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J. Buhler, H. W. Lenstra and C. Pomerance, “Factoring Integers with the Number Field Sieve,” In: A. K. Lenstra and H. W. Lenstra, Eds., The Development of the Number Field Sieve, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Vol. 1554, 1993, pp. 50-94. doi:10.1007/BFb0091539

has been cited by the following article:

• TITLE: Integer Factorization of Semi-Primes Based on Analysis of a Sequence of Modular Elliptic Equations

  AUTHORS: Boris S. Verkhovsky

  KEYWORDS: Integer Factorization, Factorization of Semi-Primes, Non-Deterministic Algorithm, Elliptic Curves, Counting Points on Elliptic Curves, Crypto-Immunity, Dual Elliptic Curves

  JOURNAL NAME: International Journal of Communications, Network and System Sciences, Vol.4 No.10, October 28, 2011

  ABSTRACT: In this paper is demonstrated a method for reduction of integer factorization problem to an analysis of a sequence of modular elliptic equations. As a result, the paper provides a non-deterministic algorithm that computes a factor of a semi-prime integer n=pq, where prime factors p and q are unknown. The proposed algorithm is based on counting points on a sequence of at least four elliptic curves y2=x(x2+b2)(modn) , where b is a control parameter. Although in the worst case, for some n the number of required values of parameter b that must be considered (the number of basic steps of the algorithm) substantially exceeds four, hundreds of computer experiments indicate that the average number of the basic steps does not exceed six. These experiments also confirm all important facts discussed in this paper.