Intractable Group-theoretic Problems Around Zero-knowledge Proofs

TL;DR

This paper explores the connection between group-theoretic intractable problems and zero-knowledge proofs, aiming to identify new problems for developing more secure and efficient cryptographic protocols.

Contribution

It provides an overview of zero-knowledge proofs and highlights group-theoretic intractable problems as potential foundations for novel ZKP schemes.

Findings

List of group-theoretic intractable problems relevant to ZKP

Analysis of how these problems can underpin new cryptographic schemes

Discussion on the security implications of using group problems in ZKP

Abstract

While the amount of data produced and accumulated continues to advance at unprecedented rates, protection and concealment of data increase its prominence as a field of scientific study that requires more action. It is essential to protect privacy-sensitive data at every phase; at rest, at run, and while computations are executed on data. The zero-knowledge proof (ZKP) schemes are a cryptographic tool toward this aim. ZKP allows a party to securely ensure the data's authenticity and precision without revealing confidential or privacy-sensitive information during communication or computation. The power of zero-knowledge protocols is based on intractable problems. There is a requirement to design more secure and efficient zero-knowledge proofs. This demand raises the necessity of determining appropriate intractable problems to develop novel ZKP schemes. In this paper, we present a brief outline of ZKP schemes, the connection of these structures to group-theoretic intractable problems, and annotate a list of intractable problems in group theory that can be employed to devise new ZKP schemes.