Implementation of Goldwasser-Kilian primality test on elliptic curves

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.