---------- Forwarded message ----------
From: Zooko O'Whielacronx
Date: Tue, Nov 12, 2013 at 11:09 PM
Subject: the new 2014 Add-Only Sets
To: tahoe-dev
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 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
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, 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.
