Abstract:
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.

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

Abstract:
Many people know the general story about RSA and large (probably) prime numbers, without having an idea of how to perform arithmetic operations with the numbers of thousands of bits. Even if they want to develop their own tool for a digital signature, they give up because they think that special hardware-software offers are required for that. In this paper we want to show that even by using a very simple console application, the tools for signature can be developed. Those tools are not as powerful and functional as the products of renowned companies, but they are sufficient to stimulate the interest in cryptography (and the coding of known algorithms is the best way for that), and that is our overriding and permanent goal[3].

Abstract:
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.

Abstract:
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.

Abstract:
In this paper, we present a complete digital signature message stream, just the way the RSAdigitalsignature scheme does it. We will focus on the operations with large numbers due to the fact that operatingwith large numbers is the essence of RSA that cannot be understood by the usual illustrative examples withsmall numbers[1]

Abstract:
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.

Abstract:
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.

Abstract:
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.

Abstract:
In categorical quantum mechanics, classical structures characterize the classical interfaces of quantum resources on one hand, while on the other hand giving rise to some quantum phenomena. In the standard Hilbert space model of quantum theories, classical structures over a space correspond to its orthonormal bases. In the present paper, we show that classical structures in the category of relations correspond to biproducts of abelian groups. Although relations are, of course, not an interesting model of quantum computation, this result has some interesting computational interpretations. If relations are viewed as denotations of nondeterministic programs, it uncovers a wide variety of non-standard quantum structures in this familiar area of classical computation. Ironically, it also opens up a version of what in philosophy of quantum mechanics would be called an ontic-epistemic gap, as it provides no direct interface to these nonstandard quantum structures.