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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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33,914 ratings · 5,904 reviews
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Uses of Randomness in Algorithms and Protocols

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

4.85 33,914 ratings · 5,904 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 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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Joshua Roberts
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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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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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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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Betty Anderson
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Laura  Davis
Laura Davis February 23, 2025
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Matthew Roberts
Matthew Roberts August 26, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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Ashley Smith January 19, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Michelle Young
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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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Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Rebecca Collins
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A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Nicholas Nelson
Nicholas Nelson February 22, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Joseph Baker
Joseph Baker November 22, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Melissa Mitchell
Melissa Mitchell March 07, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Michelle Thomas
Michelle Thomas June 14, 2025
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Donald Lewis
Donald Lewis March 29, 2025
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
John Collins
John Collins December 19, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Rebecca Anderson
Rebecca Anderson May 03, 2025
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Ryan Roberts
Ryan Roberts April 29, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Laura White
Laura White June 27, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Sarah Adams
Sarah Adams October 05, 2024
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
Steven Perez
Steven Perez January 04, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Michelle Sanchez
Michelle Sanchez December 10, 2024
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Charles  Davis
Charles Davis September 27, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Mary Scott
Mary Scott April 14, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Kenneth Robinson
Kenneth Robinson May 14, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Sharon Harris
Sharon Harris September 27, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Sharon Reyes
Sharon Reyes June 10, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Linda Ramirez
Linda Ramirez February 16, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Kenneth Anderson
Kenneth Anderson November 16, 2024
An acceptable diversion. Certain acts were fascinating, while others felt like a slight endeavor to complete. Suitable if your reading queue is empty.
David Wilson
David Wilson October 15, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Patricia Williams
Patricia Williams December 27, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Laura Anderson
Laura Anderson October 06, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Margaret Lewis
Margaret Lewis November 06, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Donald Perez
Donald Perez May 13, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Anthony Diaz
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Jessica Turner
Jessica Turner October 05, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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