Quantum-safe Cryptographic protocols

虽然量子计算机的物理实现似乎仍然遥不可及，但这种实现的前景对密码学世界来说是如此深刻，以至于已经值得考虑的是，在建造量子计算机后，这门科学将变成什么样子。对量子安全(又名后量子)密码工具和协议的研究源于这样一种信念，即我们必须从现在开始为未来做准备。**量子安全不经意传输和完全同态Encryption**********************************************************In经典世界过去有非常通用的技术来从各种密码学假设实现不经意传输。在量子安全的密码学世界里，我们没有这样的东西：已经提出了几种技术来获得量子安全的不经意传输，但还没有出现通用的技术。寻找这样一种普遍的方法将是我们研究的目标之一。我们还将考虑在有错误学习假设或近似整数GCD假设下实现的完全同态加密的不经意传输与相关任务之间的关系。我们想要证明，在量子世界中，OT本质上比FHE更容易实现。*交互散列和统计零知识Arguments*****************************************************Another的具体目标是研究一种强大的工具来构造安全协议，称为交互散列。这一工具在经典的信息理论和计算框架中都被使用过。目前，涉及交互散列的协议的安全性证明在量子环境下都不是有效的。我们将开发新技术来建立量子世界的安全证明。我们希望得到与经典世界相同的结果：在量子单向函数存在的唯一假设下，可以为NP建立统计零知识论点。**非交互量子安全零知识Proofs***********************************************Another经典密码学情形在量子安全世界中不再可用，它是计算假设下非交互零知识协议的原型。这样的协议已经被提出用于在没有计算假设的情况下完全或统计地非交互零知识证明(尽管使用量子通信来实现)。然而，它似乎不适用于只有计算性零知识可实现的情况(例如，对于NP-完全语言)，或者证明系统的可靠性只有在某个计算假设不能被打破的情况下才有效(完美或统计零知识论点)。**本研究计划将仅包含理论工作，但将产生重要的HQP培训。

While physical implementation of a quantum computer still seems far away, the perspective of such a realization is so profound to the world of cryptography that it is worth considering already what this science will become after the construction of a quantum computer. The study of Quantum-safe (aka Post-Quantum) cryptographic tools and protocols follow from the belief that we must start now to prepare for this future.**Quantum-Safe Oblivious Transfer and Fully Homomorphic Encryption**********************************************************In the classical world there used to be very general techniques to achieve Oblivious Transfer from various cryptographic assumption. In the Quantum-safe cryptographic world we have no such things: several techniques have been proposed to obtain Quantum-safe Oblivious Transfer but no general technique has emerged yet. The search for such a general approach will be one objective of our research. We will also consider the relation between Oblivious Transfer and the related task of Fully Homomorphic Encryption as implemented under the Learning with error assumption or the Approximate Integer GCD assumption. We would like to show that in the quantum world OT is inherently easier to achieve than FHE.***Interactive Hashing and Statistical Zero-Knowledge Arguments*****************************************************Another specific target is to study a powerful tool to construct secure protocols known as "Interactive Hashing". This tool was used in the classical setting both in the information theoretical and computational framework. Currently, none of the proofs of security of protocols involving interactive hashing is valid in the quantum setting. We will develop new techniques to establish security proofs in the quantum world. We hope to achieve the same result as in the classical world: It is possible to build statistical zero-knowledge arguments for NP under the sole assumption that a quantum one-way function exists.**Non-Interactive Quantum-Safe Zero-Knowledge Proofs***********************************************Another classical cryptographic situation that is no longer available in the Quantum-safe world, is the primitive of Non-Interactive Zero-Knowledge protocols under computational assumptions. Such protocols have been proposed for prefect or statistical Non-Interactive Zero-Knowledge proofs under no computational assumption (although using quantum communication to achieve that). However, it does not seem to apply to situations where only Computational Zero-Knowledge is achievable (for NP-complete languages for example) or where the soundness of the proof system is only valid because a certain computational assumption cannot be broken (Perfect or Statistical Zero-Knowledge Arguments).**This research program will contain theoretical work only but will produce significant training of HQPs.