A cryptanalytic attack on the LUC cryptosystem using continued fractions

The LUC cryptosystem is a modification of the RSA cryptosystem based on Lucas sequences. In this paper we extend the Verheul - van Tilborg and Dujella variants of the Wiener attack on RSA to the LUC cryptosystem. We describe an algorithm for finding a secret key $d$ of the form $d = r q_{m+1} pm s q_m$, for some $mgeq -1$ and nonnegative integers $r$ and $s$, using continued fractions. We derive bounds for $r$ and $s$ using results on Diophantine approximations

Causes of Student Success in School

The article presents the contribution of socio-demographic, socio-economic, employment status and level of education of parents/guardians to students’ school success. The aim of this article is to discover the causes of school (un)success given the contribution of predictor variables. The predictor set of variables consists of four scales: socio-demographic status (total number of brothers, total number of sisters, marital status of parents, distance from home to school and number of members households), socio-economic status (total monthly income of parents/guardians, place to study in the house/apartment, possession of laptop/computer, constant internet access in the house/apartment and the way they come to school), employment status of parents/guardian and educated status of parent/guardian. In addition to the set of predictors, a criterion variable was used, which consists of three dimensions, namely school success at the end of the sixth, seventh and eighth grade of primary school. The results of the research confirm a statistically significant correlation between socio-demographic, socio-economic, employment status and the level of education of parents/guardians and school success of children, provided that socio-demographic status has a higher predictive power on students’ school success. It was confirmed that students have a positive attitude about the importance of the grade as well as that they perceive that their parents have the same attitude

Digital Signature

Razmjena ključeva među osobama koje sudjeluju u komunikaciji nije uvijek izvediva na siguran način u komunikacijskom sustavu preko kojeg se vrši razmjena ključeva. Jedan od mogućih načina rješavanja ovog problema je u korištenju kriptosustava javnog ključa prilikom slanja poruke. Cilj nam je očuvati njenu vjerodostojnost, netaknutost i nepobitnost. Tu mogućnost nudi nam digitalni potpis, a kako je RSA jedan od najsigurnijih kriptosustava s javnim ključem koji ujedno omogućuje direktno potpisivanje poruke, u radu je opisano RSA digitalno potpisivanje.A digital signature is a mathematical scheme for demonstrating the authenticity of a message stored in electronic form. A valid digital signature gives a recipient reason to believe that the message was created by a known sender. Digital signatures are commonly used in everyday situations such as writing a letter, software distribution and financial transactions, etc. The first practical public-key cryptosystem is the RSA. One of the primary applications of RSA is in the use of digital signature. In this paper we describe the RSA digital signature sheme

Divisibility rules

Pravila djeljivosti nam služe za ispitivanje je li dani broj djeljiv s fiksnim djeliteljem, ali bez provođenja postupka dijeljenja. Najčešće se ispitivanje provodi ispitujući znamenke danog broja. U ovom članku dajemo pregled nekih pravila djeljivosti prirodnih brojeva.A divisibility rule is a shorthand way of discovering whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits. In this paper we present some rules for positive integers