# Patent

## Title
Authentication of an electromagnetic terminal-transponder couple by the transponder

## Abstract

A method of authentication of a terminal generating a magnetic field, by a transponder including an oscillating circuit from which a D.C. voltage is generated, wherein the transponder: receives first data relative to the current in an oscillating circuit of the terminal, measured by the terminal for a first value of the resistive load of the transponder; and exploits these first data and second data relative to the level of said D.C. voltage, respectively measured for the first resistive load value and for a second resistive load value.

## Background
CROSS REFERENCE TO RELATED APPLICATIONS
This application claims the priority benefit of French patent application Ser. No. 09/54347, filed on Jun. 25, 2009, entitled “AUTHENTICATION OF AN ELECTROMAGNETIC TERMINAL-TRANSPONDER COUPLE BY THE TRANSPONDER,” which is hereby incorporated by reference to the maximum extent allowable by law.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention generally relates to electronic systems, and more specifically to systems using electromagnetic transponders, that is, transceivers capable of being interrogated in a contactless and wireless manner by a read and/or write terminal.
2. Discussion of the Related Art
Many communication systems are based on a modulation of an electromagnetic field generated by a terminal. They range from the simplest electronic tag used as a theft-prevention device to more complex systems where a transponder intended to communicate with the terminal when it is in its field, is equipped with calculation functions (electronic purse, for example) or data processing functions.
Electromagnetic transponder systems are based on the use of oscillating circuits comprising a winding forming an antenna, on the transponder side and on the terminal side. Such circuits are intended to be coupled by a near magnetic field when the transponder enters the field of the terminal. The oscillating circuits of the terminal and of the transponder are generally tuned to the same frequency corresponding to the excitation frequency of the oscillating circuit of the terminal.
In most cases, transponders have no autonomous power supply and extract the power supply necessary to their circuits from the high-frequency field radiated by the antenna of the terminal.
When a transponder needs to communicate with a terminal, the transponder may have to authenticate the terminal before accepting a data exchange. For example, in applications where the transponder is used as a payment means (be it in money or units of account), it may reserve payments to certain terminals. According to another example, a transponder of chip card type, associated with electronic equipment (for example, a personal digital assistant or a cell phone) identifies or authenticates a user in a communication with other electronic equipment (for example, a laptop or desktop computer).
Symmetrically, the terminal may have to authenticate the transponder before transmitting certain data thereto.
Currently, authentication processes use cryptography algorithms and a data exchange between the terminal and the transponder. Such processes require significant power- and time-intensive calculations. Further, any cryptographic process is more or less sensitive to attacks aiming at discovering the secret of the authentication to hack the system.
SUMMARY OF THE INVENTION
It would be desirable for a transponder to be able to authenticate a terminal with which it needs to communicate before it has to transmit data to the terminal, and for the terminal to also be able to authenticate the transponder.
It would also be desirable to have an authentication process independent from any cryptography.
It would also be desirable to have a fast, less power- and calculation-intensive authentication process.
To achieve all or part of these objects as well as other, at least one embodiment of the present invention provides a method of authentication of a terminal generating a magnetic field, by a transponder comprising an oscillating circuit from which a D.C. voltage is generated, wherein the transponder:
receives first data relative to the current in an oscillating circuit of the terminal, measured by the terminal for a first value of the resistive load of the transponder; and
exploits these first data and second data relative to the level of said D.C. voltage, respectively measured for said first resistive load value and for a second resistive load value.
According to an embodiment of the present invention, the transponder:
evaluates, based on said data, a ratio between values of the current in the oscillating circuit of the terminal; and
compares this ratio with said first data.
According to an embodiment of the present invention, the transponder:
evaluates, based on said data, a value of said voltage; and
compares this evaluated value with the measured value.
According to an embodiment of the present invention, the first data correspond to the ratio of the current in the oscillating circuit of the terminal while no transponder is present in its field to a value of this current with the first resistive load value of the transponder.
According to an embodiment of the present invention, in the absence of an authentication, the transponder sends intentionally incorrect data.
The present invention also provides a method for authenticating a terminal generating a magnetic field and of a transponder which is present in this field, wherein:
the terminal is authenticated by the transponder; and
to authenticate the transponder, the terminal:
receives third data relative to the current in the oscillating circuit of the terminal, evaluated for a second value of the resistive load of the transponder; and
compares the third data with fourth corresponding data obtained by measurement.
According to an embodiment of the present invention, the third and fourth data are ratios of the current in the oscillating circuit of the terminal while no transponder is present in its field and of this same current with the second value of the resistive load.
According to an embodiment of the present invention, in the absence of an authentication by the terminal, said terminal sends intentionally incorrect data.
At least one embodiment of the present invention also provides an electromagnetic transponder comprising:
an oscillating circuit upstream of a rectifying circuit capable of providing a D.C. voltage when the transponder is present in the magnetic field of a terminal; and
at least one processing unit capable of implementing the authentication method.
The present invention also provides a terminal capable of generating an electromagnetic field for a transponder, comprising means capable of implementing the authentication method.
The foregoing objects, features, and advantages of the present invention will be discussed in detail in the following non-limiting description of specific embodiments in connection with the accompanying drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a very simplified representation of a transponder system of the type to which the present invention applies as an example;
FIG. 2 is a simplified block diagram of a terminal and of a transponder of an electromagnetic transponder communication system;
FIG. 3 is a functional block diagram illustrating an embodiment of the method of authentication of a terminal by a transponder;
FIG. 4 illustrates a variation of the embodiment of FIG. 3; and
FIG. 5 is a block diagram of an embodiment of a transponder capable of authenticating a terminal.



DETAILED DESCRIPTION
The same elements have been designated with the same reference numerals in the different drawings. For clarity, only those steps and elements which are useful to the understanding of the present invention have been shown and will be described. In particular, the coding and the modulation of the communications between the transponder and the terminal have not been detailed, the present invention being compatible with any usual communication. Further, the functions that can be implemented by a terminal or by a transponder, other than the authentication by this transponder have not been detailed either, the present invention being here again compatible with any usual function of a terminal or of a transponder.
FIG. 1 is a block diagram of an electromagnetic transponder communication system. A terminal 1 (TERMINAL) is capable of communicating in near field (for example according to a near field communication protocol NFC) with a distant element, that is, a transponder (TRANS).
The terminal may take different forms, for example, a transport ticket validation terminal, an electronic passport reader, a laptop computer, a mobile telecommunication device (GSM phone, PDA, etc.), an electronic control unit for starting an automobile vehicle, etc.
The transponder may similarly take different forms, for example, a chip card, an electronic transport ticket, an electronic passport, a telecommunication terminal (GSM phone, PDA, etc.), an electronic tag, etc.
FIG. 2 very schematically shows a simplified example of a terminal 1 and of a transponder 2.
Terminal 1 comprises an oscillating circuit, generally series, formed of an inductance L1 in series with a capacitor C1 and a resistor R1. This series oscillating circuit is, in the example of FIG. 2, connected between an output terminal 12 of an amplifier or antenna coupler 14 and a terminal 13 at a reference voltage (generally the ground). An element 15 for measuring the current in the oscillating circuit is interposed, for example, between capacitive element C1 and ground 13. Measurement element 15 belongs to a phase regulation loop which will be described hereafter. Amplifier 14 receives a high-frequency transmission signal originating from a modulator 16 (MOD) which receives a reference frequency (signal OSC), for example, from a quartz oscillator (not shown). Modulator 16 receives, if need be, a signal Tx originating from a circuit 11 for controlling and exploiting the transmissions. Circuit 11 is generally provided with a control and data processing microprocessor, communicating with different input/output circuits (keyboard, display, element of exchange with a server, etc.) and/or processing circuits, not shown. The elements of terminal 1 most often draw the power necessary to their operation from a supply circuit (not shown) connected, for example, to the power line distribution system (mains) or to a battery (for example, that of an automobile vehicle or of a portable telephone or computer). Modulator 16 provides a high-frequency carrier (for example, at 13.56 MHz) to series oscillating circuit L1-C1 which generates a magnetic field.
Capacitive element C1 is, for example, a variable-capacitance element controllable by a signal CTRL. This element takes part in the phase regulation of current I1 in antenna L1 with respect to a reference signal. This regulation is a regulation of the high-frequency signal, that is, of the signal of the carrier corresponding to the signal provided to amplifier 14 in the absence of data Tx to be transmitted. The regulation is performed by varying capacitance C1 of the oscillating circuit of the terminal to maintain the current in the antenna in constant phase relationship with a reference signal. This reference signal, for example, corresponds to signal OSC provided to modulator 14. Signal CTRL originates from a circuit 17 (COMP) having the function of detecting the phase interval with respect to the reference signal and of accordingly modifying the capacitance of element C1. The comparator receives data MES about current I1 in the oscillating circuit detected by measurement element 15 (for example, an intensity transformer or a resistor).
A transponder 2, capable of cooperating with terminal 1, comprises an oscillating circuit, for example, parallel, formed of an inductance L2 in parallel with a capacitor C2 between two terminals 21 and 22. The parallel oscillating circuit (called receive mode resonant circuit) is intended to capture the magnetic field generated by oscillating circuit L1-C1 of terminal 1. Circuits L2-C2 and L1-C1 are tuned to a same resonance frequency (for example, 13.56 MHz). Terminals 21 and 22 are connected to two A.C. input terminals of a rectifying bridge 23 (most often, fullwave). The rectified output terminals of bridge 23 respectively define a positive terminal 24 and a reference terminal 25. A capacitor Ca is connected between terminals 24 and 25 to smooth the rectified voltage. The recovered power is used to recharge a battery, not shown.
When transponder 2 is in the field of terminal 1, a high-frequency voltage is generated across resonant circuit L2-C2. This voltage, rectified by bridge 23 and smoothed by capacitor Ca, provides a supply voltage to electronic circuits of the transponder via a voltage regulator 26 (REG). Such circuits generally comprise a processing unit 27 (for example, a microcontroller μC) associated with a memory (not shown), a demodulator 28 (DEM) of the signals that may have been received from terminal 1, and a modulator 29 (MOD) for transmitting data to the terminal. The transponder is generally synchronized by means of a clock (CLK) extracted, by a block 20, from the high-frequency signal recovered, to before rectification, from one of terminals 21 and 22. Most often, all the electronic circuits of transponder 2 are integrated in the same chip.
To transmit data from terminal 1 to the transponder, circuit 16 modulates (generally in amplitude) the carrier (signal OSC) according to signal Tx. On the side of transponder 2, these data are demodulated by demodulator 28 based on voltage VCa. The demodulator may sample the signal to be demodulated upstream of the rectifying bridge.
To transmit data from transponder 2 to terminal 1, modulator 29 controls a stage 30 of modulation (retromodulation) of the load formed by the transponder circuits on the magnetic field generated by the terminal. This stage is generally formed of an electronic switch K30 (for example, a transistor) and of a resistor R30 (or a capacitor), in series between terminals 24 and 25. Switch K30 is controlled at a so-called sub-carrier frequency (for example, 847.5 kHz), much lower (generally with a ratio of at least 10) than the frequency of the excitation signal of the oscillating circuit of terminal 1. When switch K30 is on, the oscillating circuit of the transponder is submitted to an additional damping with respect to the load formed by circuits 20, 26, 27, 28, and 29 so that the transponder samples a greater amount of power from the high-frequency magnetic field. On the side of terminal 1, amplifier 14 maintains the amplitude of the high-frequency excitation signal constant. Accordingly, the power variation of the transponder translates as an amplitude and phase variation of the current in antenna L1. This variation is detected by an amplitude or phase demodulator of the terminal. In the embodiment illustrated in FIG. 2, comparator 17 integrates a phase demodulator also used to demodulate the signal originating from the transponder. Accordingly, comparator 17 provides a signal Rx giving back to circuit 11 a possible retromodulation of data received from a transponder. Other demodulation circuits may be provided, for example, a circuit exploiting a measurement of the voltage across capacitor C1.
Many variations exist to encode/decode and modulate/demodulate communications between a transponder and a terminal.
The response time of the phase regulation loop is sufficiently long to avoid disturbing the possible retromodulation from a transponder and sufficiently short as compared with the speed at which a transponder passes in the field of the terminal. One can speak of a static regulation with respect to the modulation frequencies (for example, the 13.56-MHz frequency of the remote supply carrier and the 847.5-kHz retromodulation frequency used to transmit data from the transponder to the terminal).
An example of a phase regulation terminal is described in document EP-A-0857981.
Regulating the phase on the terminal side enables using current and voltage measurements in the oscillating circuit of the transponder to deduce from these measurements information relative to the transponder coupling when it is in the field of the terminal. The coupling coefficient between the oscillating circuit of the terminal and of the transponder essentially depends on the distance separating the transponder from the terminal. The coupling coefficient, noted k, is always between 0 and 1. It can be defined by the following formula:




  
    
      
        
          k
          =
          
            M
            
              
                L
                ⁢
                
                  
                
                ⁢
                
                  1
                  ·
                  L
                
                ⁢
                
                  
                
                ⁢
                2
              
            
          
        
        ,
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          1
        
        )
      
    
  




where M represents the mutual inductance between inductances L1 and L2 of the oscillating circuits of the terminal and of the transponder.
An optimum coupling is defined as being the position at which voltage VC2 across the oscillating circuit of the transponder is maximum. This optimum coupling, noted kopt, may be expressed as:




  
    
      
        
          
            k
            opt
          
          =
          
            
              
                
                  L
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
                
                  L
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
              
              ·
              
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
              
            
          
        
        ,
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          2
        
        )
      
    
  




where R2 represents the resistance equivalent to the load formed by the elements of the transponder on its own oscillating circuit. In other words, resistance R2 represents the equivalent resistance of all the circuits of transponder 2, placed in parallel on capacitor C2 and inductance L2 (before or after the rectifying bridge). The conductance due to the transponder circuits will be called “resistive load”. The level of this load is symbolized by resistor R2 in parallel across the oscillating circuit. In above formula 2, the series resistance of inductance L1 (terminal antenna) has been neglected. It can also be considered that the value of this series resistance is, for simplification, included in the value of resistor R1.
Formula 2 represents a signature of the terminal-transponder couple. For the same transponder and given operating conditions (load R2), the optimum coupling coefficient varies according to the terminal which conditions values L1 and R1.
It is provided to take advantage of this feature to enable a transponder to authenticate the terminal in the range of which it is located by indirectly verifying this signature and, similarly, to enable the terminal to authenticate the transponder.
To authenticate the terminal-transponder couple, the value of voltage VC2 across capacitive element C2 of its oscillating circuit is exploited. This voltage is provided by the following relation:




  
    
      
        
          
            V
            
              C
              ⁢
              
                
              
              ⁢
              2
            
          
          =
          
            
              I
              ⁢
              
                
              
              ⁢
              2
            
            
              ω
              ⁢
              
                
              
              ·
              
                C
                2
              
            
          
        
        ,
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          3
        
        )
      
    
  




where I2 represents the current in the oscillating circuit of the transponder, and where ω represents the pulse of the signal.
Current I2 is equal to:




  
    
      
        
          
            I
            ⁢
            
              
            
            ⁢
            2
          
          =
          
            
              
                M
                ·
                ω
                ·
                I
              
              ⁢
              
                
              
              ⁢
              1
            
            
              Z
              ⁢
              
                
              
              ⁢
              2
            
          
        
        ,
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          4
        
        )
      
    
  




where I1 represents the current in the oscillating circuit of the terminal and where Z2 represents the transponder impedance.
Impedance Z2 of the transponder is provided by the following relation:




  
    
      
        
          
            Z
            ⁢
            
              
            
            ⁢
            
              2
              2
            
          
          =
          
            
              X
              ⁢
              
                
              
              ⁢
              
                2
                2
              
            
            +
            
              
                (
                
                  
                    L
                    ⁢
                    
                      
                    
                    ⁢
                    2
                  
                  
                    R
                    ⁢
                    
                      
                    
                    ⁢
                    
                      2
                      ·
                      C
                    
                    ⁢
                    
                      
                    
                    ⁢
                    2
                  
                
                )
              
              2
            
          
        
        ,
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          5
        
        )
      
    
  




where X2 represents the imaginary part of the impedance of the oscillating circuit




  (
  
    
      X
      ⁢
      
        
      
      ⁢
      2
    
    =
    
      
        
          ω
          ·
          L
        
        ⁢
        
          
        
        ⁢
        2
      
      -
      
        1
        
          
            ω
            ·
            C
          
          ⁢
          
            
          
          ⁢
          2
        
      
    
  
  )




and where R2 represents the resistance equivalent to the load formed by the transponder elements on its own oscillating circuit. In other words, resistance R2 represents the equivalent resistance of all the circuits (microprocessors, retromodulation means, etc.) of transponder 2, brought in parallel on capacitor C2 and inductance L2 (before or after the rectifying bridge). The conductance due to the transponder circuits, and thus their power consumption, will be called “resistive load”. The level of this load is symbolized by resistor R2 in parallel across the oscillating circuit.

Further, current I1 in the oscillating circuit of the terminal is given by the following relation:




  
    
      
        
          
            I
            ⁢
            
              
            
            ⁢
            1
          
          =
          
            Vg
            
              Z
              ⁢
              
                
              
              ⁢
              
                1
                app
              
            
          
        
        ,
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          6
        
        )
      
    
  




where Vg designates a so-called generator voltage, exciting the oscillating circuit of the terminal, and where Z1app represents the apparent impedance of the oscillating circuit.
The fact of regulating the phase of the oscillating circuit of the terminal enables for all the variations which would tend to modify, statically with respect to the modulation frequencies, the imaginary part of the load formed by the transponder, to be compensated by the phase regulation loop. It is thus ensured that in static operation, the imaginary part of impedance Z1app is zero. Accordingly, impedance Z1app becomes equal to apparent resistance R1app (real part of the impedance) and may be expressed as:




  
    
      
        
          Z
          ⁢
          
            
          
          ⁢
          
            1
            app
          
        
        =
        
          
            R
            ⁢
            
              
            
            ⁢
            
              1
              app
            
          
          =
          
            
              R
              ⁢
              
                
              
              ⁢
              1
            
            +
            
              
                
                  
                    
                      k
                      2
                    
                    ·
                    
                      ω
                      2
                    
                    ·
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    1
                    ·
                    L
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    2
                    2
                  
                
                
                  Z
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      2
                      2
                    
                    ·
                    R
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    2
                    ·
                    C
                  
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
              
              .
            
          
        
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          7
        
        )
      
    
  




In above formula 7, the series resistance of inductance L1 (terminal of the antenna) has been neglected. It can also be considered that the value of this series resistance is, for simplification, included in the value of resistance R1.
Since the oscillating circuits are tuned, it can be considered that imaginary part X2 of impedance Z2 is, as a first approximation, close to zero. As a result, the value of impedance Z2 can be written as:




  
    
      
        
          Z
          ⁢
          
            
          
          ⁢
          2
        
        =
        
          
            
              L
              ⁢
              
                
              
              ⁢
              2
            
            
              R
              ⁢
              
                
              
              ⁢
              
                2
                ·
                C
              
              ⁢
              
                
              
              ⁢
              2
            
          
          .
        
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          8
        
        )
      
    
  




By inserting this simplification into formulas 4 and 7, and inserting formula 4 into formula 3, the following formula can be obtained for voltage VC2 recovered across the oscillating circuit of the transponder:




  
    
      
        
          V
          
            C
            ⁢
            
              
            
            ⁢
            2
          
        
        =
        
          k
          ·
          
            
              
                L
                ⁢
                
                  
                
                ⁢
                1
              
              
                L
                ⁢
                
                  
                
                ⁢
                2
              
            
          
          ·
          
            
              
                V
                ⁢
                
                  
                
                ⁢
                g
              
              
                
                  
                    R
                    ⁢
                    
                      
                    
                    ⁢
                    1
                  
                  
                    R
                    ⁢
                    
                      
                    
                    ⁢
                    2
                  
                
                +
                
                  
                    k
                    2
                  
                  ·
                  
                    
                      L
                      ⁢
                      
                        
                      
                      ⁢
                      1
                    
                    
                      L
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                
              
            
            .
          
        
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          9
        
        )
      
    
  




Formula 9 shows that, for a given terminal (fixed values of Vg, R1, and L1) and for a fixed impedance L2 (and thus a fixed value of C2), voltage VC2 only depends on coupling k and on the resistive load (equivalent to resistor R2) formed by the transponder circuits and brought in parallel on the oscillating circuit.
It should be noted that formula 9 can only be applied when the oscillating circuit of transponder L2-C2 is considered to be set to the tuning frequency, that is, ω·√{square root over (L2·C2)}=1.
For a given coupling value k, considering that the impedance of the oscillating circuit of the terminal does not vary and that the circuits remain tuned, the ratio between values VC2]R21 and VC2]R20 of voltage VC2, respectively for values R21 and R20 of resistor R2, provides, according to formula 2 and 9, the following relation:




  
    
      
        
          
            V
            
              
                
                  C
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
                ]
              
              ⁢
              R
              ⁢
              
                
              
              ⁢
              21
            
          
          
            V
            
              
                
                  C
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
                ]
              
              ⁢
              
                
              
              ⁢
              R
              ⁢
              
                
              
              ⁢
              20
            
          
        
        =
        
          
            
              
                
                  (
                  
                    k
                    
                      k
                      
                        
                          opt
                          ]
                        
                        ⁢
                        
                          
                        
                        ⁢
                        R
                        ⁢
                        
                          
                        
                        ⁢
                        20
                      
                    
                  
                  )
                
                2
              
              +
              1
            
            
              
                
                  (
                  
                    k
                    
                      k
                      
                        
                          opt
                          ]
                        
                        ⁢
                        
                          
                        
                        ⁢
                        R
                        ⁢
                        
                          
                        
                        ⁢
                        20
                      
                    
                  
                  )
                
                2
              
              +
              
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  20
                
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  21
                
              
            
          
          .
        
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          10
        
        )
      
    
  




Formula 10 shows that by increasing the value of resistor R2 from a first value R20 to a second greater value R21 (which amounts to decreasing the load of the transponder circuits on oscillating circuit L2-C2), voltage VC2]R21 will be greater than voltage VC2]R20. Conversely, a decrease in the value of transistor R2 causes a decrease in recovered voltage VC2.
Another characteristic operating condition of the terminal-transponder couple is linked to an off-load operation of the terminal.
Formulas 6 and 7 enable to write:




  
    
      
        
          I
          ⁢
          
            
          
          ⁢
          1
        
        =
        
          
            Vg
            
              
                R
                ⁢
                
                  
                
                ⁢
                1
              
              +
              
                
                  
                    k
                    2
                  
                  ·
                  
                    
                      L
                      ⁢
                      
                        
                      
                      ⁢
                      1
                    
                    
                      L
                      ⁢
                      
                        
                      
                      ⁢
                      2
                    
                  
                  ·
                  R
                
                ⁢
                
                  
                
                ⁢
                2
              
            
          
          .
        
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          11
        
        )
      
    
  




The off-load values represent the current and the voltage on the terminal side when no transponder is present in the field of the terminal. In this off-load operation, the apparent impedance of the oscillating circuit of the terminal now to only depends on its components R1, C1, and L1. Further, due to the phase regulation, the imaginary part of this impedance is always zero. Formula 11 becomes:




  
    
      
        
          I
          ⁢
          
            
          
          ⁢
          
            1
            
              off
              -
              load
            
          
        
        =
        
          
            Vg
            
              R
              ⁢
              
                
              
              ⁢
              1
            
          
          .
        
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          12
        
        )
      
    
  




Formulas 11 and 12 enable to write that, for a same current coupling k:




  
    
      
        
          k
          2
        
        =
        
          
            
              R
              ⁢
              
                
              
              ⁢
              1
            
            
              R
              ⁢
              
                
              
              ⁢
              2
            
          
          ·
          
            
              L
              ⁢
              
                
              
              ⁢
              2
            
            
              L
              ⁢
              
                
              
              ⁢
              1
            
          
          ·
          
            
              (
              
                
                  
                    I
                    ⁢
                    
                      
                    
                    ⁢
                    
                      1
                      
                        off
                        -
                        load
                      
                    
                  
                  
                    I
                    ⁢
                    
                      
                    
                    ⁢
                    1
                  
                
                -
                1
              
              )
            
            .
          
        
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          13
        
        )
      
    
  




The combination of formulas 12 and 13 provides:




  
    
      
        
          
            (
            
              k
              
                k
                opt
              
            
            )
          
          2
        
        =
        
          
            
              I
              ⁢
              
                
              
              ⁢
              
                1
                
                  off
                  -
                  load
                
              
            
            
              I
              ⁢
              
                
              
              ⁢
              1
            
          
          -
          1.
        
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          14
        
        )
      
    
  




The current ratios thus provide information about the optimum coupling coefficient, and thus about the system signature for a given load.
Further, when a transponder is present in the field of the terminal with a given resistive load (for example, equivalent to a resistor R2 of value R20), the terminal can measure the value of current I1]R20 in its oscillating circuit L1-C1.
When the ratio of the recovered voltages with two values R20 and R21 of resistor R2 is expressed, for a given coupling k, and combining formulas 10 and 14, the following relation is obtained:




  
    
      
        
          
            V
            
              
                
                  C
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
                ]
              
              ⁢
              R
              ⁢
              
                
              
              ⁢
              21
            
          
          
            V
            
              
                
                  C
                  ⁢
                  
                    
                  
                  ⁢
                  2
                
                ]
              
              ⁢
              R
              ⁢
              
                
              
              ⁢
              20
            
          
        
        =
        
          
            
              
                I
                ⁢
                
                  
                
                ⁢
                
                  1
                  
                    off
                    -
                    load
                  
                
              
              
                I
                ⁢
                
                  
                
                ⁢
                
                  1
                  
                    ]
                    R
                    ⁢
                    
                      
                    
                    ⁢
                    20
                  
                
              
            
            
              
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  20
                
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  21
                
              
              +
              
                (
                
                  
                    
                      I
                      
                        off
                        -
                        load
                      
                    
                    
                      I
                      ⁢
                      
                        
                      
                      ⁢
                      
                        1
                        
                          ]
                          R
                          ⁢
                          
                            
                          
                          ⁢
                          20
                        
                      
                    
                  
                  -
                  1
                
                )
              
            
          
          .
        
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          15
        
        )
      
    
  




This relation may also be written, for R20<R21, as:




  
    
      
        
          
            
              I
              ⁢
              
                
              
              ⁢
              
                1
                
                  off
                  -
                  load
                
              
            
            
              I
              ⁢
              
                
              
              ⁢
              
                1
                
                  ]
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  20
                
              
            
          
          =
          
            
              1
              -
              
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  20
                
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  21
                
              
            
            
              1
              -
              
                
                  V
                  
                    
                      
                        C
                        ⁢
                        
                          
                        
                        ⁢
                        2
                      
                      ]
                    
                    ⁢
                    R
                    ⁢
                    
                      
                    
                    ⁢
                    20
                  
                
                
                  V
                  
                    
                      
                        C
                        ⁢
                        
                          
                        
                        ⁢
                        2
                      
                      ]
                    
                    ⁢
                    R
                    ⁢
                    
                      
                    
                    ⁢
                    21
                  
                
              
            
          
        
        ,
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          16
        
        )
      
    
  




or, for R20>R21, as:




  
    
      
        
          
            I
            ⁢
            
              
            
            ⁢
            
              1
              
                off
                -
                load
              
            
          
          
            I
            ⁢
            
              
            
            ⁢
            
              1
              
                ]
                R
                ⁢
                
                  
                
                ⁢
                20
              
            
          
        
        =
        
          
            
              
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  20
                
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  21
                
              
              -
              1
            
            
              
                
                  V
                  
                    
                      
                        C
                        ⁢
                        
                          
                        
                        ⁢
                        2
                      
                      ]
                    
                    ⁢
                    R
                    ⁢
                    
                      
                    
                    ⁢
                    20
                  
                
                
                  V
                  
                    
                      
                        C
                        ⁢
                        
                          
                        
                        ⁢
                        2
                      
                      ]
                    
                    ⁢
                    R
                    ⁢
                    
                      
                    
                    ⁢
                    21
                  
                
              
              -
              1
            
          
          .
        
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          
            16
            ′
          
        
        )
      
    
  




When ratio R21/R20 is expressed based on formula 16, the following relation is obtained:




  
    
      
        
          
            
              R
              ⁢
              
                
              
              ⁢
              20
            
            
              R
              ⁢
              
                
              
              ⁢
              21
            
          
          =
          
            
              
                
                  I
                  ⁢
                  
                    
                  
                  ⁢
                  
                    1
                    
                      off
                      -
                      load
                    
                  
                
                
                  I
                  ⁢
                  
                    
                  
                  ⁢
                  
                    1
                    
                      ]
                      R
                      ⁢
                      
                        
                      
                      ⁢
                      21
                    
                  
                
              
              -
              1
            
            
              
                
                  I
                  ⁢
                  
                    
                  
                  ⁢
                  
                    1
                    
                      off
                      -
                      load
                    
                  
                
                
                  I
                  ⁢
                  
                    
                  
                  ⁢
                  
                    1
                    
                      ]
                      R
                      ⁢
                      
                        
                      
                      ⁢
                      20
                    
                  
                
              
              -
              1
            
          
        
        ,
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          17
        
        )
      
    
  




whether value R20 is smaller or greater than value R21.
Relation 17 may also be expressed as:




  
    
      
        
          
            I
            ⁢
            
              
            
            ⁢
            
              1
              
                off
                -
                load
              
            
          
          
            I
            ⁢
            
              
            
            ⁢
            
              1
              
                ]
                R
                ⁢
                
                  
                
                ⁢
                21
              
            
          
        
        =
        
          
            
              
                R
                ⁢
                
                  
                
                ⁢
                21
              
              
                R
                ⁢
                
                  
                
                ⁢
                20
              
            
            ·
            
              (
              
                
                  
                    I
                    ⁢
                    
                      
                    
                    ⁢
                    
                      1
                      
                        off
                        -
                        load
                      
                    
                  
                  
                    I
                    ⁢
                    
                      
                    
                    ⁢
                    
                      1
                      
                        ]
                        R
                        ⁢
                        
                          
                        
                        ⁢
                        20
                      
                    
                  
                
                -
                1
              
              )
            
          
          +
          1.
        
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          18
        
        )
      
    
  




It is provided to use these ratios between off-load currents and under a given resistive load (equivalent to a resistor R2 of value R20 or R21) to have the terminal authenticate the transponder and to have the transponder authenticate the terminal.
FIG. 3 is a functional block diagram of an embodiment of a procedure of mutual authentication of a terminal and of a transponder.
The off-load current in the oscillating circuit of the terminal is assumed to have been previously stored and recorded. Preferably, this off-load current determination is performed while the terminal is in its functional environment to take into account possible static disturbances that can influence the measurement. According to a preferred variation, the value of the off-load current is periodically updated (for example, it is programmed to be measured in off-load periods of the system when it is known that no transponder is present).
When the terminal detects a transponder in the field, it measures (block 41, MES I1]R20) current I1 in its oscillating circuit (for example, by means of element 15), then calculates (block 42, CALC (I1off-load/I1]R20)MES) the ratio between the measured value and the off-load current. The result is transmitted to the transponder, which stores it (block 52, STORE (I1off-load/I1]R20)MES).
The transponder measures and stores (block 51 MES VC2]R20, before or after having received the information relative to the current from the terminal, voltage VC2 across capacitor C2 with a first value R20 of resistor R2.
Then (block 53, R20→R21), it modifies its resistive load so that equivalent resistor R2 takes a value R21. Value R21 is, for example, selected to be greater than value R20. The transponder then measures (block 54, MES VC2]R21) voltage VC2 with this value R21 and stores the result.
The transponder then calculates (block 55, CALC (I1off-load/I1]R20)EVAL) an expected value of the ratio between the values of currents I1 of the off-load terminal and of the terminal with resistor R20, and compares (block 56, (I1off-load/I1]R20)MES=(I1off-load/I1]R20)EVAL?) the evaluated value with the measured value received from the terminal.
In case of a divergence (output N of block 56), this means that the oscillating circuit of the terminal does not respect the signature.
If test 56 confirms identical values, the transponder considers the terminal as authentic (block 58, OK). Otherwise (output N of block 56), it starts an error processing (block 59, ERROR). This processing for example corresponds to a transaction denial, to a transponder reset, to a fail-soft operation (without performing the functions which are critical as to the manipulated information), etc. It may also be provided for the transponder to send messages to mislead or confuse the terminal with intentionally incorrect information, for example, messages comprising random data. Various other processings may be envisaged, for example, any error processing usually provided in the absence of an authentication by a ciphering mechanism.
If the terminal is considered as authentic, the transponder calculates and transmits to the terminal (block 57, CALC (I1off-load/I1]R21)EVAL) an evaluated value of the ratio between currents I1, in the off-load state and with value R21.
Simultaneously (at any time after step 53), the transponder notifies the terminal that it has switched its resistive load to another value to cause a new measurement of current I1.
The terminal (block 43, MES I1]R21) measures current I1, then calculates (block 44, CALC (I1off-load/I1]R21)MES) the ratio of off-load current I1 to current I1]R21 and stores the result.
The terminal then verifies (block 45, (I1off-load/I1]R21)MES=(I1off-load/I1]R21)EVAL?) the value that it has measured against the value evaluated by the transponder. In case of an identity (output Y of block 45), the terminal considers the transponder as authentic (block 46, OK). Otherwise, it starts an error processing (block 47, ERROR). As with the transponder, different error processings may be envisaged according to the application (for example, a blocking, the sending of intentionally incorrect information, etc.).
FIG. 4 partially illustrates a variation of FIG. 3 in which calculation 55 and test 56 are replaced with an evaluation (block 55′, CALC (VC2]R21)EVAL) of voltage VC2 with value R21 of resistor R2, and a comparison (block 56′, (VC2]R21)EVAL=(VC2]R21)MES?) of this evaluated value with respect to the value measured at step 54. The rest is identical to the embodiment of FIG. 3. The variation of FIG. 4 may be combined with the embodiment of FIG. 3.
Accordingly, for a given terminal (fixed values of Vg and R1) and a system in the tuned state, the transponder-terminal couple can be authenticated by exploitation of the voltages obtained on the transponder side with two resistive loads (equivalent to resistors R20 and R21) and of the corresponding currents in the oscillating circuit of the terminal.
In practice, voltage VC2 is not directly measured across the oscillating circuit of the transponder, but the smoothed voltage across voltage VCa at the output of rectifying bridge 23. Voltage VCa is proportional to voltage VC2. Since voltage ratios are evaluated, it is not necessary to know the proportionality factor between voltages VC2 and VCa. In a specific embodiment, the measurement is performed by the microprocessor. The storage of the values of the measured voltages is performed either in analog fashion or, preferentially in digital fashion over several bits, the number of which depends on the desired analysis accuracy.
The tests may be performed in an order different from that indicated hereabove. However, they are preferentially performed in an order of increasing calculation complexity, which enables to more rapidly reject a terminal which is not adapted to the transponder.
Further, different intermediary values may be stored to be reused in the successive tests or, conversely, calculated on the fly.
A minimum value may be taken into account to decrease the value of resistor R2, this value corresponding to the minimum acceptable value to preserve a sufficient supply voltage for the transponder circuits. This value is obtained by considering ratio R20/R2min according to formula 16′. Noting VC2min the voltage with resistance R2min, this formula becomes:




  
    
      
        
          
            I
            ⁢
            
              
            
            ⁢
            
              1
              
                off
                -
                load
              
            
          
          
            I
            ⁢
            
              
            
            ⁢
            
              1
              
                ]
                R
                ⁢
                
                  
                
                ⁢
                20
              
            
          
        
        =
        
          
            
              
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  20
                
                
                  R
                  ⁢
                  
                    
                  
                  ⁢
                  2
                  ⁢
                  min
                
              
              -
              1
            
            
              
                
                  V
                  
                    
                      
                        C
                        ⁢
                        
                          
                        
                        ⁢
                        2
                      
                      ]
                    
                    ⁢
                    R
                    ⁢
                    
                      
                    
                    ⁢
                    20
                  
                
                
                  V
                  
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    2
                    ⁢
                    
                      
                    
                    ⁢
                    m
                    ⁢
                    
                      
                    
                    ⁢
                    i
                    ⁢
                    
                      
                    
                    ⁢
                    n
                  
                
              
              -
              1
            
          
          .
        
      
    
    
      
        (
        
          formula
          ⁢
          
            
          
          ⁢
          19
        
        )
      
    
  




Tolerances or acceptable ranges of values may be introduced into the tests to take into account possible operating drifts of the terminal or, in the case of a category of authorized terminals, possible acceptable dispersions among the terminals of this category.
It is thus possible, based on two voltages measurements with two resistance values of the oscillating circuit of the transponder, to authenticate the terminal.
Further, the terminal may authenticate the transponder based on two current measurements in its oscillating circuit with these two resistance values.
These authentications may be used by the terminal, by the transponder, or by both.
FIG. 5 is a block diagram of an embodiment of a transponder 2, equipped to automatically determine, when it is in the field of a terminal (not shown), whether this terminal is authorized. The representation of FIG. 5 is simplified with respect to that of FIG. 2. In particular, the means of demodulation, retromodulation, and for obtaining the clock frequency have not been illustrated.
As previously, transponder 2 is based on a parallel oscillating circuit L2-C2 having its terminals 21 and 22 connected to the input terminals of a rectifying bridge 23. An element for measuring the current Ic intended for the processing unit may be provided at the output of regulator 26. Further, a switchable resistive circuit 40 is provided between terminals 24 and 25 of rectifying bridge 23. For example, two resistors R43 and R45 are connected in parallel, each being in series with a switch K43, respectively K45. Switches K43 and K45 (for example, MOS transistors) are intended to be switched to implement the method for determining the coupling position. Processing unit 27 (PU) receives information about voltage VCa on an input MES to implement the above-described method. In the example of FIG. 5, when the two resistors R43 and R45 are functionally connected, resistor R2 (load of the transponder circuits) has value R20. The disconnection of one of the resistors (for example, resistor R43) increases resistance R2 towards value R21. Other connections and switchings may be provided according to the embodiment of the implemented method. For example, a single switchable resistor may be used, considering that one of the two values of resistor R2 corresponds to the resistive load of the other transponder circuits.
According to a preferred embodiment, the switchable resistor corresponds to that used for a resistive retromodulation. For example, a first measurement is performed by switching the retromodulation resistor so that it is functionally in the circuit (switch K30 in the on state in the example of FIG. 2). Voltage VC2]R20 is measured. Then, switch K30 is turned off and voltage VC2]R21 is measured.
As a variation, the increase or the decrease of equivalent resistance R2 is caused by a variation of the power consumption of the transponder circuits, typically of processing unit 27. For example, to decrease the value of resistor R2 (increase the consumption), the execution of calculations or of processings by unit 27 is triggered. An increase of equivalent resistance R2 may also be caused by decreasing the power consumption of unit 27 by interrupting certain calculations. As a variation, the execution speed conditioned by the clock is slowed down (block 20). The variation of resistance R2 is known from the time when the power consumption of different tasks to be executed by unit 27 is known.
The calculations required to authenticate a terminal are sufficiently simple for their execution time to be negligible with respect to the displacement speed of a transponder in front of a terminal (and thus the variation speed of the coupling coefficient). Such is in particular the case for transponders equipped with microcontrollers executing cryptography functions in which these calculation-intensive functions are themselves executed in a duration for which it can be considered that the coupling does not vary. In other cases, the transponder remains laid on a reception surface of the terminal and the coupling thus does not vary for an even longer period.
It should be noted that if a hacker element attempts to intercept the exchanged values during the authentication, its simple presence in the field modifies the impedances seen by the terminal and/or the transponder and causes a failure of the authentication.
It should be noted that the authentication is performed by simple calculations and measurements.
Various embodiments with different variations have been described hereabove. It should be noted that those skilled in the art can combine various elements of these various embodiments and variations without showing any inventive step. In particular, the selection and the order of the tests to be performed depend on the application, for example, on the time available to perform the authentication, on the calculating capacity of the transponder, etc.
Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and the scope of the present invention. Accordingly, the foregoing description is by way of example only and is not intended to be limiting. The present invention is limited only as defined in the following claims and the equivalents thereto.

## Claims

1. A method of authentication of a terminal generating a magnetic field, by a transponder comprising an oscillating circuit from which a D.C. voltage is generated, wherein the transponder:
receives first data relative to a current in an oscillating circuit of the terminal, measured by the terminal for a first value of a resistive load of the transponder;
exploits the first data, and second data relative to levels of said D.C. voltage, the levels of the D.C. voltage respectively measured for said first resistive load value and for a second resistive load value; and
determines an authenticity of the terminal based on a result of the exploiting.

2. The method of claim 1, wherein exploiting the first data comprises:
evaluating, based on said second data, a ratio between values of the current in the oscillating circuit of the terminal; and
comparing this ratio with said first data.

3. The method of claim 1, wherein exploiting the first data comprises:
evaluating, based on said first data, a value of said D.C. voltage; and
comparing this evaluated value with the level of said D.C. voltage measured for the second resistive load value.

4. The method of claim 1, wherein the first data correspond to a ratio of a value of the current in the oscillating circuit of the terminal while no transponder is present in its field to a value of this current with the first resistive load value of the transponder.

5. The method of claim 1, wherein in the absence of a determination that the terminal is authentic, the transponder sends incorrect data.

6. A method for authenticating a terminal generating a magnetic field and a transponder which is present in this field, wherein:
the terminal is authenticated by the transponder according to claim 1; and
to authenticate the transponder, the terminal:
receives third data relative to the current in the oscillating circuit of the terminal, evaluated for a second value of the resistive load of the transponder;
compares the third data with fourth corresponding data obtained by measurement; and
determines an authenticity of the transponder based on a result of the comparing.

7. The method of claim 6, wherein the third and fourth data are ratios of a value of a current in the oscillating circuit of the terminal while no transponder is present in its field and a value of this same current with the second value of the resistive load.

8. The method of claim 6, wherein, in the absence of a determination that the terminal is authentic, said terminal sends incorrect data.

9. An electromagnetic transponder comprising:
an oscillating circuit upstream of a rectifying circuit capable of providing a D.C. voltage when the transponder is present in a magnetic field of a terminal; and
at least one processing unit capable of implementing the method of claim 1.

10. The method of claim 1, wherein determining the authenticity of the terminal comprises verifying that the terminal is inauthentic.

11. The method of claim 1, wherein determining the authenticity of the terminal comprises verifying that the terminal is authentic.

12. The method of claim 1, wherein the first data correspond to a ratio of first and second levels of the current in the oscillating circuit of the terminal, the first level corresponding to the current when no transponder is within a range of the magnetic field of the terminal, the second level corresponding to the current when the transponder is within the range of the magnetic field and the resistive load of the transponder corresponds to said first resistive load value.

13. The method of claim 6, wherein determining the authenticity of the transponder comprises verifying that the transponder is inauthentic.

14. The method of claim 6, wherein determining the authenticity of the transponder comprises verifying that the transponder is authentic.

15. The method of claim 6, wherein the third and fourth data are ratios of first and second levels of the current in the oscillating circuit of the terminal, the first level corresponding to the current when no transponder is within a range of the magnetic field of the terminal, the second level corresponding to the current when the transponder is within the range of the magnetic field and the resistive load of the transponder corresponds to said first resistive load value.

16. A transponder comprising:
an oscillator configured to provide a signal in response to a magnetic field of a terminal;
a rectifier configured to rectify a voltage of the signal provided by the oscillator;
one or more circuits configured to form a resistive load on the oscillator; and
a processor configured to determine an authenticity of the terminal based on a result of comparing a first value with a second value,
wherein the first value relates to a current of an oscillating circuit of the terminal,
wherein the second value relates to a level of the voltage of the signal provided by the oscillator,
and wherein the transponder is configured to receive data corresponding to the current of the oscillating circuit from the terminal.

17. The transponder of claim 16, wherein the one or more circuits comprise a switchable resistive element configured to vary the resistive load on the oscillator.

18. The transponder of claim 16, wherein the switchable resistive element is connected to the output terminals of the rectifying circuit.

19. The transponder of claim 16, wherein the switchable resistive element is configured to perform resistive retromodulation.

20. The transponder of claim 16, wherein the first value corresponds to a ratio of first and second levels of the current in the oscillating circuit of the terminal, the first level corresponding to the current when no transponder is within a range of the magnetic field of the terminal, the second level corresponding to the current in the oscillating circuit of the terminal when the transponder is within the range of the magnetic field and the resistive load corresponds to a first resistive load value.

21. The transponder of claim 20, wherein the second value corresponds to a value of the following expression:




  
    1
    -
    
      (
      
        
          R
          ⁢
          
            
          
          ⁢
          20
        
        
          R
          ⁢
          
            
          
          ⁢
          21
        
      
      )
    
  
  
    1
    -
    
      
        V
        
          
            
              C
              ⁢
              
                
              
              ⁢
              2
            
            ]
          
          ⁢
          R
          ⁢
          
            
          
          ⁢
          20
        
      
      
        V
        
          
            
              C
              ⁢
              
                
              
              ⁢
              2
            
            ]
          
          ⁢
          R
          ⁢
          
            
          
          ⁢
          21
        
      
    
  



wherein R20 is the first resistive load value, R21 is a second resistive load value, VC2]R20 is a first level of the voltage of the signal provided by the oscillator for the first resistive load value, and VC2]R21 is a second level of the voltage of the signal provided by the oscillator for the second resistive load value.

22. The transponder of claim 16, wherein the first value corresponds to a value of the following expression:




  
    
      I
      ⁢
      
        
      
      ⁢
      
        1
        offload
      
    
    
      I
      ⁢
      
        
      
      ⁢
      
        1
        
          ]
          R
          ⁢
          
            
          
          ⁢
          20
        
      
    
  
  *
  
    
      V
      
        
          
            C
            ⁢
            
              
            
            ⁢
            2
          
          ]
        
        ⁢
        R
        ⁢
        
          
        
        ⁢
        20
      
    
    /
    
      (
      
        
          
            R
            ⁢
            
              
            
            ⁢
            20
          
          
            R
            ⁢
            
              
            
            ⁢
            21
          
        
        +
        
          
            I
            ⁢
            
              
            
            ⁢
            
              1
              offload
            
          
          
            I
            ⁢
            
              
            
            ⁢
            
              1
              
                ]
                R
                ⁢
                
                  
                
                ⁢
                20
              
            
          
        
        -
        1
      
      )
    
  



wherein R20 is a first resistive load value of the resistive load of the transponder, R21 is a second resistive load value of the resistive load of the transponder, I1offload is a first level of the current in the oscillating circuit of the terminal when no transponder is within a range of the magnetic field of the terminal, I1]R20 is a second level of the current in the oscillating circuit of the terminal when the transponder is within the range of the magnetic field and the resistive load corresponds to the first resistive load value, and VC2]R20 is a first level of the voltage of the signal provided by the oscillator for the first resistive load value.

23. The transponder of claim 22, wherein the second value corresponds to a second level of the voltage of the signal provided by the oscillator for the second resistive load value.

24. A transponder comprising:
an oscillator configured to provide a signal in response to a magnetic field of a terminal;
a rectifier configured to rectify a voltage of the signal provided by the oscillator;
one or more circuits configured to form a resistive load on the oscillator; and
means for determining an authenticity of the terminal based on a result of comparing a first value with a second value,
wherein the first value relates to a current of an oscillating circuit of the terminal,
wherein the second value relates to a level of the voltage of the signal provided by the oscillator,
and wherein the transponder is configured to receive data corresponding to the current of the oscillating circuit from the terminal.

25. A system comprising:
a transponder including:
an oscillator configured to provide a signal in response to a magnetic field of a terminal,
a rectifier configured to rectify a voltage of the signal provided by the oscillator,

one or more circuits configured to form a resistive load on the oscillator, and
a processor configured to determine an authenticity of the terminal based on a result of comparing a first value with a second value; and

a terminal configured to generate a magnetic field for the transponder,
wherein the first value relates to a current of an oscillating circuit of the terminal,
wherein the second value relates to a level of the voltage of the signal provided by the oscillator,
and wherein the transponder is configured to receive data corresponding to the current of the oscillating circuit from the terminal.

26. The system of claim 25, wherein the terminal includes means for regulating a phase of the current of the oscillating circuit of the terminal.

27. The system of claim 26, wherein the means for regulating the phase of the current are configured to maintain a constant phase relationship between the current and a reference signal.

28. The system of claim 26, wherein the means for regulating the phase of the current are configured to regulate the phase of the current such that an imaginary part of an apparent impedance of the oscillating circuit is zero.

29. The system of claim 26, wherein the means form regulating the phase of the current comprise means for varying a capacitance of the oscillating circuit and means for detecting a value of the current.

30. The system of claim 25, wherein the terminal includes:
a variable capacitor;
a control circuit configured to regulate a phase of the current of the oscillating circuit of the terminal by controlling a capacitance of the variable capacitor,
wherein controlling the capacitance of the variable capacitor includes:
detecting a phase interval between the current of the oscillating circuit and a reference signal, and
adjusting the capacitance of the variable capacitor so as to reduce the phase interval.

31. The system of claim 30, wherein the control circuit is configured to maintain a constant phase relationship between the current and a reference signal.

32. The system of claim 30, wherein the control circuit is configured to regulate the phase of the current such that an imaginary part of an apparent impedance of the oscillating circuit is zero.

33. The system of claim 30, wherein the control circuit comprises a current measurement element.

34. The system of claim 25, wherein the terminal is further configured to measure the current of the oscillating circuit and to send data to the transponder regarding the current of the oscillating circuit when the transponder is within range of the magnetic field and the resistive load of the transponder corresponds to a first resistive load value.

35. The system of claim 34, wherein the terminal is further configured to receive data from the transponder regarding the current of the oscillating circuit when the transponder is within range of the magnetic field and the resistive load of the transponder corresponds to a second resistive load value.

36. The transponder of claim 16, wherein the second value further relates to a second level of the voltage of the signal provided by the oscillator.

37. The transponder of claim 16, wherein the second value further relates to a value of the resistive load.

38. The transponder of claim 16, wherein the second value further relates to a second value of the resistive load.