  Internet platforms depend on accurately determining the geographical
locations of online users to deliver targeted services (e.g., advertising). The
advent of decentralized platforms (blockchains) emphasizes the importance of
geographically distributed nodes, making the validation of locations more
crucial. In these decentralized settings, mutually non-trusting participants
need to {\em prove} their locations to each other. The incentives for claiming
desired location include decentralization properties (validators of a
blockchain), explicit rewards for improving coverage (physical infrastructure
blockchains) and regulatory compliance -- and entice participants towards
prevaricating their true location malicious via VPNs, tampering with internet
delays, or compromising other parties (challengers) to misrepresent their
location. Traditional delay-based geolocation methods focus on reducing the
noise in measurements and are very vulnerable to wilful divergences from
prescribed protocol.
  In this paper we use Internet delay measurements to securely prove the
location of IP addresses while being immune to a large fraction of Byzantine
actions. Our core methods are to endow Internet telemetry tools (e.g., ping)
with cryptographic primitives (signatures and hash functions) together with
Byzantine resistant data inferences subject to Euclidean geometric constraints.
We introduce two new networking protocols, robust against Byzantine actions:
Proof of Internet Geometry (PoIG) converts delay measurements into precise
distance estimates across the Internet; Proof of Location (PoLoc) enables
accurate and efficient multilateration of a specific IP address. The key
algorithmic innovations are in conducting ``Byzantine fortified trigonometry"
(BFT) inferences of data, endowing low rank matrix completion methods with
Byzantine resistance.
