Feldman's Verifiable Secret Sharing for a Dishonest Majority

Feldman's Verifiable Secret Sharing for a Dishonest Majority

2024-03-05 | Yi-Hsiu Chen and Yehuda Lindell
This paper presents a variant of Feldman's Verifiable Secret Sharing (VSS) protocol for the dishonest majority setting, along with additional operations such as adding and removing parties, and refreshing a sharing. The protocol ensures security in the presence of a dishonest majority, achieving security with abort. The main differences from the standard Feldman VSS include the use of a simple echo-broadcast instead of a full broadcast, the use of zero-knowledge proofs for polynomial extraction, and the absence of a "complaint" phase. The protocol also supports publicly-verifiable secret sharing, secure addition of parties, and refreshing of existing shareings. The protocols are proven to be UC secure for appropriately defined ideal functionalities. The paper also discusses the use of Feldman VSS in key generation, the security model, and the use of the ideal functionality for access structures. The protocols are designed to work with more general access structures and support asynchronous computation with minimal rounds of communication. The paper concludes with the security proofs for the protocols and their applications in threshold cryptography.This paper presents a variant of Feldman's Verifiable Secret Sharing (VSS) protocol for the dishonest majority setting, along with additional operations such as adding and removing parties, and refreshing a sharing. The protocol ensures security in the presence of a dishonest majority, achieving security with abort. The main differences from the standard Feldman VSS include the use of a simple echo-broadcast instead of a full broadcast, the use of zero-knowledge proofs for polynomial extraction, and the absence of a "complaint" phase. The protocol also supports publicly-verifiable secret sharing, secure addition of parties, and refreshing of existing shareings. The protocols are proven to be UC secure for appropriately defined ideal functionalities. The paper also discusses the use of Feldman VSS in key generation, the security model, and the use of the ideal functionality for access structures. The protocols are designed to work with more general access structures and support asynchronous computation with minimal rounds of communication. The paper concludes with the security proofs for the protocols and their applications in threshold cryptography.
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