使用同态承诺方案的零知识多方交互证明
Zero-Knowledge MIPs using Homomorphic Commitment Schemes
AI总结：
本文利用特定多方承诺方案的同态性质，为子集和问题与3SAT构造了多项式时间零知识协议，在证明者无计算限制且可共享量子纠缠的条件下仍安全，并在轮数和计算量上优于其他实用量子安全零知识协议。
摘要：
零知识协议（ZKP）允许一方向另一方证明某个事实，而除了该事实的有效性之外不泄露任何额外知识。例如，它可以用于让客户向一台可能恶意的银行机器证明自己的身份，而不会泄露诸如个人识别码之类的隐私信息。这样，恶意银行机器在交互过程中获得的任何知识，之后都无法被用来危害客户的银行账户。许多零知识协议中的一个重要工具是比特承诺，它本质上是一种数字方式，让发送方将消息放入一个锁箱中，锁上它，然后发送给接收方。之后，密钥被发送给接收方，用于打开锁箱并读取消息。这样，消息在接收方收到密钥之前对其隐藏，而发送方在发送锁箱之后也无法改变主意。本文利用一种特定多方承诺方案的同态性质，允许接收方对承诺执行运算，从而为两个NP完全问题——子集和问题与3SAT——得到多项式时间的零知识协议。这些零知识协议在证明者没有任何计算限制的情况下是安全的，即使存在共享量子纠缠也是如此。在效率方面，子集和零知识协议与文献中其他实用的量子安全零知识协议相比具有竞争力，所需轮数更少，计算量也更少。
英文摘要：
A Zero-Knowledge Protocol (ZKP) allows one party to convince another party of a fact without disclosing any extra knowledge except the validity of the fact. For example, it could be used to allow a customer to prove their identity to a potentially malicious bank machine without giving away private information such as a personal identification number. This way, any knowledge gained by a malicious bank machine during an interaction cannot be used later to compromise the client's banking account. An important tool in many ZKPs is bit commitment, which is essentially a digital way for a sender to put a message in a lock-box, lock it, and send it to the receiver. Later, the key is sent for the receiver to open the lock box and read the message. This way, the message is hidden from the receiver until they receive the key, and the sender is unable to change their mind after sending the lock box. In this paper, the homomorphic properties of a particular multi-party commitment scheme are exploited to allow the receiver to perform operations on commitments, resulting in polynomial time ZKPs for two NP-Complete problems: the Subset Sum Problem and 3SAT. These ZKPs are secure with no computational restrictions on the provers, even with shared quantum entanglement. In terms of efficiency, the Subset Sum ZKP is competitive with other practical quantum-secure ZKPs in the literature, with less rounds required, and fewer computations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
