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We present ShorTor, a protocol for reducing latency on the Tor network. ShorTor uses multi-hop overlay routing, a technique typically employed by content delivery networks, to influence the route Tor traffic takes across the internet. ShorTor functions as an overlay on top of onion routing-Tor's existing routing protocol and is run by Tor relays, making it independent of the path selection performed by Tor clients. As such, ShorTor reduces latency while preserving Tor's existing security properties. Specifically, the routes taken in ShorTor are in no way correlated to either the Tor user or their destination, including the geographic location of either party. We analyze the security of ShorTor using the AnoA framework, showing that ShorTor maintains all of Tor's anonymity guarantees. We augment our theoretical claims with an empirical analysis. To evaluate ShorTor's performance, we collect a real-world dataset of over 400,000 latency measurements between the 1,000 most popular Tor relays, which collectively see the vast majority of Tor traffic. With this data, we identify pairs of relays that could benefit from ShorTor: that is, two relays where introducing an additional intermediate network hop results in lower latency than the direct route between them. We use our measurement dataset to simulate the impact on end users by applying ShorTor to two million Tor circuits chosen according to Tor's specification. ShorTor reduces the latency for the 99th percentile of relay pairs in Tor by 148 ms. Similarly, ShorTor reduces the latency of Tor circuits by 122 ms at the 99th percentile. In practice, this translates to ShorTor truncating tail latencies for Tor which has a direct impact on page load times and, consequently, user experience on the Tor browser.