The ‐protocols for homomorphism relations are one of the cryptographic protocols which are used to prove knowledge of homomorphism relations. The Schnorr protocol is one of the most famous ‐protocols used for proving knowledge of discrete logarithm (DL) relation in which the verifier essentially performs one double‐exponentiation (i.e. a group computation of the form a x b y ). A direct application of the Schnorr protocol for proving simultaneous knowledge of n DLs with a common base leads to a ‐protocol in which the verifier performs n double‐exponentiations. In this study, the authors propose another ‐protocol for homomorphism relations. The proposed ‐protocol has fast verification when is used to prove the simultaneous homomorphism relations with a common homomorphism. Also, when the DL instantiation (DL‐instantiation) of the proposed ‐protocol is used to prove simultaneous knowledge of n DLs with a common base, it leads to a ‐protocol in which the verifier performs n +1 single‐exponentiations.