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Uses of Randomness in Algorithms and Protocols

Uses of Randomness in Algorithms and Protocols (ACM Distinguished Dissertation)

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87,355 ratings · 6,291 reviews
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Uses of Randomness in Algorithms and Protocols

Uses of Randomness in Algorithms and Protocols (ACM Distinguished Dissertation)

4.85 87,355 ratings · 6,291 reviews
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Overview: Uses of Randomness in Algorithms and Protocols makes fundamental contributions to two different fields of complexity theory: computational number theory and cryptography. The most famous result is Goldwasser and Kilian's invention of a new approach to distinguish prime numbers from composites, using methods from the theory of elliptic curves over finite fields. The Goldwasser-Kilian algorithm is the first to yield a polynomial size proof of its assertions, ensuring correctness while still provably running fast on most inputs. This new primality test implies for the first time and without any assumptions that large certified primes can be generated in expected polynomial time under a distribution that is close to uniform. It provides a provocative new link between algebraic geometry and primality testing, one of the most ancient algorithmic problems in number theory. Heuristic implementations of the algorithm are currently considered to be the fastest existing methods to certify primes. Kilian also provides two elegant and original contributions to theoretical cryptography. He shows how to base general two-party protocols on a simple protocol, known as "oblivious transfer," proving the first completeness result of this kind. He also introduces a generalization of interactive proof systems, known as "multi-prover interactive proof systems," and shows that anything provable in this model is provable in zero knowledge. Joe Kilian is a National Science Foundation Postdoctoral Fellow at MIT and Harvard. Contents: Introduction. New Techniques in Primality Testing. Committing Bits Using Oblivious Transfer. Circuit Evaluation Using Oblivious Transfer: The NC1 Circuit Base. ObliviousEvaluation of Arbitrary Circuits. Interactive Proof Systems with Multiple Provers.

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Published October 22, 1990
ISBN 4544089
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Joe Kilian writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. Joe Kilian lives with their spouse and a very vocal rescue cat.

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Nicholas Lee
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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