A Zero-Knowledge Proof System with Algebraic Geometry Techniques

Abstract

Current requirements for ensuring data exchange over the internet to fight against security breaches have to consider new cryptographic attacks. The most recent advances in cryptanalysis are boosted by quantum computers, which are able to break common cryptographic primitives. This makes evident the need for developing further communication protocols to secure sensitive data. Zero-knowledge proof systems have been around for a while and have been considered for providing authentication and identification services, but it has only been in recent times that its popularity has risen due to novel applications in blockchain technology, Internet of Things, and cloud storage, among others. A new zero-knowledge proof system is presented, which bases its security in two main problems, known to be resistant, up to now, against quantum attacks: the graph isomorphism problem and the isomorphism of polynomials problem.

Keywords

• graph isomorphism
• isomorphism of polynomials
• interactive proof system
• multivariate cryptography
• zero-knowledge proof