Abstract:
An integrated circuit ( 1 . . . 1′″, 1   a  . . . I c) with a true random number generator ( 2 . . . 2 ′″), which true random number generator ( 2 . . . 2 ″) comprises at least one instable physically uncloneable function ( 3 . . . 3′″, 3   a,    3   a ′) for generating true random numbers ( 8 ). Hence, each device of a group of devices can be provided with a unique true random generator, so that each device of the group is provided with different true random numbers even when said devices are applied to identical environmental conditions. Such a random number generator ( 2 . . . 2 ′″) may be part of a smart card as well as of a module for near field communication, for example.

Description:
FIELD OF THE INVENTION 
       [0001]    The invention relates to an integrated circuit with a true random number generator. The invention further relates to the use of a physically uncloneable function for generating random numbers. 
       BACKGROUND OF THE INVENTION 
       [0002]    The document WO2004/051458 discloses an integrated circuit as defined in the opening paragraph. According to the disclosure of this document, true random numbers are generated by means of a microprocessor operating at a first frequency, a counter for generating bits, a shifter for scrambling bits, a first oscillator for cooperating with the counter and a second oscillator cooperating with the shifter, wherein the oscillators provide a frequency perturbation based on digital input signals to generate a random signal. This random signal is sampled and used to derive single random bits. The bits are collected and a user can request a random byte after at least eight random bits have been collected. A disadvantage of this approach is that it usually takes a lot of CPU clocks before a new random bit can be retrieved. Thus, in the case of using a bigger amount of random bytes (e.g. for blinding in cryptographic operations), the execution time of the algorithm is limited by the speed of the random number generator. A further disadvantage of this embodiment is that since the circuitry for generating an input signal is an active piece of hardware, it is possible to attack it such that the random numbers are not random anymore. This way the blinding of a cryptographic algorithm could be broken. To avoid this, it is required to carry out randomness tests on the random number generator all the time. Since these tests take very long they slow down cryptographic algorithms. 
       OBJECT AND SUMMARY OF THE INVENTION 
       [0003]    It is an object of the invention to provide an integrated circuit of the type defined in the opening paragraph and a use therefore of the type defined in the second paragraph, wherein the disadvantages defined above are avoided. 
         [0004]    This object is achieved by a device according to the invention having such characteristic features that a device according to the invention can be characterized in the way defined below, that is: 
         [0005]    An integrated circuit with a true random number generator, which true random number generator comprises at least one instable physically uncloneable function for generating true random numbers. 
         [0006]    The object defined above is achieved by a use according to the invention, which provides such characteristic features that the use of a physically uncloneable function according to the invention can be characterized in the way defined below, that is: 
         [0007]    Use of an instable physically uncloneable function embedded in an integrated circuit to generate a random number. 
         [0008]    The characteristic features according to the invention provide the advantage that true random numbers can be generated very efficiently, because it is not necessary to run the time and memory consuming tests on the random number generator, since the random numbers are not generated by an active circuit but by means of an instable physically uncloneable function. The meaning of the term “instable” in the present context is that the physically uncloneable function changes its characteristics unpredictably as a result of environmental influences such as temperature, humidity, electromagnetic fields, etc., or due to ageing. Thus, generation of the random numbers is based on accidental processes, that are very difficult to be influenced by an attacker. 
         [0009]    Physically uncloneable functions are in general well known in the prior art. One example is disclosed in WO 03/046986 which describes a semiconductor device comprising security elements in a passivation layer of the device. The passivation structure has an effective dielectric constant that varies laterally over the circuit in an unpredictable way, thereby enabling the authentication verification of said semiconductor device. Whereas different circuits have different physically uncloneable functions, a physically uncloneable function on one circuit should not change over time, so that an identification procedure delivers always an unambiguous result. 
         [0010]    A further example of the use of a physically uncloneable function as stated above is described in US 2003/0204743, which discloses a group of devices having a common design but also a corresponding plurality of measurable characteristics that is unique to a device. Here a physically uncloneable function is again used for authentication. Hence, a variation of said characteristics over time has to be suppressed for the reasons stated above. 
         [0011]    Finally, U.S. Pat. No. 6,711,342 discloses an optical random number generator including an interferometer. The optical interferometer has a chaotic output depending upon temperature fluctuations in the surroundings. In fact, the document is related to a true random number generator, but because of the size of an interferometer it cannot be integrated into an electronic circuit. Thus, such a random number generator is not applicable to smart cards or other small devices such as a mobile phone for instance. U.S. Pat. No. 6,711,342 furthermore does not disclose a method where each device of a group of devices has a different random number generator. 
         [0012]    By contrast, the invention provides a method where each device of a group of devices includes a physically uncloneable function which naturally varies for different devices in an unpredictable way. Thereby each device has its own unique physically uncloneable function which—in contrast to the prior art—is furthermore designed to deliver an output signal varying over time even when the same challenge is input. Hence, each device of said group is provided with a unique true random generator, so that each device of the group is provided with different true random numbers even when said devices are applied to identical environmental conditions. In this way security for e.g. cryptographic tasks, wherein random numbers play an important role, is substantially increased. A practical example of the invention would be a random number generator on a smart card as well as in a module for near field communication, which is nowadays part of various devices such as mobile phones, PDAs and the like. It is easy to imagine that one skilled in the art can derive other applications as well without extensive effort and without departing from the scope of the invention. 
         [0013]    According to an advantageous embodiment of the invention, the integrated circuit comprises means for measuring a physical property of the physically uncloneable function. This embodiment provides the advantage that producing random numbers can be done in a very simple and secure way based on measured changes of physical values of the physical property. 
         [0014]    According to another advantageous embodiment of the invention, the integrated circuit comprises a signal generator connected with the physically uncloneable function for challenging the physically uncloneable function with an input signal. This embodiment of the invention provides the advantage of producing random numbers in a very simple and secure way based on a response from the physically uncloneable function to the input signal. 
         [0015]    If the integrated circuit comprises a pseudo random number generator cooperating with the physically uncloneable function in such a way that an output signal of the physically uncloneable function or values measured by means of the measurement means are a seed for the pseudo random number generator, the advantage is provided that if environmental influences such as temperature, humidity, etc. change slowly, random numbers can be generated in a very easy and secure way anyway. 
         [0016]    According to another advantageous embodiment of the invention, the physically uncloneable function is realized by means of a porous dielectric material which is arranged between at least two electrodes. This embodiment achieves the advantage that random numbers can be generated very effectively, since the generation of random numbers is based on fluctuations in humidity. 
         [0017]    If the physically uncloneable function is realized by means of a photosensitive semiconductor material, the advantage is achieved that the generation of random numbers can be executed very fast. 
         [0018]    However, it has proved to be particularly advantageous if the physically uncloneable function is realized by means of a metal with an electric resistance depending on temperature. This metal achieves the advantage of a high sensitivity to temperature changes. 
         [0019]    In a further embodiment of the invention, the measurement means are arranged to measure an inductance and/or capacitance of the physically uncloneable function. This provides the advantage of easy integration of the measurement means into an integrated circuit. 
         [0020]    If the physically uncloneable function is realized by means of at least one electric circuit and the measurement means are arranged to measure a runtime delay of signals of the at least one electric circuit, the advantage is achieved that the true random number generator can be implemented very easily using conventional integrated circuit design techniques. 
         [0021]    According to another embodiment of the invention, the signal generator is capable of applying a first mechanical vibration serving as the input signal for the physically uncloneable function, so as to cause a second mechanical vibration as the output signal of the physically uncloneable function. This has the advantage that the generation of random numbers can be executed very fast, since this embodiment is very sensitive to temperature fluctuations. 
         [0022]    The aspects defined above and further aspects of the invention are apparent from the examples of embodiment to be described hereinafter and are explained with reference to these examples of embodiment. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0023]    The invention will be described in more detail hereinafter with reference to examples of embodiment, but these are not to be construed as limiting the scope of the invention. 
           [0024]      FIG. 1  shows a first embodiment of an integrated circuit according to the invention in the form of a schematic block circuit diagram. 
           [0025]      FIG. 2  shows a second embodiment of an integrated circuit according to the invention in the form of a schematic block circuit diagram. 
           [0026]      FIG. 3  shows a third embodiment of an integrated circuit according to the invention in the form of a schematic block circuit diagram. 
           [0027]      FIG. 4  shows a fourth embodiment of an integrated circuit according to the invention in the form of a schematic block circuit diagram. 
           [0028]      FIG. 5  shows means for measuring the value of a parameter characteristic of the physically uncloneable function of  FIG. 6 . 
           [0029]      FIG. 6  shows a first embodiment of a physically unclonable function according to the invention in the form of a schematic circuit diagram. 
           [0030]      FIG. 7  shows a cross-section of an integrated circuit according to the invention with a second embodiment of a physically uncloneable function. 
           [0031]      FIG. 8  shows a cross-section of an integrated circuit according to the invention with a third embodiment of a physically uncloneable function. 
           [0032]      FIG. 9  shows an integrated circuit according to the invention with means for measuring the value of a parameter characteristic of the physically uncloneable function of  FIG. 7  or  FIG. 8 . 
           [0033]      FIG. 10  shows a cross-section of an integrated circuit according the invention with a further embodiment of a physically uncloneable function. 
       
    
    
     DESCRIPTION OF EMBODIMENTS 
       [0034]    The Figures are schematically drawn and not true to scale, and identical reference numerals in different Figures refer to corresponding elements. It will be clear to those skilled in the art that alternative but equivalent embodiments of the invention are possible without deviating from the true inventive concept, and that the scope of the invention will be limited by the claims only. 
         [0035]      FIG. 1  shows an integrated circuit  1  according to the invention. In the following, the abbreviation “IC” is used instead of “integrated circuit”. An IC  1  comprises a true random number generator  2 , hereinafter referred to as “TRNG”, with an instable physically uncloneable function  3 . 
         [0036]    A physically uncloneable function, hereinafter abbreviated as “PUF”, is in general defined as a function that maps challenges to responses, that is embodied by a physical device such as the IC  1 , and that verifies the following property. PUFs shall be easy to evaluate and hard to characterize. 
         [0037]    Easy to evaluate means that the IC  1  is easily capable of evaluating the PUF  3  in a short amount of time. 
         [0038]    Hard to characterize means that from a large number of plausible physical measurements (in particular, determination of chosen challenge-response pairs), an attacker who no longer has the device, and who can only use a finite amount of resources (time, matter etc.) can only extract a negligible amount of information about the response to a randomly chosen challenge. 
         [0039]    The PUF  3  is characterized by a physical property, or to be more exact by a physical parameter, such as the inductance or capacitance or runtime delays of signals. Due to the instability of the PUF  3 , the physical property or parameter characterizing the PUF  3 , such as its inductance or capacitance, changes its values in the course of time unpredictably. 
         [0040]    Furthermore, according to a preferred embodiment of the invention, the PUF  3  is “controlled”. This means that it can only be accessed via one or more access means that are physically linked to the PUF  3  in an inseparable way, e.g. an algorithm realized by means of hard- or software embedded in the integrated circuit, such as means  4  for measuring changes of the physical parameter of the PUF  3 . Thus, any attempt to circumvent this access means will lead to the destruction of the PUF  3 . In particular this access means can restrict the challenges that are presented to the PUF  3  and can limit the information about responses that is given to the outside. 
         [0041]    Since PUFs  3  are in general manufacturer resistant, as they use characteristics that are beyond the control of the fabrication process, the PUF  3  cannot be copied even with a reasonable amount of effort. Thus, it is essentially technically impossible to produce two identical PUFs  3  of the same type. 
         [0042]    Values of the physical parameter characterizing the PUF  3  are collected by means of measuring means  4  physically connected to the PUF  3 . According to the preferred embodiment of the invention, the impedance of the PUF  3  is measured. Hereinafter, the term impedance will be used in general for capacitances and inductances. 
         [0043]    In general, the implementation of the measuring means  4  depends on the specific type of impedance to be measured. The impedance may be measured for instance with a conventional circuit, as it is known from the state of the art. 
         [0044]    In a preferred implementation, the measuring means  4  comprise an oscillator and a binary counter. With the oscillator, the imaginary part of the impedance of the PUF  3  can be measured, which results in a signal with a frequency that depends on said part of the impedance. The advantage of this implementation lies in its use of standard components, such as oscillators and binary counters. These are usually present in the IC  1  already and can be applied as measuring means  4 . 
         [0045]    In another embodiment, the impedance of the PUF  3  can be measured by feeding into the PUF  3  a square wave of known frequency and amplitude generated within the IC  1  as it is known from the state of the art. The calculated actual value  5  thereof is then digitized, by means of an A/D converter  6  within the IC  1 , into a value  7 , that is indicated as “measured value”  7  in the following. 
         [0046]    The measured value  7  is true random, since it depends on statistical environmental influences, that cause a change of the impedance of the PUF  3  in the course of time. 
         [0047]    A measured value  7  corresponds to a random bit. In the case where the PUF&#39;s  3  parameter looked at changes very quickly, a random number  8  is generated by collecting several measured values  7  by means of a collecting means  9  such as a register or shift register. By thus collecting eight measured values  7 , one random byte of the random number  8  can be generated. The TRNG  2  bases its output, i.e. the random number  8 , on the underlying random physical process, i.e. the change of the values of the parameter of the PUF  3  caused by environmental influences. 
         [0048]    Another embodiment of the invention, which comprises an IC  1 ′ with an TRNG  2 ′, is shown in  FIG. 2 . Here an input signal  10 , constant or variable, is fed into the PUF  3  instead of measuring the change of a parameter of the PUF  3  directly. The input signal  10  of the PUF  3  is produced by means of a signal generator  11  embedded in the true random number generator  2 ′ of the IC I′. The input signal  10  for example may be a random number from signal generator  11  as well as the random number  8  which is looped back to provide PUF  3  with random challenges (loopback not shown in  FIG. 2 ). The system response of the PUF  3 —the output signal  12 —then will depend in an unpredictable way on the change of the parameters&#39; values caused by environmental influences, and thus will be random. In the embodiment shown in  FIG. 2 , the output signal  12  constitutes the random number. As is the case with the embodiment shown in  FIG. 1 , the output signal  12  is digitized by means of the A/D converter  6 . The digitized signal  13  then is collected by the collecting means  9  to produce the random number  8 . 
         [0049]    According to another embodiment of the invention, which comprises an IC  1 ″ with a TRNG  2 ″ as shown in  FIG. 3 , the measured values  7  of the parameter of the PUF  3  serve as a seed for a pseudo random number generator  14 , in the following abbreviated as PRNG  14 , which is also embedded in an IC  1 ″. This is of advantage especially in the case where the PUF  3  is not sensitive enough for environmental influence to provide really fast random numbers  8 . The calculated value  5  is read from the measurement means  4  and then digitized by the A/D converter  6 . The output of the A/D converter  6 , the measured value  7 , is subsequently collected by the collecting means  9 . The resulting value  15  is then used in the PRNG  14  for further generation of the random number  8 . The PRNG  14  comprises an algorithm, as is known to those skilled in the art, which is initialized with one or several resulting values  15 . This algorithm produces a much longer output sequence than the input sequence provided by the PUF  3 . The output sequence of the PRNG  14 , i.e. the random number  8 , appears to be random too, since the value  15 , on which the calculation is based, is true random. After being initialized with the value  15 , the internal state of the PRNG  14  completely determines the next bit to be generated. Thus, given the same seed value  15  the PRNG  14  will always produce the same output sequence. As the seed is determined by statistical and unpredictable environmental influences, the seed value  15  is always random and, as already mentioned above, the output sequence of the PRNG  14 —the random number  8 —thus cannot be predicted. 
         [0050]    The embodiments of  FIGS. 1 and 3  can be realized independently of one another or in combination with one another. In the latter case the IC  1 ″ can comprise decision means to decide whether to use the measured and digitized signal  7  of the PUF  3  directly or as a seed for the PRNG  14  to produce the random number  8 . The decision means can, for instance, be realized by means of a respectively configured processor. 
         [0051]    In the embodiment of the invention as shown in  FIG. 4 , the PUF  3  of the IC  1 ′″ is fed with the signal  10  generated by the signal generator  11 . Due to the changes of the PUF  3  caused by environmental influences, the signal  10  is mapped in an unpredictable way to the output signal  12 , as already mentioned above with respect to  FIG. 2 . Again a random number from signal generator  11  as well as the random number  8 , which is looped back, is imaginable as an input signal  10 . If the PUF  3  does not react very quickly to environmental changes, the output signal  12  does not change very quickly either. In this case it is of advantage if the output signal  12  of the PUF  3  serves as a seed for the PRNG  14  of the TRNG  2 ′″, analogous to the embodiment shown in  FIG. 3 . The output signal  12  is then digitized by means of the A/D converter  6  and collected with the collecting means  9  as well. The resulting value  15  is then used in the PRNG  14  for further generation of the random number  8 . 
         [0052]      FIG. 5  shows measurement means  4   a , which are an embodiment of the measurement means  4  shown in  FIGS. 1-4  and which are embedded in one of the ICs  1 ,  1 ′,  1 ″,  1 ′″. Accordingly, a PUF  3   a  is also shown in  FIG. 5  which is realized by means of a circuit embedded in the IC indicated by means of  1 ,  1 ′,  1 ″,  1 ′″ in the  FIGS. 1-4 . This circuit is hereinafter referred to as “delay circuit” and indicated by means of reference number  3   a , since it is an embodiment of the PUF  3  shown in  FIGS. 1-4 . The physical parameter that is measured is the runtime delay of signals in the delay circuit  3   a . The measurement means  4   a  comprise a parameterized self-oscillating circuit  17  built up of a first AND-gate  21 , the PUF  3   a , and an inverter  20  in a feedback loop. The frequency of the signal available at the output of the self-oscillating circuit  17  is a function of the delay of signals of the delay circuit  3   a , which delay depends on the input signal  10  fed into PUF  3   a  and on environmental changes. The rising edges of the resulting waveform is subsequently counted by a frequency counter  18  which is activated for a predefined number of clock cycles, after which the frequency of the self-oscillating circuit  17  can be read out of the counter  18 . The activation of the self-oscillating circuit  17  as well as of the counter  18  can be performed by an enable signal  22  which is fed into the first and a second AND-gate  21  and  19 , respectively. The counter  18  itself is clocked by a clock signal  23 . It should further be noted that measurement means  4   a  may comprise further modules, which are not shown. For instance the output signal of the self-oscillating circuit  17  can be synchronized by a clocked latch. Furthermore, the frequency of said output signal can be divided by additional counters. 
         [0053]      FIG. 6  now shows a delay circuit  3   a ′, which is an embodiment of the delay circuit  3   a  of  FIG. 5 , and which is made up of n−1 stages, where n is the number of bits in the input signal  10 . Each stage comprises two multiplexers  24 ,  25 ;  26 ,  27 . At the input to the delay circuit  3   a ′, a rising or falling edge gets sent into both the upper and lower path of the delay circuit  3   a ′. At each stage of the delay circuit  3   a ′, depending on the value of the bit of the input signal  10  allocated to the respective stage, the edges may cross one another, that is, the edge from the lower path goes to the higher path and vice versa. One of the two edges is then selected by the output multiplexer  28  to be looped back to the input of the delay circuit  3   a ′ in order for self oscillations to occur. Delays of paths are measured by means of the frequency counter  18  mentioned above. The delays in the delay circuit  3   a ′ will vary due to environmental conditions, mainly temperature variations. The measured delay of the delay circuit  3   a ′ either constitutes a bit of a random number  8  or can serve as a seed for a pseudo random number generator  14 . 
         [0054]    In  FIG. 7  an IC  1   a  is shown in a cross-sectional view, thus depicting its physical structure. The functional structure of IC  1   a  may be that of one of the ICs  1 ′ to  1 ′″ of  FIGS. 1-4 . IC  1   a  in general has a substrate  29  of silicon with a first side A. On this side A the IC  1   a  is provided with active elements  35  such as bipolar or field effect transistors. As is known to those skilled in the art, other elements such as capacitors, resistors and diodes may be integrated in the IC  1   a  as well. These active elements  35  are not necessarily related to functions with respect to the invention. Rather they can serve for any other function as known in the prior art, thus combining a known electronic device with the inventive TRNG. 
         [0055]    The PUF  3 ′ is realized, according to the embodiment shown, by means of two electrodes  31 ,  32  defined in a metal layer of the integrated IC  1   a . The electrodes  31 ,  32  are arranged at a distance from one another in a layer  33  of a dielectric material that is capable of absorbing humidity. The layer  33  consists, according to a first embodiment, of porous SiLK. Porous SILK is a dielectric resin with a polymer matrix that incorporates a pore structure with distributed pores  34 . The pores  34  are unpredictably distributed over the layer  33 , which is symbolized through varying distances between pores  34 . In this embodiment the PUF  3 ′ has an impedance which depends on the actual amount of humidity taken up by the pores  34 . Thus the PUF  3 ′ is very sensitive to humidity. 
         [0056]    Alternatively to using porous SiLK, the layer  33  can be made of porous silicate spin-on glass. The porous glass is bonded onto the substrate of the IC  1   a  in a way known to those skilled in the art. The parameter looked at in the case of this embodiment is the inductance of the PUF  3 ′. The impedance of the PUF  3 ′ is measured by means of measuring means  4   b  connected to the PUF  3 ′, as they are shown in  FIG. 9   
         [0057]      FIG. 8  shows an IC  1   b  as a further embodiment according to the invention, which again may have the functional structure of one of the ICs  1 ′ . . .  1 ′″ of  FIGS. 1-4 . IC  1   b  comprises a PUF  3 ″, which is an embodiment of a general PUF  3 . PUF  3 ″ is an LC-structure which comprises a capacitor with a first electrode  36 , a second electrode  37 , a dielectric layer  33  of porous material, as mentioned above, and a coil  38 . The windings of the coil  38  can be arranged so that the axis of the coil  38  is in parallel with the dielectric layer  33  (shown in  FIG. 8 ) or so that the axis of the coil  38  crosses the dielectric layer  33  (not shown). In the latter case there can be one winding below dielectric layer  33  and one above said layer. Anyway, a change of the physical characteristics of dielectric layer  33  leads to a change of the inductance of the coil  38 . It is easy to imagine that the invention applies to any combination of capacitors and inductors. Thus,  FIG. 8  only serves as a simplified example. 
         [0058]    Contrary to the embodiment of  FIG. 7 , the first and the second electrode  36 ,  37  are not present in the same layer on the same side of the layer  33 . The first electrode  36  as well as a part of the coil  38  are present in a metal layer attached to the layer  33 . The second electrode  37  as well as a further part of the coil  38  are present in an additional metal layer between the layer  33  and the active elements  35 . Interconnections between the elements are not shown in  FIG. 8  (nor in  FIG. 7 ) for reasons of brevity. By renunciation of an additional protective layer for the metal layer, in which the first electrode  36  is defined, a very high sensitivity of the PUF  3 ″ to environmental influences can be obtained. The changes in impedance of the PUF  3 ″ again can be measured by the measuring means  4   b  as shown in  FIG. 9 . 
         [0059]      FIG. 9  shows measuring means  4   b  which are an embodiment of the general measuring means  4  shown in  FIGS. 1-4  and which are integrated in an IC  1   b  according to the invention. Certainly the functional structure of IC  1   b  again could refer to one of the ICs  1 ′ . . .  1 ′″ of  FIGS. 1-4 . The PUF  3 ″ of  FIG. 8  is shown as well, but it is possible that the IC  1   b  comprises more than one PUF  3 ″ or another type of PUF. 
         [0060]    The measuring means  4   b  of this embodiment measure the imaginary part of the impedance of the PUF  3 ″. In fact the oscillator  39 , whose frequency depends on said imaginary part of the measured PUF  3 , provides a signal to a counter  40  via an upcount input UP. The counter  40  compares this frequency with a signal having a known clock frequency. This signal originates from oscillator  43  whose frequency is defined by means of an external capacitor  41  and an external resistor  42 , which both have a precise and well known value. The signal from oscillator  43  is then fed into counter  40  via a downcount input DN. The result of the binary counter  40  is the digitized signal  7 ′ which represents a value for the deviation of the signal from oscillator  39  with respect to the known clock frequency. Said digitized signal  7 ′ therefore represents a value representative of the impedance of the measured PUF. The actual value  7 ′ may be present in any kind of SI-unit, or else in any semiconductor specific value, and can be stored in the collecting means  9 ′ to constitute the random number  8 ′ or to serve as the seed for the PRNG  14  of  FIG. 3  or  4 . 
         [0061]    According to a further embodiment of the invention, the PUF  3  is realized as an “acoustic” PUF. For the description of this embodiment, reference will again be made to  FIG. 2 . For realizing the acoustic PUF  3  any piece of inhomogeneous material can be used in principle, in any suitable shape, for example parallelepiped or cylindrical. The PUF  3  can comprise a resin in cured state having inhomogeneities dispersed therein. As an alternative it may consist of two or more layers of different materials, conjoined by irregular interfaces. In order for the PUF  3  to be unique, the inhomogeneous material is produced by means of a random non reproducible process, like for example dispersing granular particles or bubbles in a resin in a fluid state, curing the resin and cutting a portion thereof. 
         [0062]    The IC  1 ′ comprises, in the case of an acoustic PUF  3 , the signal generator  11  for generating a challenge for the PUF  3 . According to this embodiment, the signal generator  11  is capable of applying as the input signal  10  for the PUF  3  a first mechanical vibration, so as to cause a second mechanical vibration as output signal  12 . The response of the PUF  3  to the challenge, i.e. the output signal  12 , is detected by means of an acoustic transducer, not shown in  FIG. 2 , embedded in the IC  1 ′. Since the acoustic PUF  3  is very temperature-sensitive, the response of the PUF  3  changes according to changes in temperature in an unpredictable way. 
         [0063]    In a further embodiment of the invention illustrated in  FIG. 10 , a PUF  3 ′″ can be realized by an IC  1   c , again comprising a substrate  29  with active elements  35  in a passivation layer  30  with an Al or Cu layer  45  on top. Layer  45  contains inhomogeneously distributed dielectric particles  44 , which inhomogeneous distribution of particles  44  can be accomplished in several ways: the layer  45  may contain particles  44  of different sizes, different compositions, different shapes, different orientations and in concentrations that vary over the area of the layer  45 . A consequence thereof is that the resistance of the PUF  3 ′″ cannot be predicted. The PUF  3 ′″ is designed such that it is extremely difficult to remove from the IC  1   c . Since the resistance of Cu and Al has a strong temperature dependence, this embodiment is very sensitive to changes in temperature too. According to this embodiment of the invention, the measurement means of the IC  1   c  are means for measuring a resistance. 
         [0064]    Alternatively, the PUF  3 ′″ can be realized by means of a light-sensitive semiconductor material, e.g. a diode made of Si wherein the diode comprises dielectric particles distributed inhomogeneously in it. Since the electric resistance of the light-sensitive semiconductor material varies unpredictably according to changes of the light falling on it, the measured resistance can be used to produce a random number. 
         [0065]    Further, it shall be stated that producing the random number  8  is not just restricted to take place completely in the integrated circuit  1  . . .  1 ′″,  1   a  . . .  1   c  itself. The measuring means  14  and/or the means for generating a challenge and detecting a respective response of the PUF  3 ,  3 ′,  3 ″,  3 ′″ can in principal be separated from the IC  1  . . .  1 ′″,  1   a  . . .  1   c  too. 
         [0066]    So, for example, the integrated circuit  1  . . .  1 ′″,  1   a  . . .  1   c  can comprise a PUF  3 ,  3 ′,  3 ″,  3 ′″ built of a transparent material that contains many scattering particles or air bubbles. A laser beam irradiates the scattering particles. The resulting speckle pattern is measured in transmission or reflection with a CCD camera. A code can then be extracted from the resulting pattern, which code can be used to produce a random number  8 . The code either constitutes a random number  8  or serves as a seed for a pseudo random number generator  14 . 
         [0067]    It should be noted that alternatively to measuring just a single PUF, several PUFs may be measured simultaneously so as to minimize the number of measuring steps. This presupposes, however, that instead of a single PUF several PUFs are applied on an IC. This simultaneous multiple measurement of PUFs accelerates the calculation of random numbers. 
         [0068]    It should further be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be capable of designing many alternative embodiments without departing from the scope of the invention as defined by the appended claims. In the claims, any reference signs placed in parentheses shall not be construed as limiting the claims. The word “comprising” and “comprises”, and the like, does not exclude the presence of elements or steps other than those listed in any claim or the specification as a whole. The singular reference of an element does not exclude the plural reference of such elements and vice-versa. In a device claim enumerating several means, several of these means may be embodied by one and the same item of hardware. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.