AF: Medium: Collaborative Research: Quantum-Secure Cryptography and Fine-Grained Quantum Query Complexity

安全的互联网通信面临着一个真正的威胁，那就是一种利用量子力学定律的新型计算机。技术界目前正在努力工作，试图建造这样的“量子”计算机。虽然关于这些设备的许多谜团仍然存在，但可以肯定的是，一台大规模的量子计算机将轻松破解支撑当前互联网的所有当前公钥加密技术。在某些攻击模型中，私钥加密的重要示例也会变得不安全。这个由三个机构组成的合作项目研究了安全基础设施面临的这些紧迫威胁背后的基本理论问题。它试图了解量子计算机的密码破解能力，集中在两个相互交织的主题上：1)身份验证的量子安全，2)用新的原语构建量子安全密码。项目活动还包括研究生和本科生的课程开发和指导。该项目还涉及旨在扩大对计算机科学的参与的具体推广活动，包括建立和发展“计算机科学中的女性”分会，向当地高中推广，为高中STEM教师举办讲习班，以及为三个伙伴机构的普通受众开发计算机科学课程。例如，身份验证--例如，电子邮件确实来自你--是一项基本的、研究得很充分的密码学挑战。在量子对手的背景下，如何恰当地表述这一基本概念尚不清楚，更不用说生产实现这一概念的具体密码工具了。该项目正在应对上述两个挑战，重点是开发强有力的身份验证公式和提供安全身份验证的新密码结构。在研究量子计算机的计算能力时，寻找“隐藏的”代数结构--比如两个数字列表只是彼此的循环移位--是一个标志性的主题。这个问题的某些变体抵制了量子算法界几十年来的共同努力，似乎相当困难。这个项目研究了这些问题在构建具有量子安全保证的新的私钥加密工具方面的应用。这个奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Secure Internet communication faces a real threat in the form of a new breed of computer that harnesses the laws of quantum mechanics. The technical community is currently hard at work attempting to construct such "quantum" computers. While many mysteries about these devices remain, it is certain that a large-scale quantum computer would easily break all current public-key cryptography that underpins the current Internet. In certain attack models, important examples of private-key cryptography would also be rendered insecure. This 3-institution collaborative project studies the basic theoretical issues underlying these urgent threats to the security infrastructure. It seeks to understand the cryptography-breaking power of quantum computers, concentrating on two interweaving themes: quantum security for 1) authenticating, and 2) constructing quantum-secure cryptography from new primitives. The project activities also include course development and mentorship at the graduate and undergraduate level. The project also involves specific outreach activities intended to broaden participation in Computer Science, including establishment and development of "women in computer science" chapters, outreach to local high schools, workshops for high-school STEM teachers, and development of computer science courses for a general audience at the three partner institutions.Authentication-proofs, for example, that an e-mail really did originate from you--is a basic and well-studied cryptographic challenge. In the setting of quantum adversaries, it is not clear how to appropriately formulate this essential notion, let alone produce specific cryptographic tools that achieve it. This project is addressing both of the challenges noted above, focusing on development of strong formulations of authentication and new cryptographic constructions that offer secure authentication. Finding "hidden" algebraic structures--like the fact that two lists of numbers are merely cyclic shifts of each other--is an emblematic theme in the study of the computing power of quantum computers. Certain variants of this problem have resisted decades of concerted effort by the quantum algorithms community, and appear to be quite difficult. This project studies applications of these problems to constructing new private-key cryptographic tools with quantum security guarantees.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.