Research output per year
Research output per year
Bill Fefferman, Ronen Shaltiel, Christopher Umans, Emanuele Viola
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
The hybrid argument allows one to relate the distinguishability of a distribution (from uniform) to the predictability of individual bits given a prefix. The argument incurs a loss of a factor k equal to the bit-length of the distributions: ε-distinguishability implies ε/k-predictability. This paper studies the consequences of avoiding this loss - what we call "beating the hybrid argument" - and develops new proof techniques that circumvent the loss in certain natural settings. Specifically, we obtain the following results: 1. We give an instantiation of the Nisan-Wigderson generator (JCSS '94) that can be broken by quantum computers, and that is o(1)-unpredictable against AC ^{0}. We conjecture that this generator indeed fools AC ^{0}. Our conjecture implies the existence of an oracle relative to which BQP is not in the PH, a longstanding open problem. 2. We show that the "INW" generator by Impagliazzo, Nisan, and Wigderson (STOC '94) with seed length O(log n log log n) produces a distribution that is 1/log n-unpredictable against poly-logarithmic width (general) read-once oblivious branching programs. Obtaining such generators where the output is indistinguishable from uniform is a longstanding open problem. 3. We identify a property of functions f, "resamplability," that allows us to beat the hybrid argument when arguing indistinguishability of (Equation Presented) from uniform. This gives new pseudorandom generators for classes such as AC ^{0}[p] with a stretch that, despite being sub-linear, is the largest known. We view this as a first step towards beating the hybrid argument in the analysis of the Nisan-Wigderson generator (which applies (Equation Presented) on correlated x _{1},...,x _{k}) and proving the conjecture in the first item.
Original language | English |
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Title of host publication | ITCS 2012 - Innovations in Theoretical Computer Science Conference |
Pages | 468-483 |
Number of pages | 16 |
DOIs | |
State | Published - 2012 |
Event | 3rd Conference on Innovations in Theoretical Computer Science, ITCS 2012 - Cambridge, MA, United States Duration: 8 Jan 2012 → 10 Jan 2012 |
Name | ITCS 2012 - Innovations in Theoretical Computer Science Conference |
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Conference | 3rd Conference on Innovations in Theoretical Computer Science, ITCS 2012 |
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Country/Territory | United States |
City | Cambridge, MA |
Period | 8/01/12 → 10/01/12 |
Research output: Contribution to journal › Article › peer-review