Relevant bibliographies by topics / Elliptic Curve Cryptography (ECC)

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Academic literature on the topic 'Elliptic Curve Cryptography (ECC)'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 September 2023

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Journal articles on the topic "Elliptic Curve Cryptography (ECC)"

1

Yan, Yuhan. "The Overview of Elliptic Curve Cryptography (ECC)." Journal of Physics: Conference Series 2386, no. 1 (December 1, 2022): 012019. http://dx.doi.org/10.1088/1742-6596/2386/1/012019.

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Abstract Elliptic Curve Cryptography (ECC) is one of the strongest and most efficient cryptographic techniques in modern cryptography. This paper gives the following introduction: The introduction of cryptography’s development; the introduction of the elliptic curve; the principle of ECC; the horizontal comparison between ECC and other types of cryptography; the modern breakthrough of ECC; the applications of ECC; by using a method of literature review. The study’s findings indicate that this factor is responsible for the rapid historical development of cryptography, from the classical password to the leap to modern cryptography. Elliptic Curve Cryptography (ECC), as one of the most important modern cryptographies, is stronger than most other cryptographies both in terms of security and strength, because it uses an elliptic curve to construct and, at the same time, uses mathematical operations to encrypt and generate keys. At the same time, elliptic curve cryptography can continue to improve the speed and intensity with the improvement of accelerators, scalar multiplication, and the speed of order operation. The applications of the elliptic curve in ECDSA and SM2 are very efficient, which further illustrates the importance of elliptic curve cryptography.
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Abhishek, Kunal, and E. George Dharma Prakash Raj. "Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography." Cybernetics and Information Technologies 21, no. 2 (June 1, 2021): 70–88. http://dx.doi.org/10.2478/cait-2021-0020.

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Abstract Short Weierstrass elliptic curves with underlying hard Elliptic Curve Discrete Logarithm Problem (ECDLP) are widely used in cryptographic applications. A notion of security called Elliptic Curve Cryptography (ECC) security is also suggested in literature to safeguard the elliptic curve cryptosystems from their implementation flaws. In this paper, a new security notion called the “trusted security” is introduced for computational method of elliptic curves for cryptography. We propose three additional “trusted security acceptance criteria” which need to be met by the elliptic curves aimed for cryptography. Further, two cryptographically secure elliptic curves over 256 bit and 384 bit prime fields are demonstrated which are secure from ECDLP, ECC as well as trust perspectives. The proposed elliptic curves are successfully subjected to thorough security analysis and performance evaluation with respect to key generation and signing/verification and hence, proven for their cryptographic suitability and great feasibility for acceptance by the community.
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Duka, Mariusz. "ELLIPTIC-CURVE CRYPTOGRAPHY (ECC) AND ARGON2 ALGORITHM IN PHP USING OPENSSL AND SODIUM LIBRARIES." Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska 10, no. 3 (September 30, 2020): 91–94. http://dx.doi.org/10.35784/iapgos.897.

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This paper presents the elliptic-curve cryptography (ECC) and Argon2 algorithm in PHP using OpenSSL and Sodium cryptographic libraries. The vital part of this thesis presents an analysis of the efficiency of elliptic-curve cryptography (ECC) and the Argon2 hashing algorithm in the Sodium library, depending on the variation of initiation parameters.
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Weku, Winsy. "Model Proyeksi (X/Z2, Y/Z2) pada Kurva Hesian Secara Paralel Menggunakan Mekanisme Kriptografi Kurva Eliptik." JURNAL ILMIAH SAINS 12, no. 1 (April 30, 2012): 65. http://dx.doi.org/10.35799/jis.12.1.2012.404.

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MODEL PROYEKSI (X/Z2, Y/Z2) PADA KURVA HESIAN SECARA PARALEL MENGGUNAKAN MEKANISME KRIPTOGRAFI KURVA ELIPTIKABSTRAK Suatu kunci publik, Elliptic Curve Cryptography (ECC) dikenal sebagai algoritma yang paling aman yang digunakan untuk memproteksi informasi sepanjang melakukan transmisi. ECC dalam komputasi aritemetika didapatkan berdasarkan operasi inversi modular. Inversi modular adalah operasi aritmetika dan operasi yang sangat panjang yang didapatkan berdasar ECC crypto-processor. Penggunaan koordinat proyeksi untuk menentukan Kurva Eliptik/ Elliptic Curves pada kenyataannya untuk memastikan koordinat proyeksi yang sebelumnya telah ditentukan oleh kurva eliptik E: y2 = x3 + ax + b yang didefinisikan melalui Galois field GF(p)untuk melakukan operasi aritemtika dimana dapat diketemukan bahwa terdapat beberapa multiplikasi yang dapat diimplementasikan secara paralel untuk mendapatkan performa yang tinggi. Pada penelitian ini, akan dibahas tentang sistem koordinat proyeksi Hessian (X/Z2, Y,Z2) untuk meningkatkan operasi penggandaan ECC dengan menggunakan pengali paralel untuk mendapatkan paralel yang maksimum untuk mendapatkan hasil maksimal. Kata kunci: Elliptic Curve Cryptography, Public-Key Cryptosystem, Galois Fields of Primes GF(p PROJECTION MODEL (X/Z2, Y/Z2) ON PARALLEL HESIAN CURVE USING CRYPTOGRAPHY ELIPTIC CURVE MECHANISM ABSTRACT As a public key cryptography, Elliptic Curve Cryptography (ECC) is well known to be the most secure algorithms that can be used to protect information during the transmission. ECC in its arithmetic computations suffers from modular inversion operation. Modular Inversion is a main arithmetic and very long-time operation that performed by the ECC crypto-processor. The use of projective coordinates to define the Elliptic Curves (EC) instead of affine coordinates replaced the inversion operations by several multiplication operations. Many types of projective coordinates have been proposed for the elliptic curve E: y2 = x3 + ax + b which is defined over a Galois field GF(p) to do EC arithmetic operations where it was found that these several multiplications can be implemented in some parallel fashion to obtain higher performance. In this work, we will study Hessian projective coordinates systems (X/Z2, Y,Z2) over GF (p) to perform ECC doubling operation by using parallel multipliers to obtain maximum parallelism to achieve maximum gain. Keywords: Elliptic Curve Cryptography , Public-Key Cryptosystem , Galois Fields of Primes GF(p)
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Taqwa, Ainur Rilo, and Danang Haryo Sulaksono. "IMPLEMENTASI KRIPTOGRAFI DENGAN METODE ELLIPTIC CURVE CRYPTOGRAPHY (ECC) UNTUK APLIKASI CHATTING DALAM CLOUD COMPUTING BERBASIS ANDROID." KERNEL: Jurnal Riset Inovasi Bidang Informatika dan Pendidikan Informatika 1, no. 1 (November 6, 2020): 42–48. http://dx.doi.org/10.31284/j.kernel.2020.v1i1.929.

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in general, information dissemination facilities in the current technological era can be done quicklyand easily through the android application media. One of the most frequently used media forinformation dissemination is chatting. The problem with this research is that the chat application allowssomeone to send messages or files to other users who have access rights, with the risk that the data willbe seen by anyone who has access rights in it. This can happen because in the chat application can seeanything that is shared as long as you have access rights, but sometimes there is some data that isprivacy. So it is necessary to add a means to secure this privacy data so it cannot be seen by other users.The solution to overcome this problem is a cryptographic system. One cryptographic method thatprovides solutions to information security problems is the Elliptic Curve Cryptography (ECC) method.Therefore this thesis proposal is to create an online system in order to implement cryptography with theElliptic Curve Cryptography (ECC) method for Android-based chat applications. The testing processin this study using 25 image data obtained, the smallest avalanche effect value is 36.52801638, thebiggest avalanche effect is 94,67749211. And obtained an average avalanche effect value of79,8881925. The average avalanche effect that produces a large enough percentage proves that theapplication is running well, because the greater the percentage obtained, the better the application isrunning. From the above test it can be concluded that the Elliptic Curve Cryptography (ECC) algorithmmethod is effective for hiding data files in chat applications that are privacy ABSTRACTIn general, information dissemination facilities in the current technological era can be done quicklyand easily through the android application media. One of the most frequently used media forinformation dissemination is chatting. The problem with this research is that the chat application allowssomeone to send messages or files to other users who have access rights, with the risk that the data willbe seen by anyone who has access rights in it. This can happen because in the chat application can seeanything that is shared as long as you have access rights, but sometimes there is some data that isprivacy. So it is necessary to add a means to secure this privacy data so it cannot be seen by other users.The solution to overcome this problem is a cryptographic system. One cryptographic method thatprovides solutions to information security problems is the Elliptic Curve Cryptography (ECC) method.Therefore this thesis proposal is to create an online system in order to implement cryptography with theElliptic Curve Cryptography (ECC) method for Android-based chat applications. The testing processin this study using 25 image data obtained, the smallest avalanche effect value is 36.52801638, thebiggest avalanche effect is 94,67749211. And obtained an average avalanche effect value of79,8881925. The average avalanche effect that produces a large enough percentage proves that theapplication is running well, because the greater the percentage obtained, the better the application isrunning. From the above test it can be concluded that the Elliptic Curve Cryptography (ECC) algorithmmethod is effective for hiding data files in chat applications that are privacy.Keywords: Cryptography, Elliptic Curve Cryptography (ECC) Algorithm, Avalanche EffectABSTRAKSecara umum, fasilitas penyebaran informasi pada era teknologi yang saat ini dapat dilakukan dengancepat dan mudah melalui media aplikasi android. Salah satu media yang paling sering digunakan untukpenyebaran informasi adalah chatting. Masalah dari penelitian ini adalah aplikasi chattingmemungkinkan seseorang dapat mengirim pesan ataupun file kepada user lain yang telah memiliki hakakses, dengan resiko datanya akan dapat dilihat oleh siapa saja yang memiliki hak akses didalamnya.Hal ini dapat terjadi karena didalam aplikasi chatting tersebut dapat melihat apapun yang dibagi selamamemiliki hak akses, namun terkadang ada beberapa data yang bersifat privasi. Sehingga perluditambahkan suatu sarana untuk mengamankan data privasi ini agar tidak dapat dilihat oleh user lain.Adapun solusi untuk mengatasi hal tersebut maka dibuatlah sebuah sistem kriptografi. Salah satumetode kriptografi yang memberikan solusi untuk permasalahan keamanan informasi adalah metodeElliptic Curve Cryptography (ECC). Oleh karena itu proposal skripsi ini untuk membuat sebuah sistemonline agar dapat mengimplementasikan cryptography dengan metode Elliptic Curve Cryptography(ECC) untuk aplikasi chatting berbasis Android. Proses pengujian pada penelitian ini menggunakan 25data citra didapatkan, nilai avalanche effect terkecil adalah 36,52801638, avalanche effect terbesaradalah 94,67749211. Dan didapatkan nilai avalanche effect rata – rata sebesar 79,8881925. Nilai rata –rata avalanche effect yang menghasilkan persentase yang cukup besar membuktikan bahwa aplikasiberjalan dengan baik, karena semakin besar persentase yang didapatkan maka semakin baik aplikasi ituberjalan. Dari pengujian diatas dapat disimpulkan bahwa metode algoritma Elliptic Curve Cryptography(ECC) ini efektif untuk menyembunyikan file data pada aplikasi chatting yang bersifat privasi.Kata Kunci : Kriptografi, Algoritma Elliptic Curve Cryptography (ECC), Avalanche Effect
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Thanh, Dinh Tien, Nguyen Quoc Toan, Nguyen Van Son, and Nguyen Van Duan. "An algorithm to select a secure twisted elliptic curve in cryptography." Journal of Science and Technology on Information security 1, no. 15 (June 8, 2022): 17–25. http://dx.doi.org/10.54654/isj.v1i15.832.

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Abstract—Fault attack is a powerful adjacency channel attack technique to break cryptographic schemes. On elliptic curve cryptography (ECC), fault attacks can be divided into three types: safeerror attacks, weak-curve-based attacks, and differential fault attacks. In the paper [1], the author has presented the fault attack on the elliptic curve cryptosystem based on the quadratic twist curve and Proposed criteria to resist elliptic fault attack on the elliptic curve. In this paper, we propose an algorithm to choose a twist secure elliptic curve and evaluate the paths published in cryptographic standards around the world. Tóm tắt— Tấn công gây lỗi là một kỹ thuật tấn công kênh kề mạnh nhằm phá vỡ các lược đồ mật mã. Tấn công gây lỗi lên mật mã đường cong elliptic (ECC) có thể được chia thành ba loại: tấn công safe-error, tấn công dựa trên đường cong yếu và tấn công gây lỗi vi sai. Trong bài báo [1], nhóm tác giả đã làm tường minh tấn công gây lỗi lên ECC dựa vào đường cong xoắn và đề xuất tiêu chí để chống lại tấn công gây lỗi trên ECC. Bài báo này nhóm tác giả đề xuất thuật toán lựa chọn đường elliptic an toàn xoắn và đánh giá an toàn xoắn cho các đường cong elliptic đã công bố trong một số chuẩn mật mã.
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Maimuţ, Diana, and Alexandru Cristian Matei. "Speeding-Up Elliptic Curve Cryptography Algorithms." Mathematics 10, no. 19 (October 7, 2022): 3676. http://dx.doi.org/10.3390/math10193676.

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In recent decades there has been an increasing interest in Elliptic curve cryptography (ECC) and, especially, the Elliptic Curve Digital Signature Algorithm (ECDSA) in practice. The rather recent developments of emergent technologies, such as blockchain and the Internet of Things (IoT), have motivated researchers and developers to construct new cryptographic hardware accelerators for ECDSA. Different types of optimizations (either platform dependent or algorithmic) were presented in the literature. In this context, we turn our attention to ECC and propose a new method for generating ECDSA moduli with a predetermined portion that allows one to double the speed of Barrett’s algorithm. Moreover, we take advantage of the advancements in the Artificial Intelligence (AI) field and bring forward an AI-based approach that enhances Schoof’s algorithm for finding the number of points on an elliptic curve in terms of implementation efficiency. Our results represent algorithmic speed-ups exceeding the current paradigm as we are also preoccupied by other particular security environments meeting the needs of governmental organizations.
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Trung, Mai Manh, Le Phe Do, Do Trung Tuan, Nguyen Van Tanh, and Ngo Quang Tri. "Design a cryptosystem using elliptic curves cryptography and Vigenère symmetry key." International Journal of Electrical and Computer Engineering (IJECE) 13, no. 2 (April 1, 2023): 1734. http://dx.doi.org/10.11591/ijece.v13i2.pp1734-1743.

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In this paper describes the basic idea of elliptic curve cryptography (ECC) as well as Vigenère symmetry key. Elliptic curve arithmetic can be used to develop elliptic curve coding schemes, including key exchange, encryption, and digital signature. The main attraction of elliptic curve cryptography compared to Rivest, Shamir, Adleman (RSA) is that it provides equivalent security for a smaller key size, which reduces processing costs. From the theorical basic, we proposed a cryptosystem using elliptic curves and Vigenère cryptography. We proposed and implemented our encryption algorithm in an integrated development environment named visual studio 2019 to design a safe, secure, and effective cryptosystem.
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Purwiko, Daniel Perdana Putra, Favian Dewanta, and Farah Afianti. "ANALISIS PENGGUNAAN ECC PADA SISTEM AUTENTIKASI DI IOT." MULTINETICS 8, no. 1 (August 29, 2022): 42–49. http://dx.doi.org/10.32722/multinetics.v8i1.4701.

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Internet of Things adalah sistem kompleks yang banyak digunakan dalam banyak cara untuk memajukan kehidupan manusia. Akibatnya, Internet of Things (IoT) memiliki banyak kerentanan keamanan dan memerlukan sistem autentikasi untuk melindungi data pengguna. Memilih jenis autentikasi yang sesuai dengan kebutuhan Anda sangat penting untuk mencapai kinerja yang sangat baik pada perangkat Internet of Things (IoT) Anda dengan spesifikasi yang relatif minimal. Karena situasi ini, algoritma Elliptic Curve Cryptography (ECC) adalah salah satu algoritma yang pasti yang mengkonsumsi lebih sedikit sumber daya dalam prosesnya. Penelitian ini bertujuan untuk menguji dan membandingkan algoritma autentikasi Elliptic Curve Cryptography(ECC) berbasis Fiat-Shamir dan Elliptic Curve Diffie-Hellman berbasis Hash Message Authentication Code (ECDH-HMAC). Parameter untuk pengujian ini adalah waktu komputasi, delay , program penyimpanan , dan biaya komunikasi dari algoritma autentikasi. Hasil eksperimen menunjukkan bahwa algoritma Elliptic Curve Diffie-Hellman berbasis Hash Message Authentication Code (ECDH-HMAC) memiliki waktu komputasi, penundaan , dan penggunaan program penyimpanan terendah, dan algoritma Elliptic Curve Cryptography (ECC) berbasis Fiat-Shamir memiliki nilaibiaya komunikasi terendah.
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Jayanti, Sravani, K. Chittibabu, and Chandra Sekhar Akkapeddi. "A Cryptosystem of Skewed Affine Cipher of Multiple Keys." ECS Transactions 107, no. 1 (April 24, 2022): 15071–80. http://dx.doi.org/10.1149/10701.15071ecst.

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In this era, where communication over technology has become vital, the reliability of the same is of utmost need. Cryptography ensures confidentiality, user authentication, and integrity of data. One of the techniques is the Elliptic Curve Cryptography (ECC). Several classical ciphers are designed based on mathematical backgrounds. In this paper, we focus on combining Affine Cipher and ECC to magnify the security provided by an Affine cipher. Hence a skewed Affine cipher that uses multiple keys over Elliptic curves is proposed. The keys chosen are derived from the points on the specified Elliptic curve, which forms a cyclic group or a cyclic subgroup.
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Dissertations / Theses on the topic "Elliptic Curve Cryptography (ECC)"

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Bommireddipalli, Nithesh Venkata Ramana Surya. "Tutorial on Elliptic Curve Arithmetic and Introduction to Elliptic Curve Cryptography (ECC)." University of Cincinnati / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1511866832906148.

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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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Lien, E.-Jen. "EFFICIENT IMPLEMENTATION OF ELLIPTIC CURVE CRYPTOGRAPHY IN RECONFIGURABLE HARDWARE." Case Western Reserve University School of Graduate Studies / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=case1333761904.

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baktir, selcuk. "Frequency Domain Finite Field Arithmetic for Elliptic Curve Cryptography." Digital WPI, 2008. https://digitalcommons.wpi.edu/etd-dissertations/272.

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Efficient implementation of the number theoretic transform(NTT), also known as the discrete Fourier transform(DFT) over a finite field, has been studied actively for decades and found many applications in digital signal processing. In 1971 Schonhage and Strassen proposed an NTT based asymptotically fast multiplication method with the asymptotic complexity O(m log m log log m) for multiplication of $m$-bit integers or (m-1)st degree polynomials. Schonhage and Strassen's algorithm was known to be the asymptotically fastest multiplication algorithm until Furer improved upon it in 2007. However, unfortunately, both algorithms bear significant overhead due to the conversions between the time and frequency domains which makes them impractical for small operands, e.g. less than 1000 bits in length as used in many applications. With this work we investigate for the first time the practical application of the NTT, which found applications in digital signal processing, to finite field multiplication with an emphasis on elliptic curve cryptography(ECC). We present efficient parameters for practical application of NTT based finite field multiplication to ECC which requires key and operand sizes as short as 160 bits in length. With this work, for the first time, the use of NTT based finite field arithmetic is proposed for ECC and shown to be efficient. We introduce an efficient algorithm, named DFT modular multiplication, for computing Montgomery products of polynomials in the frequency domain which facilitates efficient multiplication in GF(p^m). Our algorithm performs the entire modular multiplication, including modular reduction, in the frequency domain, and thus eliminates costly back and forth conversions between the frequency and time domains. We show that, especially in computationally constrained platforms, multiplication of finite field elements may be achieved more efficiently in the frequency domain than in the time domain for operand sizes relevant to ECC. This work presents the first hardware implementation of a frequency domain multiplier suitable for ECC and the first hardware implementation of ECC in the frequency domain. We introduce a novel area/time efficient ECC processor architecture which performs all finite field arithmetic operations in the frequency domain utilizing DFT modular multiplication over a class of Optimal Extension Fields(OEF). The proposed architecture achieves extension field modular multiplication in the frequency domain with only a linear number of base field GF(p) multiplications in addition to a quadratic number of simpler operations such as addition and bitwise rotation. With its low area and high speed, the proposed architecture is well suited for ECC in small device environments such as smart cards and wireless sensor networks nodes. Finally, we propose an adaptation of the Itoh-Tsujii algorithm to the frequency domain which can achieve efficient inversion in a class of OEFs relevant to ECC. This is the first time a frequency domain finite field inversion algorithm is proposed for ECC and we believe our algorithm will be well suited for efficient constrained hardware implementations of ECC in affine coordinates.
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Krisell, Martin. "Elliptic Curve Digital Signatures in RSA Hardware." Thesis, Linköpings universitet, Informationskodning, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-81084.

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A digital signature is the electronic counterpart to the hand written signature. It can prove the source and integrity of any digital data, and is a tool that is becoming increasingly important as more and more information is handled electronically. Digital signature schemes use a pair of keys. One key is secret and allows the owner to sign some data, and the other is public and allows anyone to verify the signature. Assuming that the keys are large enough, and that a secure scheme is used, it is impossible to find the private key given only the public key. Since a signature is valid for the signed message only, this also means that it is impossible to forge a digital signature. The most well-used scheme for constructing digital signatures today is RSA, which is based on the hard mathematical problem of integer factorization. There are, however, other mathematical problems that are considered even harder, which in practice means that the keys can be made shorter, resulting in a smaller memory footprint and faster computations. One such alternative approach is using elliptic curves. The underlying mathematical problem of elliptic curve cryptography is different to that of RSA, however some structure is shared. The purpose of this thesis was to evaluate the performance of elliptic curves compared to RSA, on a system designed to efficiently perform the operations associated with RSA. The discovered results are that the elliptic curve approach offers some great advantages, even when using RSA hardware, and that these advantages increase significantly if special hardware is used. Some usage cases of digital signatures may, for a few more years, still be in favor of the RSA approach when it comes to speed. For most cases, however, an elliptic curve system is the clear winner, and will likely be dominant within a near future.
En digital signatur är den elektroniska motsvarigheten till en handskriven signatur. Den kan bevisa källa och integritet för valfri data, och är ett verktyg som blir allt viktigare i takt med att mer och mer information hanteras digitalt. Digitala signaturer använder sig av två nycklar. Den ena nyckeln är hemlig och tillåter ägaren att signera data, och den andra är offentlig och tillåter vem som helst att verifiera signaturen. Det är, under förutsättning att nycklarna är tillräck- ligt stora och att det valda systemet är säkert, omöjligt att hitta den hemliga nyckeln utifrån den offentliga. Eftersom en signatur endast är giltig för datan som signerades innebär detta också att det är omöjligt att förfalska en digital signatur. Den mest välanvända konstruktionen för att skapa digitala signaturer idag är RSA, som baseras på det svåra matematiska problemet att faktorisera heltal. Det finns dock andra matematiska problem som anses vara ännu svårare, vilket i praktiken innebär att nycklarna kan göras kortare, vilket i sin tur leder till att mindre minne behövs och att beräkningarna går snabbare. Ett sådant alternativ är att använda elliptiska kurvor. Det underliggande matematiska problemet för kryptering baserad på elliptiska kurvor skiljer sig från det som RSA bygger på, men de har en viss struktur gemensam. Syftet med detta examensarbete var att utvärdera hur elliptiska kurvor presterar jämfört med RSA, på ett system som är designat för att effektivt utföra RSA. De funna resultaten är att metoden med elliptiska kurvor ger stora fördelar, även om man nyttjar hårdvara avsedd för RSA, och att dessa fördelar ökar mångfaldigt om speciell hårdvara används. För några användarfall av digitala signaturer kan, under några år framöver, RSA fortfarande vara fördelaktigt om man bara tittar på hastigheten. För de flesta fall vinner dock elliptiska kurvor, och kommer troligen vara dominant inom kort.
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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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Hitchcock, Yvonne Roslyn. "Elliptic Curve Cryptography for Lightweight Applications." Queensland University of Technology, 2003. http://eprints.qut.edu.au/15838/.

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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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Murdica, Cédric. "Sécurité physique de la cryptographie sur courbes elliptiques." Thesis, Paris, ENST, 2014. http://www.theses.fr/2014ENST0008/document.

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La Cryptographie sur les Courbes Elliptiques (abréviée ECC de l'anglais Elliptic Curve Cryptography) est devenue très importante dans les cartes à puces car elle présente de meilleures performances en temps et en mémoire comparée à d'autres cryptosystèmes asymétriques comme RSA. ECC est présumé incassable dans le modèle dit « Boite Noire », où le cryptanalyste a uniquement accès aux entrées et aux sorties. Cependant, ce n'est pas suffisant si le cryptosystème est embarqué dans un appareil qui est physiquement accessible à de potentiels attaquants. En plus des entrés et des sorties, l'attaquant peut étudier le comportement physique de l'appareil. Ce nouveau type de cryptanalyse est appelé cryptanalyse physique. Cette thèse porte sur les attaques physiques sur ECC. La première partie fournit les pré-requis sur ECC. Du niveau le plus bas au plus élevé, ECC nécessite les outils suivants : l'arithmétique sur les corps finis, l'arithmétique sur courbes elliptiques, la multiplication scalaire sur courbes elliptiques et enfin les protocoles cryptographiques. La deuxième partie expose un état de l'art des différentes attaques physiques et contremesures sur ECC. Pour chaque attaque, nous donnons le contexte dans lequel elle est applicable. Pour chaque contremesure, nous estimons son coût en temps et en mémoire. Nous proposons de nouvelles attaques et de nouvelles contremesures. Ensuite, nous donnons une synthèse claire des attaques suivant le contexte. Cette synthèse est utile pendant la tâche du choix des contremesures. Enfin, une synthèse claire de l'efficacité de chaque contremesure sur les attaques est donnée
Elliptic Curve Cryptography (ECC) has gained much importance in smart cards because of its higher speed and lower memory needs compared with other asymmetric cryptosystems such as RSA. ECC is believed to be unbreakable in the black box model, where the cryptanalyst has access to inputs and outputs only. However, it is not enough if the cryptosystem is embedded on a device that is physically accessible to potential attackers. In addition to inputs and outputs, the attacker can study the physical behaviour of the device. This new kind of cryptanalysis is called Physical Cryptanalysis. This thesis focuses on physical cryptanalysis of ECC. The first part gives the background on ECC. From the lowest to the highest level, ECC involves a hierarchy of tools: Finite Field Arithmetic, Elliptic Curve Arithmetic, Elliptic Curve Scalar Multiplication and Cryptographie Protocol. The second part exhibits a state-of-the-art of the different physical attacks and countermeasures on ECC.For each attack, the context on which it can be applied is given while, for each countermeasure, we estimate the lime and memory cost. We propose new attacks and new countermeasures. We then give a clear synthesis of the attacks depending on the context. This is useful during the task of selecting the countermeasures. Finally, we give a clear synthesis of the efficiency of each countermeasure against the attacks
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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
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Felding, Eric. "Simuleringar av elliptiska kurvor för elliptisk kryptografi." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-158133.

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This thesis describes the theory behind elliptic-curve Diffie-Hellman key exchanges. All the way from the definition of a group until how the operator over an elliptic curve forms an abelian group. This is illustrated with clear examples. After that a smaller study is made to determine if there is a connection betweenthe size of the underlying field, the amount of points on the curve and the order of the points to determine how hard it is to find out the secret key in elliptic-curve Diffie-Hellman key exchanges. No clear connection is found. Since elliptic curves over extension fields have more computational heavy operations, it is concluded that these curves serve no practical use in elliptic-curve Diffie-Hellman key exchange.
Denna rapport går igenom teorin bakom Diffie-Hellmans nyckelutbyte över elliptiska kurvor. Från definitionen av en grupp hela vägen till hur operatorn över en elliptisk kurva utgör en abelsk grupp gås igenom och görs tydligt med konstruktiva exempel. Sedan görs en mindre undersökning av sambandet mellan storleken av den underliggande kroppen, antal punkter på kurvan och ordning av punkterna på kurvan, det vill säga svårigheten att hitta den hemliga nyckeln framtagen med Diffie-Hellmans nyckelutbyte för elliptiska kurvor. Ingen tydlig koppling hittas. Då elliptiska kurvor över utvidgade kroppar har mer beräkningstunga operationer dras slutsatsen att dessa kurvor inte är praktiska inom Diffie-Hellman nyckelutbyte över elliptiska kurvor.
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Books on the topic "Elliptic Curve Cryptography (ECC)"

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Stevens, Zac Roger Julius. Elliptic Curve Cryptography. Oxford: Oxford Brookes University, 2003.

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Implementing elliptic curve cryptography. Greenwich: Manning, 1999.

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F, Blake Ian, Seroussi G. 1955-, and Smart Nigel P. 1967-, eds. Advances in elliptic curve cryptography. Cambridge, UK: Cambridge University Press, 2005.

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Menezes, A. J. Elliptic curve public key cryptosystems. Boston: Kluwer Academic Publishers, 1993.

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Henri, Cohen, and Frey Gerhard 1944-, eds. Handbook of elliptic and hyperelliptic curve cryptography. Boca Raton, FL: Taylor and Francis, 2005.

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Blake, Ian F., Gadiel Seroussi, and Nigel P. Smart, eds. Advances in Elliptic Curve Cryptography. Cambridge University Press, 2005. http://dx.doi.org/10.1017/cbo9780511546570.

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Guide to Elliptic Curve Cryptography. New York: Springer-Verlag, 2004. http://dx.doi.org/10.1007/b97644.

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Blake, Ian F., Nigel P. Smart, and Gadiel Seroussi. Advances in Elliptic Curve Cryptography. Cambridge University Press, 2009.

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Blake, Ian F., Nigel P. Smart, and Gadiel Seroussi. Advances in Elliptic Curve Cryptography. Cambridge University Press, 2005.

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Blake, Ian F., Nigel P. Smart, and G. Seroussi. Advances in Elliptic Curve Cryptography. Cambridge University Press, 2005.

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Book chapters on the topic "Elliptic Curve Cryptography (ECC)"

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Wohlgemuth, Martin. "ECC — Elliptic Curves Cryptography." In Mathematisch für fortgeschrittene Anfänger, 305–15. Heidelberg: Spektrum Akademischer Verlag, 2010. http://dx.doi.org/10.1007/978-3-8274-2607-9_24.

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Raghav, Piyush, and Amit Dua. "Security and Cryptography in Images and Video Using Elliptic Curve Cryptography (ECC)." In Cryptographic and Information Security, 141–70. Boca Raton, Florida : CRC Press, [2019]: CRC Press, 2018. http://dx.doi.org/10.1201/9780429435461-6.

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Liu, Zhe, Erich Wenger, and Johann Großschädl. "MoTE-ECC: Energy-Scalable Elliptic Curve Cryptography for Wireless Sensor Networks." In Applied Cryptography and Network Security, 361–79. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07536-5_22.

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Moosavi, Sanaz Rahimi, and Arman Izadifar. "End-to-End Security Scheme for E-Health Systems Using DNA-Based ECC." In Silicon Valley Cybersecurity Conference, 77–89. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-96057-5_6.

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AbstractToday, the amount of data produced and stored in computing Internet of Things (IoT) devices is growing. Massive volumes of sensitive information are exchanged between these devices making it critical to ensure the security of these data. Cryptography is a widely used method for ensuring data security. Many lightweight cryptographic algorithms have been developed to address the limitations of resources on the IoT devices. Such devices have limited processing capabilities in terms of memory, processing power, storage, etc. The primary goal of exploiting cryptographic technique is to send data from the sender to the receiver in the most secure way to prevent eavesdropping of the content of the original data. In this paper, we propose an end-to-end security scheme for IoT system. The proposed scheme consists of (i) a secure and efficient mutual authentication scheme based on the Elliptic Curve Cryptography (ECC) and the Quark lightweight hash design, and (ii) a secure end-to-end communication based on Deoxyribonucleic Acid (DNA) and ECC. DNA Cryptography is the cryptographic technique to encrypt and decrypt the original data using DNA sequences based on its biological processes. It is a novel technique to hide data from unauthorized access with the help of DNA. The security analysis of the proposed scheme reveals that it is secure against the relevant threat models and provides a higher security level than the existing related work in the literature.
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Ech Chkaf, Ayoub, Abdelhadi El Allali, Siham Beloualid, Taoufiq El Harrouti, Sanaa El Aidi, Abderrahim Bajit, Habiba Chaoui, and Ahmed Tamtaoui. "Applying Lightweight Elliptic Curve Cryptography ECC to Smart Energy IoT Platforms Based on the CoAP Protocol." In Advances in Information, Communication and Cybersecurity, 206–18. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-91738-8_20.

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Joglekar, Jyoti, Simran Bhutani, Nisha Patel, and Pradnya Soman. "Lightweight Elliptical Curve Cryptography (ECC) for Data Integrity and User Authentication in Smart Transportation IoT System." In Sustainable Communication Networks and Application, 270–78. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-34515-0_28.

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Hamza, Fatima Zahra, Sanaa El Aidi, Abdelhadi El Allali, Siham Beloualid, Abderrahim Bajit, and Ahmed Tamtaoui. "Applying Lightweight Elliptic Curve Cryptography ECC and Advanced IoT Network Topologies to Optimize COVID-19 Sanitary Passport Platforms Based on Constrained Application Protocol." In Advances on Intelligent Informatics and Computing, 512–23. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-98741-1_42.

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Easttom, William. "Elliptic Curve Cryptography." In Modern Cryptography, 245–56. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-63115-4_11.

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Paar, Christof, and Jan Pelzl. "Elliptic Curve Cryptosystems." In Understanding Cryptography, 239–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-04101-3_9.

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Easttom, Chuck. "Elliptic Curve Cryptography." In Modern Cryptography, 253–63. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-12304-7_11.

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Conference papers on the topic "Elliptic Curve Cryptography (ECC)"

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Ponomarev, Oleg, Andrey Khurri, and Andrei Gurtov. "Elliptic Curve Cryptography (ECC) for Host Identity Protocol (HIP)." In 2010 Ninth International Conference on Networks. IEEE, 2010. http://dx.doi.org/10.1109/icn.2010.68.

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Asaker, Ahmed A., Zeinab F. Elsharkawy, Sabry Nassar, Nabil Ayad, O. Zahran, and Fathi E. Abd El-Samie. "A Novel Iris Cryptosystem Using Elliptic Curve Cryptography." In 2021 9th International Japan-Africa Conference on Electronics, Communications, and Computations (JAC-ECC). IEEE, 2021. http://dx.doi.org/10.1109/jac-ecc54461.2021.9691307.

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Hu, Yu, Qing Li, Lei Huang, and Chung-Chieh Jay Kuo. "Efficient implementation of elliptic curve cryptography (ECC) on embedded media processors." In Electronic Imaging 2004, edited by Sethuraman Panchanathan and Bhaskaran Vasudev. SPIE, 2004. http://dx.doi.org/10.1117/12.532449.

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Chauhan, Miss Manorama. "An implemented of hybrid cryptography using elliptic curve cryptosystem (ECC) and MD5." In 2016 International Conference on Inventive Computation Technologies (ICICT). IEEE, 2016. http://dx.doi.org/10.1109/inventive.2016.7830092.

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S. Gornale, Shivanand, and A. C. Nuthan. "Discrete Wavelet Transform (DWT) Based Triple-stegging With Elliptic Curve Cryptography (ECC)." In Second International Conference on Signal Processing, Image Processing and VLSI. Singapore: Research Publishing Services, 2015. http://dx.doi.org/10.3850/978-981-09-6200-5_o-59.

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MuthuKumar, B., and S. Jeevananthan. "High speed hardware implementation of an elliptic curve cryptography (ECC) co-processor." In Computing (TISC). IEEE, 2010. http://dx.doi.org/10.1109/tisc.2010.5714634.

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Gao, Lili, Fangyu Zheng, Niall Emmart, Jiankuo Dong, Jingqiang Lin, and Charles Weems. "DPF-ECC: Accelerating Elliptic Curve Cryptography with Floating-Point Computing Power of GPUs." In 2020 IEEE International Parallel and Distributed Processing Symposium (IPDPS). IEEE, 2020. http://dx.doi.org/10.1109/ipdps47924.2020.00058.

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Maldonado-Ruiz, Daniel, Jenny Torres, and Nour El Madhoun. "3BI-ECC: a Decentralized Identity Framework Based on Blockchain Technology and Elliptic Curve Cryptography." In 2020 2nd Conference on Blockchain Research & Applications for Innovative Networks and Services (BRAINS). IEEE, 2020. http://dx.doi.org/10.1109/brains49436.2020.9223300.

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Hossain, Md Rownak, and Md Selim Hossain. "Efficient FPGA Implementation of Modular Arithmetic for Elliptic Curve Cryptography." In 2019 International Conference on Electrical, Computer and Communication Engineering (ECCE). IEEE, 2019. http://dx.doi.org/10.1109/ecace.2019.8679419.

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Hooda, Reena, Himanhu, and Vikas Poply. "To Design & Implement the Image Encryption Algorithm, using Phase Retrieval in Elliptic Curve Cryptography (ECC)." In 2022 5th International Conference on Contemporary Computing and Informatics (IC3I). IEEE, 2022. http://dx.doi.org/10.1109/ic3i56241.2022.10072750.

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Reports on the topic "Elliptic Curve Cryptography (ECC)"

1

Jivsov, A. Elliptic Curve Cryptography (ECC) in OpenPGP. RFC Editor, June 2012. http://dx.doi.org/10.17487/rfc6637.

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Lochter, M., and J. Merkle. Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation. RFC Editor, March 2010. http://dx.doi.org/10.17487/rfc5639.

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Merkle, J., and M. Lochter. Elliptic Curve Cryptography (ECC) Brainpool Curves for Transport Layer Security (TLS). RFC Editor, October 2013. http://dx.doi.org/10.17487/rfc7027.

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Blake-Wilson, S., D. Brown, and P. Lambert. Use of Elliptic Curve Cryptography (ECC) Algorithms in Cryptographic Message Syntax (CMS). RFC Editor, April 2002. http://dx.doi.org/10.17487/rfc3278.

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Turner, S., and D. Brown. Use of Elliptic Curve Cryptography (ECC) Algorithms in Cryptographic Message Syntax (CMS). RFC Editor, January 2010. http://dx.doi.org/10.17487/rfc5753.

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McGrew, D., D. Bailey, M. Campagna, and R. Dugal. AES-CCM Elliptic Curve Cryptography (ECC) Cipher Suites for TLS. RFC Editor, June 2014. http://dx.doi.org/10.17487/rfc7251.

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Bruckert, L., J. Merkle, and M. Lochter. Elliptic Curve Cryptography (ECC) Brainpool Curves for Transport Layer Security (TLS) Version 1.3. RFC Editor, February 2020. http://dx.doi.org/10.17487/rfc8734.

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Blake-Wilson, S., N. Bolyard, V. Gupta, C. Hawk, and B. Moeller. Elliptic Curve Cryptography (ECC) Cipher Suites for Transport Layer Security (TLS). RFC Editor, May 2006. http://dx.doi.org/10.17487/rfc4492.

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Zhu, L., K. Jaganathan, and K. Lauter. Elliptic Curve Cryptography (ECC) Support for Public Key Cryptography for Initial Authentication in Kerberos (PKINIT). RFC Editor, September 2008. http://dx.doi.org/10.17487/rfc5349.

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Merkle, J., and M. Lochter. Using the Elliptic Curve Cryptography (ECC) Brainpool Curves for the Internet Key Exchange Protocol Version 2 (IKEv2). RFC Editor, July 2013. http://dx.doi.org/10.17487/rfc6954.

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