What a lovely hat
Is it made out of tin foil , paper 2008/100, accelerating the scalar multiplication on elliptic curve cryptosystems over prime fields.
Patrick Longa
Elliptic curve cryptography (ECC), independently introduced by Koblitz and Miller in the 80's, has attracted increasing attention in recent years due to its shorter key length requirement in comparison with other public-key cryptosystems such as RSA. Shorter key length means reduced power consumption and computing effort, and less storage requirement, factors that are fundamental in ubiquitous portable devices such as PDAs, cellphones, smartcards, and many others. To that end, a lot of research has been carried out to speed-up and improve ECC implementations, mainly focusing on the most important and time-consuming ECC operation: scalar multiplication. In this thesis, we focus in optimizing such ECC operation at the point and scalar arithmetic levels, specifically targeting standard curves over prime fields. At the point arithmetic level, we introduce two innovative methodologies to accelerate ECC formulae: the use of new composite operations, which are built on top of basic point doubling and addition operations; and the substitution of field multiplications by squarings and other cheaper operations. These techniques are efficiently exploited, individually or jointly, in several contexts: to accelerate computation of scalar multiplications, and the computation of pre-computed points for window-based scalar multiplications (up to 30% improvement in comparison with previous best method); to speed-up computations of simple side-channel attack (SSCA)-protected implementations using innovative atomic structures (up to 22% improvement in comparison with scalar multiplication using original atomic structures); and to develop parallel formulae for SIMD-based applications, which are able to execute three and four operations simultaneously (up to 72% of improvement in comparison with a sequential scalar multiplication). At the scalar arithmetic level, we develop new sublinear (in terms of Hamming weight) multibase scalar multiplications based on NAF-like conversion algorithms that are shown to be faster than any previous scalar multiplication method. For instance, proposed multibase scalar multiplications reduce computing times in 10.9% and 25.3% in comparison with traditional NAF for unprotected and SSCA-protected scenarios, respectively. Moreover, our conversion algorithms overcome the problem of converting any integer to multibase representation, solving an open problem that was defined as hard. Thus, our algorithms make the use of multiple bases practical for applications as ECC scalar multiplication for first time.
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Home > Graduate Research > Master's Theses > 3794
Master's Theses
Elliptic curves and cryptography.
Senorina Ramos Vazquez , San Jose State University Follow
Publication Date
Spring 2010
Degree Type
Degree name.
Master of Science (MS)
Mathematics
Timothy Hsu
Cryptography, Elliptic Curves, Group of an Elliptic Curve
Subject Areas
In this expository thesis we study elliptic curves and their role in cryptography. In doing so we examine an intersection of linear algebra, abstract algebra, number theory, and algebraic geometry, all of which combined provide the necessary background. First we present background information on rings, fields, groups, group actions, and linear algebra. Then we delve into the structure and classification of finite fields as well as construction of finite fields and computation in finite fields. We next explore logarithms in finite fields and introduce the Diffie-Hellman key exchange system. Subsequently, we take a look at the projective and affine planes and we examine the action of the general linear group of degree 3 (over K) on the points of the projective plane P2(K). We then explore the geometry of the projective plane with Desargues Theorem. Next, we study conics, quadratic forms, and methods of counting intersection of curves. Finally, we study forms of degree 3 and we are able to explore cubics and the group law on an elliptic curve which leads us to our ultimate goal of examining the role of elliptic curves in cryptography.
Recommended Citation
Vazquez, Senorina Ramos, "Elliptic Curves and Cryptography" (2010). Master's Theses . 3794. DOI: https://doi.org/10.31979/etd.6fat-tnvm https://scholarworks.sjsu.edu/etd_theses/3794
Since December 15, 2010
https://doi.org/10.31979/etd.6fat-tnvm
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Home > Office of Graduate Studies > Electronic Theses, Projects, and Dissertations > 1440
Electronic Theses, Projects, and Dissertations
An exposition of elliptic curve cryptography.
Travis Severns Follow
Date of Award
Document type, degree name.
Master of Arts in Mathematics
Mathematics
First Reader/Committee Chair
Meyer, Jeffrey
Protecting information that is being communicated between two parties over unsecured channels is of huge importance in today’s world. The use of mathematical concepts to achieve high levels of security when communicating over these unsecured platforms is cryptography. The world of cryptography is always expanding and growing. In this paper, we set out to explore the use of elliptic curves in the cryptography of today, as well as the cryptography of the future. We also offer our own original cryptosystem, CSDH. This system on its own offers some moderate level of security. It shares many similarities to the post-quantum, SIDH system. The parallels between these two systems can lead to a deeper understanding of the systems offered for our post-quantum world.
Recommended Citation
Severns, Travis, "AN EXPOSITION OF ELLIPTIC CURVE CRYPTOGRAPHY" (2022). Electronic Theses, Projects, and Dissertations . 1440. https://scholarworks.lib.csusb.edu/etd/1440
Since April 28, 2022
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Simulative analysis and performance evaluation of various computations–using elliptic curve cryptography
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Raman Kumar , Sandeep Thakur , Harpreet Kaur Bajaj; Simulative analysis and performance evaluation of various computations–using elliptic curve cryptography. AIP Conf. Proc. 30 May 2024; 2900 (1): 020011. https://doi.org/10.1063/5.0209083
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In today’s era Information Security plays vital role in daily life. We use various information security tools and techniques like ATM PIN, e-commerce portal and various PDA security related issues. In this research paper we may use ECC. As ECC provides more security as compared to earlier authentication algorithms. ECC provides more security for all kind of prime numbers. We may apply multiserver authentication scheme using ECC. We have tested and analyze the performance for the guessing attack, reply attack, insider attack, DoS attack and dictionary attack. The proposed scheme is impractical against various attacks.
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IMAGES
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COMMENTS
Elliptic Curve Cryptography Implementation and Performance Testing of Curve ... Master's Thesis Spring 2017. Elliptic Curve Cryptography Implementation and Performance Testing of Curve Representations Olav Wegner Eide 30th April 2017. ii. Abstract Public-key cryptography makes it possible to create digital signatures and do key
A Master's Thesis Presented to The Graduate College of Missouri State University In Partial Ful llment Of the Requirements for the Degree Master of Science, Mathematics By Henry H. Hayden IV July 2021. ELLIPTIC CURVES AND THEIR PRACTICAL APPLICATIONS ... 7 Elliptic Curve Cryptography 68
Master of Arts in Mathematics by Travis Severns May 2022. An Exposition of Elliptic Curve Cryptography A Thesis Presented to the Faculty of California State University, San Bernardino by Travis Severns May 2022 Approved by: Dr. Je rey S Meyer, Committee Chair Dr. Bronson Lim, Committee Member
A mathematical object called an elliptic curve can be used in the construction of public key cryptosystems. This thesis focuses on speeding up elliptic curve cryptography which is an attractive alternative to traditional public key cryptosystems such as RSA. Speeding up elliptic curve cryptography can be
Reconfigurable Elliptic Curve Cryptography. by. Aarti Malik. A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in Computer Engineering Approved. By: Supervised by Dr. Pratapa Reddy, Professor Department of Computer Engineering Kate Gleason College of Engineering Rochester Institute of Technology ...
ELLIPTIC CURVES AND CRYPTOGRAPHY by Senorina R. V¶azquez In this expository thesis we study elliptic curves and their role in cryptography. In doing so we examine an intersection of linear algebra, abstract algebra, number theory, and algebraic geometry, all of which combined provide the necessary background.
Thesis Prepared for the Degree of MASTER OF SCIENCE UNIVERSITY OF NORTH TEXAS August 2007 . Huang, Jian. FPGA Implementations of Elliptic Curve Cryptography and Tate Pairing over Binary Field. Master of Science (Computer Engineering), August 2007, 70 pp., 12 tables, ... 21 figures, references, 52 titles. Elliptic curve cryptography (ECC) is an ...
Elliptic Curve Cryptography (ECC), independently proposed by Miller [Mil86] and Koblitz [Kob87] in mid 80's, is finding momentum to consolidate its status as the public-key system of ... thesis, are brought together to realize four high-speed implementations on x86-64 processors at the 128-bit security level. Presented results set new speed ...
Emphasis is given to elliptic curve cryptography methods which make use of more advanced mathematical concepts. Contents 1. Introduction 1 2. Public-key Cryptography Systems Overview 2 2.1. Preliminaries 2 2.2. Discrete Logarithm Problem 3 2.3. Di e-Hellman Key Exchange 3 2.4. Other Public Cryptosystems 4 3. Elliptic Curve Cryptography 5 3.1.
life. In this master thesis we present a lightweight BSD-based implementation of the Elliptic Curve Cryptography (ECC) for the Contiki OS and its evaluation. We show the feasibility of the implementation and use of this cryptography in the IoT by a thorough evaluation of the solution by analyzing the performance using
tation of elliptic curve cryptography. Elliptic curve cryptography has proven to be adaptable given its broad presence across various electronics of di ering sizes and capabilities. Elliptic curve cryptography is known for utilizing the discrete logarithm problem, modern algebra, and elliptic curves that have encouraged continued research into ...
In this thesis, we study the uses of elliptic curves in the cryptography. We discuss the elliptic curves over finite fields, attempts to attack; discrete logarithm, Pollard's rho algorithm, baby-step giant-step algorithm, ... This thesis is written as part of Master's Degree programme in Information Security and Cryptography at University ...
Public-key cryptography Publication info Published elsewhere. Master's Thesis, University of Ottawa, June 2007 Keywords Elliptic curve cryptography multibase NAF Contact author(s) plonga @ uwaterloo ca History 2008-03-10: received Short URL https://ia.cr/2008/100 License CC BY
A thesis submitted for the degree of Master of Science of Fiji National University October 2020. ii We certify that, as the assessors, we have read this thesis and that in our ... [25], elliptic curve cryptography (ECC) began to be employed for commercial applications. As a result, a significant amount of research has been devoted to analyzing the
In this expository thesis we study elliptic curves and their role in cryptography. In doing so we examine an intersection of linear algebra, abstract algebra, number theory, and algebraic geometry, all of which combined provide the necessary background. First we present background information on rings, fields, groups, group actions, and linear algebra. Then we delve into the structure and ...
To ensure the security of sensitive data, elliptic curve cryptography (ECC) is adopted as an asymmetric method that balances security and efficiency. Nevertheless, embedding messages into elliptic curve (EC) points poses a significant challenge. The intricacies of this process can greatly affect the overall security and efficiency of the cryptosystem, reflecting security vulnerabilities ...
It has been accepted for inclusion in EWU Masters Thesis Collection by an authorized administrator of EWU Digital Commons. For more information, please contact [email protected]. EWU Digital ... While the focus of this paper is on cryptography, elliptic curves appear all over mathematics. In mathematics, elliptic curves have applications in number the-
CERTIFICATE This is to certify that the M.Phil dissertation entitled "A Brief study of Elliptic Curve Cryptography" submitted to Madurai Kamraj University, Madurai, for the award of Master of Philosophy in Computer Science, is a bonafied record of research work and investigations done by Sri. E. Kesavulu Reddy (A5A6686903), under my supervision as a Research Scholar (Part - Time) of the ...
Elliptic Curve (EC) is the most recent and advanced technique of Elliptic Curve Cryptography (ECC). EC is often used to improve the security of open communication networks and to let specific persons with confirmed identities into the Modern Digital Era (MDE). Users of MDE make use of many technologies, such as social media, the cloud, and the ...
The world of cryptography is always expanding and growing. In this paper, we set out to explore the use of elliptic curves in the cryptography of today, as well as the cryptography of the future.We also offer our own original cryptosystem, CSDH. This system on its ownoffers some moderate level of security. It shares many similarities to the ...
Step 1: the curve is used as the general formula: y = x + ax + b where the values a and b are the curve. paramete rs [20] [21]. Step 2: two prim n umbers should be selec ted [21] Step 3: calcul ...
Raman Kumar, Sandeep Thakur, Harpreet Kaur Bajaj; Simulative analysis and performance evaluation of various computations-using elliptic curve cryptography. AIP Conf. Proc. 30 May 2024; 2900 (1): 020011.
This document discusses how a website called HelpWriting.net can assist students struggling with writing a master's thesis on elliptic curve cryptography. It offers customized solutions, thorough research, clear writing, timely delivery, and unlimited revisions. Their team of experts specializes in cryptography and related fields to ensure high-quality support. Students can have their thesis ...