--- Log opened Tue May 29 00:00:30 2018
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03:04 < swagwise> Hello everyone, is this channel still active?
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03:13 < ZmnSCPxj> Good morning bsm117532, I believe gwern had an essay about timelocks: https://www.gwern.net/Self-decrypting-files
03:13 < ZmnSCPxj> It might not be appropriate for your use-case, though
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03:14 < bsm117532>  Thanks ZmnSCPxj i'll read it
03:15 < bsm117532> I was just thinking of digging into bulletproofs.  Because if you can prove the set of sequential statements y_1=x*x, y_2=y_1*y_1, y_3=y_2*y_2... then y_n=x^(2^n) and you can aggregate the proofs.
03:16 < bsm117532> Which, ultimately, is something similar to bramc's idea, but hopefully faster than Snarks.
03:21 < bsm117532> It seems like a lot of overhead to me.  All I really want is for the prover to present x^(2^n) and for the verifier to have some way to verify or know 2^n.
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03:25 < ZmnSCPxj> Good morning bsm117532, I believe what is commonly investigated, is that some entity first provides the timelock puzzle, the prover/grinder operates the timelock
03:25 < ZmnSCPxj> When the timelock is completed, it yields a private key which the first entity has published the public key for (or encrypted some file using the public key for)
03:27 < ZmnSCPxj> I do not know, what you want to use as X
03:27 < ZmnSCPxj> How is X selected in your scheme?
03:29 < ZmnSCPxj> One can argue that timelocks is what cryptocurrency mining *is*.
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03:37 < ZmnSCPxj> Perhaps "chained hashing" in the gwern article would be of help.
03:38 < ZmnSCPxj> For instance, we can get 256 x 32bytes random data from some public random source (e.g. the most recent block hash as seed for some PRNG)
03:39 < ZmnSCPxj> The first 32-bytes, when hashed 64 (or however many) times, serves as the decryption key for the next 32-bytes.
03:40 < ZmnSCPxj> the next 32-bytes, when hashed 64 times, serves as the decryption key for the next next 32-bytes.
03:40 < ZmnSCPxj> and so on
03:40 < ZmnSCPxj> the prover needs to execute all of those in sequence
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03:40 < ZmnSCPxj> And show the decryption key and the decrypted value for each 32-byte section of the original random data
03:41 < ZmnSCPxj> the verifier(s) can perform the hashing in parallel, i.e. it checks the decrypted value for one 32-byte section, hashed 64 times, is the decryption key for the next 32-byte section
03:42 < ZmnSCPxj> the verifier(s), with some probability, can sample only some of the hashes rather than the entire proof the prover provides
03:42 < ZmnSCPxj> according to how much time it has in order to verify
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03:47 < bsm117532> ZmnSCPxj that's the usual way of doing timelocks.  I'm doing something different.  The prover presents a proof based on x which is derived from public data (e.g. using sha512 to map it into an elliptic curve point) and computes x^(2^n). Unlike the usual timelock puzzle, this is not created by a "challenger", and has no trusted setup.
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03:47 < bsm117532> This puzzle is a proof that a certain amount of time has elapsed since the public data x was revealed to the world (e.g. a block header)
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03:48 < ZmnSCPxj> Yes, my latter proposal based on chained hashing should work for your application...?
03:48 < bsm117532> Yes, it's just ugly. ;-)  That's how bramc's proposal works, using a ZK-Snark to prove chained hashing.
03:49 < ZmnSCPxj> I am almost certain that for some elliptic curve point X, X^(2^n) can be computed in O(1) time for all n.......
03:49 < bsm117532> Parallel vs serial hashing only provides a constant-time speedup
03:49 < bsm117532> x^2 can be computed in constant time.  x^4 requires twice as much constant time ;-)
03:49 < ZmnSCPxj> In the sub-second times you are measuring, perhaps constant-time speedup is sufficient?
03:50 < bsm117532> Maybe.  But I think we can do better
03:50 < ZmnSCPxj> merkle trees?
03:51 < bsm117532> That would work but they're large and I think the verifier still needs to recompute everything
03:52 < bsm117532> There's also the problem that the verifier can't add this new block to his parents list until he's verified it, which is a significant amount of extra latency in the parallal-verification case
03:52 < ZmnSCPxj> the verifier could probabilistically prove some subset of the entire proof
03:53 < ZmnSCPxj> as long as the prover has no access to the RNG the verifier is using, the prover has to provide the entire proof anyway
03:53 < ZmnSCPxj> and if there are multiple verifiers, then the prover can only fool some subsection of verifiers if it does not provide a correct entire proof
03:53 < bsm117532> I'm not sure how the probabilities would work. I can present z=w^2 as a component which has nothing to do with the input x.
03:53 < ZmnSCPxj> the verifier selects only some subsection of the proof to verify
03:53 < bsm117532> Really there's only one relevant verifier, and it's the miner who builds on your block.
03:54 < bsm117532> So an interactive proof?  Using Fiat-Shamir?  I've been thinking of that too...
03:54 < ZmnSCPxj> not interactive, just a probabilistic one.
03:55 < ZmnSCPxj> if you have verified the entire proof, then you know with certainty 1.0 that it is correct
03:55 < ZmnSCPxj> if you have verified 0.5 of the entire proof, then you know with certainty (some complex mathematical formula) that it is correct
03:55 < bsm117532> Well if I have a set of {y_i^2} and a bit-field from some entropy saying which ones I have to provide (common PRNG) I can do it.
03:56 < bsm117532> Adds an O(n) space component, but I don't think that's a huge problem
03:56 < ZmnSCPxj> Possibly, although I would prefer that the prover be required to provide the entire proof
03:56 < ZmnSCPxj> the verifier uses some hidden entropy source to decide which parts of the proof to check
03:56 < bsm117532> He would.  For instance let the entropy for the proof be hash(x, x^(2^n)) for the solution n
03:56 < ZmnSCPxj> which would improve the verification time compared to proving time
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03:57 < bsm117532> Yes at the expense of a longer "finalization" phase once the prover has found his solution
03:57 < bsm117532> I think with bulletproofs they can be incrementally aggregated
03:57 < ZmnSCPxj> ok ^^
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03:58 < bsm117532> https://github.com/apoelstra/secp256k1-mw/tree/bulletproofs
03:58  * bsm117532 reads the bulletproofs paper again...
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04:29 < bsm117532> The relevant metric for a good proof of time for this usage is (finalization time + verification time)/(mean block time).
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04:30 < bsm117532> With a braid the mean block time is expected to be 1-5 seconds or so.
04:32 < bsm117532> Given recent advances in block propagation I'm expecting it to be closer to 1s.
04:32 < bsm117532> bulletproofs range proofs take ~2ms to verify
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04:59 < bsm117532> Wait.  Given that a polynomial y = x^(2^n) can be defined by 3 points on the curve, is there a way to present three points without the verifier having to recompute the curve?
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05:26 < bsm117532> No...this is the same as presenting x, x^(2^n)...
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09:09 < swagwise> Can I ask a question? I would be happy if anyone could answer me :)
09:09 < swagwise> How are miners affected by increasing the block size to let's say 133 MB?
09:10 < swagwise> Other than network latency and block propagation
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09:24 < kanzure> http://diyhpl.us/wiki/transcripts/gmaxwell-2017-11-27-advances-in-block-propagation/
09:24 < kanzure> swagwise: ^
09:25 < swagwise> perfect! exactly what I was looking for :) Thanks!
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13:15 < kanzure> well you had asked for "other than block propagation" and my link was primarily about block propagation...
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15:18 < bsm117532> 133 MB is an awfully specific number.
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23:14 < merskiasa> Is Elio19 around?
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--- Log closed Wed May 30 00:00:31 2018