Zero-knowledge proofs (零知识证明)

Abstract

English

In cryptography, a zero-knowledge proof (ZKP) is a method by which one party (the prover) can prove to another party (the verifier) that a certain statement is true, without revealing any other information beyond the fact that the statement is true.

ZKPs are typically used in applications where it is important to verify the authenticity of information without revealing the information itself. For example, ZKPs can be used to verify the identity of a user without revealing their personal information, or to verify the validity of a document without revealing the contents of the document.

ZKPs work by using mathematical proofs that are designed to be both sound and zero-knowledge. A sound proof is one that is guaranteed to be correct, while a zero-knowledge proof is one that reveals no information beyond the fact that the proof is correct.

There are two main types of ZKPs: interactive and non-interactive. Interactive ZKPs require the prover and the verifier to engage in a back-and-forth dialogue in order to complete the proof. Non-interactive ZKPs, on the other hand, allow the prover to generate a proof that can be verified by the verifier without any further interaction.

ZKPs are a powerful cryptographic tool with a wide range of potential applications. They are still under development, but they have the potential to revolutionize the way we interact with information in the digital world.

Chinese

在密码学中，零知识证明（ZKP）是一种方法，其中一个方（证明者）可以向另一方（验证者）证明某一命题为真，而不透露任何其他信息之外的事实，即该命题为真。

ZKP通常用于应用程序，在这些应用程序中，验证信息的真实性很重要，而无需泄露信息本身。例如，ZKP可用于验证用户的身份而不泄露其个人信息，或验证文档的有效性而不泄露文档的内容。

ZKP的工作原理是使用设计为既健壮又零知识的数学证明。健壮的证明是保证正确的证明，而零知识证明是除了证明正确之外不泄露任何信息的证明。

ZKP有两种主要类型：交互式和非交互式。交互式ZKP要求证明者和验证者进行往返对话以完成证明。另一方面，非交互式ZKP允许证明者生成一个可以由验证者在没有进一步交互的情况下验证的证明。

ZKP是一种强大的密码学工具，具有广泛的潜在应用。它们仍在开发中，但它们有可能彻底改变我们在数字世界中与信息互动的方式。

Here are some specific examples of how ZKPs can be used:

• Identity verification: ZKPs can be used to verify the identity of a user without revealing their personal information. For example, a user could use a ZKP to prove their age to a website without revealing their date of birth.
• Document verification: ZKPs can be used to verify the validity of a document without revealing the contents of the document. For example, a user could use a ZKP to prove that they have a valid passport without revealing the passport number.
• Financial transactions: ZKPs can be used to verify the authenticity of financial transactions without revealing the details of the transaction. For example, a bank could use a ZKP to verify that a customer has sufficient funds to cover a transaction without revealing the customer's account balance.
• Voter verification: ZKPs can be used to verify that voters have voted correctly without revealing how they voted. This could help to prevent voter fraud and ensure that elections are fair and accurate.

ZKPs are a powerful tool that has the potential to revolutionize the way we interact with information in the digital world. They are still under development, but they are already being used in a variety of applications.

On the one hand

The Spy and the Secret Code

Jason was an intelligence agent tasked with an important mission - to infiltrate the enemy's research lab and photograph their new cryptographic algorithm. The algorithm was rumored to be uncrackable, and could be used to secure military communications.

After weeks of planning, Jason managed to break into the lab. He quickly snapped photos of the algorithm scribbled on the blackboards and encrypted it to send back to his agency. But suddenly, alarms blared and security guards rushed in, surrounding Jason.

The head of security, Komarov, interrogated Jason. "You claim you came here just to use the bathroom. But we both know you photographed something. Tell me, what did you see?" he demanded.

Jason paused, then said "I can prove I photographed the algorithm without revealing what it actually is. I'll just need a deck of cards."

Komarov, intrigued, handed Jason a deck. Jason demonstrated a complex series of steps, mixing up the deck in elaborate shuffles, occasionally showing Komarov certain cards.

After 5 minutes, Komarov was baffled. "All you've shown me is a series of random cards. But you say this proves you have a photo of the algorithm?"

"Yes," said Jason. "I've just performed a zero-knowledge proof. Through a clever interactive protocol, I've proven I have knowledge of something without revealing what that actual knowledge is. You'll just have to trust me."

Komarov paused, then laughed. "You are a clever spy. Very well, I will let you go just this once. But do not think we will fall for such a trick again!"

Jason smiled and briskly walked out, successfully completing his mission with his agency's new secret weapon - zero-knowledge proofs.