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Alice has a secp256k1 key pair that she used some time ago when she communicated with Bob. Bob can no longer user secp256k1 but he only uses ed25519 instead. Alice and Bob cannot exchange any messages.

Is there a secure algorithm that Bob can use to derive an ed25519 pubkey from original Alice's secp256k1 pub key and also Alice can derive the matching ed25519 private key from her original secp256k1 private key

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Secp256k1 and Ed25519 are completely different algorithms using different elliptic curves. There is no algorithm that could convert one to the other because the keys cannot match. It's just impossible.

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