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Here's an implementation that combines the paper you referenced with http://www.cs.uwaterloo.ca/research/tr/1999/09/CS-99-09.pdf, which gives dynamic sizing: https://github.com/KevinStern/software-and-algorithms/blob/m...


Unless I misread, I don't believe I saw anything that implied that the poster was claiming that anyone with a modicum of smarts could contribute significantly to the study of elliptic curves as relates to Diophantine equations. That being said, there are a mind-boggling number of extremely specific sub-specialties in mathematics, each of which would demand a significant investment of time from even a very intelligent person to reach a deep understanding of the state of the art. The fact that only a handful of folks are sufficiently versed in a particular sub-specialty to evaluate a long, involved and presumably brilliant proof attempt that draws significantly upon the state of the art of that sub-specialty does not imply that only a handful of folks are sufficiently intelligent to evaluate the proof. This reminds me of the recent attempt on the P/NP problem by Vinay Deolalikar - plenty of extremely talented mathematicians watched from the sidelines because they did not have sufficient specialized knowledge to properly evaluate the proof; though, that did not imply that the proof was particularly brilliant or even correct (http://michaelnielsen.org/polymath1/index.php?title=Deolalik...).


I wrote a bit about this awhile back here (http://software-and-algorithms.blogspot.com/2012/06/password...). Basically, I use HMAC to generate passwords based upon a single strong password and an account-specific phrase.


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