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Sigma protocol for faster proof of simultaneous homomorphism relations

Sigma protocol for faster proof of simultaneous homomorphism relations

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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 axby ). 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.

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