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Relevant bibliographies by topics / Elliptic Curve Discrete Logarithm (ECDL) / Dissertations / Theses

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Dissertations / Theses on the topic 'Elliptic Curve Discrete Logarithm (ECDL)'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Taufer, Daniele. "Elliptic Loops." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/265846.

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Given an elliptic curve E over Fp and an integer e ≥ 1, we define a new object, called “elliptic loop”, as the set of plane projective points over Z/p^e Z lying over E, endowed with an operation inherited by the curve addition. This object is proved to be a power-associative abelian algebraic loop. Its substructures are investigated by means of other algebraic cubics defined over the same ring, which we named “shadow curve” and “layers”. When E has trace 1, a distinctive behavior is detected and employed for producing an isomorphism attack to the discrete logarithm on this family of curves. St

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2

Taufer, Daniele. "Elliptic Loops." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/265846.

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Given an elliptic curve E over Fp and an integer e ≥ 1, we define a new object, called “elliptic loop”, as the set of plane projective points over Z/p^e Z lying over E, endowed with an operation inherited by the curve addition. This object is proved to be a power-associative abelian algebraic loop. Its substructures are investigated by means of other algebraic cubics defined over the same ring, which we named “shadow curve” and “layers”. When E has trace 1, a distinctive behavior is detected and employed for producing an isomorphism attack to the discrete logarithm on this family of curves. St

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3

Kouchaki, Barzi Behnaz. "Points of High Order on Elliptic Curves : ECDSA." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-58449.

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This master thesis is about Elliptic Curve Digital Signature Algorithm or ECDSA and two of the known attacks on this security system. The purpose of this thesis is to find points that are likely to be points of high order on an elliptic curve. If we have a point P of high order and if Q = mP, then we have a large set of possible values of m. Therefore it is hard to solve the Elliptic Curve Discrete Logarithm Problem or ECDLP. We have investigated on the time of finding the solution of ECDLP for a certain amount of elliptic curves based on the order of the point which is used to create the digi

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4

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

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5

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

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6

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 vul

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7

Falk, Jenny. "On Pollard's rho method for solving the elliptic curve discrete logarithm problem." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-85516.

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Cryptosystems based on elliptic curves are in wide-spread use, they are considered secure because of the difficulty to solve the elliptic curve discrete logarithm problem. Pollard's rho method is regarded as the best method for attacking the logarithm problem to date, yet it is still not efficient enough to break an elliptic curve cryptosystem. This is because its time complexity is O(√n) and for uses in cryptography the value of n will be very large. The objective of this thesis is to see if there are ways to improve Pollard's rho method. To do this, we study some modifications of the origina

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8

Bradley, Tatiana. "A Cryptographic Attack: Finding the Discrete Logarithm on Elliptic Curves of Trace One." Scholarship @ Claremont, 2015. http://scholarship.claremont.edu/scripps_theses/716.

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The crux of elliptic curve cryptography, a popular mechanism for securing data, is an asymmetric problem. The elliptic curve discrete logarithm problem, as it is called, is hoped to be generally hard in one direction but not the other, and it is this asymmetry that makes it secure. This paper describes the mathematics (and some of the computer science) necessary to understand and compute an attack on the elliptic curve discrete logarithm problem that works in a special case. The algorithm, proposed by Nigel Smart, renders the elliptic curve discrete logarithm problem easy in both directions fo

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9

Wilcox, Nicholas. "A Computational Introduction to Elliptic and Hyperelliptic Curve Cryptography." Oberlin College Honors Theses / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1528649455201473.

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10

Pönisch, Jens. "Kryptoggraphie mit elliptischen Kurven." Universitätsbibliothek Chemnitz, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-156488.

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11

Bouvier, Cyril. "Algorithmes pour la factorisation d'entiers et le calcul de logarithme discret." Thesis, Université de Lorraine, 2015. http://www.theses.fr/2015LORR0053/document.

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Dans cette thèse, nous étudions les problèmes de la factorisation d'entier et de calcul de logarithme discret dans les corps finis. Dans un premier temps, nous nous intéressons à l'algorithme de factorisation d'entier ECM et présentons une méthode pour analyser les courbes elliptiques utilisées dans cet algorithme en étudiant les propriétés galoisiennes des polynômes de division. Ensuite, nous présentons en détail l'algorithme de factorisation d'entier NFS, et nous nous intéressons en particulier à l'étape de sélection polynomiale pour laquelle des améliorations d'algorithmes existants sont pr

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12

Bouvier, Cyril. "Algorithmes pour la factorisation d'entiers et le calcul de logarithme discret." Electronic Thesis or Diss., Université de Lorraine, 2015. http://www.theses.fr/2015LORR0053.

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Dans cette thèse, nous étudions les problèmes de la factorisation d'entier et de calcul de logarithme discret dans les corps finis. Dans un premier temps, nous nous intéressons à l'algorithme de factorisation d'entier ECM et présentons une méthode pour analyser les courbes elliptiques utilisées dans cet algorithme en étudiant les propriétés galoisiennes des polynômes de division. Ensuite, nous présentons en détail l'algorithme de factorisation d'entier NFS, et nous nous intéressons en particulier à l'étape de sélection polynomiale pour laquelle des améliorations d'algorithmes existants sont pr

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13

Lin, Kuei-Nuan. "The discrete logarithm problem on an elliptic curve." 1999. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0021-1804200714504002.

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14

Kuei-Nuan, Lin, and 林桂暖. "The discrete logarithm problem on an elliptic curve." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/72594273947630879727.

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碩士<br>國立臺灣師範大學<br>數學研究所<br>88<br>In this master thesis, we talk about the discrete logarithm on an elliptic curve, and this is a reorganization of M-O-V's, Semaev's, and Voloch's papers. Let E be an elliptic curve over a finite field F and char(F)=p, the discrete logarithm problem on an elliptic curve is to compute an integer m such that Q=[m]P, where P and Q are rational points on E. If P has order n, we consider two cases: (1)gcd(n,p)=1 (2)gcd(n,p) is not 1 Finally, we can use the Chinese remainder theorem to compute m

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15

TebbieTung, Iu-Chui, and 董蕘翠. "Finding the secret key in Bitcoin: A review on mathematical approaches to Elliptic Curve Discrete Logarithm Problem." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/bkwnf4.

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碩士<br>國立成功大學<br>數學系應用數學碩博士班<br>107<br>With the popular usage of Bitcoin, safety in making payments or transactions becomes a topic of concern. In brief, the security chiefly relies on the easiness of finding the secret key/ private key in Bitcoin. To a large extent, this depends on how easy it is to resolve an Elliptic Curve Discrete Logarithm Problem (ECDLP). With that in mind, the main focus of this paper is to review any mathematical approaches and their variants that can theoretically tackle an ECDLP in Bitcoin. The objective is to discuss the security of Bitcoin by studying methods of unc

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