DE102015121626B4 - Chaotic circle with changeable dynamic states as a safe information store - Google Patents

Abstract

A storage device comprising at least one electronic component that realizes a chaotic circle, wherein the chaotic circle can be converted into at least one of a plurality of chaotic systems by changing a dependency of at least one property of the at least one electronic component on at least one system variable of the chaotic circle represent the information stored in the storage device, the change in dependency being defined as one or more point changes or as one or more small area changes of the at least one property dependent on the at least one system variable.

Description

The present invention relates to a secure storage device and a method for providing a secure information store. Furthermore, the present invention can relate to a device with a chaotic circle with changeable dynamic states, which can be used as a secure information store.

Portable electronic devices, for example smart cards, smartphones or tablets, are widely used in many areas. These areas are often security-relevant, for example electronic banking or secure communication, and require sensitive handling of data, which are often stored in a memory area of the electronic device and are protected against unauthorized access by means of a security mechanism which is recognized as secure, for example an encryption method.

However, since the security mechanism is independent of the storage area and the storage mechanism used, the encrypted data can be read out and is then only secured by encryption. In addition, since keys required for encryption and decryption or authentication often have to be stored in the same memory area or in a further memory of the electronic device, they are themselves worthwhile targets of attack. If the keys can be extracted from the memory, the security mechanism is broken.

Such attacks can be carried out successfully, in particular, if the electronic device can be examined directly, for example in a laboratory, so that physical access to the memory of the electronic device is possible.

Since the content of the memory is no longer protected, both the encrypted or unencrypted data and the entire memory of the electronic device can be reproduced or cloned as often as desired. Memory cloned in this way can be used in a modified electronic device and thus simulate the presence of an original, for example for authentication or in the event of a replay attack.

In order to make it more difficult to read out the contents of storage devices, storage devices can be protected against unauthorized access by passive or active physical barriers, for example by temperature sensors or by means of shielding. However, such security mechanisms can be bypassed by dedicated attacks and ultimately broken. Attackers can also deal with sufficient time for an investigation of the electronic device, for example after theft, to secure mechanisms by means of modeling or mathematical characterization.

DE 10 2014 115 736 A1 discloses a method for reading out a storage device with a plurality of chaotic systems which are coupled to one another in such a way that the storage device exhibits hyperchaotic behavior.

JC Sprott: "Simple chaotic systems and circuits", American Journal of Physics, 68 (8), 2000 , reveals chaotic circles with chaotic properties.

Chaotic systems that are based on deterministic equations, but have an unpredictable temporal development, are from Wikipedia: "Chaos Theory", 2015 , known.

It is therefore an object of the present invention to provide a storage device which or its storage mechanism itself protects the information. In particular, the object of the present invention is to specify a storage device which, even with occasional physical access, cannot be read completely and can neither be cloned nor modeled.

The invention, which solves the aforementioned objects, is specified by a storage device with the features of the main claim and by a method according to the independent claim. Advantageous embodiments of the invention are defined in the dependent claims.

According to an advantageous embodiment, a storage device is specified which comprises at least one electronic component which realizes a chaotic circle, the chaotic circle by changing a dependency of at least one property of the at least one electronic component on at least one system variable of the chaotic circle can be converted into a multiplicity of chaotic systems which represent the information stored in the storage device.

A "chaotic system" in the context of this invention is a chaotic circle set in a defined state. The chaotic system exhibits a chaotic dynamic (a chaotic behavior related to its system variables). The chaotic system can be characterized by measuring physical state variables, for example the system variables, the chaotic system or the chaotic circle in the respective state, as a result of which corresponding information is represented by the chaotic system. The structure and configuration of chaotic systems are described in S.H. Strogatz: "Nonlinear Dynamics and Chaos", Westview Press, 1994.

Although chaotic systems can be mathematically described by relatively simple systems of ordinary nonlinear differential equations, the solutions to these equations depend crucially on the system parameters and the initial conditions due to the nonlinear dynamics. The chaotic dynamics thus prevent exact modeling by a computer, since rounding errors inevitably occur. These deviations increase exponentially in chaotic systems. Chaotic systems are also topologically transitive and therefore cannot be broken down into several, easier to characterize subsystems. This property makes modeling difficult because the computing effort increases exponentially with the number of system parameters to be taken into account.

Chaotic systems are also highly sensitive, so that apparently identical chaotic systems can be clearly distinguished from one another due to the smallest variations in their component properties. This means that you cannot replicate a chaotic system exactly enough to create a second chaotic system with identical behavior. Because of this intrinsic individuality, chaotic systems are particularly suitable for use as security components, since they remain distinguishable despite identical components and are therefore difficult to copy.

The minimal component variations, which make the chaotic behavior so unique, can hardly be measured and cannot be calculated from the observable dynamics, so that, in terms of security technology, they are a "secret" and the chaotic system is an "intrinsically safe memory" “This secret can be viewed. Security is guaranteed by the fact that the secret makes the dynamics of the chaotic security component unique, but always remains hidden and cannot be reconstructed from the dynamics. The stored information can thus already be determined by random fluctuations in the production process of the electronic components. If these fluctuations are quantitatively random, the stored information can be used as the basis for generating cryptographic key material. Furthermore, the stored information can be used as authentication information, regardless of production-related fluctuations. However, this does not exclude other areas of application.

Although a chaotic system can practically not be copied in hardware, the chaotic dynamics of a single chaotic system could still be recorded and presented as part of a replay attack. However, this is prevented according to the invention by a single chaotic circle being deterministically convertible into a large number of chaotic systems. However, the measurement of all state variables for each of the large number of chaotic systems is not practical in a reasonable period of time.

The present invention thus does not require the integration of a large number of chaotic circles into an electronic device or the coupling of individual chaotic circles in order to implement a large number of resulting chaotic systems in a storage device which cannot be read out in a reasonable time. This reduces hardware requirements and complexity and increases the associated reliability.

When constructing chaotic circles to implement chaotic systems, the properties of individual electronic components must not leave very narrow intervals. These intervals are further limited by the interdependencies of the components. As a rule, a constant or global change in a property of an electronic component, for example an increase in a resistance value by 10 Ω, does not lead to a stable chaotic system, since the narrow interval limits are left. According to the invention, it is now provided that a chaotic circle, which can already represent a stable chaotic system, can be converted into a further stable chaotic system in that the dependency of a property of a component of the chaotic circle on at least one system variable of the chaotic circle is changed. For example, a 1600 Ω resistor can be changed so that it only acts as a 1620 Ω resistor in a voltage range of 2.1 V to 2.2 V, but again acts like a 1600 Ω resistor in the remaining voltage range behaves. By changing properties according to the invention by changing the dependency on a system variable, a chaotic circle can be converted into further chaotic systems which have a different, but still chaotic, dynamic behavior, and therefore ultimately into a large number of stable and distinguishable chaotic systems. The chaotic circle thus represents a secure information store, which irreversibly depicts a stored secret about its chaotic process, whereby the chaotic circle by changing component properties, which are based on a change in their dependence on system variables, into many states that can be distinguished from one another by measurement (chaotic systems ) which can be individualized by the secret.

The chaotic circle can be implemented by at least one or a plurality of electronic components, which can be arranged in a circuit or a circuit. The electronic components can each be an electronic component of the four elementary passive components (resistance, inductance, capacitor and memristor) in any combination, the properties of which can be varied depending on at least one system variable of the chaotic circle in order to transform the chaotic circle into a chaotic system to transfer from the multitude of chaotic systems. An electronic component can also define a complex circuit, for example a Chua diode.

The advantageous transfer of the chaotic circle into a multiplicity of chaotic systems in accordance with the storage device according to the invention leads to a particularly secure information store which can neither be reproduced by modeling nor read out in its entirety in a relatively short time of less than a few months. Reading out the information stored in the storage device is therefore only possible at certain points even with direct physical access to the storage device, which means that the entirety of the stored information cannot be read out at all or only with a disproportionately high expenditure of time of several months or even years .

In a preferred embodiment, the chaotic circle is characterized by a multiplicity of differential equations, at least one term of the multiplicity of differential equations defining the dependence on the at least one system variable of the chaotic circle. At least one of the terms of the differential equation describing the chaotic circle is preferably not constant, but takes on different values as a function of one or more system variables. Accordingly, the variations that reflect the change in component property cannot be applied to the constant terms, but to the form of the functional dependency.

According to a further embodiment, the dependency of the at least one property on the at least one system variable is defined in a large number of value ranges of the at least one system variable. For example, the dependency can be varied such that a continuous dependency of the value of the property on the system variable, for example a simple linear dependency, is only (strongly) changed in value ranges of the system variables that are (very) small compared to the total range of variation of the system variables . The change in the dependency can preferably be defined as one or more point changes or as one or more small area changes of the property dependent on the system variable. As a result, new chaotic systems can be generated with high probability starting from a chaotic system or an output system that is implemented by the chaotic circle in a current state, since the point change is so small that the chaotic behavior is retained. However, it is sufficient to create a new chaotic system that differs in its dynamics from the original system. By using several point changes at the same time, an extremely high number of different chaotic systems can be generated by varying a single component, for example a Chua diode.

möglichen Veränderungen der Systemdynamik, welche zu einem chaotischen System führen können.In a preferred embodiment, the dependency on the at least one system variable can be changed in a subset from the plurality of value ranges of the at least one system variable. An extremely large number of different chaotic systems can be generated by changing the dependency of the property in a subset from the large number of value ranges. A total range of values over which the state parameter of the property of the component varies as a function of a system variable can, for example, be divided into k ranges of values, of which l can be selected for change. If m changes in the corresponding value ranges are provided, this leads to $\left(\begin{array}{c}k\\ l\end{array}\right)\ast {\left(m\right)}^l$

possible changes in system dynamics, which can lead to a chaotic system.

In a further embodiment, the storage device comprises an input unit, which is configured to convert the chaotic circle into a chaotic system from the plurality of chaotic systems in response to an address by changing the dependency. The address can be entered by changing the dependency of the at least one property on the at least one system variable, preferably in a subset from the large number of defined value ranges.

In a further preferred embodiment, the storage device comprises an output unit which is set up to output one or more values which characterize the information stored in the device in accordance with a current state of the chaotic circle. The values characterizing the information stored in the storage device can be determined by measuring physical state variables or system variables of the chaotic circle, for example voltages and / or currents, according to a current state which represents a single chaotic system.

In a further embodiment, the storage device comprises an analysis unit which is set up to measure and evaluate a time profile of system variables in a current state of the chaotic circle in order to determine the one or more values. Due to the chaotic dynamics of the chaotic circle, values measured at specific points cannot be reproduced, since the current state of the storage device and thus the initial conditions of the measurement cannot be adequately controlled. Accordingly, the time course of the measured system variables can be analyzed over a predefined period of time, which is less sensitive to the initial conditions prevailing at the start of the measurement.

The analysis unit is preferably set up to evaluate the time profile of the system variables by determining parameters of the time profile of the system variables. The parameters can have one or more statistical moments in the configuration space or in the phase space. An evaluation based on statistical moments in the configuration space or phase space allows an analysis of the time course of the system variables, which is essentially independent of the initial conditions. While the phase space includes the local coordinates and their first time derivative (pulse) of the variables as physical quantities, the configuration space arises from the phase space by omitting the pulse information.

The parameters of the time profile of the system variables are preferably determined in the phase space. The resulting structures can also be called attractors. Since the shape of attractors remains the same over a large parameter range, for example over a time series with a predefined longer time period, the shape of an attractor can be used in order to obtain reproducible values which can characterize the information stored in the device. On the other hand, at least one time series with a sufficient number of measurements must be available to determine the attractors and thus to determine the information stored in the storage device. Depending on the behavior of the individual chaotic systems, 10 to 100, several hundred or several thousand cycles may be necessary to reliably determine the attractors for a given addressing, which means that a time window of several microseconds or even several milliseconds per address is necessary for the measurement can. If a sufficient number of chaotic systems are generated according to the invention by changing the dependency of the component properties on system variables, a high number of addresses can be achieved. In order to read out the entire secured memory using a brute force attack, a period of several months or even years would be required. Accordingly, even in the case of direct physical contact with the storage device according to the invention and under laboratory conditions, the stored information can only be determined after a disproportionately long period of time. The storage device according to the invention therefore already protects the entirety of the information stored therein on the basis of its configurability according to the invention.

According to one embodiment, the chaotic circle is implemented by an FPAA. The dependency can preferably be changed by changing values in a value table of the FPAA. Field Programmable Analog Arrays (FPAAs) are chips on which analog components are integrated, which can be linked to one another via appropriate programming. This enables basic and complex functions to be implemented, for example adders, multipliers or integrators, so that FPAAs for solving Differential equations can be used, which can describe a configurable chaotic circle and corresponding chaotic systems. FPAAs are therefore programmable analog systems, ie the system parameters can be loaded from a non-volatile memory when the system is started, similar to field programmable gate arrays (FPGAs). The entry can then be made by loading corresponding parameters, e.g. B. a certain value for a resistor can be specified by the user.

For example, an FPAA can emulate a system's behavior with chaotic dynamics. Individually configured FPAAs can, for example, implement components of Chua's Circuits, for example Chua diodes, differently. Here, the FPAA can access a value table with entries in order to generate a desired chaotic behavior or a change in the dependency on a system variable in the chaotic circle. Other parameters can also be used to generate the chaotic behavior by means of chaotic systems implemented in FPAAs. For example, a value table can be implemented for the generation of the characteristic curve of a component and can be specifically changed in these values in order to implement the change in the dependency. Since FPAAs have analog outputs, the outputs can be obtained in exactly the same way as with discrete Chua's Circuits, as explained below.

In a particularly preferred embodiment, the chaotic circuit is implemented by electronic components of a Chua circuit. The Chua's circuit can be implemented using discrete components or using an FPAA. A "Chua's Circuit" is an electronic resonant circuit that represents a chaotic system implemented in hardware, cf. for example LO Chua: "The Genesis of Chua's Circuit", Archives for Electronics and Transmission Technology, 46 (4), pp. 250-257, 1992 .

According to a further embodiment, the Chua's Circuit comprises a configurable electronic component, the at least one property of which can be changed as a function of the at least one system variable. For example, the Chua's circuit can comprise a non-linear negative resistor, which can depend on a system voltage and can be changed accordingly.

In another embodiment, the system variables have at least one: a capacitor voltage or a current through a coil in the Chua's circuit, or any combination thereof. Thus, after the chaotic circle has been brought into a specific state, which corresponds to an addressing of the storage device, by tapping the capacitor voltage and the current through the coil of the Chua circuit, the time course of the system variables can be measured in order to determine the values which are used in the Characterize device stored information.

According to one embodiment, the chaotic circle is arranged in a module. The device can therefore preferably comprise a plurality of modules, each of which has a chaotic circle implemented by at least one electronic component, which can be converted into a plurality of chaotic systems by changing a dependency of at least one property of the at least one electronic component on at least one system variable of the chaotic circle which represent the information stored in the respective module. As a result, a storage device can be provided with a plurality of independent, secure information stores which cannot be read out in their entirety. An information store configured in this way has an increased amount of information and thus increases the effort for an attacker. However, it should be clear that the security of the information store does not have to be based on a coupling of the individual modules, but is already ensured by the convertibility of each individual module into a large number of chaotic systems.

In a preferred embodiment, the storage device is arranged on an electronic device, preferably as a security component, comprising at least one: a digital sovereign document, a means of payment, a processor or a secured memory or any combination thereof. The storage device according to the invention in accordance with embodiments of the present invention can thus be part of a further electronic device or a non-electronic device, which can have means for accessing the storage device.

According to a further aspect of the present invention, a method for providing a secure information store is defined which comprises realizing a chaotic circle by at least one electronic component, converting the chaotic circle into a plurality of chaotic systems by changing a dependency on at least one property of the at least one electronic component Component of comprises at least one system variable of the chaotic circle and a representation of the information stored in the storage device by the plurality of chaotic systems.

According to further embodiments, the method according to one aspect of the present invention can comprise method steps which define a functionality of features of the device according to one or more embodiments of the present invention. Furthermore, embodiments of the device can define a functionality of the structural features of the device according to method steps of embodiments of the present invention.

According to one aspect of the present invention, there is provided a computer readable medium or media that includes commands that, when installed and executed by a computing device, cause the computing device to perform a method in accordance with embodiments of the present invention.

• 1 ein schematisches Diagramm eines Chua's Circuit nach dem Stand der Technik, welcher in einer Speichervorrichtung gemäß einer Ausführungsform der vorliegenden Erfindung einsetzbar ist,
• 2 eine Darstellung einer geänderten Abhängigkeit einer Bauteileigenschaft von einer Systemvariablen einer Speichervorrichtung gemäß einer Ausführungsform der vorliegenden Erfindung,
• 3 eine Darstellung einer Auswertung von Attraktoren eines chaotischen Systems einer Speichervorrichtung gemäß einer Ausführungsform der vorliegenden Erfindung,
• 4a und 4b eine Kennlinie einer nichtlinearen Funktion und einen Attraktor eines entsprechenden chaotischen Systems gemäß einer Ausführungsform der vorliegenden Erfindung,
• 5a und 5b eine punktuell veränderte Kennlinie und einen Attraktor eines entsprechenden chaotischen Systems gemäß einer Ausführungsform der vorliegenden Erfindung,
• 6a und 6b Darstellungen von Ergebnissen einer Veränderung einer Kennlinie eines chaotischen Systems einer Speichervorrichtung gemäß einer Ausführungsform der vorliegenden Erfindung,
• 7a und 7b Darstellungen von Vergleichen von baugleichen und unterschiedlichen Chips mit Speichervorrichtungen gemäß Ausführungsformen der vorliegenden Erfindung,
• 8 ein Diagramm eines Vergleichs unterschiedlicher chaotischer Systeme, welche durch einen chaotischen Kreis gemäß einer Ausführungsform der vorliegenden Erfindung realisiert sind,
• 9a und 9b einen Schaltplan eines konfigurierbaren elektronischen Bauteils, das in einer Speichervorrichtung gemäß einer Ausführungsform der vorliegenden Erfindung einsetzbar ist, bzw. dessen Kennlinie,
• 10a und 10b einen Schaltplan eines Chua's Circuit für eine Speichervorrichtung gemäß einer Ausführungsform der vorliegenden Erfindung bzw. einen resultierenden Attraktor,
• 11 ein Verfahren zum Auslesen einer Speichervorrichtung gemäß einer Ausführungsform der vorliegenden Erfindung und
• 12 ein Verfahren zum Bestimmen der Authentizität einer Speichervorrichtung gemäß einer Ausführungsform der vorliegenden Erfindung.

Further advantages of the storage device according to the invention and of the method result from the following description, in which the invention is explained in more detail using exemplary embodiments with reference to the accompanying drawings. In it show:

• 1 1 shows a schematic diagram of a Chua circuit according to the prior art, which can be used in a storage device according to an embodiment of the present invention,
• 2nd 1 shows a representation of a changed dependency of a component property on a system variable of a memory device according to an embodiment of the present invention,
• 3rd 2 shows an illustration of an evaluation of attractors of a chaotic system of a storage device according to an embodiment of the present invention,
• 4a and 4b a characteristic of a non-linear function and an attractor of a corresponding chaotic system according to an embodiment of the present invention,
• 5a and 5b a point-modified characteristic curve and an attractor of a corresponding chaotic system according to an embodiment of the present invention,
• 6a and 6b Representations of results of a change in a characteristic curve of a chaotic system of a storage device according to an embodiment of the present invention,
• 7a and 7b Representations of comparisons of identical and different chips with memory devices according to embodiments of the present invention,
• 8th 1 shows a diagram of a comparison of different chaotic systems which are implemented by a chaotic circle according to an embodiment of the present invention,
• 9a and 9b 1 shows a circuit diagram of a configurable electronic component that can be used in a storage device according to an embodiment of the present invention, or its characteristic curve,
• 10a and 10b 1 shows a circuit diagram of a Chua circuit for a storage device according to an embodiment of the present invention or a resulting attractor,
• 11 a method for reading a memory device according to an embodiment of the present invention and
• 12th a method for determining the authenticity of a storage device according to an embodiment of the present invention.

In this description, the conjunction "or" is understood as a non-exclusive disjunction, so that the expression " A or B "Either" A "Or" B "Or" A and B "can mean. For example, the parameters can have one or more statistical moments in the configuration space and / or in the phase space.

1 shows a schematic diagram of a chua circuit according to the prior art, which can be used in a memory device according to an embodiment of the present invention in order to implement a chaotic circle which represents a chaotic system. Chaotic systems are also known in the art as nonlinear dynamic systems. The development of chaotic systems over time seems unpredictable, although the underlying equations are deterministic. This behavior is also known as deterministic chaos and arises when such systems are sensitive to the Depend on initial conditions. Supposedly identical repetitions of an experiment thus lead to very different measurement results. However, a chaotic system has the property that it shows a similar behavioral pattern of the system variables for different initial conditions, which can be expressed in a convergence of the associated trajectories to a specific subspace in the phase space, which can be called an attractor. In particular, the probability distribution of the trajectories can be characteristic of the chaotic system.

The Chua's Circuit 100 is an electronic resonant circuit with a chaotic behavior. The Chua's Circuit 100 can comprise two parts: an RLC resonant circuit, which consists of a capacitor connected in parallel C2 with a series connection from a coil L and a resistance R0 consists, and a part that is responsible for the chaotic behavior and is composed of a further parallel connection, comprising a capacitor C1 and a negative resistance N _R . Both parts are over a linear resistor R connected with each other. The chaotic behavior of the Chua's Circuit 100 is reflected in the time course of its variables, the tensions V ₁ and V ₂ on the capacitors C1 respectively. C2 as well as the current I ₃ on the coil L contrary. A certain sequence of vibrations in a period does not occur again in later periods. The prediction of the future course of the vibrations, based on the observation of the previous behavior, is also not possible or not readily possible. The Chua's Circuit also responds 100 sensitive to changes in its environmental parameters. Multiple voltage curves too V ₁ or V ₂ The same system with supposedly the same boundary conditions can run completely differently, for example because different residual voltages at the capacitors for each measurement C1 , C2 can be present.

A chaotic system with chaotic behavior or dynamics is preferably given if the system has at least two unstable equilibrium points. The components of the Chua's Circuit 100 and their characteristics are in a certain relationship to each other, in particular the linear components, the capacitors C1 , C2 , the sink L and the resistors R , R0 . Furthermore, the negative resistance N _R , which can also be called a Chua diode, are fundamental for the occurrence of the chaotic behavior.

The chaotic circle and the chaotic systems realized with it can be modeled by the following system of equations: $$\begin{array}{c}{\dot{V}}_1=\frac{1}{{\mathrm{C.}}_1}\left(G\left(V_{\mathrm{2nd}}-V_1\right)-f\left(V_1\right)\right)\\ {\dot{V}}_{\mathrm{2nd}}=\frac{1}{{\mathrm{C.}}_{\mathrm{2nd}}}\left({\mathrm{I.}}_{\mathrm{3rd}}-G\left(V_{\mathrm{2nd}}-V_1\right)\right)\\ {\dot{\mathrm{I.}}}_{\mathrm{3rd}}=\frac{-1}{L}\left(V_{\mathrm{2nd}}+{\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="DE102015121626B4\_0010.png,DE102015121626B4\_0011.png"\; state="\{\{state\}\}">R</figure-callout>}}_0{\mathrm{I.}}_{\mathrm{3rd}}\right)\end{array}$$

In the system of equations (1), G denotes the reciprocal of the linear resistance R and f (V ₁ ) a special non-linear function that enables the chaotic behavior of the circle. This function is shown in the circuit diagram of the Chua's Circuit 100 through the element N _R implemented and can be implemented as a sectionally linear function with two different negative slopes, which can be denoted by a or b. A chaotic behavior of the circle can be achieved, for example, with the following component values: C1 = 10 nF, C2 = 100 nF, L = 18 mH, R0 = 12.5 Ω, R = 1600 Ω (or G = 625 µS); the negative slopes of the function f (V ₁ ) should preferably correspond to the guide values G _a = -455 µS and G _b = -758 µS. However, the present invention is not limited to any particular configuration of the Chua's Circuit 100 limited.

2nd FIG. 12 shows a representation of a changed dependency of a component property on a system variable of a memory device according to an embodiment of the present invention. According to one embodiment, the storage device, for example a storage device based on the Chua's circuit 100 as he is in 1 is shown, or based on a differently configured chaotic circle, by changing the dependency of the component property of a system variable into another chaotic system and thus addressed. The address can be entered at the Chua's Circuit 100 for example by modifying a characteristic curve of the linear resistance R respectively. This can lead to a modified characteristic curve 200 of a linear conductance G according to the system of equations (1). On the x axis it is at the resistor R applied voltage in volts, on the y-axis the current in amperes. 2nd presents the modified characteristic in a UI diagram 200 for a resistance value of 1600 Ω (625 µS), which was changed in the range between 2.1 V and 2.2 V to 1620 Ω (617.3 µS) as it was in the enlarged section 210 the characteristic 200 is shown. Because the characteristic 200 corresponds to the conductance G, this decreases with an increase of R accordingly.

To generate different chaotic systems, one or more value ranges, for example in the 2nd shown range of values between 2.1 V and 2.2 V, the component property can be changed further, for example in the range from 1600 Ω to 1660 Ω, the change being able to take place in steps, for example in 10 Ω steps.

3rd FIG. 4 shows an illustration of an evaluation of attractors of a chaotic system of a storage device according to an embodiment of the present invention.

To characterize the chaotic circle, i.e. to read out the information about a given address, which converts the chaotic circle into one of a large number of chaotic systems, individual system variables can be measured and statistical properties of the attractors can be examined. For example, a probability of residence of an attractor in a two-dimensional subspace of the phase space can be analyzed. For this purpose, the phase space can be divided into smaller areas with an imaginary grid and the distribution of the attractor over the individual grid cells can be examined. However, the present invention is not limited to a specific evaluation.

In general, statistical moments of the temporal course of the system variables can be examined to determine the stored information, for example mean value, standard deviation, skew or curvature of all system variables for a given address. These can be calculated or combined, thereby obtaining a value that characterizes the information stored in the storage device.

Furthermore, in addition or as an alternative, statistical moments of the distances between the measurement points in the configuration space can be considered, it being possible to determine a center point of a respective attractor and then to calculate a distance between each measurement value and this center point. The calculated distances can in turn be statistically analyzed by using statistical moments such as B. mean, standard deviation, skewness or curvature, can be calculated and suitably combined so as to characterize the information stored in the storage device.

The analysis of the temporal course of the system variables in the phase space is preferably carried out by examining the attractors in a preferably two-dimensional subspace of a higher-dimensional phase space of the overall system. For this purpose, the phase space can be divided into discrete areas. For example, a regular or irregular grid or any other partitioning of the subspace can be selected for this. The distribution of the attractor over the individual areas, for example grid cells, can be examined. An example of a partitioning of a two-dimensional subspace 302 with plotted values of an attractor that has been derived on the basis of a storage device with a Chua's Circuit, for example the Chua's Circuit 100 out 1 , is in the diagram 300 in 3rd shown. The voltages on the capacitors of the Chua's Circuit form a so-called double spiral tractor. The points in the grid correspond to the two voltage values at the same time. The number of points per grid cell can also be calculated for evaluating data sets.

The difference between two attractors that occurs in different system configurations, i. H. Another change in the dependency of a component property on a system variable, with regard to its spatial position or extent, can be quantified by determining and quantizing the differences in the distribution of the respective attractors over the discrete areas. Preferably, the absolute values of the differences between the grids can be summed up in order to obtain a key figure for the difference between two attractors which occur in different system configurations.

The aforementioned direct statistical analysis methods reduce the information contained in the behavior of the system variables to one, two or more scalar values. However, the direct statistical analysis methods do not differentiate between individual effects that lead to a modification of the quantities, i.e. to a change in the values derived from the data. This can be achieved by the latter method, in which the subspace is discretized, for example with a grid with an adjustable number of cells above the attractor, which can be represented by a matrix A.

1. 1. Initialisieren. Das Verfahren kann initialisiert werden, indem zwei Systemvariablen, beispielsweise Spannungen, die den Attraktor definieren, und eine Auflösung der Matrix A bestimmt werden.
2. 2. Suchen nach Minimal- und Maximalwerten. Das Verfahren kann die ausgewählten Werte isolieren und nach Minimal- und Maximalwerten der jeweiligen Systemvariablen, beispielsweise V₁ und V₂ , suchen.
3. 3. Skalieren von Werten. Der Bereich von dem größten Maximalwert zu dem kleinsten Minimalwert der entsprechenden Dimension wird als das Intervall gewählt, auf das alle Daten skaliert werden.
4. 4. Abbilden der Punkte auf die Matrix. Die skalierten Werte können auf die Gitterbereiche des Gitters abgebildet werden und es kann ermittelt werden, wie oft eine Trajektorie durch die entsprechende Zelle führt. Wenn die Trajektorie auf eine Zelle a_ij von A abgebildet ist, wird der Inhalt von a_ij um 1 inkrementiert. Hierdurch wird eine Matrix A erzeugt, die die Verteilung des Attraktors in einem zweidimensionalen Unterraum des Phasenraums darstellt.
5. 5. Berechnen von Unterschieden. Die Analyse kann für zwei oder mehr unterschiedliche Attraktoren durchgeführt werden, sodass mindestens zwei Matrizen, A und B, gemäß den vorhergehenden Schritten berechnet werden können, von denen jede die Werte eines Attraktors umfasst. Die Unterschiede können zwischen sich entsprechenden Zellen der Matrizen berechnet werden, beispielsweise mittels eines Absolutwerts der Unterschiede, und in einer dritten Matrix, C, gespeichert werden, C =|A-B|.
6. 6. Aufsummieren der Unterschiede. Die Inhalte der Zellen der Matrix C entsprechen dem Unterschied zwischen zwei Attraktoren bezüglich ihrer Form, Ausdehnung und Position sowie der Aufenthaltswahrscheinlichkeitsverteilung der Trajektorien im Phasenraum. Die Gesamtsumme aller Einträge bestimmt die Größe dieses Unterschieds, somit ergibt die Summation aller Einträge von C eine dimensionslose Maßzahl für den Unterschied zwischen zwei Attraktoren.
7. 7. Berechnen der Maßzahlen. Die Schritte 1-6 werden mit einem Datensatz in mehreren Zeitfenstern beliebiger Länge, z. B. 10 s, durchgeführt. Der Mittelwert der Werte aller Fenster kann dann als die Maßzahl betrachtet werden. Ferner kann die Standardabweichung bzw. der Standardfehler dieses Mittelwerts betrachtet werden.

An exemplary evaluation of the discretized subspace can be done by the contents of the individual cells, which represent the frequency of the sampling points of the attractor falling into these cells, can be interpreted as a grayscale image, wherein a difference image can be formed from the grayscale images for two attractors. The grayscale images can provide information about the local distribution of the attractor in the phase space. One or more of the following method steps can be provided to analyze the time course of the system variables:

1. 1. Initialize. The method can be initialized by determining two system variables, for example voltages that define the attractor, and a resolution of the matrix A.
2. 2. Search for minimum and maximum values. The method can isolate the selected values and according to minimum and maximum values of the respective system variables, for example V ₁ and V ₂ , search.
3. 3. Scaling values. The range from the largest maximum value to the smallest minimum value of the corresponding dimension is chosen as the interval to which all data is scaled.
4. 4. Map the points on the matrix. The scaled values can be mapped onto the grid areas of the grid and it can be determined how often a trajectory leads through the corresponding cell. If the trajectory to a cell a _ij of A is shown, the content of a _ij incremented by 1. This creates a matrix A generated, which represents the distribution of the attractor in a two-dimensional subspace of the phase space.
5. 5. Calculate differences. The analysis can be performed for two or more different attractors so that at least two matrices, A and B, can be calculated according to the previous steps, each of which comprises the values of an attractor. The differences can be calculated between corresponding cells of the matrices, for example by means of an absolute value of the differences, and in a third matrix, C. , are saved, C = | AB |.
6. 6. Sum up the differences. The contents of the cells of matrix C correspond to the difference between two attractors in terms of their shape, extent and position as well as the probability distribution of the trajectories in the phase space. The total of all entries determines the size of this difference, so the summation of all entries of C gives a dimensionless measure for the difference between two attractors.
7. 7. Calculate the dimensions. Steps 1-6 are performed with a data record in several time windows of any length, e.g. B. 10 s performed. The mean of the values of all windows can then be regarded as the measure. The standard deviation or the standard error of this mean value can also be considered.

1. 1. Ein „Selbstvergleich“, bei dem die Stabilität eines Attraktors über die Messdauer untersucht wird. In diesem Fall wird ein Intervall aus der Messreihe herausgenommen und mit anderen, gleichlangen Zeitintervallen derselben Messreihe verglichen. Auf diesen Vergleich wird im Folgenden und in den Figuren als SDA-Selbst Bezug genommen.
2. 2. Ein „Differenzvergleich“, bei dem Intervalle einer Messreihe mit den entsprechenden Intervallen einer zweiten Messreihe verglichen werden. Diese Methode wird im Folgenden und in den Figuren als SDA-Diff bezeichnet.

An evaluation can be carried out, for example, using the following tests, the present invention not being limited to a specific test method.

1. 1. A "self-comparison" in which the stability of an attractor is examined over the duration of the measurement. In this case, an interval is taken out of the series of measurements and compared with other, equally long time intervals of the same series of measurements. This comparison is referred to below and in the figures as an SDA self.
2. 2. A “difference comparison”, in which the intervals of a series of measurements are compared with the corresponding intervals of a second series of measurements. This method is referred to below and in the figures as SDA diff.

Since each data set originates from the same chaotic system in the first test method, the differences between these time intervals should be smaller than when (as in the second test method) data from different systems are compared with one another.

Results of a configuration of a chaotic circle in a variety of chaotic systems are summarized in Table 1. Since comparisons were carried out over several time intervals, the results are given in the form: "mean value of the intervals ± standard deviation". The resistance values relate to a modification of a characteristic curve, for example the modified characteristic curve 200 out 2nd . Table 1: Analysis of configurations of a chaotic circle. The results of the self-comparison are entered in the main diagonal, and the respective difference comparisons in the upper triangular matrix. R / Ω 1600 1610 1620 1630 1640 1650 1660 1600 69,450 ± 394 78,004 ± 931 86,121 ± 546 100,252 ± 694 112,287 ± 512 130,296 ± 738 184,623 ± 1,236 1610 72,685 ± 735 80,498 ± 881 95,167 ± 1,130 107,213 ± 1,139 126,622 ± 1,336 180,177 ± 1,298 1620 68,598 ± 543 81,744 ± 686 96,825 ± 862 117,667 ± 668 173,923 ± 1,274 1630 71,157 ± 766 87.106 ± 684 106,461 ± 864 164,868 ± 1,316 1640 71,342 ± 470 90,598 ± 558 144,279 ± 1,057 1650 69,919 ± 426 121,190 ± 1,575 1660 67,619 ± 637

The entries in the main diagonal of Table 1 correspond to results of the comparison of the attractors with themselves at different times. The values are stable and lie in the same range of values. When comparing attractors from different chaotic systems (upper triangular matrix), the differences are significantly larger.

In a preferred embodiment, a memory device according to the invention can be implemented by means of an FPAA implementation of a chua circuit with a variable characteristic of a non-linearity f (x). For this purpose, a chaotic circle can be implemented on special ICs, so-called field programmable analog arrays (FPAAs).

FPAAs are integrated circuits on which analog modules can be reconfigurably connected to one another, similar to FPGAs in the digital field. Typical components on FPAAs are e.g. B. summers, multipliers and integrators, i.e. assemblies, which can be used to solve differential equations, as they also describe chaotic systems. This technology does not require any further integration steps and is dynamically reconfigurable, which means that multiple systems can be implemented with just one chip. Furthermore, any chaotic systems can be easily implemented, since only the equations describing the system are transferred to the FPAA. Such systems are described for example in EN Lorenz: "Deterministic Nonperiodic Flow", Journal of the Atmospheric Sciences, 1963 , or OE Rössler: "An Equation for Continuous Chaos", Physics Letters, 1976 .

To implement a Chua's circuit on an FPAA, the system of equations (1) can be brought into a dimensionless form: $$\begin{array}{c}\dot{x}=\alpha \left(y-x-f\left(x\right)\right)\\ \dot{y}=x-y+\mathrm{e.g.}\\ \dot{\mathrm{e.g.}}=-\beta y+\gamma \mathrm{e.g.}\end{array}$$

wobei a und b Steigungswerte in einzelnen Abschnitten bezeichnen.For f (x), as for f (V ₁ ) described, a section-wise linear parameterization can be used: $$f\left(x\right)=bx+0.5\left(a-b\right)\left(\left|x+1\right|-\left|x-1\right|\right)$$

where a and b denote slope values in individual sections.

1. a) f(x)=bx+0.5(a-b)(|x+c|-|x-c|) mit a=-1.27,b=-0.68,c=1
2. b) f(x) =h₁x-h₂x³ mit h₁ =-1.27, h₂=-0.0157
3. c) f(x) =-atanh(bx) mit a= 2, b=0.38
4. d) f(x) = d₁x + d₂x|x| mit $d_{}$${}_1=-\frac{8}{7},{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="DE102015121626B4\_0010.png,DE102015121626B4\_0011.png"\; state="\{\{state\}\}">d</figure-callout>}}_2=\frac{4}{63}$
   

According to further embodiments, other implementation options for a Chua diode of a Chua circuit are possible. For example, in the case of FPAAs, an implementation using a LUT , whereby a segmentally linear characteristic is generated, is replaced by a structure with two multipliers, which can then generate a cubic characteristic. For example, one of the following equations can be implemented that generate the required characteristic of the Chua diode:

1. a) f (x) = bx + 0.5 (ab) (| x + c | - | xc |) with a = -1.27, b = -0.68, c = 1
2. b) f (x) = h ₁ xh ₂ x ³ with h ₁ = -1.27, h ₂ = -0.0157
3. c) f (x) = -atanh (bx) with a = 2, b = 0.38
4. d) f (x) = d ₁ x + d ₂ x | x | With $d_1=-\frac{\mathrm{8th}}{7},d_{\mathrm{2nd}}=\frac{\mathrm{4th}}{63}$
   

An individual system behavior can be generated by each of these equations, even if the rest of the circuit remains unchanged. This can advantageously be implemented using FPAAs, although other implementations are conceivable.

4a and 4b represent a characteristic of a nonlinear function and an attractor of a corresponding chaotic system according to an embodiment of the present invention. The underlying chaotic behavior of a Chua circuit implemented by an FPAA can be, for example, with parameter values of α = 10, β = -14.87, γ = 0 , a = - 1.27 and b = -0.687 can be achieved, whereby individual values can be adapted to the respective FPAA due to component fluctuations. However, the present invention is not limited to these values. An address is entered by modifying the system parameters when configuring the FPAA. The nonlinear function can be used with a value table, a so-called lookup table ( LUT ), will be realized.

4a shows the corresponding characteristic 400 the nonlinear function. The LUT can connect an output of an analog-to-digital converter (ADC) to an input of a digital-to-analog converter (DAC) of the FPAA. This means that the analog system can contain a digital component at this point, because voltages that are present at the input of the ADC are quantized and the resulting value then with the entries of the LUT compared. The DAC then generates the output voltage stored at the corresponding address. In 4a are the 256 ADC value ranges plotted on the x-axis. The DAC value assigned to the respective points in the range from -2 V to +2 V is plotted on the y-axis.

4b shows an attractor of a chaotic system one with the characteristic 400 out 4a configured chaotic circle.

Will over the LUT Influence on the shape of the characteristic 400 taken, there is a decisive intervention in the dynamics of the chaotic circle, which is transferred into another chaotic system. The systems created after changing the characteristic curve can therefore be viewed as new, independent chaotic systems or Chua's Circuits with an individual nonlinear characteristic curve. For this, the entries in the value table can be changed.

In an exemplary implementation in hardware, a Chua circuit with FPAA ICs can be implemented, for example chips from the company ANADIGM, e.g. B. an AN221E04 integrated on the development board AN221K04. These represent one LUT With 256 Entries ready, in turn 256 different initial values are possible.

5a shows a modified linear characteristic curve, which is based on the in 4a shown basic configuration was created. For this, 10 points each were awarded LUT in amplitude by each 10th to 256 Values moved, whereby the dependency of component properties on system variables can be changed. An attractor of the chaotic system is in 5b shown.

The effect of such a modification becomes clear when you look at the attractor 4b with the attractor 5b compares that with the characteristic curve 5a was generated.

6a , 6b , 7a , 7b and 8th show results of exemplary studies of each 150 different systems on two structurally identical chips, the chaotic circles of which were converted into a large number of chaotic systems by changing the dependency of component properties on system variables.

The analysis of the attractors was carried out using the analysis methods described above, as described in connection with Table 1 and the associated figures.

A self-comparison serves as the basis for the assessment. As already described above, comparing different systems with each other should result in higher key figures than comparing one system with itself.

The one described below 7a and 8th it can be seen that the self-comparisons of the chaotic systems are all in a defined area with a sufficiently small standard deviation, so that comparative comparisons of different chaotic systems should exceed these values.

Results of examining a single chip are shown in 6a and 6b shown. Here it was examined how strongly the change in a characteristic curve should advantageously be so that distinguishable chaotic systems are obtained.

6a shows the change in the amplitudes at the 10 points of the modified characteristic 5a . The x-axis shows the number of steps by which the amplitudes at the 10 points have been shifted. The y-axis shows the difference between the resulting systems and the system 5a shown. 6b adjusts the shift of the 10 points of the modified characteristic 5a represents, on the x-axis the number of steps by which the points were shifted, and on the y-axis the difference between the resulting systems and the system 5a are applied. The results show that the resulting chaotic systems can be distinguished from each other in a statistically significant manner, both when the amplitudes at identical points are only changed by one step in terms of value, as described in 6a is shown, as well as if all points are shifted by one position without changing the valences, as is shown in 6b is shown.

In the 7a and 7b The results shown are based on a measurement and configuration of a further chip of identical construction, with statistically significantly different results being able to be measured with the same configurations.

7a shows the comparison of identical addresses on two identical chips. The identification (address) of the respective chaotic system is plotted on the x-axis, and the identification number determined for the difference between the systems is plotted on the y-axis. In the lower "band" the comparison of the respective system on each of the two chips with itself is shown, in the upper one the differences of the same addresses on the two chips are shown.

7b shows a comparison of the basic configuration 5a from chip 1 with each 150 modified systems of both chips. The identifier of the respective system is plotted on the x-axis, with identifiers 0 to 150 chip 1 match and identifiers 151 to 300 chaotic systems from Chip 2nd describe. On the y-axis is the difference between the respective system and the basic configuration 5a determined key figure plotted. The results show that equally configured chaotic circles on the two chips cause different deviations.

This is due to manufacturing-related fluctuations in the production of the chips, which should always be kept as low as possible, but nevertheless lead to sufficiently large deviations when measuring the chaotic dynamics of the respective chaotic systems and thus the chaotic systems and the stored ones represented thereby Make information distinguishable. Furthermore, the information content of an original chip cannot be reproduced by using an identical chip, so that the memory device according to the invention comprising the chip cannot be cloned.

8th represents an extension of 7b to all 150 examined systems. 8th shows the comparison of each 150 Systems on 2nd Chips with each other. As in 7b the designation of the respective address is plotted on the x-axis and the resulting key figure is plotted on the y-axis. 8th it can be seen that the change according to the invention of the dependence on properties of the chaotic circle as a function of system variables leads to a large number of chaotic systems. Except for non-chaotic systems in the lowest band of 8th , which run towards a stable equilibrium point and therefore do not behave chaotically, and few unstable systems in a medium band show the other systems a chaotic behavior. Out 8th it can be seen that the respective self-comparisons occur in a range of approximately 70,000 to 130,000, while the difference comparisons occur in the range of approx. 220,000 to 650,000. The standard deviation of the respective values is so small that an overlap of the ranges almost never occurs.

A change in the properties of the chaotic circle converts the chaotic circle with a high probability into chaotic systems with chaotic behavior when changes are made in limited areas or at points in a limited number, based on a basic configuration. The number of chaotic systems generated in this way is significantly higher than if individual components were changed directly.

abgeschätzt werden. Selbst wenn es nötig sein sollte, sich auf 128 der 256 Punkte zu beschränken und die Veränderung der Wertigkeiten auf 50 zu begrenzen, beliefe sich die Zahl der Systeme immer noch auf ca. $\left(\begin{array}{c}128\\ 10\end{array}\right)*{50}^{10}\approx 2.2*{10}^{31}.$

Da für eine Charakterisierung eines chaotischen Systems mindestens ein kompletter Umlauf des Attraktors benötigt wird und dieser eine Grundfrequenz von etwa 3 kHz aufweist, würde ein Brute-Force-Angriff auf eine solche Speichervorrichtung ca. $\frac{2.2*{10}^{31}}{3000}\approx 7.3*{10}^{27}$

Sekunden dauern, was ungefähr 2.3 * 10²⁰ Jahren entspricht, was die Speichervorrichtung gegen diese Art von Angriffen immun macht.Starting from the in 5a shown approach of a change at 10 points, which were simultaneously changed by at least 10 values, the resulting number of systems can be approx $\left(\begin{array}{c}256\\ \mathrm{10th}\end{array}\right)*{246}^{\mathrm{10th}}\approx 2.3*{\mathrm{10th}}^{41}$

can be estimated. Even if it should be necessary to limit yourself to 128 of the 256 points and change the weights 50 limit, the number of systems would still be approx. $\left(\begin{array}{c}128\\ \mathrm{10th}\end{array}\right)*{50}^{\mathrm{10th}}\approx 2.2*{\mathrm{10th}}^{31}.$

Since at least one complete revolution of the attractor is required to characterize a chaotic system and this has a basic frequency of approximately 3 kHz, a brute force attack on such a memory device would approx. $\frac{2.2*{\mathrm{10th}}^{31}}{3000}\approx 7.3*{\mathrm{10th}}^{27}$

It takes seconds, which is approximately 2.3 * 10 ²⁰ years, which makes the storage device immune to this type of attack.

According to a further embodiment, one or more digital potentiometers can be provided as components in order to change resistance values. Digital potentiometers are integrated components (IC) that operate in a specific resistance range, e.g. B. 10 Ω to 1 MΩ, and with a certain resolution, for. B. 256 Steps that can be programmed to a resistance value. This can be achieved by connecting discrete resistors using analog switches. In a structure that contains such an IC, a certain resistance value can be selected each time the chaotic circuit is started, which then results in an individual system behavior. Several linear resistors can be provided in the Chua's circuit. So the Chua diode can be built using 2nd Operational amplifiers and 6 discrete resistors. In addition, the linear resistance R can be used as a free parameter for setting the system behavior. If these resistors are replaced by digital potentiometers, this leads to a chaotic circle that can be set in a variety of states (chaotic systems).

9a shows an embodiment of a configurable electronic component for a Chua's circuit, the at least one property of which can be changed as a function of at least one system variable. With a voltage controlled switch, another resistor, R2 , in a certain value range of a system variable, for example a voltage V1 , parallel to an existing linear resistance R1 be switched. This reduces the total resistance in this voltage range. This in 9a Component shown can be voltage controlled switches S1 and S2 and Schmitt trigger A1 and A2 include. The linear resistors R1 and R2 can each be 1620 Ω. The voltage controlled switches S1 and S2 are about the Schmitt trigger A1 and A2 addressed, whereby S2 via the inverted output of A2 is controlled. The voltage source V1 can generate a triangular voltage in the range of -9 V to +9 V. The Schmitt trigger A1 , A2 can be set so that in the range from 2.1 V to 2.2 V both switches are closed and the total resistance is only 810 Ω because in this case R1 parallel to R2 lies.

9b shows a voltage-current diagram of a resulting total resistance, for example that in FIG 9a shown component. In the UI diagram, the current is through R1 and R2 , so R_otal, against tension V1 applied.

According to a further embodiment, a configurable electronic component for use in a chaotic circuit of a device according to an embodiment of the present invention can be implemented with switches which can be closed in the basic state and open in a selected range of values. In this case, a resistance can be increased from 810 Ω to 1620 Ω, for example. 10a shows an integration of a circuit according to the embodiment in a Chua's circuit. The circuit includes voltage controlled switches S1 and S2 , which can connect a parallel resistance of 129.6 kΩ, the one resistor R with 1620 Ω reduced to R = 1600 Ω.

The one in one 10a shown chaotic circle generated attractor is in 10b shown. The in 10b The double spiral attractor shown (simulation duration 50 ms) has a visual similarity to attractors from chaotic circles with constant resistances.

If Chua diodes from Chua's Circuits are implemented in accordance with embodiments of the present invention with 2 operational amplifiers and 6 linear resistors, these resistors can be implemented by the in FIG 10a The circuit and resistors shown are replaced with suitable values, as a result of which a characteristic curve of the Chua diode can be influenced in such a way that a dependency of at least one property of the Chua diode on at least one system variable of the chaotic circuit is changed. As a result, the chaotic circle can be converted into a large number of chaotic systems with distinguishable system dynamics.

11 FIG. 5 illustrates a method of reading a memory device in accordance with an embodiment of the present invention.

According to a preferred embodiment, the method for reading out the memory device comprises receiving an address, mapping the address to a change in a dependency of at least one property of a chaotic circle of the memory device on a system variable, changing the property in accordance with the changed dependency, as a result of which the chaotic circle is converted into one of a plurality of chaotic systems, and outputting one or more values which characterize the information stored in the device according to the chaotic system.

The method for reading out a memory device according to embodiments of the present invention can preferably be used. The storage device can be implemented, for example, by means of one or more Chua's Circuits or FPAAs, which can represent a single chaotic circle, which can be converted into a large number of chaotic systems by changing the dependency of properties of the chaotic circle on system variables. Accordingly, mapping an address may include changing dependency values in one or more ranges of values. Furthermore, outputting the one or more values may include measuring capacitor voltages and currents through coils in the Chua's Circuits or system variables of the FPAAs.

The procedure 800 can in step 802 begin as soon as the storage device is to be read out, for example when the storage device is placed on a reading device or is connected to this reading device in a wireless or wired manner. The storage device may include a configurable chaotic circle. An input module of the storage device can in step 804 receive an address, for example from the reader. For example, the address may be received from an entity, such as a trusted server, that is external to the storage device. The address can be mapped to a state of the storage device. So in step 806 the method may continue, for example, to map the address to a functional dependency of properties of the chaotic circle on system variables. Individual value ranges of the functional dependency can, for example, be changed by one or more values, which can be controlled by a binary form of the address. Any mapping functions can be used to map an address space to the available change areas.

After mapping the address to the state of the memory device, corresponding state values of the memory device can be determined. So after mapping the addresses in step 806 and after changing the dependency of the properties, the system variables of the chaotic circle are determined and analyzed. Based on the analysis of a time course of the system variables, for example in a configuration space or phase space, characteristic values can be derived from the analysis, which in step 808 are output, preferably via an output module of the memory device.

The process can be done in step 810 check whether the storage device is actively queried, for example by continuing to apply it to a reading device or to connect it to it wirelessly or by wire. If this is the case, the method continues with step 804 away. If the storage device is inactive, the method may proceed in step 812 end up.

12th illustrates a method for authenticating a storage device according to an embodiment of the present invention.

According to one embodiment, a distributed system can be specified, which comprises secure storage and at least one trustworthy server. The secured memory stores a set of addresses for a plurality of memory devices according to an embodiment of the present invention. The at least one trustworthy server is coupled to the secured memory and is set up to provide corresponding addresses for reading out a memory device from the plurality of memory devices.

According to the invention, provision of physically stored information in one or more storage devices or a corresponding module can thus be provided, which can only be read out if addresses are known externally to the storage device or the module, which means that these addresses are not on the storage device or stored in the module. For this purpose, an attacker with access to the storage device or the module should both be impossible to read out all of the information stored in the storage device or the module in a relative time (brute force attack), and also to simulate the storage device or the module in this way or to clone that the attacker would be able to determine the stored information as soon as the address is known, even without access to the storage device or module. Ignorance of the external addresses thus protects the physically stored information in the same way that ignorance of cryptographic keys protects a cryptogram.

In one embodiment, the system further comprises at least one authentication component that is coupled to the at least one trustworthy server. The secured memory can store a set of pairs of values for each storage device, each pair of values having an address and a value stored for this address in the respective storage device, the at least one trustworthy server being set up to ensure the authenticity of one coupled to the at least one authentication component Check storage device from the plurality of storage devices. Preferably, the secure storage device may be a storage device according to embodiments of the present invention.

In this way, a trustworthy network can advantageously be set up, in which the authenticity can be checked via secure storage devices.

In a preferred embodiment, the at least one trustworthy server checks the authenticity of a storage device by sending an address stored in the secure memory to the storage device upon a request from the authentication component and comparing the response with the associated value stored in the secured memory. Because each secure storage device comprises a configurable chaotic circle, the information stored therein cannot be read out, or cannot be read out completely within a practical time frame, so that the secure storage device cannot be copied or cloned. Accordingly, a successful query with high reliability can ensure that the secure storage device is the original.

After a value pair has been used for authentication, it can preferably be identified as used, so that it is no longer used in the case of a renewed request. This can ensure even more reliably that a correct answer can only come from a secure storage device that is the original and therefore authentic.

According to yet another embodiment, a method for checking the authenticity of a plurality of storage devices according to embodiments of the present invention is specified, which comprises receiving a request from an authentication component of a distributed system for authentication of a storage device, sending an address stored in secure memory to the storage device to the authentication component, receiving a response from the authentication component and comparing the response from the authentication component with the value stored in the secure memory for the address.

Preferably, the method further comprises sending an authentication confirmation to the authentication component if the comparison is successful and sending a rejection to the authentication component if the comparison is not successful.

So can the procedure 900 out 12th for example, used in a trusted distributed system in which a variety of storage devices with configurable chaotic circles According to embodiments of the present invention, is issued by a trustworthy entity, which can then be used in checking the authenticity of the storage devices.

The procedure 900 can in step 902 begin, for example, when a secure storage device is attached to a reader or is connected to it wirelessly or by wire and the reader wants to check the authenticity of the storage device. For this purpose, the reading device or the computer system connected to it can send a request to a trustworthy server, which in step 904 can receive. The trustworthy server can step from data that are transmitted in the request, for example an identity of the storage device, or by any other method suitable for identification, the secure storage device 906 identify. Based on the result of the identification, the trusted server can step 908 a database 910 Interrogate.

Database 910 can each store a set of pairs of values for the plurality of secure storage devices that have been issued by the trustworthy entity, each pair of values having an address and a value stored for the address in the respective storage device.

The set of pairs of values for each storage device may include all of the information stored in the storage device. Security can also be increased by using only a subset of the value pairs. These pairs of values or the subset can be determined when the storage device is delivered or during the “enrollment”. For example, a subset of 10 ⁴ addresses or any other subset can be specified. The selected addresses can be created in a secure environment and the corresponding responses measured, which are then stored in the database 910 get saved. After use, the addresses used can be marked as invalid.

Is an entry to that in step 906 identified secure storage device in the database 910 included, so the database delivers 910 in response to the request in step 908 an address 912 and the value stored in it 914 . Database 910 can be configured such that an address stored in the database for the identified secure storage device is selected pseudorandomly and the associated data record, including the address 912 and the value 914 , is returned. Furthermore, the selection of the address 912 in the request in step 908 can be influenced, for example by suitable parameters or by specifying the desired address 912 itself. The database 910 can check which of the addresses or whether the desired address 912 is available. For example, the addresses can be marked as invalid after use, which can further increase security. However, the addresses can also be reused, whereby the number of reuses can be marked and only a maximum number of repeated uses can be permitted. Database 910 can also be set up to delete a pair of values from the stored data set as soon as it has been used once.

The procedure 900 can in step 916 proceed to the address 912 to be transmitted to the reading device. The reading device can transfer the transmitted address to the secure storage device, which according to the method in 11 can be read out. The reader reads the value stored in the secure storage device for the address and sends it back to the trusted server, which in step 918 the answer with the value 914 can compare.

If there is agreement, step 920 a confirmation of authenticity can be transmitted. However, if the values do not match, on the one hand no response or confirmation can be sent, or a negative confirmation or a rejection can be sent to the reading device, which then requests a new step 904 may send to the trusted server or may refuse to use the secure storage device and, for example, a device or electronic device coupled to it.

Regardless of the comparison and the confirmation sent in the steps 918 and 920 can the procedure 900 with step 904 continue and wait for further inquiries.
Accordingly, a challenge-response authentication method can be specified, based on a challenge, which of the address 912 can correspond, a response can be generated, which corresponds to a current state or a current chaotic system of the chaotic circle, which then with the stored value 914 is compared. It should be understandable that the value 914 can also be represented by a hash, so the value 914 does not have to be transmitted in plain text.

Storage devices according to embodiments of the present invention can thus be used to check the authenticity of the storage device itself and a device or electronic device coupled to it. For example, storage devices according to embodiments of the present invention can be provided on official documents, for example an electronic identity card or passport, which makes it significantly more difficult to forge the official document since the storage device cannot be cloned. Furthermore, such storage devices according to embodiments of the present invention can be attached to particularly valuable or security-critical devices or electronic devices, for example medicines, smart cards, portable computing devices, high-performance computing devices and the like. a. to enable proof of origin or authenticity of the device or the electronic device. In addition, since only a single chaotic circle has to be implemented in the storage device, the hardware requirements are low. In addition, such storage devices can be mass-produced without affecting the individuality of the individual storage devices.

It should be understood that the present invention is not limited to the specific configuration of a chaotic circle. In addition, the individual process steps in the 11 and 12th The methods shown can be carried out in a different order than the order shown and individual steps can be omitted, supplemented, repeated, permuted or in particular carried out in parallel. So can the procedure 900 for example, for each individual secure storage device in parallel to the database 910 access and carry out the subsequent check. Furthermore, the illustrated methods and further methods according to embodiments of the present invention can be carried out in a computer-assisted manner on one or more computing units or data processing units or can be stored as program code on data carriers which, when installed and / or executed on a computing device, causes the computing device to perform the corresponding method according to an embodiment of the present invention.

The features disclosed in the above description, the claims and figures can be of importance both individually and in any combination for realizing the invention in its various embodiments.

Claims (18)

A storage device comprising at least one electronic component that realizes a chaotic circle, wherein the chaotic circle can be converted into at least one of a plurality of chaotic systems by changing a dependency of at least one property of the at least one electronic component on at least one system variable of the chaotic circle represent the information stored in the storage device, the change in dependency being defined as one or more point changes or as one or more small area changes of the at least one property dependent on the at least one system variable. Device after Claim 1 , wherein the chaotic circle is characterized by a multiplicity of differential equations, at least one term of the multiplicity of differential equations defining the dependence on the at least one system variable of the chaotic circle. Device after Claim 1 or 2nd , wherein the dependency of the at least one property on the at least one system variable is defined in a plurality of value ranges of the at least one system variable. Device according to one of the preceding claims, wherein the dependency on the at least one system variable can be changed in a subset from the plurality of value ranges of the at least one system variable. Device according to one of the preceding claims, further comprising an input unit, which is configured to convert the chaotic circle based on an address into a chaotic system from the plurality of chaotic systems by changing the dependency. Device according to one of the preceding claims, further comprising an output unit that is configured to output one or more values that characterize the information stored in the device according to a current state of the chaotic circle. Device after Claim 6 , further comprising an analysis unit which is set up to measure and evaluate a time profile of system variables in a current state of the chaotic circle in order to determine the one or more values. Device after Claim 7 , wherein the analysis unit is also set up to evaluate the time profile of the system variables by determining parameters of the time profile of the system variables. Device after Claim 8 , wherein the parameters have one or more statistical moments in the configuration space or phase space. Device according to one of the preceding claims, wherein the chaotic circle is realized by an FPAA. Device after Claim 10 , wherein the at least one property can be changed by changing values in a value table of the FPAA. Device according to one of the preceding claims, wherein the chaotic circuit is realized by electronic components of a Chua circuit (100). Device after Claim 12 , The Chua's circuit (100) comprising a configurable electronic component, the at least one property of which can be changed as a function of the at least one system variable. Device after Claim 12 or 13 wherein the system variables include at least one: a capacitor voltage or a current through a coil in the Chua's circuit (100). Device according to one of the preceding claims, wherein the chaotic circle is arranged in a module. Device according to one of the preceding claims, comprising a plurality of modules, each having a chaotic circle realized by at least one electronic component, which by changing a dependency of at least one property of the at least one electronic component on at least one system variable of the chaotic circle into a plurality chaotic systems can be converted, which represent the information stored in the respective module. Device according to one of the preceding claims, wherein the storage device is arranged on an electronic device, comprising at least one: a digital official document, a means of payment, a processor or a secured memory. A method of providing a secure information store comprising: Realization of a chaotic circle by at least one electronic component; Converting the chaotic circle into at least one of a plurality of chaotic systems by changing a dependency of at least one property of the at least one electronic component on at least one system variable of the chaotic circle, the changing of the dependency as one or more point changes or as one or more small area changes of the at least one property is defined dependent on the at least one system variable; and Represent the information stored in the storage device through the plurality of chaotic systems.

Images