Abstract
Various cryptosystems have been proposed whose security relies on the difficulty of factoring integers of the special form N = pq 2. To factor integers of that form, Peralta and Okamoto introduced a variation of Lenstra’s Elliptic Curve Method (ECM) of factorization, which is based on the fact that the Jacobi symbols (a/N) and (a/P) agree for all integers a coprime with q. We report on an implementation and extensive experiments with that variation, which have been conducted in order to determine the speed-up compared with ECM for numbers of general form.KeywordsPrime FactorElliptic CurveEquality CheckGreat Common DivisorDecimal DigitThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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