Abstract
Given that the Schnorr's protocol for Discrete Logarithm (DLOG) exchanges three messages, it is an interesting problem whether a constant round zero-knowledge protocol exists for the Double Discrete Logarithm problem (DDLOG), i.e., to demonstrate the knowledge of a secret witness x in ghx. In this paper, we show that it exists for a fragment of DDLOG with two restrictions: (1) The outer group of DDLOG supports bilinear pairing, and it needs a trusted set-up for common reference string (CRS). (2) x<t where t is the size of KZG commitment key in CRS. The protocol is zero knowledge and constant round, with O(1) complexity for prover and verifier, regardless of the desired security strength. The contributions of the work are mainly theoretical due to its restrictions and concrete performance.
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