PRIMES is in P
TLDR
In this paper, an unconditional deterministic polynomial-time algorithm that determines whether an input number is prime or composite is presented. But the algorithm is not deterministic in the sense thatAbstract:
We present an unconditional deterministic polynomial-time algorithm that determines whether an input number is prime or composite.read more
Citations
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Journal ArticleDOI
Modern computer algebra
TL;DR: This highly successful textbook, widely regarded as the “bible of computer algebra”, gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems.
Journal ArticleDOI
Advances in quantum cryptography
Stefano Pirandola,Ulrik L. Andersen,Leonardo Banchi,Mario Berta,Darius Bunandar,Roger Colbeck,Dirk Englund,Tobias Gehring,Cosmo Lupo,Carlo Ottaviani,Jason Pereira,Mohsen Razavi,Jesni Shamsul Shaari,Marco Tomamichel,Vladyslav C. Usenko,Giuseppe Vallone,Paolo Villoresi,Petros Wallden +17 more
TL;DR: This review begins by reviewing protocols of quantum key distribution based on discrete variable systems, and considers aspects of device independence, satellite challenges, and high rate protocols based on continuous variable systems.
Book
Modern Cryptography: Theory and Practice
TL;DR: This book explains why "textbook crypto" is only good in an ideal world where data are random and bad guys behave nicely, and reveals the general unfitness of "textbooks crypto" for the real world by demonstrating numerous attacks on such schemes, protocols and systems under various real-world application scenarios.
Book
A Computational Introduction to Number Theory and Algebra
TL;DR: The introductory book as discussed by the authors emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience, and it alternates between theory and applications in order to motivate and illustrate the mathematics.
Proceedings ArticleDOI
Delegating computation: interactive proofs for muggles
TL;DR: This work shows how to construct short (polylog size) computationally sound non-interactive certificates of correctness for any log-space uniform NC computation, in the public-key model, and settles an open question regarding the expressive power of proof systems with such verifiers.
References
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The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
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Introduction to analytic number theory
TL;DR: The Mathematics 160 course at the California Institute of Technology as discussed by the authors was the first volume of a two-volume textbook which evolved from a course (Mathematics 160) offered at the University of California during the last 25 years.
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Handbook of theoretical computer science
TL;DR: The Handbook of Theoretical Computer Science provides professionals and students with a comprehensive overview of the main results and developments in this rapidly evolving field.
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WHO Technical Report.
TL;DR: The Feather River Coordinated Resource Management Group (FR-CRM) has been restoring channel/ meadow/ floodplain systems in the Feather River watershed since 1985 and recognized the possibility of a significant change in carbon stocks in these restored meadows and valleys.