Uses of Randomness in Algorithms and Protocols

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

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Uses of Randomness in Algorithms and Protocols

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

Written by Joe Kilian
4.85 15,444 ratings
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About this ebook:
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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Pages N/A
Published October 22, 1990
ISBN 4544089
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Joe Kilian
About the Author
Joe Kilian

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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Ryan Adams
Ryan Adams February 11, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Ryan Baker
Ryan Baker July 15, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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James Reyes
James Reyes April 25, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
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Ryan Hernandez October 21, 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.
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Barbara Carter January 24, 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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Anthony Martin January 30, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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Anthony Jackson February 29, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Carol Hernandez June 02, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Melissa Parker January 10, 2025
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
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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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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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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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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. A wonderful companion for a quiet weekend.
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Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Paul Torres
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Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Donna Diaz
Donna Diaz May 31, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
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I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Deborah Gomez
Deborah Gomez November 02, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Kevin  Davis
Kevin Davis June 24, 2024
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Jessica Lee
Jessica Lee November 24, 2025
Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
Sandra Miller
Sandra Miller June 27, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Andrew Walker
Andrew Walker October 20, 2024
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.
David Walker
David Walker August 11, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Paul Anderson
Paul Anderson March 26, 2024
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. Perfectly average.
Thomas Nelson
Thomas Nelson November 09, 2025
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.
James Phillips
James Phillips September 13, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Donna Jackson
Donna Jackson March 04, 2024
Not entirely to my refined tastes. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes.
Michael Young
Michael Young May 18, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Joseph Hernandez
Joseph Hernandez May 26, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Anthony Martin
Anthony Martin February 25, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Jessica Harris
Jessica Harris August 25, 2025
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.
Richard  Parker
Richard Parker April 14, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Patricia Hall
Patricia Hall June 14, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Elizabeth Scott
Elizabeth Scott December 25, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Donald Clark
Donald Clark February 18, 2025
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Laura Clark
Laura Clark January 08, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Barbara Carter
Barbara Carter November 10, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Donna Diaz
Donna Diaz December 20, 2024
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Dorothy Gonzalez
Dorothy Gonzalez July 05, 2025
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Mark Perez
Mark Perez January 11, 2024
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
William Harris
William Harris November 04, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
David Young
David Young November 04, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Linda Robinson
Linda Robinson April 02, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Jessica Anderson
Jessica Anderson April 07, 2025
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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