[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.