Motivation. Genomic data and derived interval datasets can carry sensitive information, and the analysis itself can reveal an analyst's intent. As genomic workloads are increasingly outsourced to third-party infrastructure, there is a need for privacy-preserving technologies that protect both the data and the queried loci. Results. We present BEDCrypt, a privacy-preserving system for genomic interval analytics based on homomorphic encryption in an honest-but-curious server setting. The server operates only on encrypted data and returns encrypted answers that the client decrypts locally, enabling core functionalities such as coverage summaries, interval intersections, proximity (window-style) queries, and set-similarity statistics, without revealing plaintext intervals or query genomic locations to the server.