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Maybe the answer to this question is a simple and unequivocal "No", followed by "How can you possibly think that this is possible?". And if I think about it rationally this seems to be the only answer. But programming and math have taught me that a lot of things one intuitively judges as impossible or pointless may have a surprising answer. So here comes one of those questions.

Is it possible to convert a gpg RSA key to an ECC key? Or, to generalize, is it possible to switch between different cryptography algorithms for one and the same key such that one retains the key's functionality; signing and encrypting etc. If so how does this work and if not, why not?

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No, not really. You can't switch because ECC and RSA are totally different algorithms that use totally different keys. The best you can do is generate a new ECC subkey which will be signed by your old RSA master key, then you can use that subkey for signing and/or encryption.

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