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06:13 < waxwing> huh, opt-in switch commitment idea is cool. sipa real_or_random am I right in saying that you could change g^{m}h^{r+H(g^{m}h^{r}, g^{r}} to just g^{m}h^{r+H(g^r)} but the former is just easier because the H() is exactly a commitment to the elgamal form?
06:13 < waxwing> (and i understood you needed the r+ because in CT you need to be able to tweak blinding factors so they add up)
06:18 < nsh> (so they add up ~ so borromean rings close into schnorr sigs by hash half-chameleon property as proof of knowledge)
06:18 < nsh> (iirc)
06:26 < waxwing> nsh, well but no i just meant the homomorphism of the pedersen commitments themselves (transaction balance being guarnateed by ped. comms. adding up to zero; blinding factors have to add up to zero, as well as values doing so).
06:34 < nsh> ah right sure; pardon me
06:34 < nsh> i was really just refreshing my understanding tangentially to your point because that is one of my bad habits :)
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07:17 < waxwing> yeah i guess the above doesn't make any sense, it's like circular reasoning, you can't commit to the hash of 'r' inside the construction of r, so prob it only makes sense to commit to a full elgamal commitment in that tweak.
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11:45 < RubenSomsen> adam3us: I was thinking why have kernels at all if you can just create two outputs, but then I realized this allows the sender to take back their money, hence my assumption that this was a weakness in MW for CT
12:12 < RubenSomsen> Adam3us: What you were saying is Alice sends Bob r1*G + v1*H, Bob splits it up into (r1-k1)*G+v1*H and kernel k1*G (normal MW so far). Then later Carol sends Bob r2*G + v2*H and Bob splits it up into (r2+k1-k2)*G + v2*H and kernel k2*G. This effectively allows pruning k1*G because Bob "spent" it inside another UTXO. Correct?
12:24 < adam3us> yes right that. would only have as many kernels as utxos. however I had the idea that people were saying MW retains one kernel for coin that ever existed in history. (though it is small at 32byte point)
12:25 < RubenSomsen> adam3us: yes, they are all kept, and they're not quite that small because every kernel also has a signature that needs to be verified, so I think it's more like 3x32 bytes?
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12:27 < RubenSomsen> I think the idea works, but I am still pondering whether claiming a kernel has any implications on privacy
12:31 < RubenSomsen> I also think you can have less kernels than UTXOs with this (one per user). In my example Bob received two UTXOs but there's only one kernel.
12:34 < adam3us> RubenSomsen: oh right. i guess could be compacted to 2x32byte with key recovery, but yes. a schnorr proof of knowledge (schnorr signature of no data)
12:34 < adam3us> you wouldnt want to reuse kernels across coins for privacy
12:37 < RubenSomsen> I vaguely remember pwuille telling me key recovery hampers batch validation
12:38 < adam3us> it does yes. space vs time tradeoff :)
12:40 < adam3us> btw an interesting and (to my thinking) more elegant way to think about the kernels is a 0-valued coin, which you do not spend to deprive the sender of knowledge of the other coin received and register for consensus as unspendable so it can not be compacted (which would allow taking coins)
12:42 < RubenSomsen> yes I especially like the analogy in the context of CT style MW
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12:59 < RubenSomsen> adam3us: Ah, the compaction problem is still there, so it doesn't work: Alice sends Bob r1*G + v1*H, Bob splits it up into (r1-k1)*G+v1*H and kernel k1*G, then Alice maliciously spends Bob's UTXO together with the kernel since this is equal to the original commitment from Alice...
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