Implementation of Goldwasser-Kilian primality test on elliptic curves

Gimadiev Marat

Type of document

diplomová práce
master thesis

Author

Gimadiev Marat

Supervisor

Al-Beywanee Bestoun S. Ahmed

Opponent

Latypov Roustem Haphisovitch

Field of study

Softwarové inženýrství

Study program

Otevřená informatika

Institutions assigning rank

katedra počítačů

Rights

A university thesis is a work protected by the Copyright Act. Extracts, copies and transcripts of the thesis are allowed for personal use only and at one?s own expense. The use of thesis should be in compliance with the Copyright Act http://www.mkcr.cz/assets/autorske-pravo/01-3982006.pdf and the citation ethics http://knihovny.cvut.cz/vychova/vskp.html
Vysokoškolská závěrečná práce je dílo chráněné autorským zákonem. Je možné pořizovat z něj na své náklady a pro svoji osobní potřebu výpisy, opisy a rozmnoženiny. Jeho využití musí být v souladu s autorským zákonem http://www.mkcr.cz/assets/autorske-pravo/01-3982006.pdf a citační etikou http://knihovny.cvut.cz/vychova/vskp.html

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Abstract

Due to the development in information security and cryptography fields, in particular public-key cryptography, the importance of searching for large prime numbers has increased. Solovay and Strassen, in 1977, and Miller and Rabin, in 1980, were developed probabilistic primality tests, using ideas of Fermat's theorem. Despite the fact that the answer of these tests is not always true, these algorithms had been used in public-key cryptography to construct a set of cryptosystems such as RSA, the Diffie-Hellman key-agreement protocol, El-Gamal scheme. The Goldwasser-Kilian primality test uses elliptic curves in order to reduce the question of the question of primality of to the question of primality q < p. Iterations of Goldwasser-Kilian scheme generate certificate of primality, which can be used by everyone who wants to make sure in primality of number p.

Due to the development in information security and cryptography fields, in particular public-key cryptography, the importance of searching for large prime numbers has increased. Solovay and Strassen, in 1977, and Miller and Rabin, in 1980, were developed probabilistic primality tests, using ideas of Fermat's theorem. Despite the fact that the answer of these tests is not always true, these algorithms had been used in public-key cryptography to construct a set of cryptosystems such as RSA, the Diffie-Hellman key-agreement protocol, El-Gamal scheme. The Goldwasser-Kilian primality test uses elliptic curves in order to reduce the question of the question of primality of p to the question of primality q < p. Iterations of Goldwasser-Kilian scheme generate certificate of primality, which can be used by everyone who wants to make sure in primality of number p.