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We consider the sale of a single item to multiple buyers by arevenue-maximizing seller. Recent work of Akbarpour and Li formalizes\emph{credibility} as an auction desideratum, and prove that the only optimal,credible, strategyproof auction is the ascending price auction with reserves(Akbarpour and Li, 2019).  In contrast, when buyers' valuations are MHR, we show that the mildadditional assumption of a cryptographically secure commitment scheme sufficesfor a simple \emph{two-round} auction which is optimal, strategyproof, andcredible (even when the number of bidders is only known by the auctioneer).  We extend our analysis to the case when buyer valuations are$\alpha$-strongly regular for any $\alpha > 0$, up to arbitrary $\varepsilon$in credibility. Interestingly, we also prove that this construction cannot beextended to regular distributions, nor can the $\varepsilon$ be removed withmultiple bidders.

Credible, Truthful, and Two-Round (Optimal) Auctions via Cryptographic Commitments