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Imagine a situation where a prover can only sign with BLS signature signing algorithm, a verifier can only verify with Schnorr signature verification algorithm. Is it possible to convert a BLS signature to a Schnorr signature, so that a verifier who can only verify Schnorr signatures can verify derived signature given public key and message?

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You can't convert the signature output from one algorithm to another, especially not ones relying on random oracles.

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