Abstract:
A passive entry system for an automotive vehicle that is configured to prevent relay attacks by analyzing magnet vectors and angles created by a plurality of antennas mounted on the vehicle is disclosed. A vehicle including a control unit configured to broadcast a wake-up signal to prompt a fob to power-up if the fob is in a low-power consumption mode and to transmit signals through a plurality of antennas coupled to the vehicle is provided, along with a fob configured to recognize the wake-up signal and to generate a response signal for the control unit in response to recognize the wake-up signal. The fob includes a controller that is programmed to receive signals transmitted from each of the plurality of antennas coupled to the vehicle, retrieve constant values from stored a memory, and calculate a magnetic integrity defining the relative position of each of the plurality of antennas. The controller allows access to the vehicle if magnetic integrity is found, and denies access to the vehicle if magnetic integrity is not found.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is the national phase of International Application No. PCT/US2014/068169, filed Dec. 2, 2014, which claims the benefit of U.S. Provisional Patent Application No. 61/911,225, filed Dec. 3, 2013, and U.S. Provisional Patent Application No. 61/975,447, filed Jan. 4, 2014, the disclosures of which are hereby incorporated by reference in their entirety. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    Traditionally, door access and authorization to start a vehicle such as an automobile has been achieved using physical key and lock systems. In these systems, inserting a correct key into the door and ignition locks enabled the user to enter and drive the car. 
         [0003]    In recent years, however, traditional key systems have been augmented with, and in many cases replaced, with remote keyless entry (RKE) devices in which users are able to open their car remotely by pressing a button on a portable communication device such as a key fob or key card. In these systems, the authorization to drive typically continued to be provided by physical key and lock systems. In some cases, however, physical keys included embedded immobilizer chips to prevent key copying. 
         [0004]    Even more recently, complex embedded electronic systems have become common to provide access and start functions, and to provide wide ranging functions to improve driver safety and convenience. These systems include Passive Entry Passive Start (PEPS) systems. In PEPS systems, a remote receiver and transmitter (or transceiver) is carried with the user in a portable communication device such as a key fob or a card. The portable communication device when successfully challenged transmits a radio frequency (RF) signal to a module within the vehicle for performing a variety of remote vehicle function such door lock/unlock, enabling engine start, or activating external/internal lighting. Passive entry systems include a transmitter and receiver (or transceiver) in an electronic control module disposed within the vehicle. The transceiver is typically in communication with one or more devices (e.g., door lock mechanism) for determining when a request for actuation of a device is initiated (e.g., lifting a door handle) by a user. 
         [0005]    Upon sensing the request for actuation, the transceiver broadcasts a passive entry interrogating signal. The fob upon receiving the interrogating signal from the ECU, the portable communication device determines if the interrogating signal is valid. If it is determined a valid signal, then the fob automatically broadcasts an output signal which includes an encrypted or rolling identification code to the electronic control module. The electronic module thereafter determines the validity of the output signal and generates a signal to the device to perform an operation (e.g., the door lock mechanism to unlock the door) if the output signal is determined valid. 
         [0006]    Passive entry systems are susceptible to security threats such as relay attack. Relay attack occurs when a first thief triggers the actuation of an interrogation signal, for example, by lifting the vehicle door handle. The passive entry system in the vehicle broadcasts the interrogation signal, since it is expected the fob is in the vicinity of a user lifting the door handle. The first thief carries a repeater which receives the interrogation signal and retransmits the interrogation signal to a second thief in close proximity to a user having an authorized fob capable of broadcasting a response signal for unlocking the vehicle. The re-transmitted signal is typically a UHF signal which can be transmitted over a long range distance as opposed to a low frequency (LF) signal. The second thief also carrying a repeater device receives the UHF signal from the first thief. The signal is decoded and the re-transmitted as a LF signal to the user carrying the authorized fob. The fob receives the re-transmitted signal from the second thief and responds to the received interrogation signal accordingly. The second thief receives the response signal having the valid coded information therein and re-transmits the signal to the first thief. The first thief receives the authenticated response signal and transmits it to the vehicle. The vehicle receives the response signal, validates the signal, and unlocks the vehicle doors. The PEPS system can also be prompted to allow the thief to start the vehicle. The present disclosure addresses methods for preventing relay attacks of the type described above. 
       SUMMARY OF THE INVENTION 
       [0007]    The present disclosure provides a passive entry system for an automotive vehicle that is configured to prevent relay attacks by analyzing magnet vectors and angles created by a plurality of antennas mounted on the vehicle. In one aspect, the disclosure provides a vehicle including a control unit configured to broadcast a wake-up signal to prompt a fob to power-up if the fob is in a low-power consumption mode and to transmit signals through a plurality of antennas coupled to the vehicle; and a fob configured to recognize the wake-up signal and to generate a response signal for the control unit in response to recognize the wake-up signal. The fob includes a controller that is programmed to receive signals transmitted from each of the plurality of antennas coupled to the vehicle, retrieve constant values from stored a memory, and calculate a magnetic integrity defining the relative position of each of the plurality of antennas. The controller allows access to the vehicle if magnetic integrity is found, and denies access to the vehicle if magnetic integrity is not found. 
         [0008]    In another aspect, the present disclosure provides a passive entry system for an automotive vehicle. The vehicle includes a control unit configured to broadcast a wake-up signal to prompt a fob to power-up if the fob is in a low-power consumption mode and to apply a driving current to and transmit signals through a plurality of antennas coupled to the vehicle, and a fob configured to recognize the wake-up signal and to generate a response signal for the control unit in response to recognizing the wake-up signal. The fob includes a fob controller programmed to receive signals transmitted from each of the plurality of antennas coupled to the vehicle, calculate a first angle between the signals transmitted by at least two of the antennas, receive an encrypted signal from the control unit describing a change in driving current applied to the antenna, and calculate a second angle between the signals transmitted by at least two of the antennas. The controller compares the first angle to the second angle and denies access to vehicle functions if the first angle is substantially equal to the second angle. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]      FIG. 1  is a block diagram of an automotive vehicle with a Passive Start and Entry System (PEPS) configured to communicate with a personal communication device or token. 
           [0010]      FIG. 2  is a simplified diagram of a vehicle illustrating a relay attack. 
           [0011]      FIG. 3 a    is a diagram illustrating a two antenna system including antennas corresponding to vehicle  12  in communication with a key fob and corresponding magnetic fields. 
           [0012]      FIG. 3 b    is a diagram illustrating an isometric view of a three antenna system and magnetic fields generated by the antennas in the system. 
           [0013]      FIG. 4  illustrates driving currents applied to antennas that can be changed to differentiate the vehicle from a relay operated by a thief. 
           [0014]      FIG. 5  illustrates another embodiment of driving currents applied to antennas that can be changed to differentiate the vehicle from a relay operated by a thief. 
           [0015]      FIG. 6  is a top view of a vehicle and corresponding fob, illustrating antennas on the vehicle and vectors corresponding to the fob. 
           [0016]      FIG. 7  is an alternate top view of a vehicle and corresponding fob, illustrating antennas on the vehicle and vectors corresponding to the fob. 
           [0017]      FIG. 8  is another top view of a vehicle and corresponding fob, illustrating antennas on the vehicle and vectors corresponding to the fob. 
           [0018]      FIG. 9  is another top view of a vehicle and corresponding fob, illustrating antennas on the vehicle and vectors corresponding to the fob. 
           [0019]      FIG. 10  is a block diagram illustrating one set of process steps for preventing RSA. 
           [0020]      FIG. 11  is a block diagram illustrating an alternate set of process steps for preventing RSA. 
           [0021]      FIG. 12  is another top view of a vehicle and corresponding fob, illustrating antennas on the vehicle and vectors corresponding to the fob. 
           [0022]      FIG. 13  is a block diagram illustrating an alternate set of process steps for preventing RSA. 
       
    
    
     DESCRIPTION 
       [0023]    Referring now to  FIG. 1 , an automotive vehicle  12  with a Passive Start and Entry System (PEPS) configured to communicate with a personal communication device or token  14 , e.g., fob, card, etc. is shown. The automotive vehicle  12  includes an internal control system that comprises a micro-controller  16  electrically coupled with a low frequency transmitter  18  and a high frequency receiver  20 , e.g., a radio frequency receiver. Other configurations and arrangements are, of course, also possible. For example, the micro-controller  16  may be electrically coupled with a high frequency transmitter (not shown) and/or a low frequency receiver (not shown). It is understood that the term passive entry system herein includes passive engine start systems in which this anti-theft system may be applied to. 
         [0024]    As used herein the phrase “low frequency” typically refers to frequencies in the range of 3-300 KHz. The phrase “high frequency” or “ultra high frequency” (UHF) typically refers to frequencies in the range of 300 MHZ-3 GHz. Other ranges, however, are also possible. LF signals are most typically transmitted at 125 kHz while high frequency signals are most typically in the 300 MHz range. 
         [0025]    In the embodiment illustrated in  FIG. 1 , antennas  22 ,  24  and  25  are electrically coupled with the low frequency transmitter  18 . An antenna  26  is coupled with the radio frequency receiver  20 . The position of the antennas  22 ,  24 ,  25  within the vehicle  12  is known by the micro-controller  16 . As discussed below, this position information may be used by the micro-controller  16  and fob  14  to determine the location of the fob  14  relative to the antennas  22 ,  24 ,  25 . For example, the antennas  22 ,  24 ,  25  may respectively be positioned on or near the roof and on or near a driver&#39;s side door and passenger&#39;s side door of the vehicle  12 . In other embodiments, additional antennas (as well as additional receivers and/or transmitters) may be positioned throughout the vehicle to, inter alia, monitor additional regions of the vehicle  12 , such as a trunk. 
         [0026]    The micro-controller  16  of  FIG. 1  may be coupled with an engine system  28  and a door system  30 . The micro-controller  16  may control/monitor the operation of the systems  28 ,  30 . For example, the micro-controller  16  may lock and unlock the door system  30  in response to receiving suitable remote keyless entry commands. In other embodiments, the micro-controller  16  may also be coupled with any suitable vehicle system to be controlled/monitored by the PEPS module to control lighting system or climate control system. 
         [0027]    In the embodiment of  FIG. 1 , the fob  14  includes a micro-controller  32  electrically coupled with a low frequency receiver  34  and a high frequency transmitter  36 , e.g., a radio frequency transmitter. In other embodiments, the micro-controller  32  may be electrically coupled with a high frequency receiver and/or a low frequency transmitter. Other configurations and arrangements are also possible. An energy storage unit  37 , e.g., a battery, capacitor, etc., supplies power to the micro-controller  32 , low frequency receiver  34  and high frequency transmitter  36 . 
         [0028]    A 3D coil antenna  38  is electrically coupled with the low frequency receiver  34 . An antenna  40  is electrically coupled with the radio frequency transmitter  36 . In other embodiments, the fob  14  may include buttons and/or a display (not shown) associated with remote keyless entry functions such as door locking/unlocking and panic alarm as well as others. 
         [0029]    In the embodiment of  FIG. 1 , the low frequency receiver  34  of the fob  14  receives wake-up signals broadcast via the low frequency transmitter  18  from the vehicle  12 . The wake-up signals prompt the micro-controller  34  to power-up from a low-power consumption mode in anticipation of further communications and in advance of executing further code. 
         [0030]    An example passive entry sequence may begin when a door handle switch (not shown) of the door system  30  generates a triggering pulse. This triggering pulse is provided to the micro-controller  16 . In response to the triggering pulse, the micro-controller  16  generates a trigger generation function. The low frequency transmitter  18  is activated to generate the low frequency wake-up signals, discussed above, associated with the trigger generation function. The low frequency wake-up signals are broadcast via the antennas  22 ,  24 ,  25 . The low frequency wake-up signals respectively broadcast by the antennas  22 ,  24 ,  25  may include information indicative of the antenna from which it was broadcast. 
         [0031]    As discussed above, the low frequency wake-up signals may facilitate locating the fob  14  relative to the antennas  22 ,  24 ,  25 . In some embodiments, the low frequency receiver  34  includes suitable circuitry (not shown) for measuring a received signal strength indicator (RSSI) of each of the low frequency wake-up signals. The micro-controller  32  includes the RSSI information in a response sent to the controller  16 . The controller  16  determines which antenna  22 ,  24 ,  25  is nearest the fob  14  based on the RSSI information. Locating the fob  14  relative to the antennas  22 ,  24 ,  25  may ensure that a user of the fob  14  is located in the area where the passive function is being requested. For example, locating the fob  14  relative to the antennas  22 ,  24 ,  25  may ensure that the user of the fob  14  is located outside the door system  30  when the door handle switch (not shown) is actuated. Likewise, locating the fob  14  relative to the antennas  22 ,  24  may reveal that the fob  14  is located within the cabin of the vehicle  12 . 
         [0032]    In certain embodiments, the micro-controller  16  generates a random number to be used as a seed number in a mathematical transformation that is also known by the micro-controller  32  as part of any suitable challenge/response validation sequence. A challenge signal that includes information indicative of the random number may be broadcast from the vehicle  12 . The fob  14  receives the challenge signal. The micro-controller  32  applies the mathematical transformation to the random number. The transformed random number, as well as the RSSI information discussed above and a fob identifier, are included in a response sent to the vehicle  12 . The micro-controller  16  may then check the fob identifier and the transformed random number to validate the fob  14 . 
         [0033]    The controller  32 , as discussed above, may permit, for example, a user to unlock and/or start the vehicle  12 . In some embodiments, a touch sensor or button on a door (not shown) triggers the controller  32  to begin the interrogation process described above. In other embodiments, a user of the fob  14  need not press/touch the fob  14  to, for example, unlock and/or start the vehicle  12 . Rather, the user simply needs to approach the vehicle  12 . In such embodiments, the controller  32  may periodically transmit, as discussed above, a wireless signal, e.g., a polling signal, to check if any fobs are within a vicinity of the vehicle  12 . An example message rate may be approximately once a second in order to trigger a fob of a user that is approaching the vehicle  12 . Any fob within the communication range may respond, as discussed above, to the polling signal. Thereafter, the controller  32  may initiate and complete the interrogation process described above before the user, for example, pulls a door handle (not shown). 
         [0034]    Returning again to  FIG. 1 , the fob  14  may, as introduced above, recognize the polling signals broadcast by the controller  32 . For example, the fob  14  may store one or more identifiers that are compared with a corresponding identifier embedded in the received polling signals. If the identifiers embedded in the polling signals match one of the stored identifiers, the fob  14  may recognize the polling signals. 
         [0035]    In some embodiments, the fob  14  may store a global identifier and a local identifier. The global identifier may be common to some or all fobs produced by a manufacturer of such fobs and may be used, for example, to test a batch of fobs produced by the manufacturer. Other uses, however, are also possible. The local identifier may be specific to a certain vehicle and may be broadcast, for example, via the polling signals. As such, fobs for different vehicles may have the same global identifier but different local identifiers. 
         [0036]    The fob  14  illustrated in  FIG. 1  may store the local identifier in memory (not shown) associated with the low frequency receiver  34  (“receiver memory”) and memory (not shown) associated with the micro-controller  32  (“micro-controller memory”). The fob  14  may store the global identifier in the micro-controller memory. During an example recognition process, the fob  14  may compare the identifier embedded in the received polling signals against the copy of the local identifier stored in the receiver memory and the copy of the global identifier stored in the micro-controller memory. If the received identifiers match any of the aforementioned stored identifiers, the fob  14  recognizes the polling signals and powers-up in anticipation of further communication, e.g., transmission of a response signal, data processing, etc. If the received identifiers do not match the stored identifiers, the fob  14  does not recognize the polling signals. As apparent to those of ordinary skill, a greater amount of power from the battery  37  is consumed if the fob  14  recognizes the polling signals because the fob  14  powers-up if it recognizes the polling signals. 
         [0037]    Referring now to  FIG. 2  in a relay-attack event, a first thief  42  actuates the passive entry system by performing an initiation event such as lifting a door handle, as described above. The first thief  42  carries a first device, such as a first repeater device (not shown), for receiving the LF signal broadcast by the controller  32  via the LF antennas  22 ,  24 , and  25 . LF signals, as described above, are typically broadcast at 125 KHz. The first device demodulates the received interrogation signal  46  and attempts to reproduce the interrogation signal  46  as a UHF signal (e.g., 800 MHz). The interrogation signal  46  is transmitted as a high frequency or UHF signal to a second repeater device carried by a second thief  44 . The second thief is positioned in close proximity to a user carrying an authorizing fob  14 . The signal transmitted by the first thief  42  is transmitted as a UHF signal so that the communication signal has sufficient signal strength for communicating the reproduced signal over a large distance (i.e., larger than that what can be achieved by a LF signal) to the second thief  44 . As a result, the user carrying the fob  14  need not be in close proximity to the vehicle  12 ; rather, the user may be at a distance far away from the vehicle  12  such that the first thief&#39;s actions at the vehicle  12  are unobservable to the user carrying the authenticating fob  14 . 
         [0038]    The second repeater device carried by the second thief  44  receives and demodulates the UHF signal in an attempt to reproduce the original interrogation signal  46 . In response to demodulating the UHF signal, the second repeater device carried by the second thief  44  modulates the data of the received signal and transmits the data as a reproduced LF signal to the fob  14  in an attempt to duplicate the original LF signal broadcast by the controller  32 . The reproduced LF signal from the second thief  44  is received by the nearby fob  14 . If the data of the received LF signal matches the authenticating data stored in fob  14 , a response signal is transmitted by the fob  14 . The second repeater device carried by the second thief  44  receives the response signal transmitted by the fob  14 . The response signal is demodulated and re-transmitted as a reproduced response signal to the first thief  42 . The repeater device carried by the first thief  42  receives the signal and broadcasts the reproduced response signal to controller  32  of the vehicle  12  for obtaining access to the vehicle  12 . 
         [0039]    In the event the LF communication signal broadcast by the second thief  44  to the fob  14  does not match the authenticating data stored in the memory of the fob  14 , then the fob  14  remains non-responsive and the relay-attack is thwarted. 
         [0040]    Referring now to  FIG. 3 a   , a diagram illustrating a two antenna system including, for example, antennas  22  (O) and  24  (O′) corresponding to vehicle  12  and key fob  14  (P) is shown to illustrate magnetic fields generated in the system. The following equations are used to define the magnetic fields, distances, and angles in the system: 
         [0000]    Coordinate systems:
 
1. XYZ with origin O
 
2. X′Y′Z′ with origin O′
 
3. UVW with origin P
 
Coil antenna O generates {right arrow over (H)} (H U , H V , H W ) at P w.r.t. UVWP frame
 
Coil antenna O′ generates {right arrow over (H)}′ (H′ U , H′ V , H′ W ) at P w.r.t. UVWP frame
 
H fields from Antenna O and Antenna O′ are linear related.
 
R=Distance from O to O′
 
At point P with Antenna O′, H′=√{square root over (H U   2 +H V   2 +H W   2 )}
 
At point P with Antenna O′, H′=H′=√{square root over (H′ U   2 +H′ V   2 +H′ W   2 )}
 
For any two vectors in space:
 
         [0000]    
       
         
           
             
               
                 H 
                 → 
               
               · 
               
                 
                   H 
                   ′ 
                 
                 → 
               
             
             = 
             
               
                 H 
                 · 
                 
                   H 
                   ′ 
                 
                 · 
                 cos 
               
                
               
                   
               
                
               β 
             
           
         
       
       
         
           
             
               cos 
                
               
                   
               
                
               β 
             
             = 
             
               
                 
                   H 
                   → 
                 
                 · 
                 
                   
                     H 
                     ′ 
                   
                   → 
                 
               
               
                 H 
                 · 
                 
                   H 
                   ′ 
                 
               
             
           
         
       
       
         
           
             
               
                 H 
                 → 
               
               · 
               
                 
                   H 
                   ′ 
                 
                 → 
               
             
             = 
             
               
                 
                   H 
                   U 
                 
                 · 
                 
                   H 
                   U 
                   ′ 
                 
               
               + 
               
                 
                   H 
                   V 
                 
                 · 
                 
                   H 
                   V 
                   ′ 
                 
               
               + 
               
                 
                   H 
                   W 
                 
                 · 
                 
                   H 
                   W 
                   ′ 
                 
               
             
           
         
       
       
         
           
             
               cos 
                
               
                   
               
                
               β 
             
             = 
             
               
                 
                   
                     H 
                     U 
                   
                   · 
                   
                     H 
                     U 
                     ′ 
                   
                 
                 + 
                 
                   
                     H 
                     V 
                   
                   · 
                   
                     H 
                     V 
                     ′ 
                   
                 
                 + 
                 
                   
                     H 
                     W 
                   
                   · 
                   
                     H 
                     W 
                     ′ 
                   
                 
               
               
                 
                   
                     
                       H 
                       U 
                       2 
                     
                     + 
                     
                       H 
                       V 
                       2 
                     
                     + 
                     
                       H 
                       W 
                       2 
                     
                   
                 
                 · 
                 
                   
                     
                       H 
                       U 
                       ′2 
                     
                     + 
                     
                       H 
                       V 
                       ′2 
                     
                     + 
                     
                       H 
                       W 
                       ′2 
                     
                   
                 
               
             
           
         
       
     
         [0041]    The angles between the two antennas can be used by the fob to determine whether a relay attack has occurred. 
         [0042]    Referring now to  FIG. 3 b   , a diagram illustrating isometric view of a three antenna system including antennas  22 (A 0 ),  24  (A 1 ), and  25  (A 2 ) corresponding to vehicle  12  and corresponding key fob  14  is shown to illustrate magnetic fields generated by the antennas in the system. As described below, constant data (m0, m1, m2, R0, R1, R2, k, l, n), relative distances between the fob and antenna, and angle data corresponding the position of the fob as compared to the antenna systems can be used to calculate a magnetic field integrity of communications between the antennas, and therefore to determine whether signals are being transmitted from an authorized fob  14  or from another transmitter. The following equations are used to define the magnetic intensity vectors, distances, and angles between the antennas and key fob, as also shown in  FIG. 3 : 
         [0000]    Coil antenna A 0  generates {right arrow over (H0)}
 
Coil antenna A l  generates {right arrow over (H1)}
 
Coil antenna A 2  generates {right arrow over (H2)}
 
R 0 =Distance from A 1  to A 2  
 
R 1 =Distance from A 0  to A 2  
 
R 2 =Distance from A 0  to A 1  
 
r0=Distance from F to A0
 
r1=Distance from F to A1
 
r2=Distance from F to A2
 
φ0=Angle between r0 and antenna A0
 
φ1=Angle between r0 and antenna A1
 
φ2=Angle between r0 and antenna A2
 
       In ΔFA0A2, let ∠FA0A2=α0, ∠FA2A0=α1 
     In ΔFA1A2, let ∠FA2A1=α2, ∠FA1A2=α3 
     In ΔFA0A1, let ∠FA1A0=α4, ∠FA0A1=α5 
     In ΔA0A1A2, let ∠A1A0 A2=A, ∠A0 A2A1=B, let ∠A0A1A2=C, 
       [0043]    
       
         
           
             
               cos 
                
               
                   
               
                
               
                 α 
                 0 
               
             
             = 
               
              
             
               
                 
                   
                     
                       r 
                       0 
                       2 
                     
                     + 
                     
                       R 
                       1 
                       2 
                     
                     - 
                     
                       r 
                       2 
                       2 
                     
                   
                   
                     2 
                      
                     
                       r 
                       0 
                     
                      
                     
                       R 
                       1 
                     
                   
                 
                  
                 
                   
 
                 
                  
                 cos 
                  
                 
                     
                 
                  
                 
                   α 
                   1 
                 
               
               = 
                 
                
               
                 
                   
                     
                       
                         r 
                         2 
                         2 
                       
                       + 
                       
                         R 
                         1 
                         2 
                       
                       - 
                       
                         r 
                         0 
                         2 
                       
                     
                     
                       2 
                        
                       
                         r 
                         2 
                       
                        
                       
                         R 
                         1 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   cos 
                    
                   
                       
                   
                    
                   
                     α 
                     2 
                   
                 
                 = 
                   
                  
                 
                   
                     
                       
                         
                           
                             r 
                             2 
                             2 
                           
                            
                           
                             R 
                             0 
                             2 
                           
                         
                         - 
                         
                           r 
                           1 
                           2 
                         
                       
                       
                         2 
                          
                         
                           r 
                           2 
                         
                          
                         
                           R 
                           0 
                         
                       
                     
                      
                     
                       
 
                     
                      
                     cos 
                      
                     
                         
                     
                      
                     
                       α 
                       3 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             r 
                             1 
                             2 
                           
                           + 
                           
                             R 
                             0 
                             2 
                           
                           - 
                           
                             r 
                             2 
                             2 
                           
                         
                         
                           2 
                            
                           
                             r 
                             i 
                           
                            
                           
                             R 
                             0 
                           
                         
                       
                        
                       
                         
 
                       
                        
                       cos 
                        
                       
                           
                       
                        
                       
                         α 
                         4 
                       
                     
                     = 
                     
                       
                         
                           
                             
                               r 
                               0 
                               2 
                             
                             + 
                             
                               R 
                               2 
                               2 
                             
                             - 
                             
                               r 
                               1 
                               2 
                             
                           
                           
                             2 
                              
                             
                               r 
                               0 
                             
                              
                             
                               R 
                               2 
                             
                           
                         
                          
                         
                           
 
                         
                          
                         cos 
                          
                         
                             
                         
                          
                         
                           α 
                           5 
                         
                       
                       = 
                       
                         
                           
                             
                               
                                 r 
                                 1 
                                 2 
                               
                               + 
                               
                                 R 
                                 2 
                                 2 
                               
                               - 
                               
                                 r 
                                 0 
                                 2 
                               
                             
                             
                               2 
                                
                               
                                 r 
                                 1 
                               
                                
                               
                                 R 
                                 2 
                               
                             
                           
                            
                           
                             
 
                           
                            
                           
                             H 
                             0 
                           
                         
                         = 
                         
                           
                             
                               
                                 m 
                                 0 
                               
                               
                                 4 
                                  
                                 
                                   πr 
                                   0 
                                   3 
                                 
                               
                             
                              
                             
                               
                                 1 
                                 + 
                                 
                                   3 
                                    
                                   
                                     cos 
                                     2 
                                   
                                    
                                   
                                     ϕ 
                                     0 
                                   
                                 
                               
                             
                              
                             
                               
 
                             
                              
                             
                               H 
                               1 
                             
                           
                           = 
                           
                             
                               
                                 
                                   m 
                                   1 
                                 
                                 
                                   4 
                                    
                                   
                                     πr 
                                     1 
                                     3 
                                   
                                 
                               
                                
                               
                                 
                                   1 
                                   + 
                                   
                                     3 
                                      
                                     
                                       cos 
                                       2 
                                     
                                      
                                     
                                       ϕ 
                                       1 
                                     
                                   
                                 
                               
                                
                               
                                 
 
                               
                                
                               
                                 H 
                                 2 
                               
                             
                             = 
                             
                               
                                 
                                   
                                     m 
                                     2 
                                   
                                   
                                     4 
                                      
                                     
                                       πr 
                                       2 
                                       3 
                                     
                                   
                                 
                                  
                                 
                                   
                                     1 
                                     + 
                                     
                                       3 
                                        
                                       
                                         cos 
                                         2 
                                       
                                        
                                       
                                         ϕ 
                                         2 
                                       
                                     
                                   
                                 
                                  
                                 
                                   
 
                                 
                                  
                                 cos 
                                  
                                 
                                     
                                 
                                  
                                 
                                   ϕ 
                                   0 
                                 
                               
                               = 
                               
                                 
                                   
                                     
                                       
                                         cos 
                                          
                                         
                                             
                                         
                                          
                                         
                                           α 
                                           0 
                                         
                                       
                                       - 
                                       
                                         cos 
                                          
                                         
                                             
                                         
                                          
                                         
                                           
                                             α 
                                             5 
                                           
                                           · 
                                           cos 
                                         
                                          
                                         
                                             
                                         
                                          
                                         A 
                                       
                                     
                                     
                                       sin 
                                        
                                       
                                           
                                       
                                        
                                       A 
                                     
                                   
                                   + 
                                   
                                     k 
                                      
                                     
                                       
 
                                     
                                      
                                     cos 
                                      
                                     
                                         
                                     
                                      
                                     
                                       ϕ 
                                       1 
                                     
                                   
                                 
                                 = 
                                 
                                   
                                     
                                       
                                         
                                           cos 
                                            
                                           
                                               
                                           
                                            
                                           
                                             α 
                                             1 
                                           
                                         
                                         - 
                                         
                                           cos 
                                            
                                           
                                               
                                           
                                            
                                           
                                             
                                               α 
                                               2 
                                             
                                             · 
                                             cos 
                                           
                                            
                                           
                                               
                                           
                                            
                                           B 
                                         
                                       
                                       
                                         sin 
                                          
                                         
                                             
                                         
                                          
                                         B 
                                       
                                     
                                     + 
                                     
                                       l 
                                        
                                       
                                         
 
                                       
                                        
                                       cos 
                                        
                                       
                                           
                                       
                                        
                                       
                                         ϕ 
                                         2 
                                       
                                     
                                   
                                   = 
                                   
                                     
                                       
                                         
                                           cos 
                                            
                                           
                                               
                                           
                                            
                                           
                                             α 
                                             3 
                                           
                                         
                                         - 
                                         
                                           cos 
                                            
                                           
                                               
                                           
                                            
                                           
                                             
                                               α 
                                               4 
                                             
                                             · 
                                             cos 
                                           
                                            
                                           
                                               
                                           
                                            
                                           C 
                                         
                                       
                                       
                                         sin 
                                          
                                         
                                             
                                         
                                          
                                         C 
                                       
                                     
                                     + 
                                     n 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
         [0000]    m0, m1, m2, are driving currents, R0, R1, R2, are the distances between antennas, and k, l, n are the angles in the preset coordinate system between the antennas. 
         [0044]    With the constants and equations above, the magnetic vectors from the coil antennas  22 ,  24 , and  25  can be calculated: {right arrow over (H0)}, {right arrow over (H1)} and {right arrow over (H2)}. This data can be combined with data collected by the 3D coil antenna  38  in the fob  14  to calculate the orientation (Roll, Pitch, Yaw) relative to the antennas. If any of the constants (m0, m1, m2, R0, R1, R2, k, l, n) are missing or incorrect, the equation identifying {right arrow over (H0)}, {right arrow over (H1)} and {right arrow over (H2)} cannot be correctly solved. Under these conditions, the magnetic fields do not match the preset condition stored in memory of the devices, and magnetic integrity does not exist. The magnetic integrity calculations, therefore, can be used to evaluate whether communications between the antennas are with the fob  14  corresponding to the vehicle  12 , or whether a relay station attack (RSA) has occurred. 
         [0045]    Referring now to  FIGS. 4 and 5 , in another aspect of the invention, the driving currents applied to antennas  22 ,  24 , and  25  can be changed to differentiate the vehicle  12  as opposed to a relay operated by a thief. Two antenna configurations  64  and  66 , respectively, that can be used as antennas  22 ,  24 , and  25  are shown. Referring first to  FIG. 4 , antenna  64  comprises a central portion  54  of a first permittivity μ 1 , left and right linear elements  50  and  52  which are separated from the central portion  54  by linking sections  56  and  58  of a second permittivity μ 2  End sections  60  and  62  are constructed of material having permittivity μ 2  Referring now to  FIG. 5 , Antenna  66  is similar in construction. Here, the right and left elements  50  and  52  are angled with respect to one another, here shown as an angle of about ninety degrees. Other angles are also possible. 
         [0046]    Referring now to  FIGS. 1, 4, 5, 6 and 10 , a first embodiment of a vehicle  12 , corresponding key fob  14  ( FIGS. 1 and 6 ), and a process  70  for preventing RSA is shown. The process  70  is started when a request for actuation of a vehicle device is initiated (e.g., lifting a door handle). Upon receipt of a request, in step  72 , the antenna  22  in vehicle  12  transmits a signal to antenna  38  in key fob  14  to wake the key fob  14 , as described above. In step  74 , the controller  32  in key fob  14  calculates the angle β 0  between vectors V 1  and V 2  produced by the 3D coil in the key fob  14  which correspond to the magnetic intensity vectors produced by antennas  22  and  24 . The controller  32  can compare this angle against stored data to determine whether the antennas are in the expected location. 
         [0047]    In an additional security step, in step  78 , the vehicle  12  can transmit an encrypted signal to the key fob  14 , identifying a change in the driving current (L1/L2) in the antenna elements  50  and  52 . In step  80 , the change in driving current on antenna  22  results in a change in the magnetic field at antenna  22 , which results in a corresponding change to the vector V 1 ′ at the fob  14 . In step  82 , the controller  32  in key fob  14  calculates the angle β 0 ′ between vectors V 1 ′ and V 2 . The controller  32  then compares angles β 0  and β 0 ′. If β 0 =β 0 ′, there was no change in driving current from the transmitting source sending the signal to key fob  14 , and an RSA likely occurred. Under these circumstances, the door locks, ignition, and other features can be immobilized or retained in a locked position, preventing access to the vehicle (step  86 ). Alternatively, if β 0 ≠β 0 ′, then the request was from a key fob  14  authorized to access the vehicle, and access is allowed. Additional mathematical verification of the expected value of β 0 ′ can also be calculated to assure authority to access functions in the vehicle. 
         [0048]    Referring now to  FIG. 7  and  FIG. 11 , an alternate embodiment of a vehicle  12 , key fob  14  and corresponding process  90  for evaluating whether RSA has occurred is shown. Here, the process  90  relies on the magnetic integrity calculations discussed above with reference to  FIG. 3 . In step  92  fob  14  is awakened as described above. In step  94 , the controller  32  in fob  14  performs the magnetic integrity calculations described based on the fob  14 , and magnetic intensity vectors H produced by antennas  22 ,  24 , and  25  on vehicle  12 . In step  96 , the controller  32  determines whether the magnetic vector equations can be solved, as described. If magnetic field integrity exists (step  96 ), the controller  32  can allow access to vehicle functions. Referring now to  FIG. 8 , as an additional security step, the driving currents in the antenna  22  can also be adjusted as described above with reference to  FIG. 10 , generating a vector V 1 ′ for comparison, as described above. Access to vehicle functions can be allowed only when both the magnetic integrity is verified, and the adjustment in angle is verified. Alternatively, if magnetic field integrity is not found in step  96 , RSA has likely occurred, and the doors and other functions can be immobilized or locked (step  100 ). 
         [0049]    Referring now to  FIG. 9 , an alternate embodiment of a vehicle  12  is shown. Here the antenna  25  is positioned adjacent a rear passenger door. Calculations at the key fob  14  are made based on the locations of antennas  22 ,  24 , and  25 , as described above. These calculations can be used alone to identify the magnetic integrity of the relationships between the antennas in the system, or can be combined with a driving current adjustment in the antennas as described above. 
         [0050]    Referring now to  FIG. 12 , another alternative embodiment of a vehicle  12  is shown. Here two antennas are used, an antenna  22  positioned in a central location in or on the vehicle, such as the center console, and another antenna  24  positioned adjacent the driver&#39;s side door. Referring now to  FIG. 13 , a series of steps for determining whether to allow access to the vehicle of  FIG. 12  is shown. Initially, in step  110 , the fob  14  is awoken from one of antenna  22  or antenna  24 . In step  112 , the controller  32  in the fob  14  evaluates field strength from signals transmitted from antennas  22  and  24 , represented by initial vectors V 1  and V 2 , and calculates an initial angle β 0  between the vectors. As part of the wakeup sequence of communications between the vehicle  12  and the fob  14 , a random number R0/R1 is encrypted and sent to the fob  14 , which includes a stored key to decrypt the data (step  114 ). A driving current R0 is applied simultaneously to the antennas  22  and  24 , resulting in a first synthesized vector V 3 . (step  116 ) The controller  32  then calculates a first verification angle β 1  between the vectors V 1  and V 3 . (step  118 ) Subsequently, a second driving current R1 (I A1 /I A2 ) is applied simultaneously to the antennas  22  and  24 , resulting in a synthesized vector V 3′ . The controller  32  then calculates a second verification angle β 2  between the vectors V 1  and V 3 ′. (step  118 ) 
         [0051]    To determine whether RSA has occurred, the controller  32  then performs one of the following calculations: 
         [0000]    
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         cos 
                          
                         
                             
                         
                          
                         
                           β 
                           0 
                         
                       
                       - 
                       
                         cos 
                          
                         
                             
                         
                          
                         
                           β 
                           1 
                         
                       
                     
                     ) 
                   
                    
                   
                     / 
                   
                    
                   
                     ( 
                     
                       
                         
                           cos 
                            
                           
                               
                           
                            
                           
                             β 
                             0 
                           
                         
                         - 
                         
                           cos 
                            
                           
                               
                           
                            
                           
                             β 
                             2 
                           
                         
                       
                       = 
                       
                         
                           k 
                           * 
                         
                          
                         R 
                          
                         
                             
                         
                          
                         0 
                          
                         
                           / 
                         
                          
                         R 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 or 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       sin 
                        
                       
                         ( 
                         
                           
                             β 
                             0 
                           
                           - 
                           
                             β 
                             2 
                           
                         
                         ) 
                       
                     
                     
                       sin 
                        
                       
                         ( 
                         
                           β 
                           2 
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         R 
                         0 
                       
                       
                         R 
                         1 
                       
                     
                     · 
                     k 
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
         [0000]    Where k is a constant that can be stored in memory in either the fob  14  or vehicle  12 . (step  124 ) If the equation is satisfied, the request to access the vehicle is determined to be valid and access to perform functions, such as open the doors, or start the ignition, is granted. If the equation is not satisfied (step  126 ), a relay station attack has occurred, and the vehicle is immobilized. Access to the doors and ignition is therefore prevented. 
         [0052]    Although the system is described with calculations performed by the controller  32  in fob  14 , the calculations can be performed by the controller  16  in vehicle  12 . The constants R0/R1 and k can be stored in memory in either the vehicle  12  or fob  14 . This verification can also be used in conjunction with other verification procedures described above. 
         [0053]    Although specific embodiments are described above, it will be apparent to those of ordinary skill that a number of variations can be made within the scope of the disclosure For example, calculations of magnetic integrity can be made by the controller  32  in the key fob  14 , the controller  16  in the vehicle  12 , or both. The number of antennas associated with the vehicle  12  and the fob  14  can vary, and the magnetic integrity equations adjusted accordingly. In some embodiments, a step of adjusting the driving current in an antenna as discussed above with reference to process  90  can be performed before magnetic integrity calculations. Although specific embodiments are described above, it will be apparent that various algorithms that include measuring the angles between two or three different antennas, determining the location of the key fob relative to the antennas, and adjusting the currents in the antennas, as described above, can be implemented in various orders to provide varying levels of assurance that a relay attack has not occurred. Additionally, the method of relay attack avoidance used by a vehicle and key fob system can be intermittently changed to further thwart attempts to steal a vehicle. Although the fob is described herein as a key fob, as described above, various types of electronic equipment that include processors and radiofrequency communication devices can be used in the present application. For example, the functions described with reference to a key fob can be provided on personal communications devices such as cellular phones, smart phones, tablets, laptops, and other types of devices. 
         [0054]    It should be understood, therefore, that the methods and apparatuses described above are only exemplary and do not limit the scope of the invention, and that various modifications could be made by those skilled in the art that would fall within the scope of the invention. To apprise the public of the scope of this invention, the following claims are made: