AI Impacts 2024年05月13日
Comment on Progress in general purpose factoring by Hugo van der Sanden
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This is an interesting article as a record of the history. It would also be useful to show how state-of-the-art algorithms at any given point in time relate to cost of factorization at different sizes; for example, GNFS is described as having “super-polynomial but sub-exponential” cost, but that doesn’t really tell you anything about what it would cost to factorize a number of a given size.

I’ve been doing some quadratic sieve work lately, and here are some times I have for that using msieve for test numbers of given length on a single 3.6GHz Intel core: 46 digits 0.11s; 61 2.19s; 70 25.89s; 80 191.85s; 88 764.24s. A graph expanding this to include lengths in the GNFS realm, and showing how that changes as new techniques are invented, would be really interesting.

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