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Black-Box Separations on Fiat-Shamir-Type Signatures in the Non-Programmable Random Oracle Model the active attack..We also show the security incompatibility between the discrete logarithm assumption and the security of the Schnorr signature via a single-instance key-preserving reduction, whereas Fischlin and Fleischhacker showed that such an incompatibility cannot be proven via a non-key-preserving reduction.