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Filename: 295-relay-crypto-with-adl.txt
Title: Using ADL for relay cryptography (solving the crypto-tagging attack)
Author: Tomer Ashur, Orr Dunkelman, Atul Luykx
Created: 22 Feb 2018
Last-Modified: 13 Jan. 2020
Status: Open
0. Context
Although Crypto Tagging Attacks were identified already in the
original Tor design, it was not before the rise of the
Procyonidae in 2012 that their severity was fully realized. In
Proposal 202 (Two improved relay encryption protocols for Tor
cells) Nick Mathewson discussed two approaches to stymie tagging
attacks and generally improve Tor's cryptography. In Proposal 261
(AEZ for relay cryptography) Mathewson puts forward a concrete
approach which uses the tweakable wide-block cipher AEZ.
This proposal suggests an alternative approach to Proposal 261
using the notion of Release (of) Unverified Plaintext (RUP)
security. It describes an improved algorithm for circuit
encryption based on CTR-mode which is already used in Tor, and an
additional component for hashing.
Incidentally, and similar to Proposal 261, this proposal employs
the ENCODE-then-ENCIPHER approach thus it improves Tor's E2E
integrity by using (sufficient) redundancy.
For more information about the scheme and a security proof for
its RUP-security see
Tomer Ashur, Orr Dunkelman, Atul Luykx: Boosting
Authenticated Encryption Robustness with Minimal
Modifications. CRYPTO (3) 2017: 3-33
available online at https://eprint.iacr.org/2017/239 .
For authentication between the OP and the edge node we use
the PIV scheme: https://eprint.iacr.org/2013/835 .
A recent paper presented a birthday bound distinguisher
against the ADL scheme, thus showing that the RUP security
proof is tight: https://eprint.iacr.org/2019/1359 .
2. Preliminaries
2.1 Motivation
For motivation, see proposal 202.
2.2. Notation
Symbol Meaning
------ -------
M Plaintext
C_I Ciphertext
CTR Counter Mode
N_I A de/encryption nonce (to be used in CTR-mode)
T_I A tweak (to be used to de/encrypt the nonce)
Tf'_I A running digest (forward direction)
Tb'_I A running digest (backward direction)
^ XOR
|| Concatenation
(This is more readable than a single | but must be adapted
before integrating the proposal into tor-spec.txt)
2.3. Security parameters
HASH_LEN -- The length of the hash function's output, in bytes.
PAYLOAD_LEN -- The longest allowable cell payload, in bytes. (509)
DIG_KEY_LEN -- The key length used to digest messages (e.g.,
using GHASH). Since GHASH is only defined for 128-bit keys, we
recommend DIG_KEY_LEN = 128.
ENC_KEY_LEN -- The key length used for encryption (e.g., AES). We
recommend ENC_KEY_LEN = 256.
2.4. Key derivation (replaces Section 5.2.2 in Tor-spec.txt)
For newer KDF needs, Tor uses the key derivation function HKDF
from RFC5869, instantiated with SHA256. The generated key
material is:
K = K_1 | K_2 | K_3 | ...
where, if H(x,t) denotes HMAC_SHA256 with value x and key t,
and m_expand denotes an arbitrarily chosen value,
and INT8(i) is an octet with the value "i", then
K_1 = H(m_expand | INT8(1) , KEY_SEED )
and K_(i+1) = H(K_i | m_expand | INT8(i+1) , KEY_SEED ),
in RFC5869's vocabulary, this is HKDF-SHA256 with info ==
m_expand, salt == t_key, and IKM == secret_input.
When used in the ntor handshake a string of key material is
generated and is used in the following way:
Length Purpose Notation
------ ------- --------
HASH_LEN forward authentication digest IV AF
HASH_LEN forward digest IV DF
HASH_LEN backward digest IV DB
ENC_KEY_LEN encryption key Kf
ENC_KEY_LEN decryption key Kb
DIG_KEY_LEN forward digest key Khf
DIG_KEY_LEN backward digest key Khb
ENC_KEY_LEN forward tweak key Ktf
ENC_KEY_LEN backward tweak key Ktb
DIGEST_LEN nonce to use in the
hidden service protocol(*)
(*) I am not sure that if this is still needed.
Excess bytes from K are discarded.
2.6. Ciphers
For hashing(*) we use GHASH(**) with a DIG_KEY_LEN-bit key. We write
this as Digest(K,M) where K is the key and M the message to be
hashed.
We use AES with an ENC_KEY_LEN-bit key. For AES encryption
(resp., decryption) we write E(K,X) (resp., D(K,X)) where K is an
ENC_KEY_LEN-bit key and X the block to be encrypted (resp.,
decrypted).
For a stream cipher, unless otherwise specified, we use
ENC_KEY_LEN-bit AES in counter mode, with a nonce that is
generated as explained below. We write this as Encrypt(K,N,X)
(resp., Decrypt(K,N,X)) where K is the key, N the nonce, and X
the message to be encrypted (resp., decrypted).
(*) The terms hash and digest are used interchangeably.
(**) Proposal 308 suggested that using POLYVAL [GLL18]
would be more efficient here. This proposal will work just the
same if POLYVAL is used instead of GHASH.
3. Routing relay cells
Let n denote the integer representing the destination node. For
I = 1...n, we set Tf'_{I} = DF_I, Tb'_{I} = DB_I, and
Ta'_I = AF_I where DF_I, DB_I, and AF_I are generated
according to Section 2.4.
3.1. Forward Direction
The forward direction is the direction that CREATE/CREATE2 cells
are sent.
3.1.1. Routing from the origin
When an OP sends a relay cell, they prepare the
cell as follows:
The OP prepares the authentication part of the message:
C_{n+1} = M
Ta_I = Digest(Khf_n,Ta'_I||C_{n+1})
N_{n+1} = Ta_I ^ E(Ktf_n,Ta_I ^ 0)
Ta'_{I} = Ta_I
Then, the OP prepares the multi-layered encryption:
For I=n...1:
C_I = Encrypt(Kf_I,N_{I+1},C_{I+1})
T_I = Digest(Khf_I,Tf'_I||C_I)
N_I = T_I ^ E(Ktf_I,T_I ^ N_{I+1})
Tf'_I = T_I
The OP sends C_1 and N_1 to node 1.
3.1.2. Relaying forward at onion routers
When a forward relay cell is received by OR_I, it decrypts the
payload with the stream cipher, as follows:
'Forward' relay cell:
T_I = Digest(Khf_I,Tf'_I||C_I)
N_{I+1} = T_I ^ D(Ktf_I,T_I ^ N_I)
C_{I+1} = Decrypt(Kf_I,N_{I+1},C_I)
Tf'_I = T_I
The OR then decides whether it recognizes the relay cell as
described below. If the OR recognizes the cell, it processes the
contents of the relay cell. Otherwise, it passes C_{I+1}||N_{I+1}
along the circuit if the circuit continues.
For more information, see section 4 below.
3.2. Backward direction
The backward direction is the opposite direction from
CREATE/CREATE2 cells.
3.2.1. Relaying backward at onion routers
When a backward relay cell is received by OR_I, it encrypts the
payload with the stream cipher, as follows:
'Backward' relay cell:
T_I = Digest(Khb_I,Tb'_I||C_{I+1})
N_I = T_I ^ E(Ktb_I,T_I ^ N_{I+1})
C_I = Encrypt(Kb_I,N_I,C_{I+1})
Tb'_I = T_I
with C_{n+1} = M and N_{n+1}=0. Once encrypted, the node passes
C_I and N_I along the circuit towards the OP.
3.2.2. Routing to the origin
When a relay cell arrives at an OP, the OP decrypts the payload
with the stream cipher as follows:
OP receives relay cell from node 1:
For I=1...n, where n is the end node on the circuit:
C_{I+1} = Decrypt(Kb_I,N_I,C_I)
T_I = Digest(Khb_I,Tb'_I||C_{I+1})
N_{I+1} = T_I ^ D(Ktb_I,T_I ^ N_I)
Tb'_I = T_I
If the payload is recognized (see Section 4.1),
then:
The sending node is I. Stop, process the
payload and authenticate.
4. Application connections and stream management
4.1. Relay cells
Within a circuit, the OP and the end node use the contents of
RELAY packets to tunnel end-to-end commands and TCP connections
("Streams") across circuits. End-to-end commands can be initiated
by either edge; streams are initiated by the OP.
The payload of each unencrypted RELAY cell consists of:
Relay command [1 byte]
StreamID [2 bytes]
Length [2 bytes]
Data [PAYLOAD_LEN-21 bytes]
The old Digest field is removed since sufficient information for
authentication is now included in the nonce part of the payload.
The old 'Recognized' field is removed and the node always tries to
authenticate the message as follows.
4.1.1 forward direction (executed by the end node):
Ta_I = Digest(Khf_n,Ta'_I||C_{n+1})
Tag = Ta_I ^ D(Ktf_n,Ta_I ^ N_{n+1})
If Tag = 0:
Ta'_I = Ta_I
The message is authenticated.
Otherwise:
Ta'_I remains unchanged.
The message is not authenticated.
4.1.2 backward direction (executed by the OP):
The message is recognized and authenticated
(i.e., C_{n+1} = M) if and only if N_{n+1} = 0.
The 'Length' field of a relay cell contains the number of bytes
in the relay payload which contain real payload data. The
remainder of the payload is padding bytes.
4.2. Appending the encrypted nonce and dealing with version-homogenic
and version-heterogenic circuits
When a cell is prepared to be routed from the origin (see Section
3.1.1 above) the encrypted nonce N is appended to the encrypted
cell (occupying the last 16 bytes of the cell). If the cell is
prepared to be sent to a node supporting the new protocol, N is
used to generate the layer's nonce. Otherwise, if the node only
supports the old protocol, N is still appended to the encrypted
cell (so that following nodes can still recover their nonce),
but a synchronized nonce (as per the old protocol) is used in
CTR-mode.
When a cell is sent along the circuit in the 'backward'
direction, nodes supporting the new protocol always assume that
the last 16 bytes of the input are the nonce used by the previous
node, which they process as per Section 3.2.1. If the previous
node also supports the new protocol, these cells are indeed the
nonce. If the previous node only supports the old protocol, these
bytes are either encrypted padding bytes or encrypted data.
5. Security
5.1. Resistance to crypto-tagging attacks
A crypto-tagging attack involves a circuit with two colluding
nodes and at least one honest node between them. The attack works
when one node makes a change to the cell (tagging) in a way that
can be undone by the other colluding party. In between, the
tagged cell is processed by honest nodes which do not detect the
change. The attack is possible due to the malleability property
of CTR-mode: a change to a ciphertext bit effects only the
respective plaintext bit in a predicatble way. This proposal
frustrates the crypto-tagging attack by linking the nonce to the
encrypted message such that any change to the ciphertext results
in a random nonce and hence, random plaintext.
Let us consider the following 3-hop scenario: the entry and end
nodes are malicious and colluding and the middle node is honest.
5.1.1. forward direction
Suppose that node I tags the ciphertext part of the message
(C'_{I+1} != C_{I+1}) then forwards it to the next node (I+1). As
per Section 3.1.2. Node I+1 digests C'_{I+1} to generate T_{I+1}
and N_{I+2}. Since C'_{I+2} is different from what it should be, so
are the resulting T_{I+1} and N_{I+2}. Hence, decrypting C'_{I+1}
using these values results in a random string for C_{I+2}. Since
C_{I+2} is now just a random string, it is decrypted into a
random string and cannot be authenticated. Furthermore, since
C'_{I+1} is different than what it should be, Tf'_{I+1}
(i.e., the running digest of the middle node) is now out of sync
with that of the OP, which means that all future cells sent through
this node will decrypt into garbage (random strings).
Likewise, suppose that instead of tagging the ciphertext, Node I
tags the encrypted nonce N'_{I+1} != N_{I+1}. Now, when Node
I+1 digests the payload the tweak T_{I+1} is fine, but using it
to decrypt N'_{I+1} again results in a random nonce for
N_{I+2}. This random nonce is used to decrypt C_{I+1} into a
random C'_{I+2} which cannot be authenticated by the end node. Since
C_{I+2} is a random string, the running digest of the end node is
now out of sync with that of OP, which prevents the end node from
decrypting further cells.
5.1.2. Backward direction
In the backward direction the tagging is done by Node I+2
untagging by Node I. Suppose first that Node I+2 tags the
ciphertext C_{I+2} and sends it to Node I+1. As per Section
3.2.1, Node I+1 first digests C_{I+2} and uses the resulting
T_{I+1} to generate a nonce N_{I+1}. From this it is clear that
any change introduced by Node I+2 influences the entire payload
and cannot be removed by Node I.
Unlike in Section 5.1.1., the cell is blindly delivered by Node I
to the OP which decrypts it. However, since the payload leaving
the end node was modified, the message cannot be authenticated by
the OP which can be trusted to tear down the circuit.
Suppose now that tagging is done by Node I+2 to the nonce part of
the payload, i.e., N_{I+2}. Since this value is encrypted by Node
I+1 to generate its own nonce N_{I+1}, again, a random nonce is
used which affects the entire keystream of CTR-mode. The cell
again cannot be authenticated by the OP and the circuit is torn
down.
We note that the end node can modify the plain message before
ever encrypting it and this cannot be discovered by the Tor
protocol. This vulnerability is outside the scope of this
proposal and users should always use TLS to make sure that their
application data is encrypted before it enters the Tor network.
5.2. End-to-end authentication
Similar to the old protocol, this proposal only offers end-to-end
authentication rather than per-hop authentication. However,
unlike the old protocol, the ADL-construction is non-malleable
and hence, once a non-authentic message was processed by an
honest node supporting the new protocol, it is effectively
destroyed for all nodes further down the circuit. This is because
the nonce used to de/encrypt all messages is linked to (a digest
of) the payload data.
As a result, while honest nodes cannot detect non-authentic
messages, such nodes still destroy the message thus invalidating
its authentication tag when it is checked by edge nodes. As a
result, security against crypto-tagging attacks is ensured as
long as an honest node supporting the new protocol processes the
message between two dishonest ones.
5.3. The running digest
Unlike the old protocol, the running digest is now computed as
the output of a GHASH call instead of a hash function call
(SHA256). Since GHASH does not provide the same type of security
guarantees as SHA256, it is worth discussing why security is not
lost from computing the running digest differently.
The running digest is used to ensure that if the same payload is
encrypted twice, then the resulting ciphertext does not remain
the same. Therefore, all that is needed is that the digest should
repeat with low probability. GHASH is a universal hash function,
hence it gives such a guarantee assuming its key is chosen
uniformly at random.
6. Forward secrecy
Inspired by the approach of Proposal 308, a small modification
to this proposal makes it forward secure. The core idea is to
replace the encryption key KF_n after de/encrypting the cell.
As an added benefit, this would allow to keep the authentication
layer stateless (i.e., without keeping a running digest for
this layer).
Below we present the required changes to the sections above.
6.1. Routing from the Origin (replacing 3.1.1 above)
When an OP sends a relay cell, they prepare the
cell as follows:
The OP prepares the authentication part of the message:
C_{n+1} = M
T_{n+1} = Digest(Khf_n,C_{n+1})
N_{n+1} = T_{n+1} ^ E(Ktf_n,T_{n+1} ^ 0)
Then, the OP prepares the multi-layered encryption:
For the final layer n:
(C_n,Kf'_n) = Encrypt(Kf_n,N_{n+1},C_{I+1}||0||0) (*)
T_n = Digest(Khf_I,Tf'_n||C_n)
N_n = T_I ^ E(Ktf_n,T_n ^ N_{n+1})
Tf'_n = T_n
Kf_n = Kf'_n
(*) CTR mode is used to generate two additional blocks. This
256-bit value is denoted K'f_n and is used in subsequent
steps to replace the encryption key of this layer.
To achieve forward secrecy it is important that the
obsolete Kf_n is erased in a non-recoverable way.
For layer I=(n-1)...1:
C_I = Encrypt(Kf_I,N_{I+1},C_{I+1})
T_I = Digest(Khf_I,Tf'_I||C_I)
N_I = T_I ^ E(Ktf_I,T_I ^ N_{I+1})
Tf'_I = T_I
The OP sends C_1 and N_1 to node 1.
Alternatively, if we want that all nodes use the same functionality
OP prepares the cell as follows:
For layer I=n...1:
(C_I,K'f_I) = Encrypt(Kf_I,N_{I+1},C_{I+1}||0||0) (*)
T_I = Digest(Khf_I,Tf'_I||C_I)
N_I = T_I ^ E(Ktf_I,T_I ^ N_{I+1})
Tf'_I = T_I
Kf_I = Kf'_I
(*) CTR mode is used to generate two additional blocks. This
256-bit value is denoted K'f_n and is used in subsequent
steps to replace the encryption key of this layer.
To achieve forward secrecy it is important that the
obsolete Kf_n is erased in a non-recoverable way.
This scheme offers forward secrecy in all levels of the circuit.
6.2. Relaying Forward at Onion Routers (replacing 3.1.2 above)
When a forward relay cell is received by OR I, it decrypts the
payload with the stream cipher, as follows:
'Forward' relay cell:
T_I = Digest(Khf_I,Tf'_I||C_I)
N_{I+1} = T_I ^ D(Ktf_I,T_I ^ N_I)
C_{I+1} = Decrypt(Kf_I,N_{I+1},C_I||0||0)
Tf'_I = T_I
The OR then decides whether it recognizes the relay cell as described below.
Depending on the choice of scheme from 6.1 the OR uses the last two blocks
of C_{I+1} to update the encryption key or discards them.
If the cell is recognized the OR also processes the contents of the relay
cell. Otherwise, it passes C_{I+1}||N_{I+1} along the circuit if the circuit
continues.
For more information about recognizing and authenticating relay cells,
see 5.4.5 below.
6.3. Relaying Backward at Onion Routers (replacing 3.2.1 above)
When an edge node receives a message M to be routed back to the
origin, it encrypts it as follows:
T_n = Digest(Khb_n,Tb'_n||M)
N_n = T_n ^ E(Ktb_n,T_n ^ 0)
(C_n,K'b_n) = Encrypt(Kb_n,N_n,M||0||0) (*)
Tb'_n = T_n
Kb_n = K'b_n
(*) CTR mode is used to generate two additional blocks. This
256-bit value is denoted K'b_n and will be used in
subsequent steps to replace the encryption key of this layer.
To achieve forward secrecy it is important that the obsolete
K'b_n is erased in a non-recoverable way.
Once encrypted, the edge node sends C_n and N_n along the circuit towards
the OP. When a backward relay cell is received by OR_I (I<n), it encrypts
the payload with the stream cipher, as follows:
'Backward' relay cell:
T_I = Digest(Khb_I,Tb'_I||C_{I+1})
N_I = T_I ^ E(Ktb_I,T_I ^ N_{I+1})
C_I = Encrypt(Kb_I,N_I,C_{I+1})
Tb'_I = T_I
Each node passes C_I and N_I along the circuit towards the OP.
If forward security is desired for all layers in the circuit, all OR's
encrypt as follows:
T_I = Digest(Khb_I,Tb'_I||C_{I+1})
N_I = T_I ^ E(Ktb_I,T_I ^ 0)
(C_I,K'b_I) = Encrypt(Kb_n,N_n,M||0||0)
Tb'_I = T_I
Kb_I = K'b_I
6.4. Routing to the Origin (replacing 3.2.2 above)
When a relay cell arrives at an OP, the OP decrypts the payload
with the stream cipher as follows:
OP receives relay cell from node 1:
For I=1...n, where n is the end node on the circuit:
C_{I+1} = Decrypt(Kb_I,N_I,C_I)
T_I = Digest(Khb_I,Tb'_I||C_{I+1})
N_{I+1} = T_I ^ D(Ktb_I,T_I ^ N_I)
Tb'_I = T_I
And updates the encryption keys according to the strategy
chosen for 6.3.
If the payload is recognized (see Section 4.1),
then:
The sending node is I. Process the payload!
6.5. Recognizing and authenticating a relay cell (replacing 4.1.1 above):
Authentication in the forward direction is done as follows:
T_{n+1} = Digest(Khf_n,C_{n+1})
Tag = T_{n+1} ^ D(Ktf_n,T_{n+1} ^ N_{n+1})
The message is recognized and authenticated
(i.e., M = C_{n+1}) if and only if Tag = 0.
No changes are required to the authentication process when the relay
cell is sent backwards.
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