TY - GEN

T1 - An efficient reduction from two-source to non-malleable extractors

T2 - 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017

AU - Ben-Aroya, Avraham

AU - Doron, Dean

AU - Ta-Shma, Amnon

N1 - Publisher Copyright:
© 2017 ACM.

PY - 2017/6/19

Y1 - 2017/6/19

N2 - The breakthrough result of Chattopadhyay and Zuckerman (2016) gives a reduction from the construction of explicit two-source extractors to the construction of explicit non-malleable extractors. However, even assuming the existence of optimal explicit non-malleable extractors only gives a two-source extractor (or a Ramsey graph) for poly(log n) entropy, rather than the optimal O(log n). In this paper we modify the construction to solve the above barrier. Using the currently best explicit non-malleable extractors we get an explicit bipartite Ramsey graphs for sets of size 2k, for k = O(log n log log n). Any further improvement in the construction of non-malleable extractors would immediately yield a corresponding two-source extractor. Intuitively, Chattopadhyay and Zuckerman use an extractor as a sampler, and we observe that one could use a weaker object - a somewhere-random condenser with a small entropy gap and a very short seed. We also show how to explicitly construct this weaker object using the error reduction technique of Raz, Reingold and Vadhan (1999), and the constant-degree dispersers of Zuckerman (2006) that also work against extremely small tests.

AB - The breakthrough result of Chattopadhyay and Zuckerman (2016) gives a reduction from the construction of explicit two-source extractors to the construction of explicit non-malleable extractors. However, even assuming the existence of optimal explicit non-malleable extractors only gives a two-source extractor (or a Ramsey graph) for poly(log n) entropy, rather than the optimal O(log n). In this paper we modify the construction to solve the above barrier. Using the currently best explicit non-malleable extractors we get an explicit bipartite Ramsey graphs for sets of size 2k, for k = O(log n log log n). Any further improvement in the construction of non-malleable extractors would immediately yield a corresponding two-source extractor. Intuitively, Chattopadhyay and Zuckerman use an extractor as a sampler, and we observe that one could use a weaker object - a somewhere-random condenser with a small entropy gap and a very short seed. We also show how to explicitly construct this weaker object using the error reduction technique of Raz, Reingold and Vadhan (1999), and the constant-degree dispersers of Zuckerman (2006) that also work against extremely small tests.

KW - Condensers

KW - Non-malleable extractors

KW - Ramsey graphs

KW - Two-source extractors

UR - http://www.scopus.com/inward/record.url?scp=85024403291&partnerID=8YFLogxK

U2 - 10.1145/3055399.3055423

DO - 10.1145/3055399.3055423

M3 - Conference contribution

AN - SCOPUS:85024403291

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1185

EP - 1194

BT - STOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

A2 - McKenzie, Pierre

A2 - King, Valerie

A2 - Hatami, Hamed

PB - Association for Computing Machinery

Y2 - 19 June 2017 through 23 June 2017

ER -