Academic Journals Database
Disseminating quality controlled scientific knowledge

Deterministic Algorithm Computing All Generators: Application in Cryptographic Systems Design

ADD TO MY LIST
 
Author(s): Boris Verkhovsky

Journal: International Journal of Communications, Network and System Sciences
ISSN 1913-3715

Volume: 05;
Issue: 11;
Start page: 715;
Date: 2012;
Original page

Keywords: Diffie-Hellman Key Exchange | ElGamal Cryptosystem | Generator | Generator of Pseudo-Random Numbers | Information Hiding | Primitive Element | Safe Prime

ABSTRACT
Primitive elements play important roles in the Diffie-Hellman protocol for establishment of secret communication keys, in the design of the ElGamal cryptographic system and as generators of pseudo-random numbers. In general, a deterministic algorithm that searches for primitive elements is currently unknown. In information-hiding schemes, where a primitive element is the key factor, there is the freedom in selection of a modulus. This paper provides a fast deterministic algorithm, which computes every primitive element in modular arithmetic with special moduli. The algorithm requires at most O(log2p) digital operations for computation of a generator. In addition, the accelerated-descend algorithm that computes small generators is described in this paper. Several numeric examples and tables illustrate the algorithms and their properties.

Tango Rapperswil
Tango Rapperswil

     Save time & money - Smart Internet Solutions