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Say I have an element $g$ of a cyclic group. Are there homomorphic signature schemes that allow deriving signatures of $g^{ax+by}$ from signatures of $g^a$ and $g^b$?

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    $\begingroup$ Such a signature scheme cannot exist for the traditional notion of unforgeability, since it would be trivial to forge new signatures. By definition, you shouldn't be able to produce a valid signature of $g^{ax+by}$ from signatures of $g^a$ and $g^b$ without the secret key. $\endgroup$
    – lamontap
    Apr 3 at 13:32
  • $\begingroup$ @lamontap Thank you for your comment. $\endgroup$
    – Adam54
    Apr 12 at 21:50
  • $\begingroup$ I seem to have misled you with my previous comment. I just realized that homomorphic signatures actually are a thing. They just adapt the unforgeability game to being unable to forge a signature for a message that is not a linear combination of previously signed messages. $\endgroup$
    – lamontap
    Apr 16 at 15:19

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