International Association
for Cryptologic Research

Private Information Retrieval(PIR) is a privacy-preserving primitive in cryptography. Significant endeavors have been made to address the variant of PIR concerning the malicious servers. Among those endeavors, list-decodable Byzantine robust PIR schemes may tolerate a majority of malicious responding servers that provide incorrect answers. In this paper, we propose two perfect list-decodable BRPIR schemes. Our schemes are the first ones that can simultaneously handle a majority of malicious responding servers, achieve a communication complexity of $ o(n^{1/2}) $ for a database of size n, and provide a nontrivial estimation on the list sizes. Compared with the existing solutions, our schemes attain lower communication complexity, higher byzantine tolerance, and smaller list size.

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 short signature sizes, 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.