Zero-knowledge proofs, explained

What are zero-knowledge proofs?

Zero-knowledge proofs (ZKPs) are an innovative cryptographic method that enables a party (the prover) to validate a claim to another (the verifier) without disclosing any detailed information about the claim itself. 

When the subject of a contract or transaction involves highly sensitive or confidential data, ZKPs ensure safe and private transactions while securing the subject matter of the transaction throughout the validation process by leveraging rigorous mathematical frameworks.

Fundamentally, ZKPs address an important problem: How can someone prove the possession of a statement, without revealing it? Revealing the substance of a transaction is the easy part, but what if the truth underlying the transaction could be safeguarded while demonstrating the impossibility of deception? 

ZKPs are best explained with the red card proof: If James wants to prove to Vincent that he has drawn a red card from a standard card deck, all he has to do is take the remaining 51 cards from the deck and systematically show Vincent all 26 black cards, which would enable Vincent to conclude that James indeed has a red card, while gaining no information on whether the held card is an ace of hearts or a three of diamonds!

ZKPs offer a safe and secure medium to conclude transactions, with their versatile nature extending their relevance and application to a range of fields from identity verification to user access controls.

The versatility of ZKPs has extended their relevance beyond traditional cryptographic applications into fields such as identity verification, secure voting and access control. 

In these use cases, zero-knowledge proofs eliminate the need to disclose private information while ensuring that only authorized individuals or entities access sensitive systems or data. 

For instance, a voter could authenticate their eligibility in an election without revealing personal details such as their address or voting history. Similarly, enterprises can implement ZKPs to streamline compliance with regulatory frameworks, verifying adherence to requirements without exposing proprietary or confidential records.

Did you know? The first theoretical articulation of ZKPs was published in an academic paper as early as 1985, when academics Shafi Goldwasser, Silvio Micali, and Charles Rackoff published their seminal paper, “The Knowledge Complexity of Interactive Proof-Systems.”

How ZKPs work in practice

In practical applications, ZKPs support scenarios involving the exchange of sensitive information, such as passwords or private keys. 

Leveraging ZKPs, sensitive information can be validated without being exposed to the risk of misuse in the wrong hands. For instance, a user could prove their ownership of a digital asset without revealing the asset’s identifier or related transaction details, and a voter could safely cast their ballot without revealing their identity. 

ZKPs use advanced mathematical constructs, such as polynomial commitments, elliptic curve cryptography or hash functions to demonstrate the continued validity of the three central properties that rationalize their existence: 

• Completeness 
• Soundness
• Zero-knowledge

Two types of ZKPs accomplish the above in different ways:

• Interactive ZKPs achieve this through a back-and-forth exchange between the prover and verifier, involving multiple steps and challenges to evidence truthfulness and removing the possibility of deception. 
• Non-interactive ZKPs simplify this process by enabling the prover to present a single proof that can be independently verified without active interaction from the verifier.

Here’s an X post that sets out the difference between the two methods:

Why ZKPs matter for cryptocurrency and CBDCs

ZKPs play a pivotal role in cryptocurrency, given the fundamental nature of public ledgers where all underlying transaction details, such as sender and recipient information or transaction amounts, are visible and verifiable. While this level of transparency shows trust and accountability, it does not allay concerns about privacy and confidentiality, which ZKPs provide.

ZKPs offer solutions to critical privacy and security challenges in cryptocurrencies and central bank digital currencies (CBDCs). The assurance provided by ZKPs concerning the privacy, security and trustworthiness of a transaction neatly supplements the trust and accountability of public ledgers such as Bitcoin, which can make all the difference to adoption at scale.

For CBDCs, adopting ZKPs is particularly useful, given that it strikes an optimal balance between regulatory oversight and individual privacy. Governments can utilize zero-knowledge proofs to ensure compliance with financial regulations while safeguarding user data against unauthorised access or misuse, creating a more secure and trusted monetary ecosystem.

Projects like Zcash and Aztec Protocol on Ethereum use ZKPs to enable private transactions, while StarkNet is advancing scalable, privacy-enhanced smart contract platforms using ZK-rollups. 

In the CBDC space, projects like Sweden’s e-krona and the European Central Bank’s digital euro have explored the theoretical use of ZKPs to balance privacy with regulatory compliance. While promising, no real-world CBDC has yet implemented ZKPs at scale, and their use remains largely experimental.

How Zcash uses ZKP to hide transaction details

Zcash, a privacy-focused cryptocurrency, uses a ZKP variant called zk-SNARKs (Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge). 

Zk-SNARKs represent cryptographic proofs that allow Zcash users to verify the validity of transactions on the blockchain without disclosing sensitive details such as the sender, recipient or transaction amount, ensuring complete confidentiality while simultaneously maintaining the integrity of the blockchain network.

Within the Zcash ecosystem, users can choose between two types of transactions: transparent and shielded. Transparent transactions operate like Bitcoin (BTC), with all associated transaction information being publicly available. 

On the other hand, shielded transactions use zk-SNARKs to obfuscate transaction details, offering enhanced privacy and security. By prioritizing user choice and privacy, Zcash has established itself as a leader in privacy-centric cryptocurrency solutions, demonstrating the real-world potential of zero-knowledge proofs.

Did you know? Zcash was built on the original Bitcoin codebase, which means it shares many similarities to the world’s largest cryptocurrency, including the fact that it has a fixed total supply of 21 million coins globally.

Benefits of ZKPs

ZKPs provide a diverse array of benefits, with wide-ranging applicability and implications across multiple fields and industries. 

Some of the key benefits of ZKPs are:

• Privacy protection: ZKPs empower users to verify truths without revealing them, ensuring robust privacy measures across digital systems.
• Regulatory compliance: ZKPs allow organizations to achieve regulatory compliance while maintaining confidentiality of their data, striking an aspirational balance between transparency and privacy.
• Enhanced security: By minimizing the exposure of sensitive data to the outside world, ZKPs reduce vulnerabilities of data breaches and hacking.
• Scalability: Non-interactive ZKPs are computationally efficient, making them well-suited for large-scale systems like CBDCs and global blockchain networks.
• Trust and transparency: ZKPs drive trust in digital interactions by cryptographically verifying truths, eliminating the need for blind trust in intermediaries or third parties.

Limitations of ZKPs

While significantly advantageous, ZKPs face certain challenges and limitations that hinder their widespread adoption and implementation.

The key drawbacks of ZKPs include:

• Complexity of implementation: Designing and deploying ZKP protocols demands exceptional technical expertise in cryptography and mathematics, which is currently the preserve of a limited set of highly specialist individuals, making adoption a challenge for smaller organizations.
• Computational overhead: Interactive ZKP implementations can be resource-intensive, requiring significant computational power for validation and processing.
• Trusted setups: Non-interactive ZKP often relies on trusted setups or reference strings, which, if compromised, can undermine the security of the entire network.

The future of ZKPs in digital finance

ZKPs are ushering in a new era of privacy and security in digital interactions, offering transformative capabilities that address critical challenges in cryptocurrencies, CBDCs and digital finance that require privacy-preserving solutions. 

Research in cryptographic optimizations and zero-trust setups is aimed at addressing existing challenges, reducing computational costs and enhancing security. These advancements will likely drive the broader adoption of ZKPs across industries like healthcare, voting systems, identity management and, most importantly, blockchain and digital finance.

An emerging development is the implementation of ZK-rollups, which bundle multiple transactions into a single batch and verify them using ZKPs. This innovation significantly improves the scalability of blockchain networks by reducing transaction costs and increasing throughput. 

In this evolving landscape, ZKPs stand as a beacon of privacy, enabling secure and transparent systems that prioritize trust and confidentiality. As ZKP technology matures, its applications will extend far beyond cryptocurrencies and digital finance, transforming how one approaches trust, privacy and security in the digital age. The continued evolution of ZKPs holds the promise of a future where privacy-enhanced solutions are integral to secure and reliable systems across sectors.