Abstract
Recently calculating the number of lattice points which is an open issue in higher dimension space is appeared. Considering a structure in higher dimension that is practical or aesthetic will be the reason for counting lattice points. Our fundamental object is to present a strategy which counts or at least to estimate how many lattice points on a polytope P in four-dimensional that makes the inconvenience of factorizing the product of the form p.q, with p and q substantial primes easy to compute, this would broke RSA cryptosystem. These approaches depend on finding the lattice point’s numbers of of 4-dimensional polytope that is approximate to the number of four dimensional balls, using the properties of the Ehrhart polynomial for a 4-polytope and the cross product of two polytopes. Results are obtained for N = pq and the factorizing of it. Two methodologies are utilized one of them is presented now and the other is in work.
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