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**Integer Factorization of Semi-Primes Based on Analysis of a Sequence of Modular Elliptic Equations** ()

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*y*mod^{2}=x(x^{2}+b^{2})(*n)*, 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.Keywords

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B. Verkhovsky, "Integer Factorization of Semi-Primes Based on Analysis of a Sequence of Modular Elliptic Equations,"

*International Journal of Communications, Network and System Sciences*, Vol. 4 No. 10, 2011, pp. 609-615. doi: 10.4236/ijcns.2011.410073.Conflicts of Interest

The authors declare no conflicts of interest.

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