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Title:
Short Code-based One-out-of-Many Proofs and Applications
Authors: Xindong Liu, Li-Ping Wang
Abstract:In this work, we propose two novel succinct one-out-of-many proofs from coding theory, which can be seen as extensions of the Stern’s framework and Veron’s framework from proving knowledge of a preimage to proving knowledge of a preimage for one element in a set, respectively. The size of each proof is short and scales better with the size of the public set than the code-based accumulator in \cite{nguyen2019new}. Based on our new constructions, we further present a logarithmic-size ring signature scheme and a logarithmic-size group signature scheme. Our schemes feature a short signature size, especially our group signature. To our best knowledge, it is the most compact code-based group signature scheme so far. At 128-bit security level, our group signature size is about 144 KB for a group with 2^{20} members while the group signature size of the previously most compact code-based group signature constructed by the above accumulator exceeds 3200 KB.
ePrint: https://eprint.iacr.org/2024/093
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