Understanding Zero-Knowledge Proofs: A Beginner’s Guide

Blockchains have been created to increase transparency, yet as the number of real-world applications has increased, privacy has become a luxury. In wallet authentication or on-chain transactions, the user is forced to reveal personal information to prove ownership, eligibility, or participation. But what if it is possible to provide proof without even revealing some information?

That is the concept behind Zero-Knowledge Proofs (ZKPs), a revolutionary technique in cryptography that enables one party to prove the existence of data without disclosing the stated data. Although the concept is not new, ZKPs are widely applied today to increase blockchain scalability, digital identity, and computing privacy. This guide will provide a detailed description of zero-knowledge proofs, including their origin, structure, applications, advantages, limitations, and their role in the modern digital architecture.

The Evolution of Zero-Knowledge Proofs

ZKPs were introduced in 1985 by cryptographers Shafi Goldwasser, Silvio Micali, and Charles Rackoff, who proposed an interactive method for proving the truth of a statement without revealing the data. Their work laid the foundation for the latest cryptographic protocols, which later earned them the Gödel Prize. 

Although ZKPs were theoretical, they gained prominence with the rise of blockchain technology. Further, with data privacy concerns increasing, they began to gain real-world relevance. Zcash became one of the first large-scale projects to use ZKPs, allowing fully confidential cryptocurrency transactions in the late 2010s.

Today, zero-knowledge technology is used more than privacy coins by playing a major role in Ethereum Layer-2 scaling solutions, digital identity systems, and even zero-knowledge machine learning (zkML), thus solidifying ZKPs as a core building block for Web3 infrastructure. 

On the other hand, platforms like Starknet use validity proofs that focus on computational integrity rather than privacy. In this, transactions are batched together and executed off-chain, and a brief proof is submitted on-chain for verification. This enables blockchains to scale efficiently without compromising on security.

The Core Principle of Zero-Knowledge Proofs

• The Prover: The prover is the party that has the confidential information at their disposal, like a password, a private key, or related information, and wants to demonstrate that they have the information without revealing it.
• The Verifier: The verifier is the one who checks the validity of the claim provided by the prover. They are meant to be persuaded that the prover is aware of the information, although they never get to know the information.

The challenge is to confirm the prover’s claim without learning any underlying information. For a proof to be classified as zero-knowledge, it must satisfy three properties such as,

• Completeness: When both sides obey the protocol and the statement of the prover is actually true, the verifier will be convinced that the statement is really true. This ensures that honest participants can always successfully complete the proof process.
• Soundness: Assuming the claim is false, there is minimal chance that a dishonest prover could cheat the verifier into accepting the claim. This prevents fraud and ensures that only valid claims can be successfully verified.
• Zero-knowledge: The verifier does not gain any new knowledge about the prover beyond the fact that the claim is valid. This protocol does not disclose any confidential data, even when the verification of the proof is taking place.

Types of Zero-Knowledge Proofs

Interactive Zero-Knowledge Proofs

They need constant interaction between the prover and verifier. The prover is challenged several times by the verifier, and has to reply accurately each time. The back-and-forth steps help establish confidence in the validity of the proof but decrease the usefulness of interactive ZKPs in distributed systems, where real-time communication between entities might not exist.

Non-Interactive Zero-Knowledge Proofs (NIZKs)

Unlike the Interactive ZKPs, this one avoids interactions. Rather, the prover produces a single proof that is applied through cryptographic methods and independently validated by the verifier. It is perfect in cases like blockchain systems, where the proofs are published, transferable, and can be authenticated by any individual without any contact.

Common Zero-Knowledge Proof Systems

• zk-SNARKs: They are short for Zero-Knowledge Succinct Non-Interactive Argument of Knowledge, and generate small proofs fast to verify, but also need a trusted setup.
• zk-STARKs: The Zero-Knowledge Scalable Transparent Arguments of Knowledge is transparent and resistant against quantum computers, which makes it suitable for high-throughput applications like those in StarkNet.
• PLONK: A universal SNARK that can transfer a large number of circuits over the same setup. It further supports a trade-off between the size of its proofs and performance and is implemented in zkEVMs such as Polygon or Aztec.
• Bulletproofs: They are compact ZKPs without a trusted setup and are ideal for range proofs and confidential transactions. Bulletproofs are slow compared to SNARKs and are applicable in privacy-centric use cases such as Monero.
• Halo 2: A recursive proof system that does not require a trusted setup and supports chaining of proofs. It is used in Mina and Celo and is especially suitable for lightweight clients.

Uses of Zero-Knowledge Proofs

● Blockchain and Rollups

ZKPs are useful in zk-Rollups, where the systems transmit thousands of off-chain transactions and only send one zk proof to the main chain thereby reducing gas fees and keeping an equivalent level of security. Examples of platforms that utilize this architecture are zkSync, Polygon zkEVM, and StarkNet.

● Privacy-Preserving Transactions

Zcash and Aleph Zero are two cryptocurrencies that apply ZKPs to protect transaction information yet maintain that it can be audited. This model supports financial privacy without compromising regulatory requirements.

● Digital Identity

Zero-knowledge proofs enable selective disclosure. For instance, a user can prove that they are an adult or reside in a specific country without revealing their exact age or address. These applications are pivotal for building self-sovereign identity systems.

● Verifiable AI (zkML)

Since decision-making by AI is being scrutinized more, zkML (zero-knowledge machine learning) allows developers to prove that a given output was produced by a model without disclosing the input or the model weights. This establishes a channel of AI audits without revealing confidential information.

● Proof of Reserves

Crypto exchanges now use ZKPs to prove they hold customer funds in full, without revealing user balances or specific asset holdings, thus boosting transparency and preventing another scandal like the FTX.

● Oracle Networks and Off-Chain Data

Using ZKPs, oracle networks can demonstrate the validity of off-chain information such as weather, prices, and other sports facts without using raw data, making data feeds to smart contracts secure and safe.

● Supply Chain Integrity

Zero-knowledge proofs serve as validation tools to check every phase of the product, be it their authenticity, compliance, and origin, without disclosing secret information, thus guaranteeing a secure and trustless supply chain 

Advantages of Zero-Knowledge Proofs

● Enhanced Privacy

In user-to-user interfaces, ZKPs can enable users to preserve personal information as well as financial data when communicating with decentralized or permissioned applications.

● Trustless Verification

ZKPs avoid intermediaries, which is a massive benefit when dealing with decentralized finance (DeFi) and the automation of smart contracts.

● Scalability

ZKPs provide the possibility to scale blockchain networks without compromising decentralization through the compression of multiple transactions into a single verification.

● Interoperability

Trustless cross-chain bridges may be feasible with ZKPs, as they can prove that a state is changed or a transaction has happened on one chain and prove it on another.

Challenges and Limitations

• Computational Overhead: A complex circuit may require hours of run time and GPUs or ASICs, but specialized networks and hardware acceleration are narrowing that gap.
• Complexity in Development: The learning curve of writing circuits of ZKPs is steep. Even though developer experience is being enhanced by tools such as Circom, Noir, and Halo 2, they are yet to evolve into user-friendly standards.
• Trusted Setup Risks: Certain ZKP systems involve a trusted setup process. A compromised arrangement of this setup may endanger the security of the whole system. To reduce this, many new systems are experimenting with transparent or universal setups.
• Regulatory Ambiguity: Although ZKPs guarantee privacy, they may cause issues in highly compliance-focused industries. Regulators are yet to find a way to balance zero-knowledge systems and KYC/AML duties.
• Terminology Confusion: Not all “ZK rollups” provide privacy. Starknet’s proofs focus on computational integrity and are more accurately known as validity rollups.

Road Ahead

One of the greatest breakthroughs in the study of cryptography is zero-knowledge proofs. They allow for demonstrating that something is true without giving away any information, thus allowing digital interactions to be safer and more intimate. With the increasing growth in blockchain and AI technology, ZKPs are emerging as an important component of the future of the internet.

In addition to this, technologies such as DECO can move the data on ordinary websites into the smart contract without revealing the data, and zk-ML can validate an AI response without viewing the model itself. Despite the speed hurdles and uninformed guidelines, the zero-knowledge technology will provide users with more privacy, thereby aiding companies to comply with the laws and increase the apps that deal with large amounts of data.