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Showing posts from April, 2018

The Ugly Duckling in factoring aka the filtering steps part I

People that knows me well are well aware that prime numbers have been my obsession since my childhood and they are source of continue interest for me. Actually thanks to cryptography they are a relevant part of my everyday life. One of the most important problem in cryptography since the discovery of RSA is factoring . The factoring problem consists of finding the prime numbers p and q given a large number , N = p x q . Unless you are still convinced that factoring is an easy peasy problem , you should know that, while probably not NP-complete, factoring is indeed reaaally hard. The faster known method for factoring is currently NFS (Number Field Sieve) and if you are interested in the topic I suggest you to read  this beautiful article from the great Carl Pomerance titled "A Tale of Two Sieves" . But it is not what I wanted to talk about today, mainly because the complete algorithm and all its shades go well beyond my current knowledge. Today instead I w