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Elementary,Middle School,High School,College,University,PHD
| Teaching Since: | May 2017 |
| Last Sign in: | 398 Weeks Ago, 5 Days Ago |
| Questions Answered: | 66690 |
| Tutorials Posted: | 66688 |
MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
Alice has a copy of a long n-bit file A = ?an-1, an-2,..., a0?, and Bob similarly has an n-bit file B = ?bn-1, bn-2,...,b0?. Alice and Bob wish to know if their files are identical. To avoid transmitting all of A or B, they use the following fast probabilistic check. Together, they select a prime q > 1000n and randomly select an integer x from {0, 1,...,q - 1}. Then, Alice evaluates and Bob similarly evaluates B(x). Prove that if A ≠ B, there is at most one chance in 1000 that A(x) = B(x), whereas if the two files are the same, A(x) is necessarily the same as B(x). (Hint: See Exercise 31.4-4.)

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