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B. Verkhovsky, “Integer Factorization of Semi-Primes Based on Analysis of a Sequence of Modular Elliptic Equations”, Int. J. of Communications, Network and System Sciences, Vol. 4, No. 10, 2011, pp. 609-615.

has been cited by the following article:

• TITLE: Deterministic Algorithm Computing All Generators: Application in Cryptographic Systems Design

  AUTHORS: Boris Verkhovsky

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

  JOURNAL NAME: International Journal of Communications, Network and System Sciences, Vol.5 No.11, November 26, 2012

  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.