[tor-dev] Request for comment: AEZ for relay cryptography

[Nick Mathewson]

[This is a draft proposal; I'm not giving it a number yet.  I'm hoping
it'll receive some good advice.]

Filename: xxx-aez-relay.txt
Title: AEZ for relay cryptography
Author: Nick Mathewson
Created: 13 Oct 2015
Status: Draft

1. Summary and preliminaries

   This proposal describes an improved algorithm for circuit
   encryption, based on the wide-block SPRP AEZ. I also describe the
   attendant bookkeeping, including CREATE cells, and several
   variants of the proposal.

   For more information about AEZ, see
           http://web.cs.ucdavis.edu/~rogaway/aez/

   For motivations, see proposal 202.

2. Specifications

2.1. New CREATE cell types.

   We add a new CREATE cell type that behaves as an ntor cell but which
   specifies that the circuit will be created to use this mode of
   encryption.

   [TODO: Can/should we make this unobservable?]

   The ntor handshake is performed as usual, but a different PROTOID is
   used:
        "ntor-curve25519-sha256-aez-1"

   To derive keys under this handshake, we still use HKDF_SHA256, but we
   produce 96 bytes of output:

     struct hkdf_output {
         u8 key_forward[48];
         u8 key_backward[48];
     };

   These two fields are constant for the lifetime of the circuit. (But
   see section 4.3 below.)

   (Also see 4.1 for a variant that uses less storage key material.)

2.2. New relay cell payload

   We specify the following relay cell payload format, to be used when
   the exit node circuit hop was created with the CREATE format in 2.1
   above:

     struct relay_cell_payload {
        u32 zero_1;
        u16 zero_2;
        u16 stream_id;
        u16 length IN [0..498];
        u8 command;
        u8 data[498]; // payload_len - 11
     };

   Note that the payload length is unchanged.  The fields are now
   rearranged to be aligned.  The 'recognized' and 'length' fields are
   replaced with zero_1, zero_2, and the high 7 bits of length, for a
   minimum of 55 bits of unambigious verification.  (Additional
   verification can be done by checking the other fields for
   correctness; AEZ users can exploit plaintext redundancy for
   additional cryptographic checking.)

   When encrypting a cell for a hop that was created using one of these
   circuits, clients and relays encrypt them using the AEZ algorithm
   with the following parameters:

       Key = Kf for forward cells, Kb for backward cells.

       # In theory, we are allowed to use a single key here, but I'm
       #

       tau = 0

       # We want no per-hop ciphertext expansion.  Instead we use
       # redundancy in the plaintext to authenticate the data.

       Nonce =
         struct {
           u64 cell_number;
           u8 is_forward;
           u8 is_early;
         }

       # The cell number is the number of relay cells that have
       # traveled in this direction on this circuit before this cell.
       # ie, it's zero for the first cell, two for the second, etc.
       #
       # is_forward is 1 for outbound cells, 0 for inbound cells.
       # is_early is 1 for cells packaged as RELAY_EARLY, 0 for
       #   cells packaged as RELAY.
       #
       # Technically these two values would be more at home in AD
       # than in Nonce; but AEZ doesn't actually distinguish N and AD
       # internally.

       AD = [ The last 32 bytes of the previous cell's plaintext,
              if this is not the first cell sent in this direction on
              this circuit ]

       # Using this as additional data guarantees that any corrupt
       # ciphertext received will corrupt the plaintext, which will
       # corrupt all future plaintexts. Using the last 32 bytes of the
       # ciphertext would not have the same property.

   This instantiates a wide-block cipher, tweaked based on the cell
   index and direction.  It authenticates part of the previous cell's
   plaintext, thereby ensuring that if the previous cell was corrupted,
   this cell will be unrecoverable.


3. Design considerations

3.1. Wide-block pros and cons?

   See proposal 202, section 4.

3.2. Given wide-block, why AEZ?

   It's a reasonably fast probably secure wide-block cipher.  In
   particular, it's performance-competitive with AES_CTR.

     (How fast is it?

     To encrypt a 509-byte relay cell with a 16 byte nonce and 32 bytes
     of additional data, AEZ only uses 360 aes rounds.  This is the same
     number of aes rounds as we'd need to CTR encrypt a 512-byte cell
     with 11.25 rounds per block.  AES128 uses 10 rounds per block;
     AES256 uses 14 rounds per block.

     We could chop out 4 of the AES rounds by optimizing the code
     for the tau=0 case, or with AD shenenegans, but that's probably
     unwise.

     Additionally, we would no longer need to maintain a running SHA-1
     of cells.)

   It seems secure-ish too.  Several cryptographers I know seem to
   think it's likely secure enough, and almost surely at least as
   good as AES.

   [There are many other competing wide-block SPRP constructions if
   you like.  Many require blocks be an integer number of blocks, or
   aren't tweakable.  Some are slow.  Do you know a good one?]

3.3. Why _not_ AEZ?

   There are also some reasons to consider avoiding AEZ, even if we do
   decide to use a wide-block cipher.

   FIRST it is complicated to implement.  As the specification says,
   "The easiness claim for AEZ is with respect to ease and versatility
   of use, not implementation."

   SECOND, it's still more complicated to implement well (fast,
   side-channel-free) on systems without AES acceleration.  We'll need
   to pull the round functions out of fast assembly AES, which is
   everybody's favorite hobby.

   THIRD, it's really horrible to try to do it in hardware.

   FOURTH, it is comparatively new.  Although several cryptographers
   like it, and it is closely related to a system with a security proof,
   you never know.

   FIFTH, something better may come along.


4. Alternative designs

4.1. Only one key

   We already use different nonces for the forward and reverse
   direction; according to the AEZ design, this is sufficient to
   give security, even if K_b and K_f are the same.  We could
   generate and store only half as much key material by using only a
   single key per circuit.

4.2. Authenticating things differently

   Adding only _a part of the plaintext_ of the previous cell seems
   a little screwy: that's usually easy information to predict.  I
   believe this is secure, however, since the only purpose here is
   to ensure that _if_ the previous cell was corrupted, subsequent
   cells will be corrupted too.

   We could authenticate more stuff, however.  We could, for
   example, authenticate the _entire_ previous ciphertext cell.  Or
   we could authenticate the last 8 bytes of ciphertext and the
   last 24 bytes of plaintext.


   (Another thing we might dislike about the current proposal is
   that it appears to requires us to remember 32 bytes of plaintext
   until we get another cell.  But that part is fixable: note that
   in the structure of AEZ, the AD is processed in the AEZ-hash()
   function, and then no longer used.  We can compute the AEZ-hash()
   to be used for the next cell after each cell is en/de crypted.)

4.3. A forward-secure variant.

   We might want the property that after every cell, we can forget
   some secret that would enable us to decrypt that cell if we saw
   it again.

   One way to do this, at a little extra expense, is to keep a 16 or
   32 byte 'chaining' value that changes after each cell.  The
   initial chaining value in each direction would be another output
   of the HKDF.  We could use it as an extra AD for the AEZ
   encryption.

   To update the chaining value, we need a one-way function.  One
   option would be your-favorite-hash-function; blake2b isn't _that_
   bad, right?

   We could also try to XOR it with a function of some hidden value
   from AEZ: E(S,-1,?) is promising, but it would require that we
   get our hands inside of our AEZ implementation.  Also it would
   require a real cryptographer to come up with it. :)

   A more severe option is to update the entire key after each
   cell. This would conflict with 4.1 above, and cost us a bit more.

   A positively silly option would be to reserve the last X bytes of
   each relay cell's plaintext for random bytes, if they are not
   used for payload.  This would help forward secrecy a little, in a
   really doofy way.

   Any other ideas?

4.4. SHA256 is stupid

   We could update the ntor definition used in this to use blake2b as
   its tweakable hash and for its KDF as well.

   (This would be faster _and_ more secure, not only because blake2b
   is lots faster than SHA256, but also because we could use the
   personalization and salt and key features of blake2b to avoid
   HMAC.)

   Or there's sha3 I guess if you want to do that.