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February 4, 2014

how fast can you factor

For no other reason than because it's there, here is the result of asking Mathematica to factor RSA 100.

In 1991,

... the factorization took a few days using the multiple-polynomial quadratic sieve algorithm on a MasPar parallel computer.

and now,

It takes four hours to repeat this factorization using the program Msieve on a 2200 MHz Athlon 64 processor.

In comparison, Mathematica took little more than an hour. Unfortunately, it was not able to parallelize it (for a real comparison, the Msieve code would have to be ported over).

{% img center http://farm6.staticflickr.com/5510/12309071334575cda01f9z_d.jpg %}

Update: This has been much better documented on this StackExchange thread, which also links to notes on internal implementation, in case you're interested:

FactorInteger switches between trial division, Pollard , Pollard rho, elliptic curve, and quadratic sieve algorithms.

Finally, more on RSA Numbers, as well as a Mathematica Notebook, here


Tags: old-post

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