Data centers increasingly host mutually distrustful users on shared infrastructure. A powerful tool to safeguard such users are digital signatures. Digital signatures have revolutionized Internet-scale applications, but current signatures are too slow for the growing genre of microsecond-scale systems in modern data centers. We propose DSig, the first digital signature system to achieve single-digit microsecond latency to sign, transmit, and verify signatures in data center systems. DSig is based on the observation that, in many data center applications, the signer of a message knows most of the time who will verify its signature. We introduce a new hybrid signature scheme that combines cheap single-use hash-based signatures verified in the foreground with traditional signatures pre-verified in the background. Compared to prior state-of-the-art signatures, DSig reduces signing time from 18.9 to 0.7 us and verification time from 35.6 to 5.1 us, while keeping signature transmission time below 2.5 us. Moreover, DSig achieves 2.5x higher signing throughput and 6.9x higher verification throughput than the state of the art. We use DSig to (a) bring auditability to two key-value stores (HERD and Redis) and a financial trading system (based on Liquibook) for 86% lower added latency than the state of the art, and (b) replace signatures in BFT broadcast and BFT replication, reducing their latency by 73% and 69%, respectively