RSA cryptosystem

Osobama koje sudjeluju u komunikaciji nije uvijek dostupan siguran komunikacijski kanal pa razmjena kljuvčeva može predstavljati veliki problem. Jedan od načina za rješenje ovog problema je korištenje kriptosustava javnog ključa. To su kriptosustavi kod kojih je iz poznavanja funkcije za šifriranje, praktički nemoguće, u nekom razumnom vremenu, izračunati funkciju za dešifriranje. Najpoznatiji kriptosustav s javnim ključem je RSA. Njegova sigurnost je zasnovana na teškoći faktorizacije velikih prirodnih brojeva.The persons involved in communication do not always have a secure communication channel and the exchange of the keys can be a big problem. One possible solution is the usage of public key cryptography. In these systems it is practically impossible to calculate the decryption function from the encryption function. The most popular public key cryptosystem in use today is the RSA. Its security is based on the difficulty of finding the prime factors of large integers

A remark on the Diophantine equation (x^3-1)/(x-1)=(y^n-1)/(y-1)

In this remark, we use some properties of simple continued fractions of quadratic irrational numbers to prove that the equation (x^3 - 1)/(x - 1) = (y^n - 1)/(y - 1), x, y, n in N, x > 1, y > 1, y > 3, n odd, has only the solutions (x,y,n) = (5,2,5) and (90,2,13)

An Attack on Small Private Keys of RSA Based on Euclidean Algorithm

In this paper, we describe an attack on RSA cryptosystem which is based on Euclid\u27s algorithm. Given a public key $(n,e)$ with corresponding private key $d$ such that $e$ has the same order of magnitude as $n$ and one of the integers $k = (ed-1)/\phi(n)$ and $e-k$ has at most one-quarter as many bits as $e$, it computes the factorization of $n$ in deterministic time $O((\log n)^2)$ bit operations