On the CCA security properties (and more) of a new variant of Paillier-ElGamal

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We solve the long-standing open question of designing a "truly" linearly homomorphic scheme -- meaning it supports homomorphic additions on arbitrary plaintexts, with no restriction, in contrast to "somewhat" ones -- that achieves CCA1 security under a standard assumption. We do so by introducing a new variant of Paillier-ElGamal, which we call Damgard-Paillier-ElGamal (DPEG) as its design follows a Knowledge-of-Exponent pattern. On top of being linearly homomorphic without any restriction, our