Non-interactive Zero-Knowledge Proofs

社会正变得越来越数字化和互联互通。在建设未来社会时，重要的是要考虑安全问题；我们需要针对犯罪组织、敌对国家和其他类型的对手的保护，这些对手可能使用窃听和窃听、黑客攻击、试图冒充等技术。简而言之，我们需要安全协议。在设计双方或多方之间的安全协议时，经常会出现两个重要问题：可验证性和隐私。例如，考虑一种协议，网上银行客户通过该协议访问她的帐户。一方面，互联网银行想要验证它是否正在与客户交谈，另一方面，客户希望她的密码保持隐私。作为一个更一般的例子，每当我们需要验证某人是否正确地遵守了特定协议，但该人或实体有一些不能透露的秘密时，就会出现可验证性和隐私问题。这项建议涉及密码学领域的技术，称为零知识证明，它同时提供验证和隐私。零知识证据允许一方在不泄露任何其他信息的情况下说服另一方相信某一陈述是真实的。例如，网上银行客户可以说服银行，她应该在甚至不通过互联网发送密码或任何其他私人信息的情况下访问她的帐户。或者在更一般的例子中，与我们交互的人可以说服我们，他们遵守了协议，而不会泄露他们的私人信息。零知识证明可以是交互的，也可以是非交互的。双方在标准的零知识证明中来回交换消息，而非交互的零知识证明由一方向另一方发送的单一消息组成。这一区别很重要，因为有许多非交互任务的例子，其中只有一方行动。例如，我们可以在不与其他各方交互的情况下对文档进行数字签名。非交互式零知识证明可用于此类非交互式任务。在本研究项目中，我们打算改进非交互式零知识证明的研究现状。我们将构造更高效的非交互零知识证明。我们将构造具有附加高级安全性质的非交互零知识证明。我们将把我们的建设建立在尽可能合理的安全假设之上。我们将把它们的适用范围扩展到比目前已知如何处理的环境更多和不同的环境。除了这些改进之外，我们还将通过具体应用来展示所取得的进步。

Society is becoming increasingly digitalized and interconnected. When building the future society it is important to think about security; we need protection against criminal organizations, hostile nations and other types of adversaries that may use techniques such as eavesdropping and wiretapping, hacking, attempts of impersonation, etc. In short, we need secure protocols.Two important issues frequently come up when designing secure protocols between two or more parties: verifiability and privacy. As an example, consider a protocol by which an internet bank customer gains access to her account. On one hand the internet bank wants to verify that it is talking to its customer, on the other hand the customer wants her password to remain private. As a more general example, verifiability and privacy issues come up whenever we need to verify that somebody is following a particular protocol correctly, yet that person or entity has some secrets that cannot be revealed.This proposal relates to techniques in the field of cryptography known as zero-knowledge proofs, which simultaneously provide verification and privacy. A zero-knowledge proof allows one party to convince another party that a certain statement is true without leaking any other information. The internet bank customer can for instance convince the bank that she should get access to her account without even sending a password or any other private information over the internet. Or in the more general example, somebody we are interacting with can convince us that they are following the protocol without divulging their private information.Zero-knowledge proofs can be both interactive and non-interactive. Whereas the two parties exchange messages back and forth in standard zero-knowledge proofs, a non-interactive zero-knowledge proof consists of a single message that is sent from one party to the other. This distinction is important since there are many examples of non-interactive tasks, where only one party acts. For instance, we can make a digital signature on a document without interacting with other parties. Non-interactive zero-knowledge proofs can be used in connection with such non-interactive tasks.In this research project we intend to improve state of the art in non-interactive zero-knowledge proofs. We will construct more efficient non-interactive zero-knowledge proofs. We will construct non-interactive zero-knowledge proofs with additional advanced security properties. We will base our constructions on as sound security assumptions as possible. We will extend their range of applicability to more and different settings than are currently known how to handle. In addition to these improvements, we will also demonstrate the advances made by giving concrete applications.