Deterministic Algorithm Computing All Generators: Application in Cryptographic Systems Design

Autor:	Boris S. Verkhovsky
Rok vydání:	2012
Předmět:	Generator (computer programming) Theoretical computer science Modular arithmetic Computer science Deterministic algorithm business.industry Cryptography Diffie–Hellman key exchange Systems design Primitive element business Algorithm ElGamal encryption Computer Science::Cryptography and Security
Zdroj:	International Journal of Communications, Network and System Sciences. :715-719
ISSN:	1913-3723 1913-3715
DOI:	10.4236/ijcns.2012.511074
Popis:	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.
Databáze:	OpenAIRE
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