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What is Zero-Knowledge Proof — Detailed Explained

Updated 2023-07-27 12:09:24

Zero-knowledge proof is a fascinating concept in the field of cryptography that has gained significant attention for its potential to enhance security and privacy. In an increasingly digital world where data breaches and privacy concerns are prevalent, zero-knowledge proofs offer a powerful tool to address these challenges. This article aims to comprehensively understand the zero-knowledge proof, exploring its definition, applications, and significance in various domains.


In today's interconnected and data-driven society, protecting sensitive information while allowing for secure interactions is essential. Zero-knowledge proof offers an innovative approach to achieving this delicate balance. By enabling one party to prove knowledge of a statement to another party without revealing any additional information, zero-knowledge proofs have the potential to develop fields such as blockchain technology, authentication systems, and secure communications.


What is Zero-Knowledge Proof

Zero-knowledge proof is a mathematical protocol that allows one party to verify another party without revealing any information beyond the statement's validity


Zero-knowledge proof is a mathematical protocol that allows one party to persuade another party to verify the truth of a statement without revealing any more information beyond the statement's validity. In essence, zero-knowledge proofs enable the prover to establish knowledge of a given fact or claim without revealing how that knowledge was attained.


The Origin of Zero-Knowledge Proof

Shafi Goldwasser, Silvio Micali, and Charles Rackoff first proposed the concept of zero-knowledge proof in 1985. It was a game-changing innovation in cryptography, allowing information to be verified without revealing sensitive information. Since then, zero-knowledge proofs have grown in importance and have found various usages in various sectors, including blockchain technology, secure authentication systems, and secure computations.


The Importance of Zero-Knowledge Proof

Zero-knowledge proofs were a breakthrough in applied cryptography because they promised to improve information security for individuals. Consider how you might verify a claim to another party (for example, a service provider) (e.g., "I am a citizen of X country"). You must present "evidence" to support your claim, such as a national passport or driver's license.


However, there are drawbacks to this strategy, most notably a need for more privacy. Personally Identifiable Information (PII) exchanged with third-party online services is stored in central databases that can be hacked. With identity theft becoming a significant concern, there is a growing desire for new privacy-protecting methods of communicating sensitive information.


The Importance of Zero-knowledge proofs is that they can eliminate the requirement to provide information to verify the validity of claims. The zero-knowledge protocol takes the assertion (a 'witness') as input and concisely demonstrates its fact. This proof ensures a statement is true without revealing the information required to create it.


Returning to our previous example, zero-knowledge proof is the only proof you need to verify your citizenship claim. The verifier needs to examine if specific aspects of the proof are valid to be convinced that the underlying statement is true.


How does Zero-Knowledge Proof Work?

How does Zero-Knowledge Proof Work?


A zero-knowledge proof allows you to demonstrate the truth of a proposition without exposing its contents or how you got the fact. Zero-knowledge protocols rely on algorithms that take some data as input and produce 'true' or 'false' as output.


Requirement of Zero-Knowledge Protocol

A zero-knowledge protocol must meet the following requirements:



The zero-knowledge protocol always returns 'true' if the input is genuine. As a result, the evidence can be accepted if the underlying proposition is true and the prover and verifier act honestly.



It is theoretically impossible to deceive the zero-knowledge protocol into returning 'true' if the input is faulty. As a result, a deceptive prover cannot fool an honest verifier into believing an invalid statement is genuine (unless with a tiny margin of probability).




The verifier knows nothing about a statement other than its truth or falsity (they have "zero knowledge" about the assertion). This criterion also precludes the verifier from deducing the original input (the contents of the statement) from the proof.


3 Elements of Zero-Knowledge Proof

A zero-knowledge proof consists of a witness, challenge, and response.




The prover uses a zero-knowledge proof to demonstrate knowledge of some confidential information. The "witness" to the evidence is the secret information, and the prover's supposed knowledge of the witness produces a series of questions that can only be answered by a party who knows the information. Thus, the prover begins the proving process by selecting a question randomly, calculating the answer, and passing it to the verifier.




The verifier chooses another question randomly from the set and asks the prover to answer it.




The prover accepts the query, computes the answer, and returns it to the verifier. The response of the prover allows the verifier to determine whether the former truly has access to the witness. The verifier selects more questions to ask to ensure the prover isn't guessing unthinkingly and receiving the correct answers by chance. By repeating this exchange numerous times, the opportunity of the prover falsifying the witness's knowledge decreases considerably until the verifier is satisfied.


The structure of an 'interactive zero-knowledge proof' is described above. Witness, Challenge and Response are also part of Zero-Knowledge proof as described in the “3 Elements of Zero-Knowledge Proof”.Early zero-knowledge protocols used interactive proving, which needed back-and-forth communication between provers and verifiers to check the truth of a statement.


2 Types of Zero-Knowledge Proof

2 Types of Zero-Knowledge Proof


There are generally two types of Zero-Knowledge Proof. They are Interactive Zero-knowledge Proofs and Non-Interactive Zero-knowledge Proofs.


1) Interactive Zero-Knowledge Proofs

Interactive zero-knowledge proofs (ZKPs) need interaction between the prover and the verifier. The prover and verifier communicate back and forth, with the prover sending a sequence of messages to the verifier. Based on the previous statements, the verifier sends a challenge message to the prover, who answers similarly. This method is repeated until the verifier is sure the assertion is true.


ZKPs are more secure than non-interactive ones because the verifier may adapt its challenges to the prover's behavior, lowering the risk of a successful attack. The disadvantage is that they consume more time and need more computational resources.


Here are some interactive zero-knowledge proof algorithms:


Protocol of Schnorr -The Schnorr protocol is a zero-knowledge interactive proof that allows the prover to exhibit knowledge of a private key associated with a public key without showing the private key itself. This mechanism is employed in digital signatures, where the prover must demonstrate ownership of the private key without disclosing it to the verifier.


·Zcash Protocol - The Zcash protocol is an interactive zero-knowledge proof that allows users to prove the existence of a transaction without revealing the sender, receiver, or transaction amount. The Zcash cryptocurrency uses this protocol to ensure transaction privacy and anonymity.


2) Non-Interactive Zero Knowledge Proofs

Non-interactive zero-knowledge proofs (Non-interactive ZKPs) do not require the prover and verifier to interact. The prover constructs an explanation based on a statement and delivers it to the verifier, who validates it. The proof is generated by hashing the information and employing a cryptographic technique to produce evidence that can be confirmed using a public key.


Non-interactive ZKPs are faster and use fewer computational resources than interactive ZKPs. Still, they are less secure since the verifier cannot adapt its challenges to the behavior of the prover.


Here are a few instances of zero-knowledge proof algorithms that are not interactive:


The Fiat-Shamir Transformation - The Fiat-Shamir transform is a non-interactive zero-knowledge proof that allows the prover to demonstrate a witness's understanding of a statement without communicating with the verifier. This type of proof is commonly used in electronic voting systems when a voter wishes to demonstrate that their vote was successfully recorded without exposing their name.


Bulletproofs - Bulletproofs are non-interactive zero-knowledge proofs used in Bitcoin transactions to validate range proofs. A range proof proves that a hidden value falls inside a specific range. Bulletproofs are especially effective in settings with limited computational resources since they can create smaller proofs than other non-interactive protocols.


Sonic - Sonic is a non-interactive zero-knowledge proof technique used to validate computations on confidential data, such as those done by smart contracts in blockchain systems. It is well-known for its scalability and efficiency, making it appropriate for large-scale applications.


Groth16 - Groth16 is a non-interactive zero-knowledge proof technique often used in privacy-preserving applications such as anonymous credential systems and private Bitcoin transactions. It is famous for large-scale applications because of its excellent efficiency and security.


·Aurora - Aurora is a non-interactive zero-knowledge proof technique used to validate calculations on encrypted material. It is helpful when numerous parties need to execute computations on sensitive data without disclosing the data to one another.


Examples of Zero-Knowledge Proof

Examples of Zero-Knowledge Proof


Anonymous Payments

Zero-Knowledge proofs are used to hide cryptocurrency transactions and enusre the privacy. Payments made with credit cards are frequently visible to several parties, including the payment provider, banks, and other interested parties (for example, government authorities). While financial surveillance might help detect unlawful activities, it also violates the privacy of ordinary persons.


Anonymizing transactions on public blockchains are also using zero-knowledge proofs. Tornado Cash, a decentralized, non-custodial service that allows users to conduct private transactions on Ethereum, is one example. Tornado Cash employs zero-knowledge proofs to conceal transaction details and ensure financial privacy.


Identity Protection

Personal information is in danger with current identity management systems. Individuals can use zero-knowledge proofs to confirm their identities while protecting sensitive data.


In the context of decentralized identification, zero-knowledge proofs are especially useful. Decentralized identification (also known as self-sovereign identity') allows individuals to manage access to personal identifiers. Proving your citizenship without disclosing your tax ID or passport information is an excellent example of zero-knowledge proof technology supporting decentralized identity.



Using online services necessitates establishing your identity and authorization to use those sites. This frequently necessitates providing personal information such as names, email addresses, birth dates, etc. You may also need to memorize long passwords to retain access.


However, zero-knowledge proofs can make authentication easier for both platforms and users. Once a ZK-proof has been constructed utilizing public inputs (such as data attesting to the user's platform membership) and private inputs (such as the user's details), the user may submit it to authenticate their identity while accessing the service. This improves the user experience and relieves enterprises of the need to keep massive volumes of user data.


Verifiable Computation

Another application of zero-knowledge proof technology for improving blockchain architectures is verifiable computation. Verifiable computing allows us to delegate computation to another entity while ensuring verifiable results. The entity submits the outcome and verifies that the program was correctly performed.


Verifiable computation is crucial for increasing blockchain processing speeds while maintaining security. Understanding this involves understanding the differences between the suggested scaling solutions for Ethereum. On-chain scaling options, such as sharding, necessitate significant changes to the blockchain's foundation layer. However, this approach is highly sophisticated, and implementation flaws can jeopardize Ethereum's security model.


Off-chain scaling solutions do not necessitate a change of the Ethereum protocol. Instead, they rely on an outsourced computing approach to boost throughput on Ethereum's foundation layer.


Verifiable computation comes into play here. When a node executes a transaction outside of Ethereum, it submits a zero-knowledge proof to validate its validity. This evidence (known as validity proof) ensures that a transaction is genuine, allowing Ethereum to apply the outcome to its state without waiting for anyone to contest it.


Validiums and zero-knowledge rollups are off-chain scaling techniques that leverage validity proofs to achieve secure scalability. These protocols execute thousands of transactions off-chain and provide evidence to Ethereum for verification. Once the proof system is verified, those results can be implemented instantly, allowing Ethereum to handle more transactions without increasing computation on the foundation layer.


Reducing Bribery and Collusion in on-chain voting.

Blockchain voting methods have numerous advantages: they are fully auditable, safe against attacks, immune to censorship, and not limited by geography. However, even on-chain voting techniques are vulnerable to collusion.


Collusion, defined as "coordinating to limit open competition by deceiving, defrauding, and misleading others," can be a malicious actor influencing voting with bribes. For example, Alice may be bribed by Bob to vote for option B on a ballot even though she favors option A.


Bribery and conspiracy restrict the effectiveness of any process that uses voting as a signaling mechanism (particularly when users can demonstrate how they voted). This can have profound effects, primarily when votes allocate scarce resources.


Quadratic funding techniques, for example, rely on donations to gauge preference for specific options among several public good projects. Each donation counts as a "vote" for a particular project, and projects with the most votes receive more funding from the matching pool.


Using on-chain voting exposes quadratic funding to collusion: because blockchain transactions are public, bribers can examine a bribee's on-chain behavior to discover how they "voted." Quadratic funding thus ceases to be an effective method of allocating cash based on the community's aggregated preferences.


Fortunately, emerging methods like MACI (Minimum Anti-Collusion Infrastructure) use zero-knowledge proofs to make on-chain voting (for example, quadratic funding mechanisms) immune to bribery and conspiracy. MACI is a collection of smart contracts and scripts that enable a central administrator (a "coordinator") to aggregate votes and tally outcomes without disclosing how each participant voted. Even so, it is still possible to establish that the votes were correctly counted or that a particular individual participated in the voting phase.


Projects that use Zero-Knowledge Proof

Projects that use Zero-Knowledge Proof


1) zkSync

ZKs have overcome scalability issues, although their process is still highly debated. For example, most validators are unable to validate the total transaction volume. As a result, the issue of censorship, DD-o-S, and centralization becomes more pressing.


A new method of validating transactions will be made feasible by Zk Sync. There will be validators and guardians, with validators assigned the duty of batching transactions and submitting security bonds that are always more than the TXs they validate. It secures the transactions in this way. At the same time, to ensure that validators do not go rogue and take control of the network, the guardians, who are majority token holders, select validators at random.


These guardians are not required to execute the computation on high-end computing systems. They can opt to control a portion of the network with a simple laptop, making the validation process totally decentralized because of the lack of an access barrier. Furthermore, they are not eligible for slashing. Thus more people will join to completely decentralize the ecosystem. That's how ZK Syncs work to give the main chains genuine decentralization, security, and scalability.


2) Starknet

Composability with the Ethereum chain is a significant challenge that has obstructed ZK technology's adoption in corporate operations. Because of its decentralization, security, and hack-proof track record, most businesses have placed their trust in the Ethereum Network. They do, however, have a concern about putting their activities on the main chain. StarkNet, a general-purpose ZKP, enables speedier dApp deployment on its ecosystem. StarkNet promotes computation integrity through the use of level 2 cryptographic proofs and current Algebra.


Furthermore, StarkNet offers the same level of composability as Ethereum, allowing developers to accelerate the development process and create complex solutions as needed. StarkNet also provides true anonymity by not allowing the user's identity to be deduced from public keys and supporting multi-calls or many transactions in a single call to settle the accounts. As a result, the flow of data from the off-chain computing layer to the main parent chain, Ethereum, is considerably reduced.


3) Miden

Miden, established in 2021, is already generating news. Miden, as a STARK-based ZKP, intends to provide 1,000 to 2,000 TPS, which will increase to 20,000 TPS once Ethereum sharding becomes online.


Polygon Miden is based on the Miden Virtual Machine, which can run any software. Miden VM has been specifically designed for STARKs, allowing for rapid proof creation on commodity hardware and significantly quicker with GPUs and/or FPGAs. It is also intended to hide all cryptographic complexities of ZK proofs and adheres to a set of architectural principles that most developers will recognize (e.g., stack machine, read-write memory, normal 32-bit integers).


Miden VM is designed with safety as one of its guiding principles. The goal is to greatly simplify the static analysis of smart contracts and to prevent many types of problems from occurring at the VM level, for example, by disabling various hazardous capabilities available on the EVM. Miden attempts to be Ethereum-compatible at the Solidity level, despite not emulating EVM one-to-one. Thus, developers will be able to use Miden to deploy the vast majority of Solidity smart contracts without making any changes. Miden will support compilation from other secure and blockchain-centric languages, such as Move and Sway, in addition to first-class Solidity compatibility.


4) Loopring

Loopring has been significant in simplifying cryptocurrency trading by providing traders with a completely non-custodial and extremely anonymous setup. The project also intends to leverage ZKP to address the issues of liquidity, scalability, and user experience. Loopring is offering a hybrid model of ZKP in its operational mode in order to scale DEX or Decentralized Exchanges. Order messaging will be handled off-chain in the Loopring Hybrid ZKP model, while settlement will take place on-chain in real-time with no delays.


The ZKP will be used by Loopring to take information to the mainchain by the prover that they have done some complex calculations. The Merkle trees will display the entire transaction history, and a smart contract will examine it to deliver real-time data sets to the mainchain for transaction recording.


Loopring seeks to completely change trading through DEX by implementing an ordering mechanism that is fast, efficient, affordable, and completely non-custodial in nature. In addition, Loopring proposes standalone exchange contracts that will make transactions totally hidden, providing users with enough privacy; therefore, allowing different DEXes to interact utilizing the ZKP model to communicate information and conduct trades. They can do so by using the same exchange contract, which will increase liquidity and speed up settlements as needed to scale decentralized exchanges.


Advantages of Zero-Knowledge Proof

3 Advantages of Zero-Knowledge Proof


Zero-knowledge proofs (ZKPs) have a number of benefits for privacy and cryptography. Here are a few significant benefits:


Privacy and Security

One of the fundamental benefits of ZKPs is their ability to maintain privacy. A prover can use a zero-knowledge proof to demonstrate the truth of a proposition without revealing any underlying information or sensitive data. This enables privacy preserving transactions and interactions in which proof of accuracy is obtained without disclosing personal information or creating transparent transaction.


By offering mathematical and cryptographic assurances, ZKPs improve trust and security. They enable verifiers to confirm a statement's veracity without relying on possibly untrustworthy or compromised sources. This is especially important when validating the integrity of complex computations or when confidence between parties is restricted.


Efficiency and Scalability

There have been substantial improvements in the effectiveness and scalability of zero-knowledge proofs. ZKPs can be implemented with lower computational and resource requirements with the development of new protocols and optimizations. This makes it possible for them to be used in more applications, such as decentralized systems and public blockchain networks.


Data Minimization

The quantity of information that needs to be disclosed between parties is reduced via zero-knowledge proofs. The risk of data breaches or leaks is decreased because only the confirmation of correctness is needed, allowing unneeded information to be kept hidden.


Disadvantages of Zero-Knowledge Proof

3 Disadvantages of Zero-Knowledge Proof


While zero-knowledge proofs (ZKPs) have many benefits, there are a few drawbacks and things to keep in mind. Some of the main drawbacks of zero-knowledge proofs are listed below:


Computation Complexity

Complex mathematical calculations and cryptographic processes are frequently needed for zero-knowledge proofs. The computational overhead can be significant, resulting in longer processing times and more resource usage. As a result, taking ZKPs into use and verifying them might be computationally demanding, which might make them less useful in some situations.


Trusted Setup

Some zero-knowledge-proof technology require a trusted setup step, which generates a set of initial settings. This provides a possible risk, as a compromise or malicious conduct during the setup process could risk the entire system's security and privacy guarantees. Maintaining a secure and trustworthy environment can be difficult and requires careful management and transparency.


Leaking Wrong Data

Even if a zero-knowledge proof does not reveal the actual data, it might nonetheless leak some information or provide statistical insights that can be utilized to generalize sensitive details in some instances. Adversaries with sufficient expertise and resources may be able to extract partial or indirect information from the proofs, thereby endangering privacy.



Zero-knowledge proofs (ZKPs) have emerged as a game-changing cryptographic tool with the potential to transform privacy, security, and trust across multiple domains. Despite their computational complexity and implementation hurdles, ZKPs provide considerable benefits in terms of data minimization, privacy protection, confidentiality, trust, and efficiency.


ZKPs let individuals and companies protect their data and maintain privacy in an increasingly linked and data-driven world by allowing the verification of statements without revealing sensitive information. ZKPs' computational overhead and trusted setup requirements are obstacles that must be properly managed, although current research and development initiatives are addressing these limits.


Overall, zero-knowledge proofs have enormous promise for addressing privacy problems, improving security, and developing trust in a wide range of applications. As technology advances and our understanding of ZKPs grows, they will play a critical role in altering how sensitive information is handled, protecting privacy rights, and encouraging innovation in the digital realm.