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

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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.