Hugh Williams invented the p+1 integer factorization method in 1982 based on John Pollard’s p-1 integer factorization method; the p+1 method finds a factor p when p is smooth with respect to a bound B. We noted in a previous exercise the similar structure of Pollard’s p-1 method and Lenstra’s elliptic curve method, and Williams’ [...]
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We have now discussed several different factorization algorithms: trial division, wheel factorization, Fermat’s method, Pollard’s rho method, Pollard’s p-1 method in both one-stage and two-stage variants, and the elliptic curve meth... Read Post
We have studied John Pollard’s p?1 algorithm for integer factorization on two previous occasions, giving first the basic single-stage algorithm and later adding a second stage. In today’s exercise we look at a somewhat different ver... Read Post
We studied John Pollard’s p-1 factorization algorithm in a previous exercise. You may recall that the algorithm finds factors of a number n by calculating the least common multiple of the integers up to some bound B, call it k, then... Read Post