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Re: [TLS] Negotiated Discrete Log DHE revision

Samuel Neves <sneves@dei.uc.pt> Wed, 09 April 2014 02:37 UTC

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Date: Wed, 09 Apr 2014 03:36:31 +0100
From: Samuel Neves <sneves@dei.uc.pt>
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Subject: Re: [TLS] Negotiated Discrete Log DHE revision
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On 09-04-2014 02:07, Daniel Kahn Gillmor wrote:
>
> I confess i don't see why the safe primes should be farther for this
> construction than a similar construction with pi, but it certainly seems
> to be the case.  Is there a reference that i should read to understand
> this better?
>

It seems to be an unlucky choice. The probability that p is prime is roughly 1/log(p) by the Prime Number Theorem.
Assuming independence, the probability that (p-1)/2 is also prime can be given by the same expression. Thus we can get a
rough approximation of the number of integers to go through: log(p)^2. In the case of p ~ 2^6144, the expected iteration
number is ~2^24.

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