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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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53,370 ratings · 7,655 reviews
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Uses of Randomness in Algorithms and Protocols

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

4.85 53,370 ratings · 7,655 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
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Joe Kilian is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Joe Kilian can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Rebecca Jackson June 15, 2025
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Susan Walker
Susan Walker April 24, 2025
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Christopher Cruz
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A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Unlikely to reread, but a reasonable expenditure of time.
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
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Mark Scott September 04, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Linda Thomas May 07, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Andrew White February 04, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Eric Allen
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A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Barbara Collins
Barbara Collins December 23, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Ashley Jones
Ashley Jones May 10, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Sharon Mitchell
Sharon Mitchell November 18, 2025
A decent, if standard, experience. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Jennifer Walker
Jennifer Walker February 10, 2024
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
George Harris
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A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Dorothy Mitchell
Dorothy Mitchell March 07, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Margaret Hall
Margaret Hall October 30, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
William King
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A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
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Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Eric Rivera
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Brian Nguyen
Brian Nguyen April 15, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Thomas Mitchell
Thomas Mitchell July 20, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Brian Robinson
Brian Robinson May 12, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Linda Adams
Linda Adams November 05, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Jessica Edwards
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Sharon Mitchell
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A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
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