparison with the original EC-DL schemes. In proposed schemes, the keys and ciphertext are computed using the ECMs. The security of trust schemes depended on the difficulty of solving the elliptic curve discrete logarithm problem (ECM-DLP). New experimental results on proposed schemes are discussed. The ECM-DL schemes consider new insights for more secure communications.

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Abdelhakim, Chillali, and M'hammed Boulagouaz. "Methods of encryption keys, example of elliptic curve." Journal of Communications and Computer Engineering 3, no. 1 (2012): 7. http://dx.doi.org/10.20454/jcce.2013.259.

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In this paper we propose an application of public key distribution based on the security depending on the difficulty of elliptic curve discrete logarithm problem. More precisely, we propose an example of Elgamal encryption cryptosystem on the elliptic curve given by the equation:

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Wu, Huangwei. "General analysis on essential mathematical principles of elliptic curve cryptography." Theoretical and Natural Science 10, no. 1 (2023): 123–29. http://dx.doi.org/10.54254/2753-8818/10/20230327.

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Prevalent is the practical application of Elliptic Curve Cryptography (ECC) in the modern public-key cryptosystem, especially the implementation of ECC algorithm in Bitcoin source code. With the thorough introduction of discrete logarithm and Diffie-Hellman key exchange, ECC has gradually progressed to be sophisticated and efficient simultaneously. Therefore, it currently has been widely regarded as the successor of RSA algorithm in terms of inheritance for its shorter lengths of keys, faster speed and higher safety under the same encryption strength. Due to the potential safety and complexity of Elliptic Curve Cryptosystem, it is apparently noticed that there is included a large volume of Maths principles related to the establishment of ECC algorithm. As a consequence, this paper will mainly focus on qualitative research and exemplary analysis to specifically elucidate the general knowledge on essential mathematical principles of ECC, including the Law of Addition, the Elliptic Curve Discrete Logarithm Problems (ECDLP) and the Elliptic Curve ElGamal (EC ElGamal), together with the corresponding applications combined with their deprivation processes.

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Sangeetha, V., T. Anupreethi, and Manju Somanath. "Cryptographic Application of Elliptic Curve Generated through Centered Hexadecagonal Numbers." Indian Journal Of Science And Technology 17, no. 20 (2024): 2074–78. http://dx.doi.org/10.17485/ijst/v17i20.1183.

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Background/Objectives: Elliptic Curve Cryptography (ECC) is a public-key encryption method that is similar to RSA. ECC uses the mathematical concept of elliptic curves to achieve the same level of security with significantly smaller keys, whereas RSA's security depends on large prime numbers. Elliptic curves and their applications in cryptography will be discussed in this paper. The elliptic curve is formed by the extension of a Diophantine pair of Centered Hexadecagonal numbers to a Diophantine triple with property D(8). Method: The Diffie–Hellman key exchange, named for Whitfield Diffie and Martin Hellman, was developed by Ralph Merkle and is a mathematical technique for safely transferring cryptographic keys over a public channel. Based on the Diffie–Hellman key exchange, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography. The generation of keys, encryption and decryption are the three main operations of the ElGamal cryptosystem. Findings: Given the relative modesty of our objectives, the fundamental algebraic and geometric characteristics of elliptic curves shall be delineated. Then the behaviour of elliptic curves modulo p: ultimately, there is a fairly strong analogy between the structure of the points on an elliptic curve modulo p and the integers modulo n will be studied. In the end, elliptic curve ElGamal encryption analogues of Diffie–Hellman key exchange will be created. Novelty: Elliptic curves are encountered in a multitude of mathematical contexts and have a varied and fascinating history. Elliptic curves are very significant in number theory and are a focus of much recent work. The earlier research works in Elliptic Curve Cryptography has concentrated on computer algorithms and pairing – based algorithms. In this paper, the concept of polygonal numbers and its extension from Diophantine pair to triples is encountered, thus forming an elliptic curve and perform the encryption-decryption process. MSC Classification Number: 11D09, 11D99,11T71,11G05. Keywords: Elliptic curves, Cryptography, Encryption, Decryption, Centered polygonal numbers

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V, Sangeetha, Anupreethi T, and Somanath Manju. "Cryptographic Application of Elliptic Curve Generated through Centered Hexadecagonal Numbers." Indian Journal of Science and Technology 17, no. 20 (2024): 2074–78. https://doi.org/10.17485/IJST/v17i20.1183.

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Abstract Background/Objectives: Elliptic Curve Cryptography (ECC) is a public-key encryption method that is similar to RSA. ECC uses the mathematical concept of elliptic curves to achieve the same level of security with significantly smaller keys, whereas RSA's security depends on large prime numbers. Elliptic curves and their applications in cryptography will be discussed in this paper. The elliptic curve is formed by the extension of a Diophantine pair of Centered Hexadecagonal numbers to a Diophantine triple with property D(8). Method: The Diffie–Hellman key exchange, named for Whitfield Diffie and Martin Hellman, was developed by Ralph Merkle and is a mathematical technique for safely transferring cryptographic keys over a public channel. Based on the Diffie–Hellman key exchange, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography. The generation of keys, encryption and decryption are the three main operations of the ElGamal cryptosystem. Findings: Given the relative modesty of our objectives, the fundamental algebraic and geometric characteristics of elliptic curves shall be delineated. Then the behaviour of elliptic curves modulo p: ultimately, there is a fairly strong analogy between the structure of the points on an elliptic curve modulo p and the integers modulo n will be studied. In the end, elliptic curve ElGamal encryption analogues of Diffie–Hellman key exchange will be created. Novelty: Elliptic curves are encountered in a multitude of mathematical contexts and have a varied and fascinating history. Elliptic curves are very significant in number theory and are a focus of much recent work. The earlier research works in Elliptic Curve Cryptography has concentrated on computer algorithms and pairing – based algorithms. In this paper, the concept of polygonal numbers and its extension from Diophantine pair to triples is encountered, thus forming an elliptic curve and perform the encryption-decryption process. MSC Classification Number: 11D09, 11D99,11T71,11G05. Keywords: Elliptic curves, Cryptography, Encryption, Decryption, Centered polygonal numbers

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Sundararajan, Ananiah Durai Durai, and Rajashree R. "A Comprehensive Survey on Lightweight Asymmetric Key Cryptographic Algorithm for Resource Constrained Devices." ECS Transactions 107, no. 1 (2022): 7457–68. http://dx.doi.org/10.1149/10701.7457ecst.

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Elliptic Curve Cryptography, being a popular lightweight asymmetric key cryptographic algorithm that is widely adapted to meet high security requirement of resource constrained devices, were surveyed in this work. Further, ECC-based ElGamal cryptosystem, Elliptic Curve Digital Signature Algorithm, and Elliptic Curve Diffie Hellman Key Exchange Algorithm have been comprehensively reviewed with its characteristics and preferred applications. In addition, few related work are analyzed and suggestions for suitable target applications were provided. Moreover, ECC being a popular asymmetric key cryptographic technique is reported to be modeled using Vivado tool for various target implementation on FPGA devices. Techniques that enhances throughput, area, and computation time that caters for IoT applications were also reviewed. Design implementations on the advanced FPGA boards for IoT device/similar applications were also analyzed and compared.

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Prabhdeep Kaur and Sheetal Kalra. "On Security Analysis of Recent Password Authentication and Key Agreement Schemes Based on Elliptic Curve Cryptography." Journal of Technology Management for Growing Economies 6, no. 1 (2015): 39–52. http://dx.doi.org/10.15415/jtmge.2015.61004.

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Secure and efficient mutual authentication and key agreement schemes form the basis for any robust network communication system. Elliptic Curve Cryptography (ECC) has emerged as one of the most successful Public Key Cryptosystem that efficiently meets all the security challenges. Comparison of ECC with other Public Key Cryptosystems (RSA, Rabin, ElGamal) shows that it provides equal level of security for a far smaller bit size, thereby substantially reducing the processing overhead. This makes it suitable for constrained environments like wireless networks and mobile devices as well as for security sensitive applications like electronic banking, financial transactions and smart grids. With the successful implementation of ECC in security applications (e-passports, e-IDs, embedded systems), it is getting widely commercialized. ECC is simple and faster and is therefore emerging as an attractive alternative for providing security in lightweight device, which contributes to its popularity in the present scenario. In this paper, we have analyzed some of the recent password based authentication and key agreement schemes using ECC for various environments. Furthermore, we have carried out security, functionality and performance comparisons of these schemes and found that they are unable to satisfy their claimed security goals.

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Lopez, Maria Isaura, and Ayad Barsoum. "Traditional Public-Key Cryptosystems and Elliptic Curve Cryptography." International Journal of Cyber Research and Education 4, no. 1 (2022): 1–14. http://dx.doi.org/10.4018/ijcre.309688.

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The need to establish safer communication channels in a world where technological development is progressing in leaps and bounds is indispensable. Thus, implementing cryptographic algorithms, which are more complex to compromise, improves the possibilities of securing our sensitive data. In this paper, the authors analyze the algorithmic foundations and perform a comparative analysis of the traditional public-key cryptographic algorithms (e.g., RSA, ElGamal, Schnorr, DSA) and elliptic curve cryptography with NIST recommended curves. In the study, they focus on six different security strengths: 80-, 96-, 112-, 128-, 192-, and 256-bit key sizes. Moreover, this study provides a benchmark among different curves (NIST, SEC2, and IEFT Brainpool) that can be used with various security levels. The authors study and compare the characteristics and performance of the traditional asymmetric algorithms and the elliptic curve algorithms for information security. The results obtained in this study will be graphically visualized through statistical graphs and tables with quantification response times.

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Rozprawy doktorskie na temat "Elliptic curve elgamal cryptosystem"

Abu-Mahfouz, Adnan Mohammed. "Elliptic curve cryptosystem over optimal extension fields for computationally constrained devices." Diss., University of Pretoria, 2004. http://hdl.handle.net/2263/25330.

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Data security will play a central role in the design of future IT systems. The PC has been a major driver of the digital economy. Recently, there has been a shift towards IT applications realized as embedded systems, because they have proved to be good solutions for many applications, especially those which require data processing in real time. Examples include security for wireless phones, wireless computing, pay-TV, and copy protection schemes for audio/video consumer products and digital cinemas. Most of these embedded applications will be wireless, which makes the communication channel vulnerable. The implementation of cryptographic systems presents several requirements and challenges. For example, the performance of algorithms is often crucial, and guaranteeing security is a formidable challenge. One needs encryption algorithms to run at the transmission rates of the communication links at speeds that are achieved through custom hardware devices. Public-key cryptosystems such as RSA, DSA and DSS have traditionally been used to accomplish secure communication via insecure channels. Elliptic curves are the basis for a relatively new class of public-key schemes. It is predicted that elliptic curve cryptosystems (ECCs) will replace many existing schemes in the near future. The main reason for the attractiveness of ECC is the fact that significantly smaller parameters can be used in ECC than in other competitive system, but with equivalent levels of security. The benefits of having smaller key size include faster computations, and reduction in processing power, storage space and bandwidth. This makes ECC ideal for constrained environments where resources such as power, processing time and memory are limited. The implementation of ECC requires several choices, such as the type of the underlying finite field, algorithms for implementing the finite field arithmetic, the type of the elliptic curve, algorithms for implementing the elliptic curve group operation, and elliptic curve protocols. Many of these selections may have a major impact on overall performance. In this dissertation a finite field from a special class called the Optimal Extension Field (OEF) is chosen as the underlying finite field of implementing ECC. OEFs utilize the fast integer arithmetic available on modern microcontrollers to produce very efficient results without resorting to multiprecision operations or arithmetic using polynomials of large degree. This dissertation discusses the theoretical and implementation issues associated with the development of this finite field in a low end embedded system. It also presents various improvement techniques for OEF arithmetic. The main objectives of this dissertation are to --Implement the functions required to perform the finite field arithmetic operations. -- Implement the functions required to generate an elliptic curve and to embed data on that elliptic curve. -- Implement the functions required to perform the elliptic curve group operation. All of these functions constitute a library that could be used to implement any elliptic curve cryptosystem. In this dissertation this library is implemented in an 8-bit AVR Atmel microcontroller. Dissertation (MEng (Computer Engineering))--University of Pretoria, 2006. Electrical, Electronic and Computer Engineering unrestricted

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Ho, Sun Wah. "A cryptosystem based on chaotic and elliptic curve cryptography /." access full-text access abstract and table of contents, 2005. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?mphil-it-b19886238a.pdf.

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Thesis (M.Phil.)--City University of Hong Kong, 2005. "Submitted to Department of Computer Engineering and Information Technology in partial fulfillment of the requirements for the degree of Master of Philosophy" Includes bibliographical references (leaves 109-111)

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Singh, Namita. "Secure communication using elliptic curve cryptosystem in ad hoc network." Thesis, University of Ottawa (Canada), 2008. http://hdl.handle.net/10393/27730.

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Ad hoc networks are standalone networks supporting "communication anytime and anywhere" using portable devices like PDAs, cell phones, laptops etc. which require no predefined organization of available links but offer constraints such as battery life, bandwidth, memory, computational ability, security, quality of service, reliability, range of the device and speed. Security framework is essential and relies on certificates to communicate with each other but requires higher battery life, bandwidth and memory space. Researchers have been using keys as an alternative. However, no protocol is complete solution due to the presence of large key lengths and high bandwidth usage. Therefore, an efficient key management system is proposed using Elliptic curve cryptosystem (ECC) aiming at secure communication among the nodes concentrating mainly on key generation, agreement and encryption/decryption with an assumption that the nodes have capabilities for efficient key storage and key security. In other words, the goal is to enable sender nodes to transmit data from sender to the destination without threats.

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Abu, Mahfouz Adnan Mohammed I. "Elliptic curve cryptosystem over optimal extension fields for computationally constrained devices." Pretoria : [s.n.], 2004. http://upetd.up.ac.za/thesis/available/etd-06082005-144557.

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Man, Kwan Pok. "Security enhancement on the cryptosystem based on chaotic and elliptic curve cryptography /." access abstract and table of contents access full-text, 2006. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?mphil-ee-b21471526a.pdf.

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Thesis (M.Phil.)--City University of Hong Kong, 2006. "Submitted to Department of Electronic Engineering in partial fulfillment of the requirements for the degree of Master of Philosophy" Includes bibliographical references (leaves 93-97)

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Cai, Zhi, and 蔡植. "A study on parameters generation of elliptic curve cryptosystem over finite fields." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31225639.

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Kultinov, Kirill. "Software Implementations and Applications of Elliptic Curve Cryptography." Wright State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=wright1559232475298514.

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Arslanian, Samuel Thomas. "An implementation of the El Gamal elliptic curve cryptosystem over a finite field of characteristic P." Fogler Library, University of Maine, 1998. http://www.library.umaine.edu/theses/pdf/ArslanianST1998.pdf.

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Poni, Sofia. "Le curve ellittiche in crittografia." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2022. http://amslaurea.unibo.it/25677/.

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Il bisogno dell'uomo di nascondere e protegge le informazioni risale ad epoca antica; infatti, la crittografia ha avuto un ruolo molto importante in diversi momenti storici, basta pensare al cifrario di Cesare o alla macchina Enigma e la macchina di Lorenz durante la Seconda guerra mondiale, e questi sono solo alcuni esempi tra i più conosciuti. Per tanto, possiamo dire quindi che la crittografia rappresenta un vasto ambito di applicazione e al giorno d'oggi, con il rapido sviluppo della tecnologia, risulta essenziale per garantici sicurezza e privacy in quanto quest'ultima è stata minuta. Quindi, dà la possibilità, per esempio, di scambairsi messaggi, effettuare chiamate vocali o salvarsi informazioni personali all'interno dei nostri dispostivi in modo che una persona non autorizzata possa accedervi. Durante il corso degli anni, in epoca recente, sono stati introdotti diversi sistemi crittografici, tra cui quelli basati su curve ellittiche (Elliptic Curve Cryptosystems - ECC) che si sono andati a presentare come alternativa ai classici sistemi asimmetrici.

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Hitchcock, Yvonne Roslyn. "Elliptic curve cryptography for lightweight applications." Thesis, Queensland University of Technology, 2003. https://eprints.qut.edu.au/15838/1/Yvonne_Hitchcock_Thesis.pdf.

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Elliptic curves were first proposed as a basis for public key cryptography in the mid 1980's. They provide public key cryptosystems based on the difficulty of the elliptic curve discrete logarithm problem (ECDLP) , which is so called because of its similarity to the discrete logarithm problem (DLP) over the integers modulo a large prime. One benefit of elliptic curve cryptosystems (ECCs) is that they can use a much shorter key length than other public key cryptosystems to provide an equivalent level of security. For example, 160 bit ECCs are believed to provide about the same level of security as 1024 bit RSA. Also, the level of security provided by an ECC increases faster with key size than for integer based discrete logarithm (dl) or RSA cryptosystems. ECCs can also provide a faster implementation than RSA or dl systems, and use less bandwidth and power. These issues can be crucial in lightweight applications such as smart cards. In the last few years, ECCs have been included or proposed for inclusion in internationally recognized standards. Thus elliptic curve cryptography is set to become an integral part of lightweight applications in the immediate future. This thesis presents an analysis of several important issues for ECCs on lightweight devices. It begins with an introduction to elliptic curves and the algorithms required to implement an ECC. It then gives an analysis of the speed, code size and memory usage of various possible implementation options. Enough details are presented to enable an implementer to choose for implementation those algorithms which give the greatest speed whilst conforming to the code size and ram restrictions of a particular lightweight device. Recommendations are made for new functions to be included on coprocessors for lightweight devices to support ECC implementations Another issue of concern for implementers is the side-channel attacks that have recently been proposed. They obtain information about the cryptosystem by measuring side-channel information such as power consumption and processing time and the information is then used to break implementations that have not incorporated appropriate defences. A new method of defence to protect an implementation from the simple power analysis (spa) method of attack is presented in this thesis. It requires 44% fewer additions and 11% more doublings than the commonly recommended defence of performing a point addition in every loop of the binary scalar multiplication algorithm. The algorithm forms a contribution to the current range of possible spa defences which has a good speed but low memory usage. Another topic of paramount importance to ECCs for lightweight applications is whether the security of fixed curves is equivalent to that of random curves. Because of the inability of lightweight devices to generate secure random curves, fixed curves are used in such devices. These curves provide the additional advantage of requiring less bandwidth, code size and processing time. However, it is intuitively obvious that a large precomputation to aid in the breaking of the elliptic curve discrete logarithm problem (ECDLP) can be made for a fixed curve which would be unavailable for a random curve. Therefore, it would appear that fixed curves are less secure than random curves, but quantifying the loss of security is much more difficult. The thesis performs an examination of fixed curve security taking this observation into account, and includes a definition of equivalent security and an analysis of a variation of Pollard's rho method where computations from solutions of previous ECDLPs can be used to solve subsequent ECDLPs on the same curve. A lower bound on the expected time to solve such ECDLPs using this method is presented, as well as an approximation of the expected time remaining to solve an ECDLP when a given size of precomputation is available. It is concluded that adding a total of 11 bits to the size of a fixed curve provides an equivalent level of security compared to random curves. The final part of the thesis deals with proofs of security of key exchange protocols in the Canetti-Krawczyk proof model. This model has been used since it offers the advantage of a modular proof with reusable components. Firstly a password-based authentication mechanism and its security proof are discussed, followed by an analysis of the use of the authentication mechanism in key exchange protocols. The Canetti-Krawczyk model is then used to examine secure tripartite (three party) key exchange protocols. Tripartite key exchange protocols are particularly suited to ECCs because of the availability of bilinear mappings on elliptic curves, which allow more efficient tripartite key exchange protocols.

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Książki na temat "Elliptic curve elgamal cryptosystem"

Martin, Keith M. Public-Key Encryption. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788003.003.0005.

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In this chapter, we introduce public-key encryption. We first consider the motivation behind the concept of public-key cryptography and introduce the hard problems on which popular public-key encryption schemes are based. We then discuss two of the best-known public-key cryptosystems, RSA and ElGamal. For each of these public-key cryptosystems, we discuss how to set up key pairs and perform basic encryption and decryption. We also identify the basis for security for each of these cryptosystems. We then compare RSA, ElGamal, and elliptic-curve variants of ElGamal from the perspectives of performance and security. Finally, we look at how public-key encryption is used in practice, focusing on the popular use of hybrid encryption.

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Części książek na temat "Elliptic curve elgamal cryptosystem"

Zheng, Zhiyong. "Elliptic Curve." In Financial Mathematics and Fintech. Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0920-7_6.

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AbstractIn 1985, mathematician v. Miller introduced elliptic curve into cryptography for the first time. In 1987, mathematician N. Koblitz further improved and perfected Miller’s work and formed the famous elliptic curve public key cryptosystem.

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Nitaj, Abderrahmane, Willy Susilo, and Joseph Tonien. "Improved Cryptanalysis of the KMOV Elliptic Curve Cryptosystem." In Provable Security. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31919-9_12.

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Akishita, Toru, and Tsuyoshi Takagi. "Zero-Value Point Attacks on Elliptic Curve Cryptosystem." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/10958513_17.

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Wong, M. M., M. L. D. Wong, and Ka Lok Man. "Compact Multiplicative Inverter for Hardware Elliptic Curve Cryptosystem." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-35606-3_58.

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Shankar, T. N., G. Sahoo, and S. Niranjan. "Digital Signature of an Image by Elliptic Curve Cryptosystem." In Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-27317-9_35.

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Chiou, C. W., Y. S. Sun, C. M. Lee, Y. L. Chiu, J. M. Lin, and C. Y. Lee. "Problems on Gaussian Normal Basis Multiplication for Elliptic Curve Cryptosystem." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23207-2_20.

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Zhang, Fangguo, and Zhuoran Zhang. "ECC$$^2$$: Error Correcting Code and Elliptic Curve Based Cryptosystem." In Cyberspace Safety and Security. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-37337-5_17.

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Kadu, Rakesh K., and Dattatraya S. Adane. "Hardware Implementation of Elliptic Curve Cryptosystem Using Optimized Scalar Multiplication." In Smart Innovation, Systems and Technologies. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0077-0_32.

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Zheng, Zhiyong, Kun Tian, and Fengxia Liu. "A Generalization of NTRUencrypt." In Financial Mathematics and Fintech. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-7644-5_7.

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AbstractNTRU cryptosystem is a new public key cryptosystem based on lattice hard problem proposed in 1996 by three digit theorists Hoffstein, Piper and Silverman of Brown University in the United States. The essence of NTRU cryptographic design is the generalization of RSA on polynomials, so it is called the cryptosystem based on polynomial rings. Its main feature is that the key generation is very simple, and the encryption and decryption algorithm is much faster than the commonly used RSA and elliptic curve cryptography. In particular, NTRU can resist quantum computing attacks and is considered to be a potential public key cryptography that can replace RSA in the post-quantum cryptography era.

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Kanda, Guard, Alexander O. A. Antwi, and Kwangki Ryoo. "Hardware Architecture Design of AES Cryptosystem with 163-Bit Elliptic Curve." In Lecture Notes in Electrical Engineering. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1328-8_55.

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Streszczenia konferencji na temat "Elliptic curve elgamal cryptosystem"

Yang, Ziyao, and Yuan Liu. "Design and Application of an International Trade Trading Platform Based on ElGamal and Elliptic Curve Cryptography." In 2024 International Conference on Intelligent Algorithms for Computational Intelligence Systems (IACIS). IEEE, 2024. http://dx.doi.org/10.1109/iacis61494.2024.10721931.

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M. GHADI, Dua. "MODIFICATION OF ELGAMAL ELLIPTIC CURVE CRYPTOSYSTEM ALGORITHM." In VI.International Scientific Congress of Pure,Applied and Technological Sciences. Rimar Academy, 2022. http://dx.doi.org/10.47832/minarcongress6-8.

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The importance of data encryption has grown dramatically, especially in terms of personal data. The elliptic curve cryptosystem is the major solution for data security because it has become more prevalent. Security and privacy are required to ensure the data has recently generated much concern within the research community. This paper's objective is to obtain a complicated and secure ciphertext and make cryptanalysis difficult. In this paper, we modified the El-Gamal Elliptic Curve Cryptosystem (ECC) by producing new secret keys for encrypting data and embedding messages by using Discrete Logarithm Problem (DLP) behavior. This modification is to offer enhanced encryption standards and improve the security. The experiential results show that the proposed algorithm is more complex than the original method.

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Fu Minfeng and Chen Wei. "Elliptic curve cryptosystem ElGamal encryption and transmission scheme." In 2010 International Conference on Computer Application and System Modeling (ICCASM 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccasm.2010.5620105.

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Wong, Tze Jin, Mohd Rushdan Md Said, Mohamed Othman, and Lee Feng Koo. "A Lucas based cryptosystem analog to the ElGamal cryptosystem and elliptic curve cryptosystem." In INTERNATIONAL CONFERENCE ON QUANTITATIVE SCIENCES AND ITS APPLICATIONS (ICOQSIA 2014): Proceedings of the 3rd International Conference on Quantitative Sciences and Its Applications. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4903592.

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Lee, Narn-Yih, Zih-Ling Chen, and Fu-Kun Chen. "Cloud Server Aided Computation for ElGamal Elliptic Curve Cryptosystem." In 2013 IEEE 37th International Computer Software and Applications Conference Workshops (COMPSACW). IEEE, 2013. http://dx.doi.org/10.1109/compsacw.2013.7.

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Udin, Md Nizam, Suhaila Abd Halim, Mohd Idris Jayes, and Hailiza Kamarulhaili. "Application of message embedding technique in ElGamal Elliptic Curve Cryptosystem." In 2012 International Conference on Statistics in Science, Business and Engineering (ICSSBE2012). IEEE, 2012. http://dx.doi.org/10.1109/icssbe.2012.6396578.

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Rachmawati, Dian, Mohammad Andri Budiman, and Muhammad Ishan Wardhono. "Hybrid Cryptosystem for Image Security by Using Hill Cipher 4x4 and ElGamal Elliptic Curve Algorithm." In 2018 IEEE International Conference on Communication, Networks and Satellite (Comnetsat). IEEE, 2018. http://dx.doi.org/10.1109/comnetsat.2018.8684121.

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Elhassani, M., A. Chillali, and A. Mouhib. "Elliptic curve and Lattice cryptosystem." In 2019 International Conference on Intelligent Systems and Advanced Computing Sciences (ISACS). IEEE, 2019. http://dx.doi.org/10.1109/isacs48493.2019.9068885.

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Bin Yu. "Establishement of elliptic curve cryptosystem." In 2010 IEEE International Conference on Information Theory and Information Security (ICITIS). IEEE, 2010. http://dx.doi.org/10.1109/icitis.2010.5689767.

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Ali, Sk Subidh, and Ozgur Sinanoglu. "Scan attack on Elliptic Curve Cryptosystem." In 2015 IEEE International Symposium on Defect and Fault Tolerance in VLSI and Nanotechnology Systems (DFTS). IEEE, 2015. http://dx.doi.org/10.1109/dft.2015.7315146.

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