Efficient statistical asynchronous verifiable secret sharing with optimal resilience

TLDR: A new statistical asynchronous verifiable secret sharing (AVSS) protocol with optimal resilience is presented and a new primitive called Asynchronous Complete Secret Sharing (ACSS) is designed which is an essential building block of asynchronous multiparty computation (AMPC).

Abstract: We present a new statistical asynchronous verifiable secret sharing (AVSS) protocol with optimal resilience; ie with n = 3t + 1, where n is the total number of participating parties and t is the maximum number of parties that can be under the control of a computationally unbounded active adversary At Our protocol privately communicates O((ln3 + n4κ)κ) bits and A-casts O(n3 log(n)) bits to simultaneously share l ≥ 1 elements from a finite field F, where κ is the error parameter There are only two known statistical AVSS protocols with n = 3t+1, reported in [11] and [26] The AVSS protocol of [11] requires a private communication of O(n9κ4) bits and A-cast of O(n9κ2 log(n)) bits to share a single element from F Thus our AVSS protocol shows a significant improvement in communication complexity over the AVSS of [11] The AVSS protocol of [26] requires a private communication of O((ln3+n4)κ) bits and A-cast of O((ln3 +n4)κ) bits to share l ≥ 1 elements However, the shared element(s) may be NULL ∉ F Thus our AVSS is better than the AVSS of [26] due to two reasons: (a) The A-cast communication of our AVSS is independent of the number of secrets ie l; (b) Our AVSS makes sure that the shared value(s) always belong to F Using our AVSS, we design a new primitive called Asynchronous Complete Secret Sharing (ACSS) which is an essential building block of asynchronous multiparty computation (AMPC) Using our ACSS scheme, we can design a statistical AMPC with optimal resilience; ie, with n = 3t + 1, that privately communicates O(n5κ) bits per multiplication gate This will significantly improve the only known statistical AMPC of [8] with n = 3t + 1, which privately communicates Ω(n11κ4) bits and A-cast Ω(n11κ2 log(n)) bits per multiplication gate