Communication Complexity with Defective Randomness

Authors Marshall Ball, Oded Goldreich, Tal Malkin

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Author Details

Marshall Ball
  • Computer Science Department, Columbia University, New York, NY, USA
Oded Goldreich
  • Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot, Israel
Tal Malkin
  • Computer Science Department, Columbia University, New York, NY, USA

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Marshall Ball, Oded Goldreich, and Tal Malkin. Communication Complexity with Defective Randomness. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 14:1-14:10, Schloss Dagstuhl – Leibniz-Zentrum fΓΌr Informatik (2021)


Starting with the two standard model of randomized communication complexity, we study the communication complexity of functions when the protocol has access to a defective source of randomness. Specifically, we consider both the public-randomness and private-randomness cases, while replacing the commonly postulated perfect randomness with distributions over 𝓁 bit strings that have min-entropy at least k ≀ 𝓁. We present general upper and lower bounds on the communication complexity in these cases, where the bounds are typically linear in 𝓁-k and also depend on the size of the fooling set for the function being computed and on its standard randomized complexity.

Subject Classification

ACM Subject Classification
  • Theory of computation β†’ Communication complexity
  • Randomized Communication Complexity
  • Randomness Extraction
  • Min-Entropy


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  1. Ran Canetti and Oded Goldreich. Bounds on tradeoffs between randomness and communication complexity. Comput. Complex., 3:141-167, 1993. Google Scholar
  2. ClΓ©ment L. Canonne, Venkatesan Guruswami, Raghu Meka, and Madhu Sudan. Communication with imperfectly shared randomness. IEEE Trans. Inf. Theory, 63(10):6799-6818, 2017. Google Scholar
  3. Benny Chor and Oded Goldreich. Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J. Comput., 17(2):230-261, 1988. Google Scholar
  4. Martin Dietzfelbinger, Juraj Hromkovic, and Georg Schnitger. A comparison of two lower-bound methods for communication complexity. Theor. Comput. Sci., 168(1):39-51, 1996. Google Scholar
  5. Yevgeniy Dodis, Shien Jin Ong, Manoj Prabhakaran, and Amit Sahai. On the (im)possibility of cryptography with imperfect randomness. In FOCS, pages 196-205. IEEE Computer Society, 2004. Google Scholar
  6. Shafi Goldwasser, Madhu Sudan, and Vinod Vaikuntanathan. Distributed computing with imperfect randomness. In DISC, volume 3724 of Lecture Notes in Computer Science, pages 288-302. Springer, 2005. Google Scholar
  7. Eyal Kushilevitz and Noam Nisan. Communication complexity. Cambridge University Press, 1997. Google Scholar
  8. James L. McInnes and Benny Pinkas. On the impossibility of private key cryptography with weakly random keys. In CRYPTO, volume 537 of Lecture Notes in Computer Science, pages 421-435. Springer, 1990. Google Scholar
  9. Ilan Newman. Private vs. common random bits in communication complexity. Inf. Process. Lett., 39(2):67-71, 1991. Google Scholar
  10. Anup Rao and Amir Yehudayoff. Communication Complexity: and Applications. Cambridge University Press, 2020. Google Scholar
  11. Ronen Shaltiel. An introduction to randomness extractors. In ICALP (2), volume 6756 of Lecture Notes in Computer Science, pages 21-41. Springer, 2011. Google Scholar
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