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I would like to get the ATECC608A microchip to sign data with ECDSA secp256k1 curve, but the chip only signs using the P256 curve.

Is there an operation I can do using the original message and the signature under P256 that would produce a signature under secp256k1?

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  • $\begingroup$ Yes, the trivial algorithm: Throw away the given signature and generate a new one using the other curve :p $\endgroup$
    – SEJPM
    Commented Feb 14, 2018 at 20:16

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There is no way to convert a signature with one curve to another. If there were, one could trivially forge signatures by starting with an insecure curve and converting it to a signature in a secure curve.

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