# Logs

<sarang> Let's go ahead and get started with GREETINGS
<kinghat> o/
<sgp_> hello
<sarang> That's long enough!
<sarang> Let's move to ROUNDTABLE
<sarang> suraeNoether: what up with you
<suraeNoether> i'm terribly ill this morning, so my update will be very brief. my work in this past week has involved three incomplete tasks:
<suraeNoether> 1) CLSAG linkable anonymity proof required some thought. sarang and i have thought about it and we have a strategy to finish writing the proof. sarang: do you want to make the changes to our LA definition or do you want i should?
<sarang> suraeNoether: I have a writeup for LA in my notebook that I'm transcribing to TeX
<suraeNoether> and proof* not just the definition
<sarang> it works just fine
<sarang> On that note
<sarang> Do you have any thoughts on linkability (not LA)
<sarang> I don't particularly like the Backes definition
<suraeNoether> uh one sec
<sarang> Triptych has a version of linkability+non-frameability that I like better
<suraeNoether> is there soemthing wrong with the definition we proposed initially?
<suraeNoether> iirc that one's from bender
<sarang> It's not formalized quite enough, in the apparent opinion of the reviewer
<sarang> I think it needs just minor work
<sarang> Triptych formalizes it a tad more IMO
<sarang> I can add that to the writeup if you like
<suraeNoether> well
<suraeNoether> for the sake of the audience, can you describe the 3 different definitions you want to consider? or 2, assuming you want to bail on backes'
<sarang> Backes requires the following for an LRS: completeness, linkable anonymity, linkability, non-frameability
<sarang> Right now we combine linkability and non-frameability with non-standard terminology
<sarang> Backes uses a particular linkability definition: can the adversary use q keys to generate q+1 non-linking signatures?
<sarang> Where q is scaled via the security parameter
<sarang> I don't particularly like this definition over the "usual" one about producing two linking signatures, but I think it's important to frame the definition as a challenger-player interaction
<sarang> Our current method does this very informally
<sarang> I propose a combined linkability definition in my Triptych writeup that's a slight formalization of what CLSAG has now
<sarang> (it could easily be split into linkability and non-frameability)
<suraeNoether> hmmmm q scaling with the security parameter is the weird part to me: if the security parameter goes up, so does q… and so this means, for example, the adversary can't produce 3 signatures using 2 keys without some linking occurring. this feels *weaker* than the statement "can't produce two signatures using the same key without them being linked"
<sarang> Yeah, which is why I don't really like it
<sarang> didn't sit well with me
<suraeNoether> and we want the property with q=1 anyway to prevent double-spending
<sarang> So I am proposing not using the Backes definition, but simply formalizing what we have now, a la Triptych
<sarang> then it's more clear what the linkability player has access to in terms of keys etc.
<suraeNoether> okay, i'm going to read more deeply into that this afternoon
<sarang> IMO it's a pretty straightforward formalization
<sarang> doesn't affect much in practice
<suraeNoether> backes' definition with q=1 seems to me to imply backes' definition with greater q, but it's possible that it doesn't technically reduce the way it seems. i'll think more about it
<sarang> That definition doesn't make assumptions about linking tags being equal AFAICT
<sarang> Whereas ours does
<sarang> I think that's part of it
<sarang> Anyway, you were talking about work you'd been doing, before I barged in =p
<suraeNoether> moving along, my next incomplete task is reviewing triptych's security proofs more deeply, which dovetails with this :P
<sarang> Yeah, a nice tie-in
<suraeNoether> finally, i'm working on matching simulations today. i'm experiencing a data management and presentation issue, but i hope for the end of the day a nice graph displaying performance of Eve as a function of ring size and churn length
<sarang> Nice!
<suraeNoether> this will come along with a push to my repo with all the code used to generate that, and explanations so people can replicate it
<sarang> word
<suraeNoether> that's it, if i had presented in the other order then your "barging" would have been a great segue into *your* work for the week :P
<sarang> We can pretend otherwise
<sarang> I have completed a draft of the Triptych preprint, which is now in suraeNoether's hands
<sgp_> suraeNoether: I'm really looking forward to that chart
<sarang> it includes my proposed linkability+non-frameability definition
<sarang> Figured out the CLSAG linkable anonymity definition, which is not as strong as Backes, but does the job IMO
<sarang> I've also been working with Aram from Zcoin on some related Groth proving system stuff
<sgp_> what's the shortfall on the linkable anonymity definition, even if there's no practical difference?
<sarang> There will be a neat paper coming out from them on that shortly, which they graciously provided to me in advance
<sarang> sgp_: Backes permits key corruption, which doesn't work with our DDH hardness assumption
<sarang> And that the adversary can pack rings with their own malicious keys
<sgp_> sarang: thanks
<sarang> (which you can assume are trivially corrupted)
<sarang> This is already stronger than the existing definition that was used
<sarang> Otherwise, I also wish to update the DLSAG paper (which will appear next year in conference proceedings) with the CLSAG security model, since they are structurally extremely similar
<sarang> So overall, a lot of tedious (but still interesting) stuff involving formal definitions and proofs
<sarang> When suraeNoether finishes his review of the Triptych preprint, it'll go to the IACR archive
<sarang> and presumably any CLSAG/DLSAG updates as well
<suraeNoether> hmm Backes' linkability definition is a puzzle i have very little intuition about: should it be harder or easier to present 2 signatures from the same key without linking the signatures than it should be to present 201 signatures from 200 different keys without any of them linking? *taps chin*
<sarang> The adversary picks which keys IIRC, right?
<suraeNoether> yeah, adversary can use KeyGen or any other way of selecting the verification keys
<suraeNoether> may not even know the secret key, so it's genuinely adversarial
<sarang> ya
<sarang> The adversarial generation isn't really a big deal, since soundness implies the adversary's choice of keys satisfy the verification equations
<sarang> and then you rely on the one-way mapping
<suraeNoether> actually, it's not clear; each verification key needs to be in \mathcal{VK}, and it's not specified where that comes from, i'm assuming from the challenger
<suraeNoether> in which case the adversary has to pick challenge keys to break linkability, it's not enough for the adversary to pack all rings with fake pubkeys
<sarang> Backes even notes that generating q such signatures is trivial, since you simply use separate keys
<sarang> Fake pubkeys should be acceptable
<sarang> since the adversary does all this offline, or otherwise generates the pubkeys in its own (seemingly) valid transactions
<sarang> The q=1 case feels like some kind of targeted linking attack, where the general q case seems like a broader "hope for a collision somewhere" attack
<sarang> suraeNoether: thoughts?
<suraeNoether> nothing concrete. the way this definition is written feels very very counter-intuitive to the way you and i have discussed linkability in the past.
<sarang> Yeah, and I haven't seen it anywhere else
<sarang> Again, I don't feel any particular need to use it
<sarang> But getting the existing definition more formalized in a challenger-player sense seems wise
<suraeNoether> agreed
<sarang> roger
<sarang> OK, that's my update
<sarang> Does anyone else have interesting (or uninteresting) research to share?
<suraeNoether> ok, dude, i think i know the problem here
<suraeNoether> with that definition
<suraeNoether> or at least my problem with it
<sarang> Ooh, go on
<suraeNoether> linkability is a property that has a "correctness" component and a "soundness" component. to correctly link two things means to link them when they should be linked. to soundly link two things is to *only* link them when they should be linked
<suraeNoether> you called this positive and negative linkability at some point
<suraeNoether> i feel like this definition is mashing the two together
<suraeNoether> or attempting to
<suraeNoether> anyway, my thoughts don't go deeper than that yet
<sarang> Backes uses non-frameability to show that you can't make signatures that _appear_ to link without knowing/using the same key
<sarang> and linkability to mean that you can't make sigs with the same key(s) but different tag(s)
<sarang> The reviewer didn't like the CLSAG paper's use of positive/negative/soundness in linkability
<suraeNoether> hmm
<suraeNoether> okay, that's going to require more thought
<suraeNoether> anywya, now i'm done. :P
<sarang> A lot of this is simply getting the right terminology for the definition(s) of choice
<sarang> I happen to like using linkability to refer to both
<sarang> since that's typically what you want
<sarang> but it's two different concepts
<sarang> OK, we can move on to any other research
<sarang> or to the next topic, QUESTIONS
<suraeNoether> i have a pretty general observation
<suraeNoether> which may be relevant in terms of independent interest
<suraeNoether> a property like linkability applies to all ZK proofs. for example, our ring signatures are ZK proofs of knowledge of a secret key. but they are *linkable* proofs of knowledge, so that if the same witness data (keys) are used for two different proofs (signatures), then an observer can link them.
<suraeNoether> so just like ZK proofs have a property of correctness (if you know a witness, the proof is valid) and a property of soundness (if you don't know a witness, your proof is invalid), a linkable ZK proof is going to have a dual pair of notions for linkability
<suraeNoether> i bring this up so that the next version of snarks has an L floating around
<sarang> There's a related-ish property in sigma protocols, quasi-unique responses
<sarang> But that relates to responses to the verifier challenge
<suraeNoether> more reading to do :\
<sarang> There's probably a subtle relationship to (SHV)ZK
<sarang> and therefore witness indistinguishability
<sarang> (which follows from SHVZK)
<suraeNoether> anyway
<sarang> Normally, providing two proofs should not reveal distinguishing information about the witnesses
<suraeNoether> right
<sarang> Hopefully you will enjoy the Triptych paper, which builds a linkable construction on top of a sigma protocol :)
<suraeNoether> i enjoyed it the last time i read it, and the tiem before that. it takes awhile to digest :P
<suraeNoether> ok, i gotta bounce, i'm not feeling well; my list of 3 unfinished tasks is also my list of action items today
<sarang> roger
<sarang> My ACTION ITEMS are getting these new definitions and proofs typeset and finalized, determining their DLSAG applicability, a few other organizational issues on the CLSAG paper to prepare it for resubmission, and getting Triptych submitted on review
<sarang> Any other final thoughts, comments, or questions before this meeting ends?
<moneromooo> I have an unrelated question.
<sarang> ?
<moneromooo> I was wondering whether atomic swaps between two cryptonotes with hte same curve etc (ie, not the general case) is possible now.
<moneromooo> Well, assuming the tooling was there of course, which it isn't.
<moneromooo> In theory I mean.
<sarang> I don't know of a good way that retains indistinguishability as well as DLSAG does, and that still has the tracing issue
<sarang> If you were willing to accept and mitigate the tracing issue, then its method could do it
<sarang> its = DLSAG's
<moneromooo> What is the tracing issue already ?
<sarang> The fixed basepoint used for dual-address key images allows determination of unwanted signature linking
<sarang> It isn't clear how to do a DLSAG-type construction with the variable-basepoint key images used currently
<sarang> I should more precisely say, the use of a fixed basepoint and having output private keys used as the corresponding key image discrete log (this doesn't exist in more recent constructions that use a fixed basepoint but in a different way)
<sarang> Oh, suraeNoether: do you think it's useful in the LA definition to include the linking tag oracle separately from the signature oracle?
<sarang> The player can get the linking tag oracle result simply by querying the signature oracle on a public key by using a random ring and message (and ignoring everything but the returned linking tag)
<sarang> Having a separate oracle only really serves to make it clear that the player doesn't necessarily need to convince a user to sign messages, but can obtain linking tags otherwise
<sarang> (although in this security model, it can do both)

Post tags : Dev Diaries, Cryptography, Monero Research Lab