Security and Communication Networks

Research Article

Broadcast Complexity and Adaptive Adversaries in Verifiable Secret Sharing

Algorithm 1

SendWithCheck.
 Inputs. Player , Player , Dealer , Message
 Goal. To deliver message from player to player with the presence of an adaptive, rushing but computationally bounded (only in memory) adversary.
(1)Private channel
 (a) sends message to .
(2)Broadcast
 (a) chooses two random pad .
 (b) sends to .
 (c) D sends and to .
 (d) sends and to .
 (e) [Internal computations:] computes the value . If the value is not equal to , rejects the message , otherwise, accepts the message .
 (f) broadcasts rejecting or accepting message plus the sender . Each player holds the set which initially is empty and keeps every which its message rejected. If then disqualified.
(3)In protocol
 (a) Each player holds the set which initially is empty. After distributing the shares (first round of ) each player assigns . If then the secret could not be reconstructed and players have to commit on alternative value .