TY - GEN

T1 - The randomness complexity of parallel repetition

AU - Chung, Kai Min

AU - Pass, Rafael

PY - 2011

Y1 - 2011

N2 - Consider a m-round interactive protocol with soundness error 1/2. How much extra randomness is required to decrease the soundness error to δ through parallel repetition? Previous work, initiated by Bell are, Goldreich and Gold wasser, shows that for public-coin interactive protocols with statistical soundness, m·O(log (1/δ)) bits of extra randomness suffices. In this work, we initiate a more general study of the above question. • We establish the first derandomized parallel repetition theorem for public-coin interactive protocols with computational soundness (a.k.a. arguments). The parameters of our result essentially matches the earlier works in the information-theoretic setting. • We show that obtaining even a sub-linear dependency on the number of rounds m (i.e., o(m)·log(1/δ)) is impossible in the information-theoretic, and requires the existence of one-way functions in the computational setting. • We show that non-trivial derandomized parallel repetition for private-coin protocols is impossible in the information-theoretic setting and requires the existence of one-way functions in the computational setting. \end{itemize} These results are tight in the sense that parallel repetition theorems in the computational setting can trivially be derandomized using pseudorandom generators, which are implied by the existence of one-way functions.

AB - Consider a m-round interactive protocol with soundness error 1/2. How much extra randomness is required to decrease the soundness error to δ through parallel repetition? Previous work, initiated by Bell are, Goldreich and Gold wasser, shows that for public-coin interactive protocols with statistical soundness, m·O(log (1/δ)) bits of extra randomness suffices. In this work, we initiate a more general study of the above question. • We establish the first derandomized parallel repetition theorem for public-coin interactive protocols with computational soundness (a.k.a. arguments). The parameters of our result essentially matches the earlier works in the information-theoretic setting. • We show that obtaining even a sub-linear dependency on the number of rounds m (i.e., o(m)·log(1/δ)) is impossible in the information-theoretic, and requires the existence of one-way functions in the computational setting. • We show that non-trivial derandomized parallel repetition for private-coin protocols is impossible in the information-theoretic setting and requires the existence of one-way functions in the computational setting. \end{itemize} These results are tight in the sense that parallel repetition theorems in the computational setting can trivially be derandomized using pseudorandom generators, which are implied by the existence of one-way functions.

KW - derandomization

KW - interactive protocols

KW - parallel repetition

KW - randomness extractors

KW - soundness amplification

UR - http://www.scopus.com/inward/record.url?scp=84863330765&partnerID=8YFLogxK

U2 - 10.1109/FOCS.2011.93

DO - 10.1109/FOCS.2011.93

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84863330765

SN - 9780769545714

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 658

EP - 667

BT - Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011

T2 - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011

Y2 - 22 October 2011 through 25 October 2011

ER -