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Vincent Granville's Blog – May 2020 Archive (2)

New Probabilistic Approach to Factoring Big Numbers

Product of two large primes are at the core of many encryption algorithms, as factoring the product is very hard for numbers with a few hundred digits. The two prime factors are associated with the encryption keys (public and private keys). Here we describe a new approach to factoring a big number that is the product of two primes of roughly the same size. It is designed especially to handle this problem and identify flaws in encryption algorithms.  …

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Added by Vincent Granville on May 27, 2020 at 12:20pm — No Comments

Simple Trick to Dramatically Improve Speed of Convergence

We discuss a simple trick to significantly accelerate the convergence of an algorithm when the error term decreases in absolute value over successive iterations, with the error term oscillating (not necessarily periodically) between positive and negative values. 

We first illustrate the technique on a well known and simple case: the computation of log 2 using its well know, slow-converging series. We then discuss a very interesting and more complex case, before finally focusing on a…

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Added by Vincent Granville on May 5, 2020 at 5:37pm — No Comments

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