have an account?【sign in】a survey of zero-knowledge proofs with applications to cryptography
barrientosauthorAbstract:
Zero-knowledge proofs are a powerful concept in the field of cryptography, enabling a prover to prove to a verifier that they possess certain knowledge without revealing any additional information. This article provides a comprehensive survey of zero-knowledge proofs, their various forms, and their applications in cryptography. We discuss the historical background, fundamental definitions, and state-of-the-art results in this area. Furthermore, we explore the various security properties of zero-knowledge proofs and their implications for secure communication and privacy-preserving protocols.
Zero-knowledge proofs, also known as zero-knowledge statements or zero-knowledge arguments, were first introduced by Goldwasser, Minsky, and Nahum in 1984. They were designed to provide a means of proving knowledge of a statement without actually revealing the statement itself, thereby ensuring privacy and security in communication and data exchange. Since then, zero-knowledge proofs have been extensively studied and applied in various fields, including cryptography, security protocols, and game theory.
Historical Background:
The concept of zero-knowledge proofs originated from the work of Goldwasser, Minsky, and Nahum, who developed the first pseudorandom function and pseudo-random kernel in the context of cryptography. Their groundbreaking results laid the foundation for the development of secure communication protocols and privacy-preserving algorithms. Subsequently, zero-knowledge proofs have been extended and generalized in various directions, leading to a rich body of literature and a diverse range of applications in cryptography.
Fundamental Definitions:
A zero-knowledge proof consists of a proof system, consisting of a prover P and a verifier V, and a proof of knowledge, such that (i) if P knows the statement S, then P can produce a valid proof P of S, and (ii) if P does not know S, then V cannot determine whether P has a valid proof P of S or not. The goal of a zero-knowledge proof is to provide a proof system that is both sound (i.e., valid proofs are indeed valid, and invalid proofs are never produced) and complete (i.e., for every valid proof P, there exists a statement S such that P is a proof of S).
Applications to Cryptography:
Zero-knowledge proofs have found numerous applications in cryptography, particularly in the design of secure communication protocols and privacy-preserving algorithms. Some notable applications include:
1. Secret-key encryption: Zero-knowledge proofs can be used to construct secret-key encryption schemes that provide unbreakable security without relying on a trust model or unapproachable cryptographic primitives.
2. Authentication and identification: Zero-knowledge proofs can be used to design authentication and identification protocols that ensure privacy and security of user data while maintaining the integrity of the communication channel.
3. Group communication and consensus: In group communication and consensus protocols, zero-knowledge proofs can be used to provide privacy-preserving voting and consensus algorithms, ensuring that the result of the consensus is unbreakable and independent of the input data.
Security Properties and Implications:
Zero-knowledge proofs are generally secure against adaptive choke attack, where the adversary can make statements about the output of the proof system. However, the proof systems may be vulnerable to the adaptive choke attack, where the adversary can make statements about the input to the proof system. To counteract this, one can use the idea of adaptive security, which provides a means of ensuring that the output of the proof system is unbreakable, even in the presence of an adaptive choke attacker.
Zero-knowledge proofs have become an essential tool in the field of cryptography, providing a means of proving knowledge of a statement without revealing any additional information. Their various forms and applications in cryptography have significantly advanced the field of security and privacy, enabling the design of secure communication protocols and privacy-preserving algorithms. As technology continues to evolve, zero-knowledge proofs are expected to play an increasingly important role in ensuring data security and privacy in the digital age.