You tell your friend that you know the password to his phone but he doesn’t believe you and tells you to prove it to him. With other people around, you wish to preserve his privacy and decide not to reveal his password. How can you prove to him that you know the password? This is the perfect use case of the Zero-Knowledge Proof (ZPK), a cryptographic method in which one party can prove to another that their statement is true without revealing the information. In the growing digital age, where identity verification is essential for online authentication, ZKPs provide a crucial application for validity in blockchain cryptocurrencies. 

How does it work? 

The ZKP method involves two parties: a prover and a verifier. In the situation above, you are the prover and your friend would be the verifier. An example of ZKP for this situation would be your friend writing a secret message in his notes app. You, the prover, unlock the phone and relay the message’s contents, convincing your friend of your knowledge of his password. His password was never mentioned, yet you showed him you know it. 

Three Key Properties of a Zero-Knowledge Proof

• Zero-Knowledge: If the statement given by the prover is true, then the verifier can’t know anything else about the statement (zero-knowledge) other than it is true. 
• Completeness: Any truthful prover can prove to the verifier that their statement is true.
• Soundness: A dishonest prover shouldn’t be able to convince a verifier of their validity. 

Figure 1

Demonstrates a basic example of a communication channel used in a ZKP proof. (1) The prover sends a commitment, (2) the verifier provides algorithmic proof, and (3) the prover sends their solution. Finally, the verifier checks the solution to determine validity. 

Source: ResearchGate

ZKPs use in the Blockchain 

The use of ZKPs in the blockchain has been growing with demands for privacy. Blockchains for major cryptocurrencies are transparent, allowing anyone to view transaction details like sender, receiver, and amount, posing privacy concerns. ZKP helped users to prove their identity, without revealing private information, strengthening transaction security.

Key ZKP Technologies Used 

• zk-SNARKs (Succinct Non-Interactive Argument of Knowledge): zk-SNARKs allows for secure transactions, mainly used by Zcash, a privacy-focused cryptocurrency. It maintains validity using cryptographic proofs that verify the correctness of a transaction while shielding transaction details (e.g., sender, receiver, amount). Its succinct and non-interactive feature means smaller data and faster efficient transactions, allowing for scalability in platforms like the Aztec Network. 

• zk-STARKs (Scalable Transparent Arguments of Knowledge): While zk-STARKs are similar to zk-SNARKS, they are much more scalable and can handle larger computations allowing them to be more resistant to quantum attacks. This power allows for its use in Ethereum where it verifies thousands of transactions with a single proof, but is computationally expensive to generate. 

• Bulletproofs: This is a subcategory of Zero-Knowledge Proofs known as range proofs, where the prover shows the value lies in a certain range, without revealing the value itself. Similar to zk-SNARKS they are so small that if all Bitcoin transactions used Bulletproofs its UTXO set size would shrink from 160 GB to 17 GB. But their small size makes them more time-complex than other methods.

Figure 2

The time complexity of the three ZKP technologies in the different stages. 

Source: Ethereum Stack Exchange

The Evolution of Zero-Knowledge Proofs 

Foundational Research and Traction of ZKPs 

In their 1985 paper “The Knowledge Complexity of Interactive Proof Systems,” Shafi Goldwasser, Silvio Micali, and Charles Rackoff (cryptographic principles researchers at MIT) introduce the concept of Zero-Knowledge Proofs. While this theoretical idea proved compelling in cryptography, due to its interactive design, time complexity became a challenge with large data. To address these limitations, researchers explored concurrent zero-knowledge (CZK) to understand ZKP performance when run continuously and the redundancy of zero-knowledge systems with multiple providers. This grew its practicality for independent environments like the Internet. 

Innovation of ZKP variants 

In 2011 a significant breakthrough came with the introduction of the Extractable Collision Resistance (ECR) hash function used to make zk-SNARKs. This progress led to Pinocchio in 2013, one of the first practical systems of zkSNARKs, with a verification time of 10ms. Following this success in 2017, Bulletproofs was announced, gaining popularity for their efficiency and non-reliance on trusted protocols. Soon enough Eli Ben-Sasson, a top researcher in cryptographic proofs and co-founder of StarkWare, and his team introduced zk-STARKs which gained traction for its quantum attack resistance by using hash functions like SHA-256 rather than elliptical curves. 

Widespread Adoption of ZKP in Blockchain 

Zk-Rollups, a layer-2 scaling solution, emerged as the leading solution for scalability in the blockchain. Its ability to bundle multiple transactions into a single proof, reduced blockchain congestion by up to 90%. Ethereum processed over $1 billion in assets through zk-rollups and other major platforms have adopted zk-rollups, showing ZKPs practical usage.  Privacy-focused protocols like Zcash leveraged ZKPs for confidential transactions, and Ethereum’s upgrade (EIP-4844) is set to enhance the efficiency of zk-Rollups with lower fees and higher output. 

Conclusion

Zero-Knowledge Proofs has revolutionized the cryptography industry by enhancing privacy and efficiency. It has become a crucial component of the blockchain in securing transactions, scalability, and faster computation has led to it becoming widely used. ZKPs will likely go on to be adopted by more cryptocurrencies, with scaling decentralized networks, and decreasing transaction costs both financially and computationally. With its potential to create a future where privacy and transparency can coexist, ZKPs ensure a more open yet secure digital ecosystem for everyone. 

References

Binance. (2023, January 18). What Is Zero-knowledge Proof and How Does It Impact Blockchain? What Is Zero-knowledge Proof and How Does It Impact Blockchain? https://academy.binance.com/en/articles/what-is-zero-knowledge-proof-and-how-does-it-impact-blockchain

Bulletproofs: Short Proofs for Confidential Transactions and More. (2017). Bulletproofs. https://crypto.stanford.edu/bulletproofs/

Chainlink. (2024, July 29). What Is a Zero-Knowledge Proof? Zero-Knowledge Proof (ZKP) – Explained. https://chain.link/education/zero-knowledge-proof-zkp#:~:text=Bulletproofs%20are%20short%20non%2Dinteractive%20zero%2Dknowledge%20proofs%20that,these%20technologies%2C%20including%20StarkNet%2C%20ZKsync%2C%20and%20Loopring.

Daphne, T. (2022, December 21). Zero-knowledge proofs explained in 3 examples. Circularise. Retrieved January 3, 2025, from https://www.circularise.com/blogs/zero-knowledge-proofs-explained-in-3-examples

Jain, S. (2024, May 21). Zero Knowledge Proof. GeeksforGeeks. Retrieved January 3, 2025, from https://www.geeksforgeeks.org/zero-knowledge-proof/

Starks, A. (2024, January 23). History of the formation of ZKP. ZKPs (Zero Knowledge Proofs) gained… | by Emil Pepil. Medium. Retrieved January 6, 2025, from https://medium.com/@emilpepil/history-of-the-formation-of-zkp-151dd7001ffa