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Re:Socat: “the hard coded 1024 bit DH p parameter was not pr... by wtbob on Monday February 01, 2016 @05:06PM (#11015919)
> 2^-80 is an incomprehensibly tiny number.

When one wants a 128-bit security margin, 2^-80 is 2^48 times too big.

Re:Socat: “the hard coded 1024 bit DH p parameter was not pr... by mrb on Monday February 01, 2016 @05:17PM (#11016018)
This is not a valid comparison.

An attacker who can bruteforce, say, 2^80 128-bit keys (approximate limit of the computational power of the largest adversaries) has 1 chance out of 2^48 to break the security.

But an attacker has only 1 chance out of 2^80 that this parameter is a non-prime.

2^80 is much larger than 2^48, therefore it is not a problem.

Re:Socat: “the hard coded 1024 bit DH p parameter was not pr... by wtbob on Monday February 01, 2016 @08:09PM (#11017042)
It's not about bruteforcing.

If I want a 128-bit security level, I'm willing for a random guess of my key to have a 2^-128 chance of being correct. I'm likewise willing for a prime I generate to have a 2^-128/uses chance of not being prime (where uses is equal to the number of times I'll actually be using it).

I can't be 100% certain that a large number is actually prime. But I can be certain enough. Having a 2^-80 chance of being wrong isn't good enough when I want a 2^-128 security level.

Re:Socat: “the hard coded 1024 bit DH p parameter was not pr... by mrb on Monday February 01, 2016 @09:04PM (#11017242)
Yes, security margins are all about what can and cannot be brute forced!

You can't compare these 2 scenarios directly, because in practice:

- attackers can take as many guesses as they want against a piece of data protected by a 128-bit key, but

- attackers get only 1 chance that a particular piece of data protected by a supposed prime is not a prime.

Re:Socat: “the hard coded 1024 bit DH p parameter was not pr... by cperciva on Monday February 01, 2016 @05:23PM (#11016065)
Apples and oranges. When we talk about 128-bit security, we mean that it takes ~2^128 work to break it; not that there's a 2^-128 chance that it is broken.
Re:Socat: “the hard coded 1024 bit DH p parameter was not pr... by marshray on Monday February 01, 2016 @06:11PM (#11016414)
Most protocols do allow the attacker to choose how many times the defender must win at some game of probability.

If the defender is somehow put in a situation to generate 2^80 primes, then he's in trouble.

Re:Socat: “the hard coded 1024 bit DH p parameter was not pr... by cperciva on Monday February 01, 2016 @06:22PM (#11016479)
Sure, I'd aim for a higher security level in a "attacker can keep asking for new primes until we screw up" scenario.
Re:Socat: “the hard coded 1024 bit DH p parameter was not pr... by wtbob on Monday February 01, 2016 @08:10PM (#11017044)
> When we talk about 128-bit security, we mean that it takes ~2^128 work to break it; not that there's a 2^-128 chance that it is broken.

But it also implies that e.g. the attacker has a 2^-128 chance of randomly guessing a key.