Privacy amplification and non-malleable extractors via character sums

Yevgeniy Dodis, Xin Li, Trevor D. Wooley, David Zuckerman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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 Gold reich 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. To achieve a polynomial running time when outputting many bits, we rely on a widely-believed conjecture about the distribution of prime numbers in arithmetic progressions. Our analysis involves a character sum estimate, which may be of independent interest. Using our non-malleable extractor, we obtain protocols for "privacy amplification": key agreement between two parties who share a weakly-random secret. Our protocols work in the presence of an active adversary with unlimited computational power, and have asymptotically optimal entropy loss. When the secret has entropy rate greater than 1/2, the protocol follows from a result of Dodis and Wichs, and takes two rounds. When the secret has entropy rate δ for any constant δ > 0, our new protocol takes a constant (polynomial in 1/δ) number of rounds. Our protocols run in polynomial time under the above well-known conjecture about primes.

Original languageEnglish (US)
Title of host publicationProceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011
Pages668-677
Number of pages10
DOIs
StatePublished - 2011
Event2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 - Palm Springs, CA, United States
Duration: Oct 22 2011Oct 25 2011

Other

Other2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011
CountryUnited States
CityPalm Springs, CA
Period10/22/1110/25/11

Fingerprint

Amplification
Entropy
Polynomials
Seed
Gold

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Dodis, Y., Li, X., Wooley, T. D., & Zuckerman, D. (2011). Privacy amplification and non-malleable extractors via character sums. In Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 (pp. 668-677). [6108229] https://doi.org/10.1109/FOCS.2011.67

Privacy amplification and non-malleable extractors via character sums. / Dodis, Yevgeniy; Li, Xin; Wooley, Trevor D.; Zuckerman, David.

Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011. 2011. p. 668-677 6108229.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Dodis, Y, Li, X, Wooley, TD & Zuckerman, D 2011, Privacy amplification and non-malleable extractors via character sums. in Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011., 6108229, pp. 668-677, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011, Palm Springs, CA, United States, 10/22/11. https://doi.org/10.1109/FOCS.2011.67
Dodis Y, Li X, Wooley TD, Zuckerman D. Privacy amplification and non-malleable extractors via character sums. In Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011. 2011. p. 668-677. 6108229 https://doi.org/10.1109/FOCS.2011.67
Dodis, Yevgeniy ; Li, Xin ; Wooley, Trevor D. ; Zuckerman, David. / Privacy amplification and non-malleable extractors via character sums. Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011. 2011. pp. 668-677
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