In this section, we review the den

In this section, we review the denitions of standard basic tools used throughout the paper.

Veriable Secret Sharing. An (n; t)-secret sharing scheme, is a protocol in which a dealer who holds a secret value shares the secret among n parties such that any set of t parties cannot gain any information about the secret, but any set of at least t+1 parties can reconstructs it. An (n; t)-veriable se- cret sharing (VSS) scheme is an (n; t)-secret sharing scheme with the additional property that after the sharing phase, a dishonest dealer is either disqualied or the honest parties can reconstruct the secret, even if shares sent by dishonest parties are spurious. In our protocol, we use the constantround VSS protocol of Katz et al. [22] that is based on Shamir's secret sharing scheme [29]. This result is described in Theorem 2.

Theorem 2. [22] There exists a synchronous linear (n; t)- VSS scheme for t < n=3 that is perfectly-secure against a static active adversary. The protocol requires one broadcast and three rounds of communication.

Quorum Building. A good quorum is a set of N = O(log n) parties that contains a majority of honest parties. King et al. [23] showed that a Byzantine Agreement (BA) protocol can be used to bring all parties to agreement on a collection of n good quorums. In this paper, we use the fast BA protocol of Braud-Santoni et al. [8] to build n good quorums.

Theorem 3. [23, 8] There exists an unconditionally-secure protocol that brings all good parties to agreement on n good quorums with high probability. The protocol has ~O(n) amor- tized communication and computation complexity2, and it can tolerate up to t < (1=3

ผลลัพธ์ (ไทย) 1:

In this section, we review the de nitions of standard basic tools used throughout the paper.Veri able Secret Sharing. An (n; t)-secret sharing scheme, is a protocol in which a dealer who holds a secret value shares the secret among n parties such that any set of t parties cannot gain any information about the secret, but any set of at least t+1 parties can reconstructs it. An (n; t)-veri able se- cret sharing (VSS) scheme is an (n; t)-secret sharing scheme with the additional property that after the sharing phase, a dishonest dealer is either disquali ed or the honest parties can reconstruct the secret, even if shares sent by dishonest parties are spurious. In our protocol, we use the constantround VSS protocol of Katz et al. [22] that is based on Shamir's secret sharing scheme [29]. This result is described in Theorem 2.Theorem 2. [22] There exists a synchronous linear (n; t)- VSS scheme for t < n=3 that is perfectly-secure against a static active adversary. The protocol requires one broadcast and three rounds of communication.Quorum Building. A good quorum is a set of N = O(log n) parties that contains a majority of honest parties. King et al. [23] showed that a Byzantine Agreement (BA) protocol can be used to bring all parties to agreement on a collection of n good quorums. In this paper, we use the fast BA protocol of Braud-Santoni et al. [8] to build n good quorums. ทฤษฎีบทที่ 3 [23, 8] มี protocol ปลอดภัยโดยไม่มีเงื่อนไขที่ทำให้ทุกฝ่ายดีข้อตกลงบนโควรัมดี n มีโอกาสสูง โพรโทคอลการสื่อสารเมอร์ tized ~O(n) และ complexity2 คำนวณ และมันสามารถทนได้ถึง t < (1 = 3