What about this for modification resistance?<br><div>We keep a count of all cells passing and use AES in CTR mode with a 2 part counter: the first part the cell counter, the second one a block counter. Then to authenticate the cell we can use a 16 byte tag and a Wegman-Carter MAC. This gives a total overhead of 48 bytes for a three hop link, which is half the cited one, and which</div>
<div>is provably as secure as AES.</div><div><br></div><div>ChaCha is a component part of one of the SHA-3 finalists, namely JH. If JH is selected as the SHA3 candidate, this may (read may) entail something about the security of ChaCha. The HAIFA construction JH uses doesn't say much about proofs of security, unlike the sponge papers.</div>
<div><br></div><div>ECC groups don't matter much: there are some really bad choices out there, but any attack against Curve25519 is</div><div>going to probably imply an attack against NIST P-256 as well. Its not that different from picking a particular DH prime: some are bad because p-1 is smooth, but if not then they all look the same.</div>
<div><br></div><div>2012 is coming soon: The schedule says between March and June of this year SHA3 will be announced. Everything after that involves bureaucracy. Why switch to SHA256 and then to SHA3 when we won't be done before March anyway?</div>
<div><br></div><div>In general options are bad in crypto: we should migrate as few times as possible to avoid various attacks that might involve degrading a negotiation. As for Certicom their patents were licensed by NIST. Unfortunately for them they openly admit on their website that these are mostly implementation patents. To my untrained eye DJB's analysis is spot on. There is also <a href="http://tools.ietf.org/html/rfc6090">http://tools.ietf.org/html/rfc6090</a> which seems to do something similar.</div>
<div><br></div><div>Sincerely,<br>Watson Ladd</div><div><div class="gmail_quote">On Mon, Oct 31, 2011 at 8:25 PM, Nick Mathewson <span dir="ltr"><<a href="mailto:nickm@torproject.org">nickm@torproject.org</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">Here's an early draft document trying to sketch out the parameters for<br>
migrating to better crypto ops and designs in the future.<br>
<br>
Comments are invited, even comments of the form "you will need to be<br>
much more specific here before I can say anything sensible."<br>
<br>
This is proposals/ideas/xxx-new-crypto-sketch.txt in the torspec repository.<br>
<br>
<br>
<br>
Title: Design sketch for new crypto ops<br>
Date: 31 Oct 2011<br>
Author: Nick Mathewson<br>
<br>
0. Overview<br>
<br>
The point of this document is to discuss what crypto we ought to be using.<br>
See "Initial Thoughts on Migrating Tor to New Cryptography" from last year<br>
for general guidelines and principles.<br>
<br>
In broad strokes, the parts of our crypto are:<br>
<br>
IDENTITY KEYS AND FINGERPRINTS<br>
Addressed here in Section 2.<br>
LINK CRYPTO (TLS) --<br>
Addressed in proposals 176, 184. We say a little here in section 5,<br>
though.<br>
CREATE/EXTEND CRYPTO --<br>
Addressed in xxx-ntor-handshake.txt and rransom's EXTEND draft at<br>
[*] and subsequent discussion on the tor-dev mailing list. Not<br>
considered here.<br>
RELAY CRYPTO<br>
Addressed here in Section 6.<br>
DIRECTORY SYSTEM<br>
Addressed here.<br>
HIDDEN SERVICE SYSTEM<br>
Addressed in a forthcoming document by rransom.<br>
<br>
[*] <a href="https://lists.torproject.org/pipermail/tor-dev/2011-March/002547.html" target="_blank">https://lists.torproject.org/pipermail/tor-dev/2011-March/002547.html</a><br>
<br>
1. Base algorithm choice<br>
<br>
There seem to be two main candidate algorithms for signatures: RSA<br>
with big keys (hereinafter "RSA>1024"); and Ed25519, which is DSA with<br>
the sharp edges filed off on an Edwards curve related to DJB's<br>
Curve25519. We can look at other ECC groups too. {But see ECC<br>
Notes in 1.1 below.}<br>
<br>
FOR DIFFIE-HELLMAN: Curve25519 seems like a decent choice; failing<br>
that, one of the NIST P-groups. Failing that, DH on Z_p with big<br>
groups (hereinafter "DH>1024"). {But see ECC Notes in 1.1 below.}<br>
<br>
FOR A HASH FUNCTION: SHA256, switching to SHA3 in 2012 when it comes<br>
out. It might be worthwhile waiting for SHA3 in most places and<br>
skipping over the SHA256 stage entirely.<br>
<br>
FOR A STREAM CIPHER: AES-CTR is in one sense a conservative choice<br>
inasmuch as AES is well-analyzed, but AES's well-known issues with<br>
cache-based timing attacks are pretty worrisome. We can mitigate that<br>
some by using random secret IVs for AES-CTR, so that we will be<br>
encrypting neither attacker-chosen nor attacker-known plaintext with<br>
our AES cipher, but that's a bit kludgy. There are also supposed to<br>
be time-invariant implementations that use Intel's AESNI instructions<br>
where available, and time-invariant implementations that use<br>
bit-slicing.<br>
<br>
Salsa20 is what rransom likes these days, but IMO we aren't competent<br>
to tell whether it looks good or not; the existing attacks against it<br>
don't look like very bad news to me, but who knows whether it's<br>
getting enough attention that we can read. See also ChaCha; see also<br>
the other eSTREAM winners/finalists; see also SHA3 if the SHA3 winner<br>
specifies a way to use it as a stream cipher, or specifies an<br>
underlying stream/block cipher.<br>
<br>
If we're feeling cautious, we could run two independently-keyed stream<br>
ciphers and xor their streams together.<br>
<br>
FOR A RANDOM NUMBER GENERATOR: We currently use OpenSSL seeded with<br>
RAND_poll and with platform entropy. OpenSSL uses a message-digest-<br>
based algorithm from SSLeay (See <a href="http://linux.die.net/man/3/sslrand" target="_blank">http://linux.die.net/man/3/sslrand</a><br>
for the ugly details.) The platform entropy management can be messy,<br>
obscure, or both. I suggest that:<br>
<br>
* We should seed our PRNG with more entropy sources if we can find<br>
some promising code with an appropriate license<br>
* Instead of just using OpenSSL's PRNG, we should use OpenSSL's<br>
MD-based PRNG xor'd with some other good PRNG. (Fortuna,<br>
maybe. Is there a combine operation better than xor? See also SHA3<br>
if the SHA3 winner is one that specifies a PRNG mode of<br>
operation.)<br>
* We should consider splicing this combined-stream PRNG into OpenSSL<br>
as the RNG it uses for SSL and key generation.<br>
* We should re-seed the RNG before and after very sensitive<br>
operations, like private key generation.<br>
<br>
1.1. ECC notes<br>
<br>
ECC is the brave new[*] crypto of the future! It's faster[**] than<br>
doing crypto in Z_n (as we do for RSA and DH now) for equivalent<br>
levels of security, and the resulting outputs are much shorter.<br>
<br>
As near as I can tell as a layman, Certicom is muddying the waters as<br>
much as possible wrt claiming that it's nigh-impractical to deploy ECC<br>
without licensing their patents. This is rather like the silliness<br>
that PKP used to pull back in the day, where they claimed that their<br>
patents covered not only the existing public key cryptography<br>
algorithms, but also the very idea of public key cryptography itself.<br>
<br>
DJB claims that for every patent he's aware of, either that patent<br>
doesn't cover his code, or that patent is invalid because of prior<br>
art. I'm not going to try to evaluate these claims, since I'm not<br>
supposed to be reading patents for typical "let's avoid the appearance<br>
of knowing infringement" reasons. But before we dive into the world<br>
of ECC, we should see if we can ask any friendly patent attorneys and<br>
ECC experts for a second or third opinion here.<br>
<br>
I note in passing that nearly all of the patents that DJB mentions in<br>
his list would appear to expire over the next 12 months or so.<br>
<br>
Additionally, there are ECC groups out there less fast than DJB's, but<br>
more widely available and analyzed. We should consider some of those<br>
too.<br>
<br>
One final issue to investigate is whether using these algorithms will<br>
make any major free software distribution decide not to include us. I<br>
seem to recall seeing that one or two of the big ones had at one point<br>
decided to ship OpenSSL only with ECC disabled, either because of real<br>
patent concerns, or because of an opinion that the Certicom license<br>
for ECC use in TLS was problematic for free software, or something<br>
like that. We should check that out.<br>
<br>
[*] Actually, it's older than onion routing, and older than some<br>
members of the Tor Project.<br>
<br>
[**] Actually, because of the common practice of choosing a small-ish<br>
prime value (65537) for e in RSA, RSA public key operations can be a<br>
little faster than equivalent-security ECDH or ECDSA operations. The<br>
private key operations in RSA are still much much slower.<br>
<br>
2. New identities<br>
<br>
Identity keys and their fingerprints are used:<br>
- To sign router descriptors.<br>
- To identify nodes in consensus directories.<br>
- To make sure we're talking to the right node in the link handshake.<br>
- To make sure that the extending node is talking to the right next<br>
node when sending an extend cell.<br>
- To identify particular nodes in the hidden service subsystem.<br>
- To identify nodes in the UI in various places.<br>
- Internally, to identify a node uniquely in the codebase.<br>
- To determine which part of the circuit ID space to use on a Tor<br>
instance's links.<br>
<br>
2.1. New identities, option 1: "RSA>1024, slow migration"<br>
<br>
In this option, we use RSA for identity keys indefinitely. Nearly all<br>
operations done with an identity key are signature checking; signing<br>
happens only a few times an hour per node even with pathological<br>
cases. Since signature checking is really cheap with RSA, there's no<br>
speed advantage for ECC here. (There is a space advantage, since the<br>
keys are much smaller.)<br>
<br>
The easiest way to migrate to longer identity keys is to tell all Tors<br>
to begin accepting longer identity keys now, and to tweak all our<br>
protocols so that longer RSA identity keys are understood. We should<br>
then have a pair of parameters in the consensus that determines the<br>
largest and smallest acceptable identity key size in the network.<br>
Clients and servers should reject any keys longer or shorter than<br>
specified. Once all versions of Tor can accept long identity keys, we<br>
raise the maximum size from 1024 to somewhere in the 2048-4096 range.<br>
<br>
2.2. New identities option 2: "RSA>1024, faster migration"<br>
<br>
In this option, we use RSA for identity keys indefinitely as above.<br>
But we allow nodes to begin having longer identities now, even though<br>
older Tors won't understand them. This implies, of course, that every<br>
such node needs to have at least 2 identities: one RSA1024 identity<br>
for backward compatibility, one RSA>1024 identity for more secure<br>
identification.<br>
<br>
We would have these identities cross-certify as follows: All keys<br>
would be listed in the router descriptor. RSA>1024 keys would be<br>
called something other than identity-key, so as not to confuse older<br>
clients. A signature with the RSA>1024 key would appear right before<br>
the current RSA1024 signature. This way, signed material would<br>
include both keys, and would be signed by both keys.<br>
<br>
[In other words, descriptors would look something like:<br>
<br>
router foo...<br>
...<br>
identity-key<br>
-----BEGIN RSA KEY-----<br>
1024-bit RSA key here<br>
-----END RSA KEY-----<br>
ext-identity-key<br>
-----BEGIN RSA KEY-----<br>
3072-bit RSA key here<br>
-----END RSA KEY-----<br>
...<br>
ext-signature<br>
-----BEGIN SIGNATURE-----<br>
signature of everything through "ext-signature\n",<br>
using the long key<br>
-----END SIGNATURE-----<br>
router-signature<br>
-----BEGIN SIGNATURE-----<br>
signature of everything through "router-signature\n",<br>
using the short key<br>
-----END SIGNATURE-----<br>
<br>
]<br>
<br>
See "UI notes" in the "new fingerprints" section below for some of the<br>
implications of letting nodes have multiple identity keys.<br>
<br>
We'll need to advertise these new identities in consensus directories<br>
too; see 4.2 below for more info there.<br>
<br>
2.3. New identities option 3: "RSA>1024 and/or Ed25519, faster migration"<br>
<br>
As in option 2 above, but new keys can also be Ed25519. If we expect<br>
that not all installations will allow Ed25519 (see "ECC Notes",<br>
section 1.1), we'll need to say that every server with an Ed25519 key<br>
must also have an RSA>1024 key.<br>
<br>
2.4. Implications for current use of identity keys<br>
<br>
Let's review our use of identity keys again and make sure that we can<br>
handle all of them with the ideas above.<br>
<br>
- To sign router descriptors.<br>
<br>
We discussed this in 2.2.<br>
<br>
- To make sure we're talking to the right node in the link handshake.<br>
<br>
The current v3 link handshake can handle presenting multiple identity<br>
certificates in the CERT cell. We should consider ourselves to be<br>
connected to a node with identity X if _any_ of the identity<br>
certificates that it presents in its authenticated CERT cell has<br>
identity X. To handle EXTEND cells correctly, we should verify every<br>
identity we can.<br>
<br>
- To make sure that the extending node is talking to the right next node<br>
when sending an extend cell.<br>
<br>
The new extend cell format needs to allow the client to tell the<br>
extending node about some identity for the destination node that the<br>
extending node will be able to understand. This is a capability of<br>
the extending node that the client needs to be able to check. (Also,<br>
the extend cell needs to hash that identity in a form the extending<br>
node can understand, but that's a fingerprint issue.)<br>
<br>
- To determine which part of the circuit ID space to use on a Tor<br>
instance's links.<br>
<br>
We can continue to use RSA1024 identity key comparison here by<br>
default. We can also use some other parameter of the v3 handshake, or<br>
introduce a new link protocol where if the initiator authenticates,<br>
the initiator always gets the low circIDs and the responder always<br>
gets the high ones.<br>
<br>
- To identify nodes in consensus directories.<br>
- To identify nodes in the UI in various places.<br>
- Internally, to identify a node uniquely in the codebase.<br>
<br>
See sections 3 and 4 below.<br>
<br>
- To identify particular nodes in the hidden service subsystem.<br>
<br>
Out of scope.<br>
<br>
2.5. Migrating away from short ID keys entirely<br>
<br>
Eventually, no version of Tor that requires 1024-bit identity keys will<br>
remain. When that happens, we should stop using them entirely. That<br>
means that if we take any path other than the "slow migration" path of<br>
2.1, we'll need to make everything that looks at a node's identity<br>
also accept nodes with _only_ a RSA>1024/Ed25519 identity.<br>
<br>
At the directory service level, we should have an option to allow<br>
nodes without RSA1024 identity keys (off until all clients and nodes<br>
accept new identity keys).<br>
<br>
2.6. Selective correctness attacks<br>
<br>
For any scheme based on having multiple signature types on a router<br>
descriptor or other document, an attacker could mount a partitioning<br>
attack by making a document which older clients will accept but newer<br>
clients will reject.<br>
<br>
It's easy to prevent this at the consensus step: directory authorities<br>
MUST NOT accept any descriptor unless all clients will be able to<br>
verify it.<br>
<br>
For bridge descriptors, we need to investigate more carefully.<br>
<br>
3. New fingerprints<br>
<br>
Right now we compute fingerprints by taking the SHA1 hash of an ASN1<br>
encoding of the RSA1024 identity key. We encode this in hex almost<br>
everywhere, and sometimes prefix it with a $.<br>
<br>
I propose that fingerprints of the future be determined by taking a<br>
digest using SHA256 or SHA3 of:<br>
<br>
"Hash Algorithm Name", "Key Type Name", encoded key<br>
<br>
When representing these internally, we should include the hash<br>
algorithm that was used. When representing them in the UI, we should<br>
use the notation %b64, where b64 is a base-64 encoding, omitting the<br>
trailing =s.<br>
<br>
(Other plausible characters to use are @, ?, +, ~, =, etc. I like %,<br>
but can be persuaded. Bikeshed bikeshed bikeshed.)<br>
<br>
Since 43 base-64 characters is enough to represent a 256-bit digest,<br>
with 2 bits left over, I propose that the b64 value encode<br>
<br>
hh | D(hash algorithm name, key type, encoded key)<br>
<br>
where hh is a 2-bit value, with one of the following values:<br>
<br>
00 -- sha256<br>
01 -- sha3<br>
10 -- to be determined<br>
11 -- reserved.<br>
<br>
We should investigate in the interface whether it's plausible to allow<br>
a prefix of a node ID where the full ID would otherwise be required.<br>
That seems risky for short prefixes, though.<br>
<br>
3.1. How many fingerprints is that anyway?!<br>
<br>
Suppose that we allow sha256 and sha3 as hash algorithms, and we allow<br>
each node to have 3 identity keys: one RSA1024, one RSA>1024, and one<br>
ECC. Then we would have 7 fingerprints (6 plus the legacy<br>
SHA1(RSA1024) fingerprint), for a total of 20+6*32==212 bytes per<br>
node.<br>
<br>
It's not a horrible problem to accept them all in the UI, but the UI<br>
isn't the only place that needs to know fingerprints. Instead, let's<br>
say that RSA1024 identities are only identified with SHA1 hashes.<br>
This limits our fingerprint load to a more manageable 20+32*2 == 84<br>
bytes per node. Still not great, though.<br>
<br>
3.2. What does this imply for the UI?<br>
<br>
In the UI we'll lose the property that no node has more than one<br>
fingerprint: I do not believe that this actually hurts us.<br>
<br>
3.3. Implications for directory information<br>
<br>
Clients must know a hash for each node's identity key, or else they<br>
can't make an authenticated connection to the node or tell ORs how to<br>
extend to the node.<br>
<br>
This means that if client Alice wants to connect to node Bob, Alice<br>
must have a fingerprint of Bob's ID key such that she understands the<br>
ID key type and the fingerprint algorithm. If Alice wants to extend<br>
from Bob to Carol, she must have a fingerprint of Carol's ID key such<br>
that Bob understands the ID key type and the fingerprint algorithm.<br>
<br>
So for every node, Alice must not only know a fingerprint that *she*<br>
can use for that node, but also a set of fingerprints such that every<br>
node can understand at least one fingerprint in the set.<br>
<br>
This implies a proliferation of fingerprints! We should tread<br>
carefully here. To prevent proliferation, the easiest solution is not<br>
to add too many new types and to have a good plan for retiring older<br>
types.<br>
<br>
3.4. Implications for EXTEND cells<br>
<br>
As mentioned in 3.3, when a client Alice tells node Bob to extend<br>
to node Carol, she needs to give Bob a fingerprint for Carol that Bob<br>
will understand: one where Bob understands the digest algorithm, and<br>
understands the identity key type.<br>
<br>
There are two ways we can do this:<br>
<br>
1) Alice's EXTEND cell contains every fingerprint for Carol that<br>
Alice knows about. Bob treats the cell as valid if every one he<br>
can verify is correct.<br>
<br>
2) Alice knows which fingerprint types Bob understands (either via<br>
his version, or something else in his directory info). She<br>
selects a fingerprint for Carol using the best one of these<br>
types.<br>
<br>
The first seems more robust to me, if we have space for enough bytes.<br>
If we proliferate too many types, though, we'll need to do the second.<br>
<br>
4. Directory changes<br>
<br>
4.1. Better cross-referencing<br>
<br>
In some places, directory objects cross-reference one another by SHA1<br>
hash. They should use a better hash algorithm instead.<br>
<br>
This does make problems in a few cases.<br>
<br>
Router descriptors and extrainfo descriptors:<br>
<br>
One problematic case is in determining node families. If node A<br>
and node B want to list each other as being in the same family,<br>
they need to do so in a way that clients can interpret. That could<br>
mean listing SHA1-RSA1024 fingerprints so old clients understand,<br>
AND new fingerprints for security. (But *that* could create<br>
interesting partitioning attacks wherein your family looks<br>
different depending on who's looking.)<br>
<br>
Solution: we need to move the responsibility for combining node<br>
families into the consensus voting process, so clients don't<br>
need to understand the cross-reference types themselves.<br>
<br>
Another case is in certifying extrainfo documents from descriptors.<br>
For that, we can list multiple extrainfo digests, either on the<br>
extrainfo line, or on additional lines.<br>
<br>
Voting and consensus documents:<br>
<br>
Adding more fingerprints in votes isn't a problem; votes are a tiny<br>
fraction of authority bw usage. Adding more hashes is easy.<br>
<br>
For consensus documents, we ought to have flavors that you can<br>
download depending on what set of fingerprint types you<br>
understand.<br>
<br>
For integrity purposes, consensuses can refer to microdescriptors<br>
or descriptors by any digest type that the client understands. But<br>
for downloading purposes, the digest type must be one that<br>
directory caches also support: see 4.4.<br>
<br>
4.2. More fingerprints<br>
<br>
Because extending from node A to node B requires that we have node B's<br>
fingerprint in a way that node A will understand, it is not enough to<br>
get a set of identity fingerprints for each node in the format that<br>
the client likes best -- see 3.3 and 3.4 above. So every flavor of<br>
consensus we serve needs to include a node identity in a format the<br>
client understands, and node identities in formats such that every<br>
node will understand at least one.<br>
<br>
4.3. An option: compound signatures on directory objects<br>
<br>
In Tor 0.2.2.x and later, when we check a signature on a directory<br>
object (not including hidden service descriptors), we only look at<br>
the first DIGEST_LEN bytes of the RSA-signed data. Once 0.2.1.x is<br>
obsolete, or on any types of signatures not checked in 0.2.1.x, we<br>
can use the rest of the space. (We're using PKCS1 padding on our<br>
signatures, which has an overhead of 11 bytes. Signing a SHA1 hash<br>
with a 1024-bit key therefore leaves 128-11-20==97 more bytes we<br>
could use for a SHA2 or a SHA3 hash.)<br>
<br>
4.4. Downloading by digest<br>
<br>
We should have directory caches support downloading objects by more<br>
hash types. Right now, descriptors are downloaded by their SHA1<br>
hashes and microdescriptors by their SHA256 hashes. This is okay for<br>
now, but once SHA3 is out, we should support downloading all of these<br>
by SHA3 digest.<br>
<br>
5. Link crypto changes<br>
<br>
Currently we use TLS. That's fine.<br>
<br>
We should however look to longer link keys, bigger DH groups, etc.<br>
<br>
Once TLS versions 1.1/1.2 are available in OpenSSL, we should move to<br>
use them, I think. We should also look into how quickly we can<br>
deprecate TLS 1.0 and SSL <= 3 usage.<br>
<br>
6. Relay crypto changes<br>
<br>
There are a few things we might want out of improved relay crypto.<br>
They include:<br>
- Resistance to end-to-end bitwise tagging attacks.<br>
- Better resistance to malleability.<br>
- If using counter mode, no block-cipher operations on any value<br>
known to the attacker.<br>
<br>
I'll try to provide these in increasing order of difficulty. None of<br>
these is necessarily correct; I should look for a security proof or a<br>
better construction for any that we seem likely to use.<br>
<br>
Rationales: Our existing malleability resistance is a kludge. Doing<br>
no block-cipher ops on attacker-known values increases our security<br>
margins a little. Our arguments about tagging attacks hold that an<br>
attacker who controls both ends has plenty of ways to win even if<br>
tagging attacks are foiled; nonetheless, most of these ways are<br>
technically slightly more difficult than xor-based tagging, and it<br>
could be useful to boost our defense-in-depth a little bit, just in<br>
case other active end-to-end attacks turn out to be harder than we'd<br>
thought.<br>
<br>
6.1. Option 1: Use AES-CTR in a less scary mode<br>
<br>
When doing key expansion, in addition to establishing Kf, Kb, Df, and<br>
Db, also establish IVf and IVb. Use the current relay crypto, except<br>
instead of starting the counters at 0, start them at IVf and IVb.<br>
This way, an attacker doesn't have any known plaintexts to work with,<br>
which makes AES a little more robust.<br>
<br>
6.2. Option 2: As 1, but tagging attacks garble the circuit after one block.<br>
<br>
Keep an HMAC of all previously received encrypted cells on a circuit.<br>
When decrypting a cell, use this HMAC value to determine the first 64<br>
bits of the counter; increment the low 64 bits of the counter as<br>
usual.<br>
<br>
This way, if an adversary flips any bits before passing the stream<br>
through an honest node, no _subsequent_ block will be recoverable.<br>
<br>
To prevent any part of the stream from being re-used, close any<br>
circuit if the low 64 bits of the counter would ever wrap (that is,<br>
around 295 million terabytes).<br>
<br>
(If we're using a stream cipher with fast re-key, then we can just<br>
have the key used for each block be an HMAC of all previously<br>
received ciphertext.)<br>
<br>
6.3. Option 3: As 1, but tagging attacks garble the circuit in the same block.<br>
<br>
Use a large-block cipher mode, such as BEAR or LIONESS (depending on<br>
whether we need a PRP or SPRP). Base the key material for each block<br>
on an HMAC of all previous blocks' ciphertexts.<br>
<br>
This way, if an adversary makes any alteration in a block, that block<br>
and all subsequent blocks will be garbled. It's more expensive than<br>
2, though, especially if we need to use a LIONESS construction.<br>
<br>
{I considered IGE here, with a trick where odd-numbered nodes on a<br>
circuit start from the front of the block and even-numbered nodes<br>
start from the end, but it didn't seem much better. We should<br>
investigate relative performance, though.}<br>
<br>
6.4. Option 4: Shall we have middle nodes be able to fast-stop bad data?<br>
<br>
In all the above options, if a cell is altered, the middle node can<br>
at best turn that cell and the rest of the cells on the circuit into<br>
garbage, which the last node won't deliver (if honest) or can't<br>
deliver (if dishonest).<br>
<br>
Might we prefer to do as in mixnets, and have nodes kill circuits<br>
upon receiving altered cells?<br>
<br>
It's not such an obvious improvement. Including more MACs is more<br>
expensive in per-cell overhead. The attacks that we would foil this<br>
way but not with Option 3 are not so much better than the the passive or<br>
timing-based-active end-to-end attacks that would still remain.<br>
<br>
Consider that if option 3 is in place, an end-to-end attacker who<br>
wants to do a tagging attack at one node can garble the rest of the<br>
circuit and see if the output is garbled at the exit node. But such<br>
an attacker could just as easily close the circuit at one of those<br>
nodes and watch for a corresponding close event, or even better --<br>
simply pause traffic on that circuit for a while and watch for a<br>
corresponding gap at the exit. The only advantage of the garbling<br>
attack would be that garbled cells are presumably rarer than circuit<br>
closes or traffic pauses, and thus easier to use to distinguish<br>
target circuits. But that's still questionable: the other attacks<br>
win fine, and the pause attack doesn't risk detection as much.<br>
<br>
So why might we want to do this? First, the overhead doesn't need to<br>
be as bad as you might first expect (see below). Second, it would be<br>
nice to increase the security margin as much as possible: "attacks<br>
only get better".<br>
<br>
So let's figure out how it would look.<br>
<br>
To do this one, we'd want to have outgoing and incoming circuits<br>
treated differently. Incoming cells would get decrypted as in 1<br>
above, except that we'd have a MAC on them. For outgoing cells,<br>
each node would check that the first N bytes of the cell<br>
match a MAC of all data seen so far, *including the rest of the<br>
cell*. They'd then remove the first N bytes, re-pad the cell<br>
with bytes from a PRNG, and decrypt the resulting re-padded cell.<br>
(This is basically how mixmaster works, and how mixminion works in<br>
the common case.)<br>
<br>
The space overhead here is kind of large: N bits per cell per node.<br>
In the most paranoid case, if we used 256-bit HMACs on 3-node paths,<br>
that's 96 bytes per cell, which is more than 20% of the total length.<br>
But we can probably do better if we let the CREATE operation also<br>
tell the node some N to check. For example, the first node doesn't<br>
need to check any bits. The second and third nodes could check 64<br>
bits apiece; that only has 16 bytes overhead total, and high<br>
probability of catching any changes. (Birthday attacks don't matter<br>
here, and an attacker who mounts this attack for long enough to<br>
accidentally find a 64-bit MAC will break so many circuits in the<br>
process as to become totally unreliable.)<br>
<br>
All of this leaks the path lengths and position on the path to<br>
various nodes. We might open ourselves up to partitioning attacks if<br>
different clients choose different numbers of bits. What's more, we<br>
might leak the length of the path to the last node by how much junk<br>
there is at the end of the cell. So we'd need to be careful!<br>
<br>
Here's a simple construction for this format, to be concrete:<br>
<br>
The CREATE operation's KDF produces the following outputs:<br>
Kf, IVf (stream cipher key and IV for forward direction)<br>
Kb, IVb (stream cipher key and IV for reverse direction)<br>
Mf (MAC key for forward direction)<br>
Mb (MAC key for reverse direction)<br>
SEEDf (PRNG key for forward direction)<br>
And it also sets the following user-selected parameter:<br>
MACBYTESf (an integer between 0 and 32 inclusive)<br>
MACBYTESb (an integer between 0 and 32 inclusive)<br>
CANEXIT (boolean: can we exit from this hop?)<br>
<br>
Let Kf[i], Mf[i], etc denote the parameter Kf, Mf, etc as shared<br>
between the client and the i'th node in its circuit.<br>
<br>
Relay cells sent towards the client have the following plaintext<br>
format:<br>
Body:<br>
Content:<br>
Relay Command [1 byte]<br>
StreamID [2 bytes]<br>
Length [2 bytes]<br>
Data [Up to CELL_DATA_LEN-5-MACBYTESb bytes]<br>
Padding [randomly generated as needed to fill the<br>
cell]<br>
MAC(All previous encrypted content + encrypted content,<br>
Mb)[:MACBYTESb] [MACBYTESb bytes]<br>
<br>
The originator of the client-bound cell encrypts the content with<br>
the next part of its Kb,IVb stream, then appends the MAC.<br>
<br>
Non-clients receiving a client-bound relay cell encrypt the entire<br>
cell body, MAC included, with the next part of the stream cipher<br>
that was keyed with Kb,IVb.<br>
<br>
When the client receives a relay cell body, it iteratively does:<br>
<br>
For node i in circuit from 1..N:<br>
Let cells_i = all previous cells which we previously decided<br>
were from node i, or relayed by node i,<br>
and let cellbody = the body of the cell, except for the last<br>
MACBYTESb[i] bytes,<br>
and let cellmac = the last MACBYTESb[i] bytes of this cell.<br>
<br>
If cellmac is nonempty, check wither cellmac = mac_received,<br>
where mac_received is the first MACBYTESb[i] bytes of<br>
MAC(cells_i | cellbody, Mb[i]). If so, this cell is from node<br>
i.<br>
<br>
If this cell is from node i, add cellbody to cells_i, then<br>
decrypt cellbody using the stream keyed with Kb[i],IVb[i].<br>
Act on it as a relay cell.<br>
<br>
Otherwise add the entire cell to cells_i, and decrypt it, MAC<br>
included, with the stream keyed with Kb[i], IVb[i].<br>
<br>
If no node sent this cell: it's junk and somebody is probably<br>
messing with us! Destroy the circuit.<br>
<br>
<br>
When the client *sends* a cell outbound to node N:<br>
<br>
Let cells[i] start at "" for all i in 1...N initially, and get<br>
updated as below.<br>
<br>
Let MACLEN = SUM(MACBYTESf[1...N])<br>
<br>
Let Body =<br>
Relay Command [1 byte]<br>
StreamID [2 bytes]<br>
Length [2 bytes]<br>
Data [Up to CELL_DATA_LEN-5-MACLEN bytes]<br>
Padding [randomly generated,<br>
CELL_DATA_LEN-5-MACLEN-len(Data) bytes]<br>
<br>
Let PAD[i] = the next MACBYTESf[i] bytes from the PRNG keyed<br>
with SEEDf[i], for i in 1...N<br>
<br>
Let STREAM[i] = the next CELL_DATA_LEN bytes of<br>
the stream keyed by Kf[i],IV[i], for i in 1...N<br>
<br>
Let PADSEEN[1] == ""<br>
<br>
For i in 2...N:<br>
Let L = len(PADSEEN[i-1]) + len(PAD[i-1])<br>
Let PADSEEN[i] = (PADSEEN[i-1] | PAD[i-1]) xor<br>
STREAM[i-1][CELL_DATA_LEN-L:]<br>
<br>
For i in N down to 1:<br>
<br>
Let Encbody = Body xor STREAM[i][:len(Body)]<br>
Let extra = "RECOGNIZED" if i == N, "OK" otherwise<br>
Let cells[i] = cells[i] | Body | PADSEEN[i]<br>
Let M = MAC(cells[i] | extra , Mf[i])<br>
<br>
Let Body = M[:MACBYTESf[i]] | EncBody<br>
<br>
<br>
To receive an outbound cell:<br>
<br>
Let M be the first MACBYTESf bytes of the cell, let REST be the<br>
rest of the cell, and let "cells" be all previous cells on this<br>
circuit. If CANEXIT, and M = MAC(cells|rest|"RECOGNIZED",<br>
Mb)[:MACBYTESf], and MACBYTESf > 0, this cell is for us. If M<br>
= MAC(cells|rest|"OK", Mb)[:MACBYTESf], this cell is not for<br>
us, but is valid. Otherwise, destroy the circuit.<br>
<br>
Let PAD = the next MACBYTESf[i] bytes of the PRNG keyed with<br>
SEEDf, and decrypt REST | PAD using the stream cipher keyed<br>
with Kf,IVf. If this cell is for us, act on it as a relay<br>
cell. Otherwise, relay it.<br>
<br>
ANOTHER VARIANT:<br>
<br>
If we restrict MACBYTESf values to range 0..HL/2, where HL is the<br>
length of the MAC output, we can replace<br>
MAC(x | "RECOGNIZED")[:MACBYTESf] and MAC(x | "OK")[:MACBYTESf]<br>
with<br>
MAC(x)[:MACBYTESf] and MAC(x)[HL-MACBYTESf:]<br>
<br>
PICKING MACBYTESf,MACBYTESb.<br>
<br>
We don't need to worry about birthday attacks:<br>
<br>
Because we're using a MAC, only the parties who are making<br>
the MACs could try to do a brute-force search for a<br>
collision, but they have no reason to do so.<br>
<br>
If a collision occurs accidentally, an adversary can't<br>
substitute an earlier-seen cell for a later one with the<br>
same MAC, since the MAC covers not only the cell, but all<br>
previous cells on the circuit.<br>
<br>
So 16 bytes is about the most we should ever do, given our<br>
usual security parameters. Let me moot the number 8 for<br>
MACBYTESb.<br>
<br>
For outbound cells, for any hop we can exit from, choosing<br>
MACBYTESf=6 gets us the current security level. For the first<br>
hop, assuming we don't exit from it, choosing MACBYTESf=0 is<br>
totally safe, since the link crypto guarantees that nothing was<br>
corrupted on the way.<br>
<br>
In general, to prevent an end-to-end tagging attack, it seems<br>
sufficient to do something like setting MACBYTES=8 for the last<br>
hop, and MACBYTES=8 for one hop in the middle.<br>
<br>
OTHER VARIANTS:<br>
<br>
Can we combine this approach with one of the approaches in 2 or<br>
3 above to ensure that if corrupt data passes (because of our<br>
use of truncated HMACs) it still corrupts the stream?<br>
<br>
Can/should we use GCM or something here instead of separate<br>
encrypt/hmac operations? It doesn't seem that GCM per se would<br>
apply without some tweaking, which we probably do not have the<br>
expertise to do.<br>
<br>
OVERHEAD NOTES:<br>
<br>
When computing additional overhead with this method, note that<br>
it lets us replace the old 4 byte "digest" field and the 2 byte<br>
"recognized" field.<br>
<br>
I note in passing that we need at most 9 bits for the length<br>
field, and at most 6 bits for the command field, yet we're using a<br>
total of 3 bytes for those 15 bits. That's an opportunity to<br>
save another byte.<br>
<br>
ACKS<br>
<br>
Lots of the good ideas and concerns here are due to Robert Ransom.<br>
<br>
Michael Stone helped some with "relay option 4" above.<br>
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</blockquote></div><br><br clear="all"><div><br></div>-- <br>"Those who would give up Essential Liberty to purchase a little Temporary Safety deserve neither Liberty nor Safety."<br>-- Benjamin Franklin <br>
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