Factorization of Large Numbers using Reconfigurable Devices

We propose to implement the Mesh Design for implementing the Number Field Sieve particularly which will be used to perform the Matrix step to do Matrix Multiplication. Mesh approach is proposed by Daniel Bernstein which brought down the cost of Number Field Sieve by significant factor especially in the matrix step[5]. The computation is done in the mesh-connected array of processors, which utilizes local memory efficiently compared to PC based implementation. Mesh Design is also used in sieving step[12][32]. Bernstein proposed the Mesh Sorting method for matrix-vector multiplication, which uses Schimmler’s sorting. The Schimmler’s sorting is used to sort m numbers in 8m-8 steps. So the complexity of matrix-vector multiplication reduces by a square root of normal computation time needed. Shamir-Tromer proposed the Mesh Routing method for the matrix-vector multiplication, which has the same complexity benefit as in Mesh Sorting [6].