Asynchronous Weak Secret Sharing | AWSS Sample Clauses

Asynchronous Weak Secret Sharing | AWSS. We construct a secret sharing protocol called Asynchronous Weak Secret Sharing (AWSS). An AWSS protocol satis es the termination and secrecy requirements of AVSS (De nition 2 on page 9). The correctness requirement is as follows. If the dealer is uncorrupted then the uncorrupted players always reconstruct the secret shared by the dealer, as in AVSS. The di erence from AVSS lies in the case where the dealer is corrupted. For AWSS we only require that: Correctness of AWSS: Once some uncorrupted player completes protocol Sh, there exists a xed value, r 2 F [ fnullg, such that the following requirements hold:

Asynchronous Weak Secret Sharing | AWSS. Like AVSS, an AWSS protocol also consists of two pro- tocols: a sharing protocol (called WSh), where the dealer shares a secret and a reconstruction protocol (called WRec), where the parties reconstruct the secret from its shares. An AWSS protocol also has three properties, namely Termina- tion, Correctness and Secrecy. The Termination and the Secrecy conditions are the same as for the AVSS (see Def- inition 2), except that Sh is replaced by WSh and Rec is replaced by WRec. The Correctness condition is also the same as for the AVSS for the case when the dealer is honest; however, the Correctness condition is weakened in AWSS for the case when the dealer is corrupted as follows: If an honest party terminates WSh then a value, say s ∈ F ∪ {⊥} is fixed. Moreover, with probability at least (1 − ϵ), each honest party will output either s or ⊥ at the end10 of WRec.