phc-discussions - Re: [PHC] Let's not degenerate when if the PRF is too narrow for desired output

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Date: Wed, 17 Apr 2013 19:10:00 +0400
From: Solar Designer <solar@...nwall.com>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Let's not degenerate when if the PRF is too narrow for desired output

On Wed, Apr 17, 2013 at 08:25:07AM -0400, Matthew Green wrote:
> I think this statement could be relaxed a bit, but I also agree that overall computational cost should be dominated by the work factor specified as input to the function -- it should not depend strongly (i.e., linearly) on output length.

Exactly.

> By the way, this would seem to be an issue for scrypt as well, since it uses PBKDF2 for the final generation.

scrypt uses PBKDF2 with 1 iteration.  Even if it did not use PBKDF2
specifically, it'd have to spend roughly as much time producing the
requested output length in some other way.

Here's a related desirable property of a good PHS: its overall
computational cost should not depend strongly (e.g., linearly) on input
length as well.  If it does, we have two problems:

1. The cost settings would have to be chosen with consideration of the
maximum input length supported on a given system, so they would likely
end up being lower than what could be afforded for typical input length.

2. The input (password or passphrase) length would be leaked via timings.
While such leaks are unavoidable e.g. with crypt(3)'s use of C strings, a
strong dependency of PHS computation time on input length would make the
leaks a whole lot worse.

Since you mentioned scrypt's use of PBKDF2: it uses PBKDF2 to process
the input as well, but it also does so with 1 iteration only.  Thus,
problem 1 above does not apply (the computational cost is dominated by
scrypt's SMix, not its initial and final uses of PBKDF2).  As to
problem 2, perhaps there's a little bit of room for improvement here,
but it's tricky and it remains not perfect even with the enhancements I
can think of (e.g., looping over the same input for up to a given
constant maximum length: can have same number of instructions, but not
same memory access pattern like we'd have for an actual higher length).

> We should discuss whether we want this to be a criteria for PHC.

I will definitely consider any proposed PHS that allows for much quicker
computation of partial output (than full output) flawed.  While for some
uses of the previous millennium's KDF this is excusable, for a PHS it is
not, and it never was.  The requirements for a PHS are stronger than
those for some uses of a KDF.

Alexander