I went through the PAKE draft on TLS 1.3, and while I certainly appreciate the 
use of a PAKE within TLS, I would like to highlight one potential security 
issue that the working group needs to be aware of.

The draft has SPAKE2+ as its sole defined parameter set; SPAKE2+ has a rather 
interesting property that if the attacker can perform a single discrete log 
problem, in particular, compute the discrete log of N to the base of M, that 
is, find k such that kM = N, then the PAKE properties go away.  That is, an 
active attacker can perform a single exchange, and then efficiently run through 
his dictionary of potential passwords and (as long as the correct password is 
in the dictionary) recover the password.

Let me repeat this: if someone can solve a single discrete log problem (for 
example, if he has a slow Cryptographically Relevant Quantum Computer), then 
the attacker can immediately attack any SPAKE2+ implementation using that 
parameter set, anywhere in the world.

If the working group endorses SPAKE2+, then they need to be aware of this, and 
should highlight it in the security considerations.
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