On the Foundations and Methods of Quantum Cryptography

该项目旨在提高我们对量子密码学基础的理解，开发量子工具，允许新的密码学原语，并更好地理解其局限性。双方可以使用量子通信（即量子密钥分发）就密钥达成一致，这一事实首次给了密码学的主要目标：数据隐私、数据真实性和数据完整性可以通过量子力学在理论上提供信息的希望，而正如我们所知，仅通过经典手段是不可能的。甚至在量子密钥分发的安全性完全建立之前，研究人员就已经证明，即使是所有强大的量子实验家，也不可能实现其他加密原语。因此，在量子世界中，密码学的图景并不像人们最初想象的那样不受约束。除了通过量子信息处理实现经典密码任务外，量子密码学还对提供将密码技术应用于量子系统的方法感兴趣。通常，经典原语有一个自然的量子解释。例如，为了公开保证文档的完整性和真实性而签署文档有一个自然的量子对应物：签署量子态。量子密码学感兴趣的是确定在什么条件下（如果有的话）这些量子原语是可能的。例如，尽管可以基于合理的计算假设安全地执行文档签名，但在这种设置中仍然不可能对量子态进行签名。另一方面，由于不确定性原理，虽然电子货币不能轻易防止双重支出，但量子货币没有这种脆弱性。

This project aims at improving our understanding of the foundations of quantum cryptography, to develop quantum tools allowing for new cryptographic primitives and a better understanding of its limits. The fact that two parties can agree upon a secret key using quantum communication (i.e. quantum key distribution) has first given hopes that the main goals of cryptography: data privacy, data authenticity, and data integrity could be provided information theoretically by quantum mechanics while, as we know, being impossible by classical means alone. Even before the security of quantum key distribution was fully established, researchers have shown that other cryptographic primitives would remain impossible even by all powerful quantum experimentalists. The picture of cryptography in a quantum world is therefore not as unconstrained as one could have first thought. In addition to the realization of classical cryptographic tasks by quantum information processing, quantum cryptography is also interested in providing means by which cryptographic techniques can be applied to quantum systems. Very often, classical primitives have a natural quantum interpretation. For instance, signing documents in order to publicly guarantee their integrity and authenticity has a natural quantum counterpart: signing quantum states. Quantum cryptography is interested in determining under what conditions, if any, these quantum primitives are possible. As an example, although signing documents can be performed securely based upon reasonable computational assumptions, signing quantum states remains impossible in this setting. On the other hand, while electronic money cannot be easily protected against double-spending, quantum money does not have this vulnerability, thanks to the uncertainty principle.