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Revision #1 to TR20-071 | 2nd September 2020 22:11

A Tight Lower Bound on Adaptively Secure Full-Information Coin Flip

Revision #1
Authors: Iftach Haitner, Yonatan Karidi-Heller
Accepted on: 2nd September 2020 22:11
Keywords:

Abstract:

In a distributed coin-flipping protocol, Blum [ACM Transactions on Computer Systems '83], the parties try to output a common (close to) uniform bit, even when some adversarially chosen parties try to bias the common output. In an adaptively secure full-information coin flip, Ben-Or and Linial [FOCS '85], the parties communicate over a broadcast channel and a computationally unbounded adversary can choose which parties to corrupt along the protocol execution. Ben-Or and Linial proved that the $n$-party majority protocol is resilient to $O(\sqrt{n})$ corruptions (ignoring poly-logarithmic factors), and conjectured this is a tight upper bound for any $n$-party protocol (of any round complexity). Their conjecture was proved to be correct for single-turn (each party sends a single message) single-bit (a message is one bit) protocols Lichtenstein, Linial and Saks [Combinatorica '89], symmetric protocols Goldwasser, Tauman Kalai and Park [ICALP '15], and recently for (arbitrary message length) single-turn protocols Tauman Kalai, Komargodski and Raz [DISC '18]. Yet, the question for many-turn protocols was left completely open.

In this work we close the above gap, proving that no $n$-party protocol (of any round complexity) is resilient to $\omega(\sqrt{n})$ (adaptive) corruptions.

Paper:

TR20-071 | 4th May 2020 17:09

A Tight Lower Bound on Adaptively Secure Full-Information Coin Flip

TR20-071
Authors: Iftach Haitner, Yonatan Karidi-Heller
Publication: 4th May 2020 17:14
the parties try to output a common (close to) uniform bit, even when some adversarially chosen parties try to bias the common output. In an adaptively secure full-information coin flip, Ben-Or and Linial [FOCS '85], the parties communicate over a broadcast channel and a computationally unbounded adversary can choose which parties to corrupt during the protocol execution. Ben-Or and Linial proved that the $n$-party majority protocol is resilient to $o(\sqrt{n})$ corruptions (ignoring log factors), and conjectured this is a tight upper bound for any $n$-party protocol (of any round complexity). Their conjecture was proved to be correct for single-turn (each party sends a single message) single-bit (a message is one bit) protocols, Lichtenstein, Linial, and Saks [Combinatorica '89], symmetric protocols Goldwasser, Kalai, and Park [ICALP '15], and recently for (arbitrary message length) single-turn protocols Tauman Kalai, Komargodski, and Raz [DISC '18]. Yet, the question for many-turn (even single-bit) protocols was left completely open.
In this work we close the above gap, proving that no $n$-party protocol (of any round complexity) is resilient to $O(\sqrt{n})$ (adaptive) corruptions.