Hi all,<div><br /></div><div>https://github.com/AdamISZ/schnorr-unembeddability/</div><div><br /></div><div>Here I'm analyzing whether the following statement is true: "if you can embed data into a (P, R, s) tuple (Schnorr pubkey and signature, BIP340 style), without grinding or using a sidechannel to "inform" the reader, you must be leaking your private key".</div><div><br /></div><div>See the abstract for a slightly more fleshed out context.</div><div><br /></div><div>I'm curious about the case of P, R, s published in utxos to prevent usage of utxos as data. I think this answers in the half-affirmative: you can only embed data by leaking the privkey so that it (can) immediately fall out of the utxo set.</div><div><br /></div><div>(To emphasize, this is different to the earlier observations (including by me!) that just say it is *possible* to leak data by leaking the private key; here I'm trying to prove that there is *no other way*).</div><div><br /></div><div>However I still am probably in the large majority that thinks it's appalling to imagine a sig attached to every pubkey onchain.</div><div><br /></div><div>Either way, I found it very interesting! Perhaps others will find the analysis valuable.</div><div><br /></div><div>Feedback (especially of the "that's wrong/that's not meaningful" variety) appreciated.</div><div><br /></div><div>Regards,</div><div>AdamISZ/waxwing</div><div><br /></div>

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