Changes between Initial Version and Version 13 of Ticket #795

Timestamp:

2013-11-13T07:06:06Z (11 years ago)

Author:

zooko

Comment:

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 "0" 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. 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.