Intractable Group-theoretic Problems Around Zero-knowledge Proofs

While the amount of data created and stored continues to increase at striking rates, data protection and concealment increases its importance as a field of scientific study that requires more effort. It is essential to protect critical data at every stage while it is being stored and transferred. One cryptographic tool that is of interest and can be widely used in this medium is zero-knowledge proof systems. This cryptographic structure allows one party to securely guarantee the authenticity and accuracy of the data at hand, without leaking any confidential information during communication. The strength of zero-knowledge protocols is mostly based on a few hard-to-solve problems. There is a need to design more secure and efficient zero-knowledge systems. This need brings the necessity of determining suitable difficult problems to design secure zero-knowledge schemes. In this study, after a brief overview of zero-knowledge proof systems, the relationship of these structures to group-theoretic algorithmic problems and an annotated list of intractable algorithmic problems in group theory are given.