Non-malleable extractors via character sums

In studying how to communicate over a public channel with an active adversary, Dodis and Wichs introduced the notion of a non-malleable extractor. A non-malleable extractor dramatically strengthens the notion of a strong extractor. A strong extractor takes two inputs, a weakly-random x and a uniformly random seed y, and outputs a string which appears uniform, even given y. For a non-malleable extractor nmExt, the output nmExt(x, y) should appear uniform given y as well as nmExt(x, A(y)), where A is an arbitrary function with A(y) = y. We show that an extractor introduced by Chor and Goldreich is non-malleable when the entropy rate is above half. It outputs a linear number of bits when the entropy rate is 1/2 + α, for any α > 0. Previously, no nontrivial parameters were known for any non-malleable extractor. We further show that our construction works even if the seed has entropy linear in the output length. To achieve a polynomial running time when outputting many bits, we rely o...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Trevor D. Wooley, David Zuckerman
• Keywords: CORR 2011, Education, Entropy, Non-malleable Extractor, Strong Extractor