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Deterministic Algorithm Computing All Generators: Application in Cryptographic Systems Design

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DOI: 10.4236/ijcns.2012.511074    3,594 Downloads   5,106 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

B. Verkhovsky, "Deterministic Algorithm Computing All Generators: Application in Cryptographic Systems Design," International Journal of Communications, Network and System Sciences, Vol. 5 No. 11, 2012, pp. 715-719. doi: 10.4236/ijcns.2012.511074.

References

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