Chapter

Advances in Cryptology – CRYPTO 2010

Volume 6223 of the series Lecture Notes in Computer Science pp 538-557

Protocols for Multiparty Coin Toss with Dishonest Majority

  • Amos BeimelAffiliated withDept. of Computer Science, Ben Gurion University
  • , Eran OmriAffiliated withDept. of Computer Science, Bar Ilan University
  • , Ilan OrlovAffiliated withDept. of Computer Science, Ben Gurion University

Abstract

Coin-tossing protocols are protocols that generate a random bit with uniform distribution. These protocols are used as a building block in many cryptographic protocols. Cleve [STOC 1986] has shown that if at least half of the parties can be malicious, then, in any https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-14623-7_29/MediaObjects/978-3-642-14623-7_29_IEq1_HTML.png -round coin-tossing protocol, the malicious parties can cause a bias of https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-14623-7_29/MediaObjects/978-3-642-14623-7_29_IEq2_HTML.png to the bit that the honest parties output. However, for more than two decades the best known protocols had bias https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-14623-7_29/MediaObjects/978-3-642-14623-7_29_IEq3_HTML.png , where https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-14623-7_29/MediaObjects/978-3-642-14623-7_29_IEq4_HTML.png is the number of corrupted parties. Recently, in a surprising result, Moran, Naor, and Segev [TCC 2009] have shown that there is an https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-14623-7_29/MediaObjects/978-3-642-14623-7_29_IEq5_HTML.png -round two-party coin-tossing protocol with the optimal bias of https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-14623-7_29/MediaObjects/978-3-642-14623-7_29_IEq6_HTML.png . We extend Moran et al. results to the multiparty model when less than 2/3 of the parties are malicious. The bias of our protocol is proportional to https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-14623-7_29/MediaObjects/978-3-642-14623-7_29_IEq7_HTML.png and depends on the gap between the number of malicious parties and the number of honest parties in the protocol. Specifically, for a constant number of parties or when the number of malicious parties is somewhat larger than half, we present an https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-14623-7_29/MediaObjects/978-3-642-14623-7_29_IEq8_HTML.png -round https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-14623-7_29/MediaObjects/978-3-642-14623-7_29_IEq9_HTML.png -party coin-tossing protocol with optimal bias of https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-14623-7_29/MediaObjects/978-3-642-14623-7_29_IEq10_HTML.png .