  Recent attention on secure multiparty computation and blockchain technology
has garnered new interest in developing auction protocols in a decentralized
setting. In this paper, we propose a secure and private Vickrey auction
protocol that addresses the challenge of maintaining auction correctness while
preserving the confidentiality of bidders' information. Our protocol leverages
secure multiparty computation (SMPC) techniques that enable decentralized
computation of the final payment price without disclosing additional
information. The total computational complexity of our proposed protocol,
including preparation, is $O(n^2 k)$, and the complexity for the main auction
is $O(n k)$. Furthermore, we show that our protocol is resistant to collusion
and the auction outcome is publicly verifiable, which prevents dishonest
bidders from altering this outcome.
