Non-interactive Zero-Knowledge Proofs

社会日益数字化和互联化。在建设未来社会时，考虑安全是很重要的；我们需要防范犯罪组织、敌对国家和其他类型的对手，他们可能使用诸如窃听和窃听、黑客攻击、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：可验证性和隐私性。例如，考虑一个协议，通过该协议，互联网银行客户可以访问其帐户。一方面，网上银行想要验证它正在与客户交谈，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，当我们需要验证某人是否正确地遵循特定协议时，可验证性和隐私问题就会出现，但是这个人或实体有一些不能透露的秘密。这个提议涉及到密码学领域中被称为零知识证明的技术，它同时提供验证和隐私。零知识证明允许一方在不泄露任何其他信息的情况下使另一方相信某一陈述是正确的。例如，网上银行的客户可以说服银行，她应该访问自己的账户，甚至不需要在互联网上发送密码或任何其他私人信息。或者在更一般的例子中，与我们互动的人可以说服我们他们在不泄露私人信息的情况下遵守协议。零知识证明既可以是交互式的，也可以是非交互式的。在标准的零知识证明中，双方来回交换消息，而非交互式的零知识证明由从一方发送到另一方的单个消息组成。这种区别很重要，因为有许多非交互式任务的例子，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。在这个研究项目中，我们打算提高非交互式零知识证明的技术水平。我们将构建更高效的非交互式零知识证明。我们将构建具有额外高级安全属性的非交互式零知识证明。我们的建设要建立在尽可能健全的安全假设基础上。我们将把它们的适用范围扩展到更多不同的设置，而不是目前已知的如何处理。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.