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.
Highlights
The increasing use of powerful electronic devices and the availability of networks that provide ubiquitous and high-performance connectivity allow applications to transfer huge volumes of data in brief periods of time
These algorithms are the base of several digital signature techniques, and authentication and identification protocols, which are commonly used for e-commerce, banking transactions, and government services, among others, and their applications have been increasing with the introduction of multifactor authentication and cryptocurrencies
Though the pair ( F1, x1 ) can be obtained in the same fashion as the pair ( F0, x0 ), i.e., by computing the polynomial set related to the corresponding graph isomorphism, a more direct approach consists of directly applying suitable permutations to the subindices k and l for the variables obtained from the edges of H and H
Summary
The increasing use of powerful electronic devices and the availability of networks that provide ubiquitous and high-performance connectivity allow applications to transfer huge volumes of data in brief periods of time. The rapid development of cryptanalysis techniques and quantum computers endanger these security measures, with the most alarming threat being the existence of an algorithm that can solve the factorization problem efficiently, provided a quantum computer can ever be built [3]. These issues make clear that new techniques must be studied and developed in preparation for possible realizations of these threats. An authentic prover will be ready to provide a solution efficiently
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