In a world like ours where anything and everything is possible, verification of statements becomes crucial. Here, comes the concept of Zero-knowledge proofs (ZKPs). This cryptographic concept plays a crucial role in allowing one party (the prover) to prove to another party (the verifier) that a statement is true without revealing any information about the statement itself. Through this notion, privacy of addresses and security concerns are maintained at all times. So, what are ZKPs exactly and why are they important? Let’s find out in more detail.
Defining Zero-Knowledge Proofs
A zero-knowledge proof is a means of demonstrating the truth of a statement without disclosing the actual content of the statement itself. In this scenario, the “prover” is the entity attempting to validate a claim, while the “verifier” is responsible for confirming the accuracy of said claim.
The concept of zero-knowledge proofs was initially introduced in a 1985 paper titled “The knowledge complexity of interactive proof systems,” which established the definition that is widely accepted today:
A zero-knowledge protocol is a technique through which one party (referred to as the prover) can convince another party (known as the verifier) that a particular assertion is correct, all the while keeping secret any details beyond the fact that this specific statement holds true.
Over time, zero-knowledge proofs have advanced significantly and are now employed in various practical applications.
Key Concepts
When it comes to zero-knowledge proofs there are some concepts that play a crucial role. These are completeness and soundness. Let’s take a deeper look at these.
Completeness pertains to the prover’s ability to convincingly demonstrate knowledge of pertinent information with a high level of probable accuracy. To satisfy the soundness requirement, the verifier should be able to accurately determine whether the prover indeed possesses the information in question.
Crucially, for a proof to be genuinely zero-knowledge, both completeness and soundness must be achieved without any exchange of the actual information between the prover and verifier.
How Zero-Knowledge Proofs Work
Zero-knowledge proof works on three notions. These are Witness, Challenge and Response.
1. Witness
In the realm of zero-knowledge proofs, the “witness” serves as the private knowledge or information that the prover possesses and intends to prove without revealing its actual content. It’s akin to a hidden secret, such as a password, possession of a certain document, or knowledge of a specific fact. The strength of a zero-knowledge proof lies in the prover’s ability to demonstrate knowledge of this witness without exposing the witness itself. The witness is the cornerstone of the proof, allowing the prover to convince the verifier of their authenticity without disclosing sensitive details.
2. Challenge
The “challenge” is the pivotal element in the interaction between the prover and verifier during a zero-knowledge proof. It is generated by the verifier and presents a unique and unpredictable query based on the prover’s initial assertion and the information available up to that point. The challenge acts as a test, requiring the prover to provide a response that demonstrates their knowledge of the witness, thereby verifying the authenticity of their claim. Importantly, the challenge must be designed so that it doesn’t leak any information about the witness or the proof, ensuring that the zero-knowledge property is upheld.
3. Response
The “response” is the prover’s answer to the challenge presented by the verifier. It is carefully crafted to reveal only enough information to satisfy the verifier’s query without disclosing the underlying witness. The response is a cryptographic construct that demonstrates the prover’s possession of the relevant knowledge or secret without revealing the secret itself. It is the prover’s way of assuring the verifier that they are legitimate without divulging any confidential information. A well-structured response ensures that the zero-knowledge proof remains secure and private, upholding the fundamental principles of zero-knowledge cryptography.
Types of Zero-Knowledge Proofs:
Following are the various types of Zero-Knowledge Proofs and their characteristics.
1. Interactive Zero-Knowledge Proofs (IZKP):
- Characteristics:
- Two-Party System: An IZKP requires active participation from both the prover and the verifier during the proof protocol.
- Multiple Rounds: Often consists of a series of questions and answers (challenges and responses) between the prover and verifier.
- Trust Dependency: The verifier needs to be genuinely interactive and not collude with potential adversaries.
- Use Cases:
- Secure Authentication: IZKPs can be used to authenticate users in systems without revealing secret credentials.
- Privacy-Preserving Protocols: Useful in systems where two parties wish to compare data without revealing the actual data, e.g., comparing secret prices between bidders.
2. Non-Interactive Zero-Knowledge Proofs (NIZKP):
- Characteristics:
- One-Time Communication: Unlike IZKP, NIZKP allows the prover to send just one message to the verifier without the need for back-and-forth interactions.
- Random Oracle Model: NIZKPs often rely on a common reference string or a random oracle model to achieve the non-interactive property.
- Universally Verifiable: Once a NIZKP is produced, anyone can verify it, not just a single dedicated verifier.
- Use Cases:
- Blockchain and Cryptocurrencies: Many modern blockchain platforms employ NIZKPs to ensure transaction privacy while still retaining transparency, like Zcash with zk-SNARKs.
- Digital Signatures: NIZKPs can prove the validity of a digital signature without revealing the actual signature or the message it’s tied to.
Applications in the Real World
Zero-knowledge proof has a lot of real world applications. Here, we will explore these in a bit of detail.
- Anonymous Payments
Credit card transactions are often visible to multiple parties, compromising user privacy. Privacy coins like Zcash and Monero use zero-knowledge proofs to shield transaction details, ensuring privacy. Zero-knowledge technology allows nodes to validate transactions without accessing transaction data.
2. Identity Protection
Zero-knowledge proofs enhance decentralized identity systems by enabling individuals to validate their identity without revealing sensitive details. For example, proving citizenship without disclosing tax ID or passport information.
3. Authentication Simplification
Zero-knowledge proofs simplify authentication for online services. Users can present a ZK-proof generated from public and private inputs to authenticate without disclosing personal information, improving the user experience and reducing the need to store extensive user data.
4. Verifiable Computation
Verifiable computation uses zero-knowledge proofs to outsource computation while ensuring correctness. It speeds up blockchains like Ethereum without compromising security. Off-chain solutions, like zero-knowledge rollups, use validity proofs to process transactions efficiently.
5. Reducing Bribery and Collusion in On-chain Voting
Zero-knowledge proofs combat collusion in blockchain voting, such as quadratic funding mechanisms. MACI (Minimum Anti-Collusion Infrastructure) uses ZK-SNARK proofs to tally votes without revealing individual choices, reducing bribery’s effectiveness.
Conclusion
All in all, zero-knowledge proofs play a crucial role in enhancing privacy and security in the digital age. Its real world application is one of a kind and users are encouraged to explore it in more detail.