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| gmaxwell | aj: I'd like to review the work here: http://lists.linuxfoundation.org/pipermail/lightning-dev/2015-November/000329.html the mention of OP_CHECK_SECP256K1_MUL_VERIFY gives me concern that something is broken. But I could use an 'extract' of the scheme that assumes I don't know or care anything about lightning. | 02:55 |
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| aj | gmaxwell: sure! | 02:56 |
| aj | gmaxwell: so the idea with HTLCs is you pay to a hash and collect the payment by revealing the preimage. using sha256 or hash160 or whatever means that to forward a htlc you have to reuse the same hash/preimage at each step. i assume you're totally familiar with that? | 02:58 |
| gmaxwell | Yes. to make the payment atomic. | 02:58 |
| aj | gmaxwell: yeah | 02:58 |
| aj | gmaxwell: so it would be nice if you could use different hash/preimages at each step, so that different nodes in the route can't conspire and work out who was paying who. the "previous message" was me trying to do that with a SNARK | 03:00 |
| gmaxwell | So in here you pay to randomly relayed pubkeys along the way. But then how is the unlock atomic? e.g. if you just sign with Q at the end, the private key is not revealed... and so the other transfers are stuck, no? | 03:00 |
| aj | gmaxwell: so the use of ecc_multiply as the hash function instead solves it much more cleverly | 03:01 |
| aj | gmaxwell: ie PUBLIC = g*PREIMAGE | 03:01 |
| aj | gmaxwell: so that's still the last step in the chain, but the step prior to that becomes PUBLIC*n = g*PREIMAGE*n, and the step before that becomes PUBLIC*n*m = g*PREIMAGE*n*m* | 03:02 |
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| aj | gmaxwell: the n and m are kept secret to the person doing the paying, and the particular node; so they're not random pubkeys, they're random multiples of the next pubkey | 03:03 |
| gmaxwell | that was supposted to be 'related'. | 03:03 |
| aj | gmaxwell: english should've been designed with a higher hamming distance | 03:04 |
| aj | gmaxwell: okay so if you're asked to forward PUBLIC*n*m to PUBLIC*n; then you need to be told PUBLIC*n*m, PUBLIC*n, and m; you can then verify the multiplication, and once the payment completes you'll find out PREIMAGE*n (because PUBLIC*n will have just cleared). But you know m, so you multiply and have PREIMAGE*n*m and can clear the next step | 03:06 |
| gmaxwell | Why not this alternative scheme; Q = xG; Q1 = Q+P1, Q2 = Q+P2, Q3 = Q+P3 where the P_n are the single keys of the participants. | 03:06 |
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| gmaxwell | And instead of revealing Q you sign with it, using a forced static R value, so all the participants learn the discrete log from the signature? | 03:07 |
| aj | gmaxwell: because then you could just subtract your key P1 to work out Q and correlate transactions? | 03:07 |
| gmaxwell | aj: the 'your key'-- the key is single use, and uniformly distributed. | 03:08 |
| aj | gmaxwell: hmm, i'm not sure how that would work | 03:08 |
| gmaxwell | (I was going to seperately say you should be doing Q+nG generally, as it is enormously faster and as far as I can tell you need no property of multiplication here) | 03:09 |
| gmaxwell | aj: What part isn't clear? | 03:09 |
| aj | gmaxwell: so "x" is the secret known by the merchant, and Q is revealed to the consumer, yes? | 03:10 |
| gmaxwell | Yes. | 03:11 |
| aj | gmaxwell: oh, or is it the signature that's revealed to the consumer, not Q? | 03:11 |
| gmaxwell | x is the hash preimage, if you will, Q is the hash. the Q+... the the derrived hashes. whos preimages will be known to the keyholders of P1, P2, P3 ... respectively (and only them), once they know x. | 03:12 |
| gmaxwell | x can be disclosed if the payment to Q at the end requires signing with a particular nonce (e.g. substr constraining the signature), and the particupants know the discrete log of that nonce already. | 03:14 |
| gmaxwell | beyond not requiring additional constructs and getting rid of the expensive multiply, I think the inner public keys can replace the need for a seperate signature, and potentially make it so that all transactions except the last look like more ordinary multisig transactions. | 03:15 |
| aj | gmaxwell: hmm | 03:15 |
| aj | gmaxwell: that /sounds/ plausible, but i'll need to work it out with pen and paper... | 03:18 |
| aj | gmaxwell: (substr is a disabled opcode though) | 03:19 |
| gmaxwell | (there is an extra constraint that you need to show that P_n wasn't generated as a function of Q but there are several ways to do that.) | 03:19 |
| gmaxwell | aj: sure, though all the other things you're talking about don't exist. And I would be much more keen to enable substr (it's there in alpha, ...) than a generic point scalar multiply, which is fairly expensive (basically the same cost as a signature verify) | 03:20 |
| gmaxwell | single show signatures tend to be useful for other things in any case. | 03:21 |
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| aj | gmaxwell: so i think "OP_DUP 16 OP_LEFT <r> OP_EQUALVERFIY <Q> OP_CHECKSIGVERIFY" would let you reveal "x" with just OP_SUBSTR/OP_LEFT; but i don't see how earlier steps could get away with just a regular multisig txn? | 03:34 |
| gmaxwell | instead of having to be a preimage + key, they're just payments to a key. | 03:36 |
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| aj | gmaxwell: but that doesn't work transitively? ie, once I know <x> I can sign with <Q+P3>, but how does that help the next guy sign with <Q+P2>? | 03:39 |
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| gmaxwell | when he knows x he can with with Q+P2. (presuming he could sign with P2 to begin with, he just adds x to his private key) | 03:41 |
| aj | gmaxwell: right, but he doesn't know <x> unless he forces me to sign with a known r too, rather than just asking me to pay to an address? | 03:42 |
| gmaxwell | I'm assuming he'll observe the Q single show payment. | 03:43 |
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| gmaxwell | same deal as with the plain hashlock, everyone tests the same preimage. | 03:44 |
| aj | gmaxwell: that only works if he knew the log of the <r> value that i chose? | 03:44 |
| gmaxwell | you can all share that in advance. (e.g. Q picks it and tells the whole channel Q,r at the start) | 03:44 |
| aj | gmaxwell: seems like that'd require trust... i don't think you'd get to see the reveal of Q normally either -- it'd be in a channel, rather than on the blockchain | 03:47 |
| gmaxwell | I don't see how this is different than the case where you are using a common Hx = H(x) everywhere. | 03:47 |
| aj | gmaxwell: not using a common Hx is the goal :) | 03:47 |
| gmaxwell | Yes for privacy! | 03:48 |
| gmaxwell | But you're not making a privacy related objection. | 03:48 |
| aj | gmaxwell: but with a common Hx each node along the chain says "Here's x!" to the previous node, who then verifies H(x)=Hx, and repeats. you forward along the same Hx each time because that's the only way you'll convince anyone to give you x | 03:49 |
| gmaxwell | okay you're counting on each step forcing there not the final being made public. | 03:50 |
| gmaxwell | Then I withdraw that optimization. Still, use of addition and single sure I hope turn out to be useful improvements. :) I'll think more about this. | 03:51 |
| aj | gmaxwell: okay :) | 03:52 |
| aj | gmaxwell: though... i think maybe you just end up with two OP_CHECKSIGVERIFIES anyway, rather than an OP_ECC_MUL + OP_CHECKSIGVERIFY (or OP_SHA256 + OP_CHECKSIGVERIFY) :( | 03:53 |
| aj | gmaxwell: revealing Q with just one OP_CSIGV would let the other guy publish the old commitment tx, then spend your output (ie, getting a refund), but then claim the original payment too (assuming they didn't rip them off in the same way) | 03:55 |
| gmaxwell | yes, if each step has to reveal then you need two keys. (a CMS with one being single show) | 03:56 |
| aj | CMS? | 03:56 |
| gmaxwell | checkmultisig. | 03:56 |
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| gmaxwell | I'm going to go try to find a single show signature in the existing system. There may well be one. | 03:58 |
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| gmaxwell | y'all are gonna hate me, but I did it: we've already got a single show signature in Bitcoin! | 04:29 |
| aj | gmaxwell: ... so what is it? | 04:30 |
| gmaxwell | So I have a scheme, where you can give me a pubkey, and I can write a unusual scriptpubkey that pays to it, which you can sign for but not without leaking your private key to the world ... with computational soundness (e.g. you could do an intractable amount of computation and break it.) | 04:32 |
| sipa | hashlock where the preimage is the pubkey? | 04:35 |
| amiller_ | guy fawkes signatures satisfy that description too | 04:35 |
| sipa | oh. leaks private key | 04:35 |
| gmaxwell | amiller_: from context, it need to be a ECDSA single show for other reasons. | 04:35 |
| amiller_ | kk, then i'm intrigued to see this | 04:36 |
| gmaxwell | b17df64bbaf96453bb63912b939861997275d03435043dcea56a68436895e10f | 04:37 |
| gmaxwell | I'll let other people stew on it for a day. Someone might invent a better one along the way. :) | 04:37 |
| gmaxwell | amiller_: simplifying the earlier discussion and removing all the LN specific stuff, here is why I want it: | 04:39 |
| gmaxwell | Here is a private atomic swap that doesn't need the multiphase "CoinSwap" transform: | 04:39 |
| gmaxwell | B computes nonce x and P = xG | 04:39 |
| gmaxwell | B sends P, single-show-signature-with P to A | 04:39 |
| gmaxwell | B pays to if() {Apub2+P} else {CLTV Bpub} | 04:39 |
| gmaxwell | A pays to if() {Bpub, force R key P} else {CLTV Apub} | 04:39 |
| gmaxwell | the two payements are unlinkable (assumping apub2 is kept private to alice and bob; uh and assuming my two bpubs above are distinct keys) | 04:40 |
| gmaxwell | And they're atomic. | 04:40 |
| amiller_ | what do you mean by B sends P, single-show-signature-with P to A.... does that reveal x to A? | 04:43 |
| gmaxwell | no, it's just a signature. then in the last payment the scriptpubkey requires a signature with P in such a way x will be made public. (e.g. if we had substr, you'd just use it to constrain R to be the R from the earlier signature) | 04:46 |
| kanzure | atomic swap should be applied to lightning transaction types at some point | 04:46 |
| gmaxwell | so the missing primitive for this private atomic swap was a way to do a signature which will leak the private key in bitcoin today. (since it's nicer if things work now...) | 04:47 |
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| amiller_ | after step 2 "B sends P, single-show-signature-with P to A", is the message that will be eventually single-show-signed predetermined? | 04:50 |
| gmaxwell | can't be, alas, it's a spend of the last transaction (pays) there, so it will commit to that txid. | 04:51 |
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| amiller_ | can you replace "A pays to if() {Bpub, force R key P} else {CLTV Apub}" with simply "A pays to if() {force R key P} else {CLTV Apub}" | 04:54 |
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| gmaxwell | amiller_: doing to means someone could see that spend and race it (now knowing x) to steal the funds. | 04:56 |
| amiller_ | i cant see why this is a signature and not just revealing the preimage..... oh i see the point is for them to be unlinkable | 04:56 |
| gmaxwell | so the requirement for a Bpubkey there is important. | 04:56 |
| gmaxwell | Yes, to be unlinkable. | 04:57 |
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| gmaxwell | amiller_: I made a generic scheme for that in the past https://bitcointalk.org/index.php?topic=321228.0 which lets you hide any smart contract from the blockchain and make it private.. including an atomic swap (of the normal hashlock type)... but it has lots of steps, which is a pain to implement, and make it malleability vulnable. | 04:58 |
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| amiller_ | ok i guess that kind of unlinkability is cool enough, that's cool it improves coinswap, i guess it's obvious it's possible in general but probably requires cleverness to do with existing script | 05:05 |
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| amiller_ | since the only tool at your disposal in bitcoin script is checking a signature over the current transaction, i imagine all you can hope to do is check multiple signatures over the same message under different but related public keys | 05:14 |
| sipa | and require related k | 05:15 |
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| amiller_ | how do you require related k? | 05:18 |
| sipa | i've been asking myself that question for the past half hour | 05:18 |
| * gmaxwell cheshire cat | 05:20 | |
| kanzure | what was the signature scheme where you can insert arbitrary text into the middle of a signature? | 05:20 |
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| kanzure | perhaps adding that sort of requirement would reveal some key info | 05:20 |
| kanzure | er, it was not arbitrary text, i am misremembering, but that's already evident by me not remembering the name :-) | 05:21 |
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| aj | hmm, i can related keys, but can't get the sigs from the related keys to be related enough but not too much | 05:23 |
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| gmaxwell | unrelated; Anyone else here read Mother Earth Mother Board? I think it's online, fun read though probably a bit dated now. In it; it talks about undersea cables, once installed being something of a 'found artifact' ... like stargates left from a prior civilization, where generations of engineers pour over them to characterize them and extract every bit of capacity available... far beyond what t | 05:25 |
| gmaxwell | hey originally did. I've thought about the bitcoin network like this at times, just because the cost ratio of upgrading it vs coming up with a crazy way to use what it has already supports doing the latter. | 05:25 |
| amiller_ | i don't think you can require related k but i also don't see why you need that | 05:28 |
| kanzure | there was some idea about using undersea sponges to make fiber optics at some point | 05:29 |
| sipa | amiller_: signing with related public keys does not automatically reveal the private key | 05:29 |
| sipa | amiller_: or BIP32 would be very broken | 05:29 |
| kanzure | like all weird scifi ideas, i am sure that orionsarm.com has shamelessly copied the idea | 05:29 |
| aj | gmaxwell: that's the neal stephenson travelogue? was hoping for a scifi story where they were literally found artifacts... | 05:30 |
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| bsm117532 | I just noticed that the Iota folks have put out a whitepaper. (It's a DAG-based crypto-currency) At first glance it looks pretty good. http://188.138.57.93/tangle.pdf | 06:10 |
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| bsm117532 | Is Serguei Popov or any of the Iota people going to be at Scaling Bitcoins? If not I'll try to cover this material... | 06:32 |
| sipa | that doesn't sound like applicable in the short term to bitcoin proper | 06:35 |
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| kanzure | "KLEE: Unassisted and Automatic Generation of High-Coverage Tests for Complex Systems Programs" http://llvm.org/pubs/2008-12-OSDI-KLEE.html (klee stuff) | 06:37 |
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| kanzure | oops didn't know about the name "coin history linearization", would have used that in scalingbitcoin-review.pdf had i known | 06:48 |
| kanzure | re: blockchain sharding proposals, https://www.reddit.com/r/Bitcoin/comments/3u1m36/why_arent_we_as_a_community_talking_about/cxbamhn | 06:48 |
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| kanzure | is there a way to do a 2-way spv peg where if the sidechain operators don't submit a conflicting proof within some number of confirmations, bitcoin users can recover their deposits to the spv address? | 07:13 |
| kanzure | spv address or er, spv mechanism | 07:13 |
| kanzure | unrelated; "segwit" == "segregated witness" (took me a few seconds..) | 07:14 |
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| sipa | kanzure: should be less.ambiguous than SW! | 07:17 |
| bsm1175321 | kanzure: I have talked about sharding, and I plan to make noise about it at Scaling Bitcoin, but I don't have any good proposal there. It's hard. (#3 here: http://blog.sldx.com/three-challenges-for-scaling-bitcoin/) | 07:21 |
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| bsm1175321 | sipa: better to take a long road to the right answer than a short-term band-aid that we'll regret the consequences of forever. To that end, DAGs can solve a lot of problems, and we should consider a route to it. | 07:22 |
| bsm1175321 | If you want to hear how I think we can add a DAG layer to bitcoin without upsetting consensus and bitcoin blocks I can talk about it more here... | 07:23 |
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| kanzure | "Asymmetric proof-of-work based on the Generalized Birthday problem" https://eprint.iacr.org/2015/946 https://eprint.iacr.org/2015/946.pdf https://www.reddit.com/r/Bitcoin/comments/3u2gk6/asymmetric_proofofwork_based_on_the_generalized/cxbbauh | 08:05 |
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| tromp__ | kanzure, that was previously discussed at https://www.reddit.com/r/bitcoinxt/comments/3n6hkc/research_paper_asymmetric_proofofwork_based_on/ | 08:12 |
| bsm1175321 | I have a hard time with word salad. Lots of salad in those last few links. | 08:14 |
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| Taek | .tell bramc you mentioned earlier working on Bitcion's peer protocol. gavinandresen was also talking about rewriting Bitcoin's peer protocol, perhaps there's value in collaboration | 08:55 |
| yoleaux | Taek: I'll pass your message to bramc. | 08:55 |
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| kanzure | "OP_CHECKWILDCARDSIGVERIFY or "Wildcard Inputs"" http://lists.linuxfoundation.org/pipermail/bitcoin-dev/2015-November/011805.html | 09:47 |
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| gwillen | kanzure: hmmm interesting | 09:50 |
| kanzure | yeah seems likely to work if you can enforce some standard about sorting | 09:50 |
| gwillen | oh hm, like sorting the candidate utxos? | 09:51 |
| kanzure | right | 09:51 |
| kanzure | but lookup time is going to be painful for validators | 09:52 |
| kanzure | especially without references | 09:52 |
| gwillen | yeah it sounds like he wants it to take them all without actually having to know what they are | 09:52 |
| kanzure | validators will always have to know them all | 09:52 |
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| gwillen | but if you instead do specify the amount | 09:52 |
| gwillen | and just have it take utxos from the beginning in sort order until you reach that amount | 09:52 |
| gwillen | and I mean, this is no more annoying for validators than SIGHASH_NO_TXID or whatever | 09:53 |
| gwillen | that would be "give me any coin with this scriptpubkey", versus this is "give me _all_ coins with this scriptpubkey" | 09:53 |
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| kanzure | how would you do miner fees with the partial one? | 09:58 |
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| kanzure | you would have to specify the fee amount in script too :) | 09:58 |
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| gwillen | kanzure: I'm imagining that you do specify an input value, contra the original mailing list suggestion | 10:01 |
| gwillen | and that value has to be the some of the values of some prefix of the list of possible inputs in whatever the sort order is | 10:01 |
| gwillen | and it unambiguously uses all of those | 10:01 |
| gwillen | err, the sum*** of the values | 10:01 |
| gwillen | and then the fee works as normal | 10:02 |
| kanzure | i think that many implementations assume that all inputs are valid, and use that as a way to reject invalid transactions, though | 10:02 |
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| kanzure | er. valid according to existing rules. | 10:02 |
| kanzure | so increases soft-fork difficulty | 10:02 |
| gwillen | hmm, can you explain a bit more? | 10:02 |
| kanzure | the input would be "invalid" according to existing rules | 10:03 |
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| kanzure | implementation details- like how validators are implemented- can influence how you choose to implement a soft-forkable feature... if a change requires too much effort, widespread deployment is unlikely. | 10:03 |
| gwillen | ahh hmm | 10:04 |
| kanzure | i haven't actually looked tho | 10:04 |
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| zookolaptop | Aw, that's nice that they thank gmaxwell and tromp_: https://eprint.iacr.org/2015/946 | 10:17 |
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| kanzure | gwillen: also; if you use the no-inputs-ever strategy, then you might accidentally spend some BTC to fees if you receive BTC to that scriptpubkey after you sign a transaction, but before the transaction is confirmed. | 10:40 |
| gwillen | kanzure: that's why you do specify a value | 10:40 |
| bsm1175321 | Hahaa I decided on some terminology: In a DAG if one of your node's parent's parent is one of your own parents, that's {\it incest} and disallowed. (Popov's tangle has incest) | 10:44 |
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| bsm1175321 | Just in case anyone else wanted to read that Iota paper I posted...don't. It's a confused mess with some poorly understood textbook statistics thrown in. | 13:42 |
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| kanzure | "Bitcoin meets strong consistency" http://www.tik.ee.ethz.ch/file/ed3e5da74fbca5584920e434d9976a12/peercensus.pdf (something about an identity layer?) | 14:07 |
| el33th4x0r | Bitcoin already provides strong consistency. | 14:09 |
| sipa | eh, no | 14:10 |
| el33th4x0r | This meme that is going around that Bitcoin is "eventually consistent" is just wrong. | 14:10 |
| sipa | bitcoin is not even eventually consistent. it's probabilistically consistent | 14:10 |
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| el33th4x0r | Correct, it's not eventually consistent. | 14:10 |
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| el33th4x0r | It provides a very strong probabilistic guarantee. | 14:11 |
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| sipa | with certain economic assumptions | 14:11 |
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| el33th4x0r | And assumptions on the hash power of colluding attackers. | 14:14 |
| el33th4x0r | but the bottom line is that one cannot look at the tail of the blockchain, observe that it's changing, and conclude that the system is "eventually consistent" or "inconsistent" | 14:15 |
| el33th4x0r | Paxos proposals can change over time. Paxos guarantees serializability, one of the strongest consistency guarantees. | 14:15 |
| el33th4x0r | When we evaluate databases, we examine their behavior with respect to a Write protocol and Read protocol. | 14:16 |
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| el33th4x0r | We do not examine the intermediate states of their internal data structures. No one cares that those change, as long as the changes are not reflected to clients through the Read()/Write() API. | 14:17 |
| el33th4x0r | I've heard various people mention casually that Bitcoin offers weak consistency. This is incorrect -- the exponentially-decaying probabilistic guarantee offered by Bitcoin is stronger than most distributed databases. | 14:19 |
| amiller_ | i think they should cite Exposing Computationally-Challenged Byzantine Impostors ftp://haskell.cs.yale.edu/pub/TR/tr1332.pdf and PoW-Based Distributed Cryptography with No Trusted Setup http://link.springer.com/chapter/10.1007/978-3-662-48000-7_19 | 14:21 |
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| bsm1175321 | el33th4x0r: Bitcoin's consistency is only asymptotic, not convergent (and certainly not exponential). Academic studies (PAXOS) generally go for convergence. | 14:35 |
| kanzure | ah gmaxwell already posted a comment https://www.reddit.com/r/Bitcoin/comments/3u3c2g/roasbeef_bitcoin_meets_strong_consistency_paper/cxbru1g | 14:36 |
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| el33th4x0r | Paxos is not an academic study, it's a protocol. | 14:37 |
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| bsm1175321 | It originated in academia and is well studied there. | 14:37 |
| el33th4x0r | Right, I'm an academic, well aware of Paxos' origins. | 14:38 |
| el33th4x0r | If we wanted to be pedantic, Synod is the original consensus protocol, and Paxos has been applied to a family of consensus protocols. | 14:39 |
| bsm1175321 | So why this dislike of "weak consistency"? Isn't it just saying "asymptotic"? | 14:39 |
| el33th4x0r | Because Bitcoin provides something stronger than weak consistency. Also, the framework people use to evaluate it is broken. | 14:40 |
| el33th4x0r | BTW "convergent" is not a well-defined term. And the probabilistic guarantee offered by Bitcoin is certainly exponential, discussed in the white paper. | 14:40 |
| bsm1175321 | Convergent is a very well defined mathematical term. | 14:41 |
| el33th4x0r | Can you please define it for consensus protocols? | 14:41 |
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| * bsm1175321 looks through notes. Would be happy to be wrong about this... | 14:44 | |
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| bsm1175321 | el33th4x0r: I think you're right. "Probabilistic Convergence" is better. If I figure out why I decided it was asymptotic I'll post about it. But the probability of an attacker with hashpower < 0.5 creating the highest-weight chain is absolutely convergent to zero. | 14:56 |
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| el33th4x0r | bsm1175321: Great. And the probability of an attacker with hashpower < 0.33 creating the highest-weight chain indeed converges to 0 with increasing block height. | 15:04 |
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| bsm1175321 | Modulo the selfish mining attack... | 15:05 |
| bsm1175321 | Which I think you wrote, no? | 15:05 |
| el33th4x0r | Right, that's me and Ittay Eyal. | 15:05 |
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| el33th4x0r | I'll head home for dinner and baby play, but let me leave on a positive note: we all have good reason to be proud of Bitcoin when it comes to claims about its consistency. | 15:07 |
| el33th4x0r | It provides stronger consistency guarantees than Mongo, for instance. | 15:07 |
| el33th4x0r | Not as strong as HyperDex, which provides a linearizability guarantee, but still stronger than many of the systems that people use to store their data. | 15:08 |
| el33th4x0r | Judging Bitcoin by the presence of change at the blockchain's tail reflects confusion, because no one would judge Paxos or Zab or RAFT by how the leader changes its proposal. | 15:10 |
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| * rusty2 pings gmaxwell... | 15:28 | |
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| bramc | Asymptotic rolling consistency, with no one single moment having absolute consensus except in retrospect, is how all databases should work. | 17:09 |
| yoleaux | 24 Nov 2015 16:55Z <Taek> bramc: you mentioned earlier working on Bitcion's peer protocol. gavinandresen was also talking about rewriting Bitcoin's peer protocol, perhaps there's value in collaboration | 17:09 |
| bramc | Taek, Right Gavin's muttering about it is why I was thinking about it. I don't actually know how Bitcoin's peer protocol works though, I just have some slightly sketchy thoughts about how I'd do it from scratch. | 17:10 |
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| bramc | So at some point I should sit down with someone who knows the current protocol well and discuss it. | 17:18 |
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| kang_ | bramc: record it | 17:19 |
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| bramc | Has anybody looked at http://eprint.iacr.org/2015/366.pdf ? It's got a nontrivial proof of time | 18:02 |
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| tromp__ | i read the first 2 sections:) | 18:18 |
| bramc | tromp__ I'm finding section 3 nontrivial, but it says that their construction is based on modular square roots, which raises the question of why not simply do repeated modular square roots | 18:25 |
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| tromp__ | those do not take more time to compute | 18:30 |
| tromp__ | for a prime field the multiplicative order is p-1 | 18:31 |
| tromp__ | so computing a square root is taking a (p-1)/2 -th power | 18:31 |
| tromp__ | a sqrt of a sqrt is cheaper, just (p-1)/4 th power | 18:31 |
| tromp__ | uhm, wait. what happens if p == 3 mod 4 | 18:32 |
| gmaxwell | tromp__: if the field is congruent to 3 mod 4, then you can use the (p+1)/4th power (and simular to get a 4th root) | 18:33 |
| gmaxwell | if P has other structure you can also construct a more efficient powering ladder (e.g. if its a repunit prime like 2^127-1 you can do most of the work by repeated squaring). | 18:35 |
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| bramc | Oh I see | 18:39 |
| gmaxwell | bramc: in any case the way sqrt works over a field is that the roots of member of the field that is a quadratic residue form a cyclic subgrop with a known number of members, so the way you find the sqrt is effectiely by going all the way around the long way, repeatly squaring to get to the members-1th step. | 18:39 |
| gmaxwell | (and since we know how big the group is, we can just efficiently raise to the relevant power) | 18:39 |
| bramc | This might be a fairly good practical speedup, because the constant multiplier has to do with number of bits instead of number of bytes | 18:40 |
| bramc | although, umm, you don't have the floating multiplier that you do in the repeated hashing constructions. Apparently I need to trudge through the rest of this paper. | 18:42 |
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| bramc | I'm not following their sloth construction, but if you're shooting for the biggest ratio of time to generate versus time to verify for a given size proof, I think it's best to just pick as large of a P which will fit. | 19:11 |
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| tromp__ | hmmm, a megabit prime? | 19:27 |
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| tromp__ | then optimization freeness may suffer, as you need these fancy FFT based multiplication methods for best performance | 19:29 |
| katu | i find their argument (well or more or less lack of) that tonneli-shanks root finding is unparallelizabl lacking | 19:29 |
| katu | its a probabilistic meet-in-the middle algorithm | 19:29 |
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| bramc | tromp__ The whole thing is going to have to assume quite a bit of known best optimization | 19:36 |
| tromp__ | yes, that's the shaky part. with iterated hash there is little worry about the optimal way to compute it:) | 19:37 |
| gmaxwell | There needs to be one of these SMBC comics that chargs "knoweldge of number theory" vs "faith that any asymmetric cryptography is actually secure in the long run" that goes up for a bit then down to almost zero then up a little bit and stays flat. :) | 19:42 |
| gmaxwell | [Another topic] Someone on reddit was complaining ( https://www.reddit.com/r/Bitcoin/comments/3u5b1d/my_exchange_with_coinbase_ceo_brian_armstrong/ ) that coinbase terminated the payment processing account for his NSFW comic book business, I responded extolling the virtues of not using third party payment processing and complained about soft-power regulation that bypasses due process by putting p | 19:49 |
| gmaxwell | ressure on commercial intermediaries but not banning things, and said I hoped tech like Bitcoin would reduce reliance on vulnerable choke-points. Apparently the name of one DOJ program doing this sort of thing is "operation chokepoint". I guess I approve of the naming! | 19:49 |
| kanzure | yes it is nice when they use independently derivable naming | 19:55 |
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| --- Log closed Wed Nov 25 00:00:35 2015 | ||
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