Zero-Knowledge Proofs: Everything to Know

By  Beluga Research August 17, 2023

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  • Cryptocurrency Zero-Knowledge proofs allow verifiable transactions without revealing sensitive information
  • Zero-Knowledge proofs were introduced in the 1980s and have since found practical applications in cryptography, blockchain and privacy-preserving systems
  • A zk-SNARK is a popular Zero-Knowledge proof that allows one party to prove a statement's truth without revealing additional information
  • Zero-Knowledge proofs offer privacy protection, enhanced security, scalability improvements and interoperability


Cryptocurrency Zero-Knowledge proofs allow verifiable transactions without revealing sensitive information. Zero-Knowledge proofs provide an elegant solution to the problem of verifying the truth of a statement without disclosing any sensitive information. In a Zero-Knowledge proof, the prover aims to convince the verifier that a given statement is true, without revealing any additional knowledge beyond the validity of that statement. This unique property allows for the verification of claims while maintaining privacy.

A Brief History

The concept of Zero-Knowledge proofs was introduced in the 1980s by researchers Shafi Goldwasser, Silvio Micali and Charles Rackoff, and this breakthrough work laid the foundation for the theoretical framework of Zero-Knowledge proofs. Since then, numerous advancements have been made, and Zero-Knowledge proofs have found practical applications in various fields, including cryptography, blockchain technology and privacy-preserving systems.

Zero-Knowledge Proofs: Everything to Know

Zero-Knowledge proofs rely on complex mathematical algorithms and cryptographic protocols to achieve goals. One widely-used type of Zero-Knowledge proof is the "Zero-Knowledge Succinct Non-Interactive Argument of Knowledge" (zk-SNARK). A zk-SNARK allows one party, the prover, to convince another party, the verifier, that a statement is true without revealing any additional information.

To understand how zk-SNARKs work, here is an example: Betty wants to prove to Aaron that she knows the solution to a mathematical problem without revealing the solution itself. In this scenario, Betty can use a zk-SNARK to generate a proof, which consists of a succinct cryptographic representation of her knowledge. Aaron can then verify the proof using a verification algorithm without gaining any insight into Betty's solution. In other words, Betty is proving her knowledge of how to solve the equation without exposing the actual solution.

The underlying mathematics behind zk-SNARKs involves elliptic curve cryptography, pairing-based cryptography and other advanced mathematical constructs. These techniques enable the prover to create a proof that can be efficiently verified by the verifier, ensuring both efficiency and security.

Zero-Knowledge proofs have gained significant attention within the cryptocurrency space due to the potential to address critical challenges such as transaction privacy and scalability. In blockchain networks like Zcash, Zero-Knowledge proofs are used to provide shielded transactions wherein the sender, receiver and transaction amount remain hidden from the public. This enhances privacy and confidentiality, offering users a higher level of control over financial information.

Getting Started

To understand Zero-Knowledge proofs, it is first essential to grasp the concept of proof without revealing. For example, perhaps Betty has a secret message, and she wants to prove to Aaron that she knows the content of that message without actually disclosing it. Zero-Knowledge proofs enable this type of verification.

At the core, Zero-Knowledge proofs allow one party, known as the "prover," to convince another party, called the "verifier," that a particular statement is true without revealing any additional information. The key idea is that the verifier can be confident in the validity of the statement without gaining any knowledge about the underlying data.

Unique Aspects

Zero-Knowledge proofs possess several unique aspects that make them valuable in the field of cryptocurrencies. One important characteristic is the ability to enhance privacy. By utilizing Zero-Knowledge proofs, users can prove ownership or knowledge of certain information without disclosing sensitive data. This property is particularly valuable in blockchain systems, where privacy is a critical concern.

Another notable aspect is the concept of verifiability. Zero-Knowledge proofs allow anyone to verify the validity of a statement without having to trust the prover. This feature is crucial in decentralized systems such as cryptocurrencies, where trust in a central authority is minimized or eliminated altogether.

Zero-Knowledge proofs also offer scalability benefits. In certain scenarios, proving a statement directly may require computationally intensive calculations or a large amount of data transmission. However, by utilizing Zero-Knowledge proofs, the prover can generate a succinct proof that can be efficiently verified. This scalability advantage is especially relevant in blockchain networks, where computational resources are limited.

Furthermore, Zero-Knowledge proofs can be used to ensure fairness in certain interactions. For example, in a two-party computation scenario in which two parties want to perform a joint computation on their private data, Zero-Knowledge proofs enable them to verify that the computation was carried out correctly without revealing inputs. This property ensures fairness and mitigates the risk of cheating.


  • Privacy Protection - Zero-Knowledge proofs allow users to prove the validity of a statement without revealing any sensitive information. This is particularly useful in cryptocurrencies where users can prove ownership of certain assets or the correctness of a transaction without disclosing account balances or transaction details.
  • Enhanced Security - Zero-Knowledge proofs can strengthen the security of cryptographic protocols. By using Zero-Knowledge proofs, users can verify the validity of information without the need for trust in a third party. This reduces the risk of data breaches, hacks or manipulation by malicious actors.
  • Scalability Improvements - Zero-Knowledge proofs can significantly enhance the scalability of blockchain networks. Through techniques like zk-SNARKs, complex computations can be compressed into concise proofs, reducing the computational and storage requirements. This enables faster transaction processing and lowers the burden on network participants.
  • Interoperability - Zero-Knowledge proofs can facilitate interoperability between different blockchain networks. By using Zero-Knowledge proofs, it becomes possible to verify the correctness of transactions or state transitions across multiple blockchains without revealing the underlying data. This opens up opportunities for cross-chain transactions and collaborations between different blockchain ecosystems.


  • Complexity - Implementing and understanding Zero-Knowledge proofs can be challenging. The underlying cryptographic concepts and mathematical algorithms can be complex, requiring specialized knowledge and expertise. This complexity can hinder the adoption and development of applications that utilize Zero-Knowledge proofs.
  • Computational Overhead - Zero-Knowledge proofs often require significant computational resources to generate and verify. The computational overhead can be a barrier to real-time or resource-constrained environments. However, ongoing research and advancements in Zero-Knowledge proof techniques aim to reduce this computational burden.
  • Trusted Setup - Some Zero-Knowledge proof systems require a trusted setup process, which involves generating initial parameters or keys. If this setup process is compromised or manipulated, it could undermine the security and privacy guarantees of the Zero-Knowledge proof system. Developing and executing a secure trusted setup can be a complex and delicate procedure.
  • Public Auditability - Zero-Knowledge proofs, by nature, hide information from verifiers. While this provides privacy benefits, it can also hinder public auditability. In certain cases, regulatory or compliance requirements may demand transparency and the ability to audit the underlying data. Striking a balance between privacy and auditability can be a challenge.