Verifiable Secret Sharing and Achieving Simultaneity in the Presence of Faults

Original paper: Verifiable secret sharing and achieving simultaneity in the presence of faults. Benny Chor, Shafi Goldwasser, Silvio Micali, and Baruch Awerbuch. 1985

• This work presents a VSS scheme.
• A simultaneous broadcast network guarantee that all nodes send messages simultaneously (at designated times) and all processors receive messages (at designated times).
• Assuming the hardness of RSA function, this paper shows how to construct a simultaneous broadcast network with \(n\) nodes and \(t\) Byzantine faults from a semi-synchronous network.
  • It uses OT.
• Their construction consists of a compiler that transforms algorithms, robust against \(t\) Byzantine faults in a simultaneous network, to equivalent algorithms robust against \(t\) Byzantine faults in a semi-synchronous network.
  • The transformation requires \(O(1)\) rounds of communication for every original round
  • \(O(2^{l})_{}\) local computation time
• This is actually a weak VSS in the modern terminology.