A Quantum-Proof Non-malleable Extractor
In privacy amplification, two mutually trusted parties aim to amplify the secrecy of an initial shared secret X in order to establish a shared private key K by exchanging messages over an insecure communication channel. If the channel is authenticated the task can be solved in a single round of communication using a strong randomness extractor; choosing a quantum-proof extractor allows one to establish security against quantum adversaries.
In the case that the channel is not authenticated, this simple solution is no longer secure. Nevertheless, Dodis and Wichs (STOC’09) showed that the problem can be solved in two rounds of communication using a non-malleable extractor, a stronger pseudo-random construction than a strong extractor.
We give the first construction of a non-malleable extractor that is secure against quantum adversaries. The extractor is based on a construction by Li (FOCS’12), and is able to extract from source of min-entropy rates larger than 1 / 2. Combining this construction with a quantum-proof variant of the reduction of Dodis and Wichs, due to Cohen and Vidick (unpublished) we obtain the first privacy amplification protocol secure against active quantum adversaries.
- 1.Aggarwal, D., Chung, K.-M., Lin, H.-H., Vidick, T.: A quantum-proof non-malleable extractor, with application to privacy amplification against active quantum adversaries. arXiv preprint arXiv:1710.00557 (2017)
- 3.Aggarwal, D., Hosseini, K., Lovett, S.: Affine-malleable extractors, spectrum doubling, and application to privacy amplification. In: 2016 IEEE International Symposium on Information Theory (ISIT), pp. 2913–2917. IEEE (2016)Google Scholar
- 8.Chandran, N., Kanukurthi, B., Ostrovsky, R., Reyzin, L.: Privacy amplification with asymptotically optimal entropy loss. In: Proceedings of the 42nd ACM Symposium on Theory of Computing, STOC 2010, Cambridge, Massachusetts, USA, 5–8 June 2010, pp. 785–794 (2010)Google Scholar
- 9.Chattopadhyay, E., Goyal, V., Li, X.: Non-malleable extractors and codes, with their many tampered extensions. arXiv preprint arXiv:1505.00107 (2015)
- 10.Chung, K.-M., Li, X., Wu, X.: Multi-source randomness extractors against quantum side information, and their applications (2014)Google Scholar
- 12.Cohen, G.: Non-malleable extractors - new tools and improved constructions. Electron. Colloq. Comput. Complex. (ECCC) 22, 183 (2015)Google Scholar
- 13.Cohen, G., Raz, R., Segev, G.: Non-malleable extractors with short seeds and applications to privacy amplification. In: 2012 IEEE 27th Annual Conference on Computational Complexity (CCC), pp. 298–308. IEEE (2012)Google Scholar
- 14.Cohen, G., Vidick, T.: Privacy amplification against active quantum adversaries (2016)Google Scholar
- 18.Dziembowski, S., Pietrzak, K.: Leakage-resilient cryptography. In: 2008 49th Annual IEEE Symposium on Foundations of Computer Science, pp. 293–302. IEEE (2008)Google Scholar
- 19.Dodis, Y., Wichs, D.: Non-malleable extractors and symmetric key cryptography from weak secrets. In: Mitzenmacher, M (ed.) Proceedings of the 41st Annual ACM Symposium on Theory of Computing, Bethesda, MD, USA, pp. 601–610. ACM (2009)Google Scholar
- 21.Gavinsky, D., Kempe, J., Kerenidis, I., Raz, R., De Wolf, R.: Exponential separations for one-way quantum communication complexity, with applications to cryptography. In: Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing, pp. 516–525. ACM (2007)Google Scholar
- 25.Li, X.: Design extractors, non-malleable condensers and privacy amplification. In: Proceedings of the 44th Symposium on Theory of Computing Conference, STOC 2012, New York, NY, USA, 19–22 May 2012, pp. 837–854 (2012)Google Scholar
- 26.Li, X.: Non-malleable condensers for arbitrary min-entropy, and almost optimal protocols for privacy amplification. CoRR, abs/1211.0651 (2012)Google Scholar
- 27.Li, X.: Non-malleable extractors, two-source extractors and privacy amplification. In: FOCS, pp. 688–697 (2012)Google Scholar
- 29.Li, X.: Improved non-malleable extractors, non-malleable codes and independent source extractors. In: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, Montreal, QC, Canada, 19–23 June 2017, pp. 1144–1156 (2017)Google Scholar