Zero-Knowledge Proofs: Definition and Applications

Definition

A zero-knowledge proof (ZK proof) is a cryptographic method by which one party (the prover) can demonstrate to another party (the verifier) that a statement is true without revealing any information beyond the validity of the statement itself. The prover convinces the verifier of a fact without disclosing the underlying data.

The concept, first described in a landmark 1985 paper by Goldwasser, Micali and Rackoff, has evolved from a theoretical curiosity into one of the most consequential technologies in blockchain and distributed systems. Zero-knowledge proofs enable privacy-preserving transactions, scalable blockchain computation and verifiable off-chain processing — capabilities that are reshaping the architecture of decentralised networks.

How It Works

Core Properties

A zero-knowledge proof must satisfy three properties:

Completeness — If the statement is true and both parties follow the protocol honestly, the verifier will be convinced of the statement’s validity.

Soundness — If the statement is false, no dishonest prover can convince the verifier that it is true, except with negligible probability.

Zero-knowledge — If the statement is true, the verifier learns nothing beyond the fact that the statement is true. No additional information about the underlying data is revealed.

Practical Example

Consider a user who needs to prove they are over eighteen years of age to access a service. In a traditional verification model, the user would present their identity document, revealing their exact date of birth, name, address and other personal data. With a zero-knowledge proof, the user can prove “I am over eighteen” without revealing their date of birth, name or any other identifying information.

Types of Zero-Knowledge Proofs

Interactive ZK proofs — The original formulation requires multiple rounds of communication between prover and verifier. The verifier poses challenges, and the prover responds. After sufficient rounds, the verifier reaches a statistical confidence in the statement’s validity.

Non-interactive ZK proofs (NIZKs) — Modern cryptographic techniques allow zero-knowledge proofs to be generated in a single step, without interaction between prover and verifier. Non-interactive proofs can be verified by anyone, making them suitable for blockchain applications where proofs must be publicly verifiable.

ZK-SNARKs (Succinct Non-Interactive Arguments of Knowledge) — A class of zero-knowledge proofs that are compact (succinct) and fast to verify. ZK-SNARKs are widely used in blockchain Layer 2 solutions and privacy-preserving protocols. They require a trusted setup — an initial ceremony that generates cryptographic parameters.

ZK-STARKs (Scalable Transparent Arguments of Knowledge) — An alternative to ZK-SNARKs that eliminates the trusted setup, using transparent (publicly verifiable) cryptographic parameters. ZK-STARKs produce larger proofs but offer stronger security assumptions and resistance to quantum computing attacks.

Blockchain Applications

ZK-rollups — Layer 2 scaling solutions that use zero-knowledge proofs to verify the validity of batched transactions before submitting them to Layer 1. ZK-rollups offer faster finality than optimistic rollups and provide mathematical guarantees of transaction validity.

Privacy — ZK proofs enable confidential transactions on public blockchains, allowing users to transact without revealing sender, receiver or amount information. Privacy-focused protocols and DeFi applications use ZK proofs to protect user data whilst maintaining the auditability required for compliance.

Identity verification — ZK proofs enable selective disclosure of identity attributes — age, nationality, accreditation status — without revealing the underlying identity documents. This capability is particularly relevant for regulated DeFi and institutional crypto applications.

Smart-contract verification — ZK proofs can verify the correct execution of complex computations off-chain, reducing the on-chain gas-fee burden and enabling applications that would be prohibitively expensive to execute on Layer 1.

Swiss Context

Research Leadership

Switzerland is a global leader in zero-knowledge cryptography research. ETH Zurich and EPFL host some of the world’s most cited research groups in applied cryptography, with particular strength in:

• Proof-system design — Development of new ZK proof systems with improved efficiency, reduced proof sizes and enhanced security properties
• Formal verification — Mathematical verification of ZK-proof implementations to ensure they satisfy completeness, soundness and zero-knowledge properties
• Hardware acceleration — Research on specialised hardware (ASICs, FPGAs) for generating ZK proofs more efficiently, reducing the computational cost of proof generation
• Post-quantum security — Developing ZK-proof systems that remain secure against quantum computing attacks

Crypto Valley ZK Projects

Crypto Valley hosts several companies and projects building zero-knowledge infrastructure:

• ZK-rollup infrastructure — Swiss teams developing ZK-rollup technology for Layer 2 scaling, targeting both general-purpose computation and application-specific use cases
• Privacy protocols — Projects building privacy-preserving transaction layers and compliance-compatible confidential computing
• Identity systems — Swiss companies developing ZK-based identity verification for regulated financial services, enabling compliance with AML requirements without exposing unnecessary personal data

Regulatory Relevance

Zero-knowledge proofs have significant regulatory implications in Switzerland. FINMA’s approach to AML compliance traditionally relies on the ability to identify transacting parties and monitor transaction flows. ZK proofs that enable privacy-preserving transactions create tension with these requirements.

However, the technology also offers potential solutions: ZK proofs can enable “compliant privacy,” in which users prove their AML/KYC compliance status without revealing their identity to the public blockchain. This approach — demonstrating regulatory compliance without sacrificing privacy — is an active area of development among Swiss blockchain companies and a topic of ongoing dialogue with FINMA.

Key Considerations

Computational cost — Generating zero-knowledge proofs is computationally intensive, particularly for complex statements. Proof generation can take seconds to minutes, depending on the proof system and the statement’s complexity. This cost is borne by the prover, not the verifier.

Trusted setup — ZK-SNARKs require a trusted setup ceremony. If the ceremony is compromised, fake proofs could be generated. ZK-STARKs and newer proof systems eliminate this requirement but produce larger proofs.

Maturity — Whilst the theoretical foundations of ZK proofs are well established, production-grade implementations are relatively new. Bugs in ZK-proof implementations have resulted in vulnerabilities in deployed systems. Rigorous auditing and formal verification are essential.

Adoption trajectory — ZK technology is rapidly moving from research to production. Major blockchain ecosystems are integrating ZK proofs into their core infrastructure, and the Swiss crypto VC community views ZK infrastructure as one of the highest-conviction investment themes for the current cycle.

Donovan Vanderbilt is a contributing editor at ZUG BLOCKCHAIN, a publication of The Vanderbilt Portfolio AG, Zurich. The information presented is for educational purposes and does not constitute investment advice.