--- layout: post title: Logs for the MRL Meeting Held on 2019-12-09 tags: [dev diaries, crypto, research] author: asymptotically / Sarang --- # Logs **\** Let's go ahead and get started with GREETINGS **\** o/ **\** hello **\** That's long enough! **\** Let's move to ROUNDTABLE **\** suraeNoether: what up with you **\** i'm terribly ill this morning, so my update will be very brief. my work in this past week has involved three incomplete tasks: **\** 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? **\** suraeNoether: I have a writeup for LA in my notebook that I'm transcribing to TeX **\** and proof\* not just the definition **\** it works just fine **\** On that note **\** Do you have any thoughts on linkability (not LA) **\** I don't particularly like the Backes definition **\** uh one sec **\** Triptych has a version of linkability+non-frameability that I like better **\** is there soemthing wrong with the definition we proposed initially? **\** iirc that one's from bender **\** It's not formalized quite enough, in the apparent opinion of the reviewer **\** I think it needs just minor work **\** Triptych formalizes it a tad more IMO **\** I can add that to the writeup if you like **\** well **\** 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' **\** Backes requires the following for an LRS: completeness, linkable anonymity, linkability, non-frameability **\** Right now we combine linkability and non-frameability with non-standard terminology **\** Backes uses a particular linkability definition: can the adversary use `q` keys to generate `q+1` non-linking signatures? **\** Where `q` is scaled via the security parameter **\** 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 **\** Our current method does this very informally **\** I propose a combined linkability definition in my Triptych writeup that's a slight formalization of what CLSAG has now **\** (it could easily be split into linkability and non-frameability) **\** 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" **\** Yeah, which is why I don't really like it **\** didn't sit well with me **\** and we want the property with q=1 anyway to prevent double-spending **\** So I am proposing not using the Backes definition, but simply formalizing what we have now, a la Triptych **\** then it's more clear what the linkability player has access to in terms of keys etc. **\** okay, i'm going to read more deeply into that this afternoon **\** IMO it's a pretty straightforward formalization **\** doesn't affect much in practice **\** 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 **\** That definition doesn't make assumptions about linking tags being equal AFAICT **\** Whereas ours does **\** I think that's part of it **\** Anyway, you were talking about work you'd been doing, before I barged in =p **\** moving along, my next incomplete task is reviewing triptych's security proofs more deeply, which dovetails with this :P **\** Yeah, a nice tie-in **\** 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 **\** Nice! **\** 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 **\** word **\** 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 **\** We can pretend otherwise **\** I have completed a draft of the Triptych preprint, which is now in suraeNoether's hands **\** suraeNoether: I'm really looking forward to that chart **\** it includes my proposed linkability+non-frameability definition **\** Figured out the CLSAG linkable anonymity definition, which is not as strong as Backes, but does the job IMO **\** I've also been working with Aram from Zcoin on some related Groth proving system stuff **\** what's the shortfall on the linkable anonymity definition, even if there's no practical difference? **\** There will be a neat paper coming out from them on that shortly, which they graciously provided to me in advance **\** sgp\_: Backes permits key corruption, which doesn't work with our DDH hardness assumption **\** Instead, we assume the adversary can obtain key images **\** And that the adversary can pack rings with their own malicious keys **\** sarang: thanks **\** (which you can assume are trivially corrupted) **\** This is already stronger than the existing definition that was used **\** 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 **\** So overall, a lot of tedious (but still interesting) stuff involving formal definitions and proofs **\** When suraeNoether finishes his review of the Triptych preprint, it'll go to the IACR archive **\** and presumably any CLSAG/DLSAG updates as well **\** 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\* **\** The adversary picks which keys IIRC, right? **\** yeah, adversary can use KeyGen or any other way of selecting the verification keys **\** may not even know the secret key, so it's genuinely adversarial **\** ya **\** The adversarial generation isn't really a big deal, since soundness implies the adversary's choice of keys satisfy the verification equations **\** and then you rely on the one-way mapping **\** 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 **\** 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 **\** Backes even notes that generating `q` such signatures is trivial, since you simply use separate keys **\** Fake pubkeys should be acceptable **\** since the adversary does all this offline, or otherwise generates the pubkeys in its own (seemingly) valid transactions **\** 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 **\** suraeNoether: thoughts? **\** 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. **\** Yeah, and I haven't seen it anywhere else **\** Again, I don't feel any particular need to use it **\** But getting the existing definition more formalized in a challenger-player sense seems wise **\** agreed **\** roger **\** OK, that's my update **\** Does anyone else have interesting (or uninteresting) research to share? **\** ok, dude, i think i know the problem here **\** with that definition **\** or at least my problem with it **\** Ooh, go on **\** 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 **\** you called this positive and negative linkability at some point **\** i feel like this definition is mashing the two together **\** or attempting to **\** anyway, my thoughts don't go deeper than that yet **\** Backes uses non-frameability to show that you can't make signatures that \_appear\_ to link without knowing/using the same key **\** and linkability to mean that you can't make sigs with the same key(s) but different tag(s) **\** The reviewer didn't like the CLSAG paper's use of positive/negative/soundness in linkability **\** hmm **\** okay, that's going to require more thought **\** anywya, now i'm done. :P **\** A lot of this is simply getting the right terminology for the definition(s) of choice **\** I happen to like using linkability to refer to both **\** since that's typically what you want **\** but it's two different concepts **\** OK, we can move on to any other research **\** or to the next topic, QUESTIONS **\** i have a pretty general observation **\** which may be relevant in terms of independent interest **\** 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. **\** 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 **\** i bring this up so that the next version of snarks has an L floating around **\** There's a related-ish property in sigma protocols, quasi-unique responses **\** But that relates to responses to the verifier challenge **\** more reading to do :\ **\** There's probably a subtle relationship to (SHV)ZK **\** and therefore witness indistinguishability **\** (which follows from SHVZK) **\** anyway **\** Normally, providing two proofs should not reveal distinguishing information about the witnesses **\** right **\** Hopefully you will enjoy the Triptych paper, which builds a linkable construction on top of a sigma protocol :) **\** i enjoyed it the last time i read it, and the tiem before that. it takes awhile to digest :P **\** ok, i gotta bounce, i'm not feeling well; my list of 3 unfinished tasks is also my list of action items today **\** roger **\** 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 **\** Any other final thoughts, comments, or questions before this meeting ends? **\** I have an unrelated question. **\** ? **\** I was wondering whether atomic swaps between two cryptonotes with hte same curve etc (ie, not the general case) is possible now. **\** Well, assuming the tooling was there of course, which it isn't. **\** In theory I mean. **\** I don't know of a good way that retains indistinguishability as well as DLSAG does, and that still has the tracing issue **\** If you were willing to accept and mitigate the tracing issue, then its method could do it **\** its = DLSAG's **\** What is the tracing issue already ? **\** The fixed basepoint used for dual-address key images allows determination of unwanted signature linking **\** It isn't clear how to do a DLSAG-type construction with the variable-basepoint key images used currently **\** 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) **\** Oh, suraeNoether: do you think it's useful in the LA definition to include the linking tag oracle separately from the signature oracle? **\** 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) **\** 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 **\** (although in this security model, it can do both)