#bitcoin-wizards on 2020-05-04 — irc logs at freenode.irclog.whitequark.org

2015-10-30 00:53 sipa changed the topic of #bitcoin-wizards to: This channel is for discussing theoretical ideas with regard to cryptocurrencies, not about short-term Bitcoin development | http://bitcoin.ninja/ | This channel is logged. | For logs and more information, visit http://bitcoin.ninja

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18:20 <jeremyrubin> is the BIP-32 weakness (ext parent key + non hardened child --> ext paretn privkey) inherent or just a choice for the scheme?

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18:22 <sipa> it is my belief that it is inevitable as long as just DL-based cryptography is used

18:22 <zmnscpxj__> I believe so as well

18:22 <sipa> by making xpubs linearly larger, they can support O(n) revelation of child private keys

18:22 <sipa> but you can't do better

18:23 <jeremyrubin> sipa: that version is also trivially true under concatenation, but there's probably a more efficient O(n) scheme

18:24 <sipa> what do you mean by concatenation?

18:24 <sipa> it's not that trivial, iirc

18:24 <jeremyrubin> e.g. P1P2P3P4 and require all 4 to sign. You can reveal a child for 3 of P1, P2, P3, P4

18:25 <sipa> no no

18:25 <sipa> there is a scheme that lets you generate 1 public key from 1 xpub, in such a way that revealing 3 child private keys is fine

18:25 <sipa> let me try to find the paper

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18:26 <jeremyrubin> Huh

18:26 <jeremyrubin> And it recurses?

18:26 <jeremyrubin> Because if you do n = 2 or 3, then you can just do key-trees

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18:26 <sipa> no

18:26 <sipa> any k<n revealed private keys in the tree below is fine

18:26 <sipa> but not more

18:26 <jeremyrubin> Ah

18:27 <sipa> same as BIP32, except BIP32 has n=1

18:27 <jeremyrubin> So if I knew some distant cousins they would still 'count'

18:27 <sipa> https://fc15.ifca.ai/preproceedings/paper_15.pdf

18:28 <jeremyrubin> Paper is still of interest since for the use case I have in mind being able to publicly derive a known N would be interesting. Out of curiosity on the larger pubkeys, that implies not bitcoin compatible correct? Or is it pubkey that is just a larger generator?

18:29 <sipa> it's bitcoin compatible

18:29 <sipa> the xpub just contains more than 1 point

18:29 <jeremyrubin> gotcha.

18:39 <jeremyrubin> This is helpful, but I'm trying to understand the benefit. So I publish a public key of length N+1, then a public individual can compute M > N sub-keys, but I can only reveal the private keys to L <= N of them? So the benefit is that I'm not precommiting to which keys I've released? Versus a simpler "Here are N keys" model.

18:40 <jeremyrubin> This does seem overall a good match for my use case, where the user will derive M > N sub-keys but only receive N of them

18:45 <jeremyrubin> I think I can even set something up within this scheme which is hierarchical-like

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18:52 <jeremyrubin> E.g., suppose you use the first N+1 group to generate and reveal 2N pubkeys and then reveal N privkeys. The other N privkeys are still secure. So then the group of N revealed privkeys can be used to create a generator for N-1 privkeys/pubkeys etc.

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18:53 <sipa> you're using the term group and generator, but i think you mean something else than the group theory meaning of those words?

18:53 <jeremyrubin> Yeah

18:54 <jeremyrubin> Group --> Sequence

18:54 <jeremyrubin> generator --> constructor?

18:54 <jeremyrubin> The base case I have is essentially revealing a single integer which corresponds to a key which corresponds to binary conditions in the sequence above.

18:55 <jeremyrubin> So you would reveal that key and all it's parents

18:55 <jeremyrubin> and the child gives you no additional information on the cousins (because it's only from info known at the parent level)

18:56 <jeremyrubin> Hmm I guess not all it's parents

18:57 <jeremyrubin> Will need to write it out to confirm it does what I think

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