Basic aspects of the zero-knowledge concept: theoretical foundations, modern ZKP systems, and conceptual representation of zk-SNARK technology

Authors

DOI:

https://doi.org/10.30837/rt.2026.1.224.02

Keywords:

zero knowledge, interactive zero-knowledge proof, non-interactive zero-knowledge proof, zero knowledge protocol, arithmetic circuit, zk-SNARK, cybersecurity

Abstract

In the context of rapid and widespread digitalization of society, active implementation of new innovative technologies, and the growth of cyber threats, the issue of organizing effective cybersecurity for enterprises is becoming particularly important. To protect today's modern digital enterprise, you need a comprehensive strategy for secure access to your corporate resources anytime, anywhere, regardless of where they are located. By following Zero Trust Architecture (ZTA) principles, which call for least privilege access and continuous verification, businesses can effectively minimize their attack surface and limit potential losses from compromised accounts. However, existing access control and authentication mechanisms alone are not always sufficient to ensure complete protection of critical data, especially in scenarios where proof of access rights or actions is required without revealing content. In such cases, an effective addition to ZTA can be the use of Zero-Knowledge (ZK) concept, which allows confirming access rights or ownership (knowledge) of certain information without the need to disclose it, which significantly reduces the risks of leaks and unauthorized access. At the same time, representatives of businesses interested in the security of their systems are not yet fully aware of the advantages of this concept. The practical application of already known Zero-Knowledge Proof (ZKP) capabilities in various relevant areas that ensure security is being hampered, among other things, by a lack of awareness and insufficient theoretical training in this area among specialists responsible for security and communicating these capabilities (their potential) to the managers of relevant IT companies. In other words, there is currently a problem related to a lack of awareness about the zero-knowledge concept (its theoretical and practical significance) for making the right decision when building a security system for a corporate information system in modern conditions. This article is exactly aimed at solving this problem. The purpose of this work is to systematize the theoretical foundations and practical application of the zero-knowledge concept using simple and obvious examples in order to understand the potential of ZKP in solving problems of confidentiality/privacy and data verification. To this end, it outlined the main aspects of the zero-knowledge concept, including an analysis of the applicability of interactive and non-interactive approaches, an assessment of existing ZKP systems, and a conceptual representation of zk-SNARK technology based on the popular Groth16 scheme with mathematical justification. This contributes to a better understanding and future use of this dynamically developing and complex concept as one of the key mechanisms of modern cryptography, providing the ability to prove the correctness of calculations without disclosing the computational process or the initial data.

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2026-04-30

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Yesin, V., & Vilihura, V. (2026). Basic aspects of the zero-knowledge concept: theoretical foundations, modern ZKP systems, and conceptual representation of zk-SNARK technology. Radiotekhnika, (224), 23–57. https://doi.org/10.30837/rt.2026.1.224.02

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No. 224 (2026): Radiotekhnika

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