March 26, 2018

**<suraeNoether>** Sarang is apparently en route from an airport and is not expected to make it for the meeting. So today i'll just babble a bit

**<suraeNoether>** and answer questions

**<rehrar>** Remind me, was he presenting at that Blockchain conference?

**<suraeNoether>** yes, that's why he's en route from the airport

**<suraeNoether>** he took it upon himself to disabuse some folks of some certain notions about hashgraph

**<suraeNoether>** which I think is neat

**<suraeNoether>** specifically, he's been reading a lot about graph-based currencies, and someone gave a rather misleading presentation, but Sarang's presentation (I believe) preceded it and it was an educational moment

**<suraeNoether>** but I shouldn't speak for him, I wasn't there. the conference organizers flew him out to give a presentation on behalf of MRL and I have confidence he did a great job representing us

**<rehrar>** Will it be posted online?

**<suraeNoether>** he can answer that later today. I don't know.

**<rehrar>** ok, thanks

**<suraeNoether>** So, before we proceed, does anyone have any other general questions for MRL?

**<sgp_[m]>** Sorry I'm here but mostly distracted by class. Looking forward to hopefully viewing the presentation online

**<suraeNoether>** ok, neato burrito. So, basically this week I've 1) been putting some copy-editing changes into the multisig paper like spelling and references 2) working on models of the spend-time distributions vs. ring mixin selection distributions, and 3) while driving between albuquerque and denver, I think I came up with a novel ECC signature scheme from one-way functions (staring into the desert sun), but I'm not

**<suraeNoether>** putting a lot of effort into that until I have more of a handle on spend-time distributions

**<suraeNoether>** I've also 4) been building the MRL Research Roadmap for 2018. I need to discuss with sarang, but I think we'll be putting that out mid-May, because we want to have a complete look at what's going on

**<suraeNoether>** uhm, also I've spent an enormous amount of time this week on a certain project for MRL related to churning and the EAE scenario. details to come later on

**<hyc>** sounds cool

**<rehrar>** if hyc thinks it's cool, then it's cool

**<suraeNoether>** hyc and I have been chatting about an asic-unfriendly POW expansion, also

**<sgp_[m]>** I'm highly looking forward to seeing your work with EAE

**<hyc>** yes and I'm now digging back into the bulletproofs paper to try to get more solid understanding

**<suraeNoether>** namely, if instead of a POW game like: find nonce x such that H(block || x) * difficulty < target…. we can run a POW game like: find a nonce x such that, for a random bit of javascript J(x) that is loop-free, H(block || J(x))*difficulty < target

**<suraeNoether>** this was the idea hyc originally brought to my attention, but verification requires executing the code, so I was thinking instead it could be a random arithmetic circuit instead. then you can present bulletproofs that you know the nonce x such that H(block || AC(x))*difficulty < target efficiently

**<rehrar>** oh yeah, I remember you guys discussing something like that. Just to clarify for me cuz it was a bit confusing at the time. The idea is that CPUs and GPUs compile code better than ASICs would, correct?

**<hyc>** compile and execute

**<suraeNoether>** the idea is that if the code is random, then an asic will presumably not even be able to compile the code, let alone execute it, but a cpu is built to deal with arbitrary code

**<suraeNoether>** maybe this is a bad analogy, but I think of an ASIC as a big manufacturing factory, fully automated. it makes lemon cakes. the random code you just spit out asked for a rotisserie chicken

**<rehrar>** making it so that an ASIC would have to be built with a CPU, which defeats the purpose because might as well have a computer at that point, right?

**<hyc>** that's the general idea yes

**<rehrar>** great, I understand now. Thank you for explaining. :)

**<suraeNoether>** yeah, it shifts the bottleneck away from the highly asic'able hash to finding the nonce for the hash, kinda

**<suraeNoether>** which is quite clever

**<endogenic>** hack the planet!

**<rehrar>** if this idea pans out, we can even do some looking into seeing if the random stuff can do something useful as well?

**<hyc>** useful?

**<rehrar>** never mind, this is something I know too little about. Sorry. Plz continue.

**<hyc>** the code must be highly random and unpredictable

**<hyc>** if it does something useful, that can be ASIC'd

**<endogenic>** rehrar: use the heat to warm your chickens

**<hyc>** there ya go

**<rehrar>** can the chickens consume the arbitrary code?

**<ArticMine>** The random code can provide space heating and in many parts of the world that is useful

**<suraeNoether>** does anyone have any other questions? i can sketch out my new signature scheme if folks are curious, but it'd be more of an algebra discussion. :D

**<ArticMine>** Sure

**<suraeNoether>** Cool. So, definition: a cartesian square of groups is a set of four groups and four group homomorphisms arranged in a square satisfying *one weird property*

**<suraeNoether>** https://www.irccloud.com/pastebin/XXZjHHp0/

**<suraeNoether>** So the square looks like this

**<suraeNoether>** and the property is this: if group elements from B and C end up *at the same element* in D, then they must have *come from* the same element in A

**<endogenic>** scientists hate it!

**<suraeNoether>** denoting the top map f, the left map g, the rihgt map h, the bottom map j, this means: if there exist some b in B and c in C such that j(c) = h(b), then there exists some a in A such that b = f(a) and c = g(a)

**<suraeNoether>** so I'm going to set A to be my private key group Zq, and D to be my public key group G

**<suraeNoether>** and i'll just assume the middle groups B and C are also equal to my public key group

**<suraeNoether>** then a message M can give me a signature this way: from M, build a one-way map from Zq (private keys) to G (signatures) called SIGN and a one-way map from G (signatures) to G (public keys) called VER

**<suraeNoether>** to sign the message, I evaluate my private key SIGN(x) and get a group element, my signature. To validate this game from me, I evaluate VER at my signature and check that the result is my public key, VER(SIGN(x)) = X

**<suraeNoether>** so my signature is SIGN(x) and the function VER

**<suraeNoether>** each message M has a different pair of one-way functions SIGN and VER

**<suraeNoether>** to forge this, I need to find a group element S such that VER(S) = VER(SIGN(x)) for someone's honestly computed SIGN(x), but that requires breaking the one-way-ness of all the arrows in my square

**<suraeNoether>** *this is all great in theory, but i have no implementation yet. :P*

**<suraeNoether>** oh, i missed a word: in the definition of the cartesian square, the diagram has to be commutative. so if I traverse from A to D along one path (through B), I get the same result as if I had traversed the other path (through C)

**<suraeNoether>** and that is *critical*

**<suraeNoether>** so, to construct an implementation, I need a way to map from message space to the space of one-way group homomorphisms to get SIGN and VER, and then I need to mod out by the ideal generated by all the functions that don't satisfy the cartesian property

**<suraeNoether>** more recently cartesian squares (mid-late 20th century terminology) have been called "pullback diagrams," and I haven't found any descritpions in the literature of EC-based digital signatures based on them

**<suraeNoether>** that doesn't mean that this is a novel signature scheme, only that I haven't found any old references to them. I'm emailing around asking folks, and if anyone comes across anything, please let me know

**<suraeNoether>** to forge this… <— also, i need to find a message M such that VER is the one-way function derived from M to compute a forgery

**<suraeNoether>** okay, abstract algebra/category theory lecture done. :P hehe

**<hyc>** whew ;)

**<suraeNoether>** ikr what a blowhard

**<suraeNoether>** also s/game/came

**<hyc>** I think I missed a part, can you explain again the bit after "now listen carefully" ?

**<suraeNoether>** "i think a few pages back, you missed a negative and the error propagates. I would have said something, but you were so excited about proving P=NP"

**<hyc>** lol

**<suraeNoether>** does anyone have any questions for MRL? I believe sarang is going to be posting another FFS to fund the third audit later today or something?

**<rehrar>** how much extra is going to be needed?

**<rehrar>** and did we sign off on anyone getting started already?

**<suraeNoether>** rehrar I don't know, and I don't know. i believe nioc was encouraging us to not worry about getting it funded and to just post it so we can get the process moving, but I don't want to speak for him.

**<rehrar>** got it

**<suraeNoether>** and sarang will be back later today to talk about that

**<suraeNoether>** days like today, i want to hire a suresh noether

**<suraeNoether>** okay, next meeting, I want to talk about planning the first monero conference, and planning travel for sarang and i to other conferences between now and then

**<suraeNoether>** i'm actually attending a bitcoin/blockchain event on april 25 in denver at one of the venues i'm looking at for the monero conference

**<suraeNoether>** and I have a few meetings next week about it too

**<suraeNoether>** other than that, I got nothing left to chat about

**<nioc>** rehrar: I believe Bunz and QuarksLab have already been signed

**<suraeNoether>** i also want to chat next week about how is everyone satisfied with MRL. I want to gauge the community on direction, depth, breadth, leadership, funding models/goals etc.

**<rehrar>** cool, thanks nioc

**<suraeNoether>** so, with that, i want folks to think about what you would say to me if you had me face-to-face. :D

**<rehrar>** oy, I need to talk with the two of you fairly soon. It's already Revuo time again.

**<suraeNoether>** rehrar i believe i'm dragging sarang out to denver for that blockchain event. make it up here around that time and maybe we can make it a MAGIC board member meeting + revuo intervuo.

**<suraeNoether>** we'll drag mike from the moneromonitor by. :P it'll be historic~

**<suraeNoether>** </meeting>

Post tags : Community, Cryptography, Monero Research Lab