1. Single or multiple radios, each transmitting at the same constant power, P c t , and frequency f c $_{t}$. 2. Single or multiple radios, each being ability to adapt its transmission frequency, f j t , over time; j is an index of adversarial radios. 3. Multiple radios with adaptive transmission capabili- ties as above, and additionally the ability to estab- lish fast communication among any of the adversarial nodes equipped with those radios. Adversarial radios in all above cases can record GNSS signals and navigation messages for long periods. For all adversaries above, we consider a nominal range R , within which adversarial transmissions can be received, with this value varying for different adversarial radios. We denote this as the area under attack . Clearly, the more powerful and the more numerous radios an adversary has, the higher its potential impact can be. In the sense, it can influence a larger system area and potentially mislead more receivers. We assume that the area under attack does not coin- cide with the wireless system area. In other words, the adversary has limited physical presence and communica- tion capabilities. This implies that nodes can lock on ac- tual GNSS signals for a period of time before entering an area under attack. We do not dwell on how frequently and under what circumstances nodes are under attack. Rather, we investigate the strength of different defense mechanisms given that a node is under attack. We abstract the phys- ical properties of the adversarial equipment and consider the periods of time it can cause unavailability and maintain the receiver locked on the spoofed signal. We emphasize that our attack model is not the worst case; this would be a receiver under attack during its cold start , that is, the first time it is turned on and searches for GNSS signals to lock on. However, our adversary model corresponds to a broad range of realistic cases and it is a powerful one. For example, returning to the cargo example of the introduction: It will be hard for an adversary to control a receiver from its installation, e.g., on a container, and then throughout a trip. But it would be rather easy to select a location and time to mount its attack. Regarding the strength of the attacker, it is noteworthy that attacks are possible without any physical access to and without tampering with the victim node(s) software and hardware. The adversary can construct a transmitter that emits sig- nals identical to those sent by a satellite, and mislead the receiver that signals originate from a visible satellite. How- ever, the attacker has to first force the receiver to lose its “lock” on the satellite signals. This can be achieved by jamming legitimate GNSS signals, by transmitting a sufficiently powerful signal that interferes with and ob- scures the GNSS signals [12]. Jammers are simple to con- struct with low cost and very effective: for example, with 3.2 Mounting Attacks against GNSS Re- ceivers 3 Received GNSS signal delayed Transmit after t replay NAV message buffering Preamble detection Victim receiver V Total delay t replay Adversary Figure 1: Illustration of the replay attack: the adversary captures and replays the signal after some time t$_{replay}$ = t min replay + τ , with the τ ≥ 0 chosen by the adversary, and t min replay > 0 imposed by the specifics of the attack configu- ration and the adversary capabilities. 1 Watt of transmission power, the reception of GNSS sig- nals is stopped within a radius of approximately 35 km radius [6,12]. Then, the adversary can spoof GNSS signals, i.e., forge and transmit signals at the same frequency and with power that exceeds that of the legitimate GNSS signal at the re- ceiver’s antenna. Satellite simulators are capable of broad- casting simultaneously signals carrying counterfeit naviga- tion data from ten satellites. 3 The spoofed signal can also be generated by manipulating and rebroadcasting actual signals ( meaconing ). As long as the lock of the victim re- ceiver V on the spoofed signal persists, loc ( V ) is under the influence or full control of the adversary. Apart from jamming, the adversary could take advan- tage of gaps in coverage , i.e., areas and periods of time for which V cannot lock on to more than three satellite sig- nals. Clearly, this can be often possible in urban areas or because of the terrain, such as tunnels or obstructions from high-rise buildings. We do not consider further this case, as such loss of satellite signals is not under the control of the attacker. Nonetheless, the tests we propose here are ef- fective independently of what causes receivers to loose lock on GNSS signals. The replay attack can be viewed as a part of a more general class of relay attacks : the attacker receives at one location legitimate GNSS signals, relays those to another location 3.3 Replay attack $^{3}$The adversary can deceive the receiver after down-conversion of the satellite signal, with one component in-phase and one in- quadrature: I ( t ) = a$_{i}$C$_{a}$ ( t ) M ( t ) cos ( ft ) (2) Q ( t ) = a$_{q}$C$_{a}$ ( t ) M ( t ) sin ( ft ) (3) C$_{a}$ is the C/A (Course/Aquisition) code, M ( t ) is the NAV message, and coefficients a$_{i}$ and a$_{q}$ represent the signal attenuation. The at- tacker could pick the amplifying coefficients a$_{i}$ and a$_{q}$ such that the received signal power exceeds the nominal power od a GPS signal [13].