Date: Wed, 20 Jan 2016 13:00:15 -0500 From: Daniel Kahn Gillmor <dkg@...thhorseman.net> To: Kurt Seifried <kseifried@...hat.com> Cc: oss-security <oss-security@...ts.openwall.com> Subject: Re: Prime example of a can of worms On Wed 2016-01-20 12:25:42 -0500, Kurt Seifried wrote: > Sorry yes, although this also applies equally to keys/etc. sure, though i hope we're not in a "few keys" scenario, that would definitely be bad :) > [dkg wrote:] >> For one, the writeup addresses probabilistic primality tests, but >> doesn't describe proofs of primality, which are significantly more >> expensive to generate (and still probably more expensive to verify than >> a short Miller-Rabin test). But these proofs provide certainty in a way >> that probabilistic tests might not. If we're talking about runtime >> primality checking when communicating with a potential adversary, are >> there proofs about the (im)possibility of generating a pseudoprime that >> is more or less likely to pass a miller-rabin test? > > I looked at this a bit and quite honestly the computational time involved > is just to much to be useful, unless we're talking about generating a small > set of highly trusted primes. For normal people, this just isn't feasible > (witness prime generation taking between less then a second, and more than > 10 minutes, nobody wants to wait 10 minutes...). right, i'm not suggesting that proof generation be done at runtime, just that it is an example of a stronger guarantee than we have for runtime checks, and that it *only* applies to the "generating a small set of highly-trusted primes" case. > Agreed, I listed the diversity more as a stop-gap for the cases where > people have older hard/software (e.g. Java) that will never support larger > primes/keys. At least then you don't get caught in dragnets for the > default/commonly used primes. I agree with this analysis, but the chart in the middle of your paper makes it looks like the diversity is "best", while the "small set of heavily-evaluated primes" (i'm assuming that's what's meant with the "few keys" side of the X axis) is merely "good". --dkg
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