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Title:
Lin2-Xor Lemma and Log-size Linkable Threshold Ring Signature
Authors: Anton A. Sokolov
Abstract:In this paper we introduce a novel method for constructing an efficient linkable threshold ring signature without a trusted setup in a group where the decisional Diffie-Hellman problem is hard and no bilinear pairings exist. Our ring signature is logarithmic in the anonymity set size and linear in the signer threshold, its verification complexity is close to linear in both the anonymity set size and the threshold. A range of the recently proposed setup- free logarithmic size signatures is based on the commitment-to-zero proving system by Groth and Kohlweiss or on the Bulletproofs inner-product compression method by Bünz et al. In contrast, we construct our signature from scratch using the Lin2-Xor and Lin2-Selector lemmas that we formulate and prove here. With these lemmas we construct an n-round public coin special honest verifier zero-knowledge membership proof protocol and instantiate the protocol in the form of a general-purpose setup-free linkable threshold ring signature in the random oracle model. Also, we show the signature is anonymous, has witness-extended emulation, is unforgeable and non-frameable.
ePrint: https://eprint.iacr.org/2020/688
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