the new 2014 Add-Only Sets

Wed Nov 13 07:09:18 UTC 2013

Folks:

(This is a copy of
https://tahoe-lafs.org/trac/tahoe-lafs/ticket/795#comment:13 .)

Here's my rendition of our discussion of add-only sets at the Tahoe-LAFS
Summit today. (As usual, I altered and embellished this story significantly
while writing it down, and people who were present to witness the original
discussion are invited to chime in.)

An add-only cap doesn't have to also be a write-only cap. It might be good
for some use cases that you can give someone a cap that lets them read the
whole set, and add elements into the set, without letting them remove
elements or change previously-added elements. It might be good in some
*other* use cases to have an "add-only&write-only" cap, which allows you to
add elements into the set but doesn't let you read elements of the set, nor
remove nor change previously-added elements. We agreed to focus on the
former case for now, because it is easier to design and implement a
solution to it. (See
#796<https://tahoe-lafs.org/trac/tahoe-lafs/ticket/796>for discussion
of write-only caps.)

We agreed to forget about erasure-coding, which makes an already-confusing
problem (how to implement add-only sets without allowing a few malicious
servers, adders, or set-repairers to perform *rollback attack* or *selection
attack*), into a *very*-confusing problem that exceeded my brain's ability
to grapple with it.

So, for now, assume that add-only sets don't use erasure-coding at all.

Now, the basic design we came up with is like this. I'll explain it in
multiple passes of successive refinement of the design.
FIRST PASS: DESIGN "0"

An authorized adder (someone who holds an add-cap) can generate "elements",
which are bytestrings that can be added into the set. (I mispronounced
"elements" as "elephants" at one point, and from that point forward the
design was expressed in terms of a circus act involving elephants.)

Elephants have an identity as well as a value (bytestring), so:

    aos = DistributedSecureAddOnlySet()
    aos.add_elephant(b"\xFF"*100)
    aos.add_elephant(b"\xFF"*100)

results in aos containing *two* elephants, not one, even though each
elephant has the same value (the bytestring with one hundred 0xFF bytes in
it).

aos.add_elephant() generates a random 256-bit nonce to make this elephant
different from any other elephant with the same value. I call this "putting
a tag on the elephant's ear" — a "tagged elephant" is a value plus a nonce.
Even if two elephants are identical twins, they can be distinguished by the
unique nonce written on their ear-tags.

aos.add_elephant() then puts a digital signature on the tagged-elephant
(using the add-only-cap, which contains an Ed25519 private key), and sends
a copy of the tagged-elephant to every one of N different servers. Putting
a digital signature on a tagged-elephant is called "wrapping a net around
it".

A reader downloads all the tagged-elephants from all the servers, checks
all the signatures, takes the union of the results, and returns the
resulting set of elephants.

Design "A" relies on *at least one* of the servers that you reach to save
you from rollback or selection attacks. Such a server does this by knowing,
and honestly serving up to you, a fresh and complete set of
tagged-elephants. “Rollback” is serving you a version of the set that
existed at some previous time, so the honest server giving you a copy of
the most recent set protects you from rollback attack. “Selection” is
omitting some elephants from the set, so the honest server giving you a
complete copy of the set protects you from selection attack.
SECOND PASS: DESIGN "1"

We can extend Design "0" to make it harder for malicious servers to perform
selection attacks on readers, even when the reader doesn't reach an honest
server who has a complete copy of the most recent set.

The unnecessary vulnerability in Design "0" is that each tagged-elephant is
signed independently of the other tagged-elephants, so malicious servers
can deliver some tagged-elephants to a reader and withhold other
tagged-elephants, and the reader will accept the resulting set, thus
falling for a selection attack. To reduce this vulnerability, adders will
sign all of the *current* tagged-elephants along with their new
tagged-elephant with a single signature. More precisely, let the "identity"
of a tagged-elephant be the secure hash of the tagged-elephant (i.e. the
secure hash of the nonce concatenated with the value). The signature on a
new tagged-elephant covers the identity of that tagged-elephant,
concatenated with the identities of all extant tagged-elephants, under a
single signature. In circus terms, you add the new tagged-elephant into a
pile of tagged-elephants and throw a net over the entire pile, including
the new tagged-elephant.

Now, malicious servers can't omit any of the older tagged-elephants without
also omitting the new tagged-elephant. Readers will not accept the new
tagged-elephant unless they also have a copy of all of the other
tagged-elephants that were signed with the same signature. This limits the
servers's options for selection attacks.
THIRD PASS: DESIGN "2"

We can refine Design "1" to make it cleaner and more CPU-efficient and
network-efficient. This will also lay the groundwork for an efficient
network protocol.

The unnecessary "dirtiness" in Design "1" is that the digital signatures on
older tagged-elephants become extraneous once you add a new digital
signature. We have a mass of tagged-elephants, we throw a net over the
whole mass, then later when we add a new tagged-elephant to the pile, we
throw a new net on top of the new (slightly larger) pile. Now the
*underlying* net has become redundant: once you've verified the signature
of the outermost net, there is no need to check the signature of the inner
net. In fact, if one implementation checks the signature of the inner net
and another implementation does not check it, then a malicious adder
colluding with a malicious server could cause the implementations to differ
in their results, by putting an invalid net (an invalid signature) topped
by a new tagged-elephant with a valid net. (Daira was the one who noticed
that issue.)

To make this cleaner and more efficient, we will never put a net around a
net, and instead we'll keep each tagged-elephant in a box. When you want to
add a new tagged-elephant to a set, you rip off and throw away any extant
nets, then you *put the new tagged-elephant in a box which is nailed on top
of the previous topmost box*. Then you wrap a net around the new topmost
box. "Nailing" box Y on top of box X means taking the secure hash of box X
and appending that to box Y (before signing box Y). A "box" is a
tagged-elephant concatenated with any number of "nails", each of which is
the secure hash of a previous box.

(Note that you can sometimes have two or more boxes precariously perched at
the top of a stack, when two adders have simultaneously added a box before
each saw the other's new box. That's okay — the next time an adder adds a
box on top of this stack, he'll nail his new box to *each* of the previous
topmost boxes.)

Boxes are a lot more CPU-efficient than nets, and more importantly nobody
(neither readers, adders, nor servers) needs to revisit a lower-down box in
order to add a new top-most box. Once you nail box Y on top of box X, then
you can later add box Z just by taking the hash of box Y, without
revisiting box X.

Note that we need two different secure hashes here: one is the identity of
a tagged-elephant, which is the secure hash of: the nonce concatenated with
the value. The other is the hash of the box, which is the secure hash of:
the identity of a tagged-elephant concatenated with the hashes of any
previous boxes. We need the identity of a tagged-elephant for finding out
whether a certain tagged-elephant already exists in a stack (regardless of
what position it occupies within that stack), and we need the hash of the
box for efficiently verifying that all the tagged-elephants in a stack were
approved by an authorized adder.

This also leads to the efficient network protocol: an adder can remember
(cache) the Directed Acyclic Graph of boxes which a given server previously
told the adder about. When the adder wants to add a new tagged-elephant or
a set of new tagged-elephants to that server, he can send just the boxes
which would be *new* to that server, assuming that the server hasn't
learned anything new since the last time they talked. Readers can do
likewise, remembering what each server previously told them about, and
asking the server to just tell them about things that are not already
covered the topmost box(es) that the reader already knows about.
CONCLUSION

Okay, that's it! I think Design "2" is a good one. It has good security
against rollback or selection attacks by malicious servers (assuming some
kind of whitelisting of servers! Which is ticket
#467<https://tahoe-lafs.org/trac/tahoe-lafs/ticket/467>and is not yet
implemented.) And, it doesn't go
*too* far over the top in terms of complexity; it seems more intuitive to
me than (my vague memories of) previous attempts to design add-only sets
for LAFS.

(By the way, there are a few other possible ways to strengthen defenses
against rollback
attack<https://tahoe-lafs.org/trac/tahoe-lafs/query?status=%21closed&keywords=%7Erollback&order=priority>,
which we've previously considered in the context of mutable files, but they
probably also apply to add-only sets.)

I'm excited about this design being feasible, because I think add-only sets
could be a critical building block in valuable use-cases such as secure
logging, secure email, secure backup, and more.

Regards,

Zooko

P.S. Thanks to Isis and Mike for showing up today and, when asked what
Tahoe-LAFS improvements they were interested in, suggesting add-only sets.
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