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feat: prove Batch verify in bip340 - #1
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- batchVerify_sound_bits: b-bit coefficients (2^b ≤ n) catch an invalid signature except with probability 2^-b - BIP340Batch: incremental coefficient derivation as a random oracle; batch_incremental_sound bounds acceptance of an invalid batch by (q + ℓ)/2^b, via a potential-based bad-event lemma (prEvent_bad_le) Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
- generalize the verifier, game and query bounds over the hash input (key L i), shared by both derivations - batch_indexed_sound: coefficients hashed from (batch, index), as in the BIP340 text; same (q + ℓ)/2^b bound - secp256k1 versions of both bounds with 128-bit coefficients Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
batch_indexed_grind: from one valid signature, an explicit attacker making q hash queries gets an invalid 2-signature batch accepted with probability at least 1 - (1 - 2^-b)^q, matching the (q + 2)/2^b upper bound of batch_indexed_sound up to the ℓ term. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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