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Full-Text Articles in Physical Sciences and Mathematics
A Cohomological Perspective To Nonlocal Operators, Nicholas White
A Cohomological Perspective To Nonlocal Operators, Nicholas White
Honors Theses
Nonlocal models have experienced a large period of growth in recent years. In particular, nonlocal models centered around a finite horizon have been the subject of many novel results. In this work we consider three nonlocal operators defined via a finite horizon: a weighted averaging operator in one dimension, an averaging differential operator, and the truncated Riesz fractional gradient. We primarily explore the kernel of each of these operators when we restrict to open sets. We discuss how the topological structure of the domain can give insight into the behavior of these operators, and more specifically the structure of their …
Quantum Computing And U.S. Cybersecurity: A Case Study Of The Breaking Of Rsa And Plan For Cryptographic Algorithm Transition, Helena Holland
Quantum Computing And U.S. Cybersecurity: A Case Study Of The Breaking Of Rsa And Plan For Cryptographic Algorithm Transition, Helena Holland
Honors Theses
The invention of a cryptographically relevant quantum computer would revolutionize computing power, transforming industry and national security. While a theoretical possibility at the time of this writing, the ability of quantum algorithms to solve the factoring and discrete logarithm problems, upon which all currently employed public-key cryptography depends, presents a serious threat to digital communications. This research examines both the mathematics and government policy behind these risks and their implications for cybersecurity. Specifically, a case study of RSA, Shor’s algorithm, and the American Intelligence Community’s plan to transition toward quantum-resistant algorithms is presented to analyze quantum threats and opportunities and …