November 04, 2019
<suraeNoether> I'm surae, I'm a taurus maybe, and i like long walks on the beach with high probability
<suraeNoether> anyone else here?
<suraeNoether> well, public logs will be posted of this meeting either way, so anyone who missed it can find the logs online
<suraeNoether> okay, well, sarang, would you like to start?
<sarang> I've been working on a few things…
<sarang> More Triptych work, on math/proof for single inputs, which are fine
<sarang> This includes some CLSAG-style key aggregation and more efficient key images
<sarang> (more on multi-input in a sec)
<sarang> Also gave a talk on transaction protocols
<sarang> And looked at using the existing transaction proofs to mitigate the Janus subaddress attack
<sarang> As to multi-input Triptych, this link is to the Overleaf paper: https://www.overleaf.com/read/ncqsdsydxvjv
<sarang> The problem with witness extraction is the last equation on page 7
<suraeNoether> you and arthur are planning on submitting for peer review, yes?
<sarang> We could, once/if the proofs work out for multi-input
<sarang> We want to show that for every spent input M, H(M) = r*J
<sarang> where J is the key image
<sarang> and M = rG
<sarang> What we instead show is that a sum of the form \sum_u (\mu_u * H(M_u)) = \sum_u (witness_u J_u)
<suraeNoether> do you have your talk powerpoint up on your github?
<suraeNoether> by chance
<sarang> It's also the case that the sum of all witness_u is equal to the witness found for the signing key check
<sarang> Two equations above that one
<suraeNoether> found it: https://github.com/SarangNoether/talks :P
<sarang> I don't see a good line of reasoning to show why such a witness extraction would be equivalent to the honest generation of those key image
<suraeNoether> i'm taking a look now.
<suraeNoether> that shouldn't discourage anyone else from looking tho
<sarang> (you have to swap the two sums in the last equation to get something of the form that's two equations above, but that's fine)
<suraeNoether> janus mitigation right now is extra schnorr signatures, right?
<sarang> Yes, but you can use the existing transaction proof method, provided you check against a complete subaddress
<sarang> It's still off-chain, but functionality that exists now
<suraeNoether> very nice. iirc sgp_ wrote something on the janus vulnerability and made a blog post about it, or has a draft prepared. is that out or does it need updating or anything like that?
<sarang> Probably, but I'd like someone else to confirm that tx proof verification does in fact require external input of the suspected subaddress
<sarang> and that it's not pulled from the proof string in any way, or otherwise influenced directly by the prover
<sarang> (since the prover could simply use the Janus-modified subaddress)
<sarang> For this witness extraction, I suspect that it may possible to show that each u-summand in the X-check is in fact equal to a particular r_u term
<sarang> If that's the case, then we could easily show that the u-summand scalars in the Y-check are those _same_ r terms
<suraeNoether> great, does anyone else have any other questions for sarang about his work on triptych, or his work on janus, or questions about his talk?
<suraeNoether> well, my work this week has been on the matching code ( https://github.com/b-g-goodell/mrl-skunkworks/tree/matching-buttercup/Matching ) which has some peculiar failings right now
<suraeNoether> my basic unit tests for graphtheory.py, which handles all the graph theoretic stuff, are passing. nodes and edges are added and deleted correctly, weighted correctly, matches are found, etc.
<suraeNoether> but when i simulate a ledger with my simulator.py tool, the result misses some nodes and/or edges
<suraeNoether> these aren't being caught lower down, but are being caught higher up
<suraeNoether> so anyone with interest in python, graph theory, traceability, etc, can contribute by trying to figure out why my code isn't adding edges/nodes appropriately all the time. it's very bizarre behavior, and i'm sure it comes down to something ridiculous like my previous buffer problem
<suraeNoether> but, i want to put it down for a few days since other folks in theory could help, and i have other things to do like help review triptych's proofs
<sarang> That seems reasonable
<sarang> Is it clear in the code (or errors) where the specific problems are?
<sarang> i.e. if someone wishes to play around with it
<suraeNoether> running sh tests.sh from the tools folder will auto detect all the tests and execute them; i've skipped all the tests i know are currently passing, so it'll go right into the brick wall immediately
<sarang> got it
<sarang> suraeNoether: if you're going to be on IRC this afternoon, we could dive into that witness extraction and see if we can't solve it
<sarang> I have some ideas
<suraeNoether> beyond that, i have a few papers i have begun reading, such as this one https://eprint.iacr.org/2019/1177.pdf on aggregation approaches, and a few others on interactive versions of concensus mechanisms like this one https://eprint.iacr.org/2019/1172.pdf
<suraeNoether> sarang: i'm catching up on the triptych paper now and whiteboarding it
<suraeNoether> if i go all pepe sylvia on the thing i may take a crazed picture for posterity
<sarang> excellent reference
<sarang> I'll add a few more lines to page 7 to show how the X and Y witnesses are related
<sarang> since that should come into play in the Y-soundness
<suraeNoether> so my action items today are: triptych whiteboarding, janus tx proof validation check (the external input issue you just mentioned)
<suraeNoether> my action items immediately are to post my work report for last month and request funding for my next quarter, but i hate that and i much prefer coding and math so i'm finding myself v avoidant
<sarang> For this week, I'd (ideally) like to figure out this soundness issue… if it's possible to do so, it provides a very interesting extension to this Groth proof scheme
<suraeNoether> does anyone have any other research to advertise, or other questions for sarang or i?
<sarang> and would make Triptych a competitive option for tx protocol
<suraeNoether> it's such a great name
<sarang> suraeNoether: here are some general notes on the witness structure for ya
<suraeNoether> afk for about 10 minutes
<suraeNoether> sarang ^ yes pls!
<sarang> The prover wants to show that it knows the discrete logs (r-terms, in notation) for each of the signing pubkeys (M terms)
<sarang> so it knows a set of r (indexed by u different spends, no index here for clarity) such that M = rG for each one
<sarang> it also wants to show that H(M) = rJ for each one, where each J is a key image provided by the prover
<sarang> When done honestly, each J is defined such that J = (r^-1)*H(M)
<sarang> In the soundness proof, the "X check" is for signing keys, and the "Y check" is for linking tags
<sarang> X-soundness allows us to extract a witness (which involves certain Vandermonde-related coefficients) r1 such that r1*G = mu_1*M_1 + mu_2*M_2 + …
<sarang> and we claim (MuSig/CLSAG-style) that knowing this witness r1 implies knowledge of each of the r terms going into the right-hand sum
<sarang> Ideally, for the Y-soundness, we want to extract a related witness that implies knowledge of the same r-terms that go into the linking tag identities
<sarang> If you stare at the rightmost terms of the bottom equation and third-from-bottom equations on page 7, you can see the u-summands match up
<sarang> If we can show (using the form of the Vandermonde coefficients, etc.) that each u-summand in the X-soundness corresponds properly to an r-value, we may be able to make a solid argument about using those same u-summands in the Y-soundness equation (since we need the _same_ r-values there)
<sarang> The construction of the Vandermonde-related coefficients \theta_e is also discussed on page 7 (and can be found in the original Bootle paper's proof)
<sarang> This might get complicated, since rows of the Vandermonde matrix correspond to different F-S challenges :/
<sarang> sarang is done talking now
<sgp_> suraeNoether: yes, the blog post should be updated to include the mitigation
<suraeNoether> sgp_: can you link the post for the meeting logs pls?
<sarang> sgp_: once it's been confirmed that the verifier externally provides the expected subaddress
<suraeNoether> showing the correspondence like that has always been a sticking point :\
<sarang> suraeNoether: unless you can think of a good argument that having the same summand terms in both the X- and Y-witnesses is sufficient already
<suraeNoether> well, i'll catch up and then i'll see what you mean by that. :P
<sarang> e.g. we already claim that knowledge of that sum-witness in the X-portion is equivalent to knowledge of each discrete log
<sarang> Just remember that the key to the linking is that we show that the _same_ r-terms are used to construct the signing keys _and_ the corresponding linking keys
<sarang> so having the same witnesses should come into play
<sarang> It gets tricky because we don't directly show knowledge of each r-term, just the mu-weighted CLSAG-style combination
<sarang> So I wonder if we in fact already have all the information we need to show this
<sarang> and perhaps don't need to mess with those Vandermonde coefficients (which would be a huge pain to do)
<suraeNoether> okay, does anyone else have any research to talk about, or questions for MRL, or requests/points to bring up/etc?
<suraeNoether> otherwise we can adjourn the meeting and continue chatting about triptych outside of that context