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Speeding the Pollard and Elliptic Curve Methods of Factorization
1987
Mathematics of Computation
Since 1974, several algorithms have been developed that attempt to factor a large number N by doing extensive computations modulo N and occasionally taking GCDs with N. These began with Pollard's p -1 and Monte Carlo methods. More recently, Williams published a p + 1 method, and Lenstra discovered an elliptic curve method (ECM). We present ways to speed all of these. One improvement uses two tables during the second phases of p ± 1 and ECM, looking for a match. Polynomial preconditioning lets
doi:10.2307/2007888
fatcat:6zfknzpvu5acflxq5gfz6vmkiy