Time-delayed broadcasting for defeating inside jammers

We address the problem of jamming-resistant broadcast communications under an internal threat model. We propose a time-delayed broadcast scheme (TDBS), which implements the broadcast operation as a series of unicast transmissions distributed in frequency and time. TDBS does not rely on commonly shared secrets, or the existence of jamming-immune control channels for coordinating broadcasts. Instead, each node follows a unique pseudo-noise (PN) frequency hopping sequence. Contrary to conventional PN sequences designed for multi-access systems, the PN sequences in TDBS exhibit correlation to enable broadcast. Moreover, they are designed to limit the information leakage due to the exposure of a subset of sequences by compromised nodes. We map the problem of constructing such PN sequences to the 1-factorization problem for complete graphs. We further accommodate dynamic broadcast groups by mapping the problem of updating the assigned PN sequences to the problem of constructing rainbow paths in proper edge-colored graphs.