AVSS for Sharing a Single Secret Sample Clauses

AVSS for Sharing a Single Secret. Before going into the details of the AVSS, we first closely look into our AWC scheme for sharing a single secret (namely the protocol AWC Single) and see why it fails to satisfy the properties of AVSS. The first easy observation is that if Committer is honest, then the protocol AWC Single pro- vides all the properties of an AVSS (namely Com can be used as the sharing protocol, while DeCom can be used as the reconstruction protocol). Moreover, even if Committer is corrupted, the Com protocol provides all the properties of a sharing protocol of an AVSS; the problem arises during the DeCom protocol, as it may fail to satisfy two important re- quirements of a reconstruction protocol of an AVSS. More specifically, if Committer is corrupted, then the following two problems may arise during the DeCom protocol: – The corrupted Committer may not initiate the protocol DeCom, in which case, the honest parties will never ter- minate the protocol. This will be a violation of the third requirement of the termination condition of AVSS, which requires that all the honest parties should terminate the reconstruction protocol, even if D (in this case Committer) is corrupted. This problem arises because the participa- tion of Committer (namely the revelation of the primary signatures) is the key step in the DeCom protocol. ∈ – The honest parties may output ⊥ during the protocol DeCom, even if an s F was committed by Committer during the Com protocol. This is because even though a corrupted Committer cannot successfully reveal (as an INT) the primary signatures of an honest Pj ∈ WCORE / on an “incorrect” share Sh′j = Shj (such that Sh′j was not given as a share to Pj during the Com), the corrupted Committer can always successfully reveal the primary signatures of a corrupted Pj ∈ WCORE on any arbi- trary share Shj′ of his choice; this is because in AICP, if Signer (in this case the party Pj) and INT (in this case the Committer) are both corrupted, then INT can suc- cessfully reveal the signature of Signer on any arbitrary value, which is “consistent” with the verification infor- mation of the verifiers. So if the revealed shares corre- sponding to the corrupted Pj’s in WCORE do not lie on the polynomial defined by the shares of the honest Pj’s in WCORE, then the parties end up outputting ⊥, even though s /= ⊥ was committed during Com. This will be a violation of the first requirement of the correctness condition of AVSS, which demands the reconstruction of the committed value ...
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