Dragan Vidakovic

Dragan Vidakovic, Dusko Parezanovic, Zoran Vucetic

In this paper we present the experimental results that more clearly than any theory suggest an answer to the question: when in detection of large (probably) prime numbers to apply, a very resource demanding, Miller-Rabin algorithm. Or, to put it another way, when the dividing by first several tens of prime numbers should be replaced by primality testing? As an innovation, the procedure above will be supplemented by considering the use of the well-known Goldbach's conjecture in the solving of this and some other important questions about the RSA cryptosystem, always guided by the motto "do not harm" - neither the security nor the time spent.

Dragan Vidakovic, Dusko Parezanovic

In this paper, we will present how to find keys elliptic curve cryptosystems (ECC) with simple tools of Delphi 7 console application, using the software problem solving of the scalar point multiplication in the field GF(p), where p is an arbitrary prime number.

Dragan Vidakovic, Olivera Nikolic, Dusko Parezanovic et al.

We believe that there is no real data protection without our own tools. Therefore, our permanent aim is to have more of our own codes. In order to achieve that, it is necessary that a lot of young researchers become interested in cryptography. We believe that the encoding of cryptographic algorithms is an important step in that direction, and it is the main reason why in this paper we present a software implementation of finding the inverse element, the operation which is essentially related to both ECC (Elliptic Curve Cryptography) and the RSA schemes of digital signature.

Dragan Vidakovic, Dusko Parezanovic, Olivera Nikolic et al.

In this paper, we present a complete digital signature message stream, just the way the RSA digital signature scheme does it. We will focus on the operations with large numbers due to the fact that operating with large numbers is the essence of RSA that cannot be understood by the usual illustrative examples with small numbers.

Dragan Vidakovic, Olivera Nikolic, Dusko Parezanovic

In order to avoid unnecessary applications of Miller-Rabin algorithm to the number in question, we resort to trial division by a few initial prime numbers, since such a division take less time. How far we should go with such a division is the that we are trying to answer in this paper?For the theory of the matter is fully resolved. However, that in practice we do not have much use. Therefore, we present a solution that is probably irrelevant to theorists, but it is very useful to people who have spent many nights to produce large (probably) prime numbers using its own software.