November 04, 2019

**<suraeNoether>** GREETINGS!

**<suraeNoether>** I'm surae, I'm a taurus maybe, and i like long walks on the beach with high probability

**<sarang>** Hi

**<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>** Sure

**<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>** (multi.tex)

**<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>** yes

**<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

**<sarang>** hmm

**<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>** https://www.youtube.com/watch?v=InbaU387Wl8

**<suraeNoether>** so my action items today are: triptych whiteboarding, janus tx proof validation check (the external input issue you just mentioned)

**<sarang>** great

**<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)

**<suraeNoether>** back

**<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>** hmmmm

**<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 :\

**<sgp_>** https://getmonero.org/2019/10/18/subaddress-janus.html

**<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>** sure

**<suraeNoether>** *nod*

**<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

**<sarang>** roger

Post tags : Dev Diaries, Cryptography, Monero Research Lab