The well-known Signed ElGamal scheme consists of ElGamal
encryption with a non-interactive Schnorr proof of knowledge. While this
scheme should be intuitively secure against chosen-ciphertext attacks
in the random oracle model, its security has not yet been proven nor
disproven so far, without relying on further non-standard assumptions
like the generic group model. Currently, the best known positive result
is that Signed ElGamal is non-malleable under chosen-plaintext attacks.
In this paper we provide evidence that Signed ElGamal may not be CCA
secure in the random oracle model. That is, building on previous work of
Shoup and Gennaro (Eurocrypt\'98), Seurin and Treger (CT-RSA 2013),
and Bernhard et al. (PKC 2015), we exclude a large class of potential
reductions that could be used to establish CCA security of the scheme.