phc-discussions - Re: [PHC] Deriving multiple keys (was RE: Mechanical tests)

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Date: Wed, 9 Apr 2014 14:27:25 +0200
From: Thomas Pornin <pornin@...et.org>
To: discussions@...sword-hashing.net
Subject: Re: [PHC] Deriving multiple keys (was RE: Mechanical tests)

On Wed, Apr 09, 2014 at 10:25:27AM +0000, Peter Gutmann wrote:
> This is how existing crypto protocols like TLS and CMS do it, typically you
> denote the operation via some diversifier, e.g. TLS uses "CLNT" and "SRVR"
> (actually for the MAC, but a similar thing)

I'll beg to differ here.

In TLS (see section 6.3 of RFC 5246), the symmetric keys are derived from
the "master secret" with a single PRF call:

   When keys and MAC keys are generated, the master secret is used as an
   entropy source.

   To generate the key material, compute

      key_block = PRF(SecurityParameters.master_secret,
                      "key expansion",
                      SecurityParameters.server_random +
                      SecurityParameters.client_random);

   until enough output has been generated.  Then, the key_block is
   partitioned as follows:

      client_write_MAC_key[SecurityParameters.mac_key_length]
      server_write_MAC_key[SecurityParameters.mac_key_length]
      client_write_key[SecurityParameters.enc_key_length]
      server_write_key[SecurityParameters.enc_key_length]
      client_write_IV[SecurityParameters.fixed_iv_length]
      server_write_IV[SecurityParameters.fixed_iv_length]

Thus, TLS exhibits the "output splitting" behaviour. Now, the PRF itself
is defined as a concatenation of HMAC outputs; however, each HMAC will
typically use SHA-256 (in TLS-1.2) for 32 bytes of output. With a cipher
suite based on AES-128 and HMAC/SHA-256, the two encryption keys will be
the result of a split of a single HMAC output.

> Exactly.  I'm not sure if this is explicitly recorded anywhere, but
> it's certainly part of the crypto folklore that you don't use the same
> PRF output to generate keys for different purposes.

"Folklore" is probably the right term: old wisdom whose actual roots are
lost in the mists of Time. In the random oracle model, output splitting
is "obviously" safe. In fact, as Dmitry indicates, the "non-splitting"
method really is the definition of a new PRF, whose output is split; so
the dichotomy between splitting and non-splitting is not ultimately a
real one.

Now I am ready to accept the idea that when the "PRF" is not a true PRF
(i.e. demonstrably deviates from the ideal construct of a PRF, as for
instance Merkle-Damgard hash functions with the "length extension
attack")(*), then all constructions using that not-PRF are not
equivalent and some may be weaker than others. However, I don't thing it
can be boiled down to a simple rule of "don't split the output". It
really depends on the details of the shortcomings of the not-PRF.

	--Thomas Pornin

(*) I also admit that I am here skipping over a lot of details, since a
random oracle, a PRF and a hash function are not the same thing. Please
fill in the blanks. The core idea is that output splitting SHOULD be
safe, and if it is not then it is a (demonstrable) weakness of the PRF.