Abstract
Murphy, Murky, Mopey, Moody, and Morose decide to write a paper together over the Internet and submit it to the prestigious CRYPTO’19 conference that has the most amazing PC. They encounter a few problems. First, not everyone is online every day: some are lazy and go skiing on Mondays; others cannot use git correctly and they are completely unaware that they are losing messages. Second, a small subset of the co-authors may be secretly plotting to disrupt the project (e.g., because they are writing a competing paper in stealth).
Suppose that each day, sufficiently many honest co-authors are online (and use git correctly); moreover, suppose that messages checked into git on Monday can be correctly received by honest and online co-authors on Tuesday or any future day. Can the honest co-authors successfully finish the paper in a small number of days such that they make the CRYPTO deadline; and perhaps importantly, can all the honest co-authors, including even those who are lazy and those who sometimes use git incorrectly, agree on the final theorem?
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- 1.
This is necessary because if a single proposer made a proposal after being elected, the adversary could make the proposer offline in that precise round.
- 2.
Later in our \({\mathsf{VSS}}\) and \({\mathsf{LE}}\) protocols that invoke \({\mathsf{RBC}}\), the fact that the \({\mathsf{RBC}}\) ’s environment
is admissible is guaranteed by construction. - 3.
Note that (a) implies that if \({{{\mathcal {E}}}}\) outputs \(\bot \), then no honest node will ever output a reconstructed secret.
- 4.
Specifically, when honest nodes running inside
want to send messages, the messages are forwarded to 
, and 
tells 
when each honest node receives what message. - 5.
For simplicity, we omit writing the randomness consumed by \({\mathsf{PKE}}.\mathsf{Enc}\) which is also part of the witness.
- 6.
Recall that the \({\mathsf{LE}}\) instance deals with its own message signing internally.
is admissible is guaranteed by construction.
want to send messages, the messages are forwarded to 
, and 
tells 
when each honest node receives what message.References
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Guo, Y., Pass, R., Shi, E. (2019). Synchronous, with a Chance of Partition Tolerance. In: Boldyreva, A., Micciancio, D. (eds) Advances in Cryptology – CRYPTO 2019. CRYPTO 2019. Lecture Notes in Computer Science(), vol 11692. Springer, Cham. https://doi.org/10.1007/978-3-030-26948-7_18
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