Interaktivna predstavitev računanja na eliptični krivulji

diplomsko delo

Katja Logar (Author), Aleksandar Jurišić (Mentor)

Abstract

Opišemo eliptične krivulje in računanje z njimi. Predstavimo problem diskretnega logaritma in njegovo uporabo v kriptografskih protokolih, kot so Diffie-Helmanov dogovor o ključu ter podpisi DSA in ECDSA. Preučimo najbolj pomembne splošne napade na problem diskretnega logaritma, s poudarkom na tistih, ki delujejo tudi v grupi na eliptični krivulji, to sta algoritem veliki korak--mali korak ter Pollardov ro algoritem s Floydovim algoritmom za iskanje ciklov. Opišemo tudi aplikacijo za interaktivno predstavitev eliptičnih krivulj ter računanje s točkami na eliptični krivulji. Razdeljena je na dve manjši aplikaciji, prva predstavlja eliptične krivulje nad realnimi števili, druga pa nad praštevilskimi obsegi.

Keywords

eliptične krivulje;končni obsegi;kriptografija z javnimi ključi;računalništvo in informatika;univerzitetni študij;diplomske naloge;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[K. Logar]
UDC:	004:512.742(043.2)
COBISS:	1538311619
Views:	543
Downloads:	158
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Interactive representation of arithmetic on elliptic curve
Secondary abstract:	We first describe elliptic curves and their arithmetic. Then we introduce the discrete logarithm problem and its implications in cryptographic protocols, such as the Diffie-Helman key agreement and the signatures DSA and ECDSA. The most important general attacks on the discrete logarithm problem are also studied, with an emphasis on those that work in the group of points on an elliptic curve, i.e., the giant step-baby step algorithm and the Pollard's rho algorithm together with the Floyd's algorithm for cycle detection. Our application for interactive representation of elliptic curves and their arithmetic is also described. It is divided into two smaller applications. The first focuses on elliptic curves over real numbers and the second one on prime fields.
Secondary keywords:	elliptic curves;finite fields;public key cryptography;computer and information science;diploma;
Type (COBISS):	Bachelor thesis/paper
Study programme:	1000468
Embargo end date (OpenAIRE):	2019-08-23
Thesis comment:	Univ. v Ljubljani, Fak. za računalništvo in informatiko
Pages:	45 str.
ID:	11204697