Gradecast

Gradecast stands for graded-broadcast protocol.
This definition is not adaptively secure! It is unclear what properties should hold when the sender is not correct.

Definition

From Optimal algorithms for Byzantine agreement. Paul Feldman, and Silvio Micali. 1988 and Gradecast in Synchrony and Reliable Broadcast in Asynchrony with Optimal Resilience, Efficiency, and Unconditional Security. Ittai Abraham, and Gilad Asharov. 2022

In Gradecast a sender has an input and each party outputs a value and a grade $\{0,1,2\}$ such that:
\begin{enumerate}
\item \emph{(Validity)} If the sender is honest then all honest parties output the sender's input and grade $2$.
\item \emph{(Non-equivocation)} If two honest parties output a grade $\ge 1$ then they output the same value.
\item \emph{(Agreement)} If an honest party outputs grade $2$ then all honest parties output the same output and with grade $\ge 1$.
\end{enumerate}

References
- First introduced by Optimal algorithms for Byzantine agreement. Paul Feldman, and Silvio Micali. 1988
- Simple Gradecast Based Algorithms. Michael Ben-Or, Danny Dolev, and Ezra N. Hoch. 2010
- Formalized again by On expected constant-round protocols for Byzantine agreement. Jonathan Katz, and Chiu Yuen Koo. 2009
- Also discussed in Gradecast in Synchrony and Reliable Broadcast in Asynchrony with Optimal Resilience, Efficiency, and Unconditional Security. Ittai Abraham, and Gilad Asharov. 2022