BACKGROUND OF THE INVENTION

1. Field of the Invention

[0001] The present invention relates to a method for performing secure computation using a solid volume of material to which a number of electrodes are attached. Applications of the invention as programmable matter include pattern recognition, audio recognition, image recognition, genetic algorithm reader and a reservoir computer.

2. Technical Field

[0002] Disclosed herein is a system that provides an entirely new way of computing. Engineered traveling or standing wave pulse patterns in certain types of materials can be interpreted as a computation. Internal pulse patterns in the materials(s) cause constructive and destructive interference and thereby manipulate internal dipoles and other supramolecular elements in a controlled way.

[0003] Aspects of the present invention relate to the field of security devices and in particular to a security device that comprises a network of capacitors that acts as a physical unclonable function used to control access to a restricted device or service.

[0004] Aspects of the present invention relate to the electrical properties of piezoelectric materials for computation. Therefore, the background further involves materials science and solid-state physics. BACKGROUND OF SECURITY ASPECTS

[0005] A wide range of security devices exist that are used to control access to restricted devices. For example, it is known to use a digital key to control access to a restricted digital device, such as a computer terminal. In order to access the restricted digital device, the authenticity of the digital key is assessed. Access to the restricted digital device is achieved upon successful verification of the

authenticity of the digital key. In practice this may comprise executing a

cryptographic protocol in order to determine the authenticity of the digital key. For example, the digital key may be stored on a dongle or similar portable storage device. In order to access the restricted digital device, the dongle is operatively coupled to the restricted digital device, and a cryptographic exchange may take place in order to verify the authenticity of the digital key. Only the bearer of an authentic digital key is provided access to the restricted digital device. In order to maintain the confidentiality of the digital key, it may be stored in an encrypted format on the dongle. This ensures that a fraudulent user cannot simply obtain the digital key by downloading it from the dongle.

[0006] In a similar way, digital keys are also used to control access to restricted services, such as computer software applications. These solutions function in fundamentally the same way as described previously. Again, a digital key is stored in encrypted format on a portable storage device, such as a dongle. The security of these solutions is also reliant on the confidentiality of the digital key being

maintained.

[0007] One shortcoming of existing prior art solutions is that their security is reliant on the confidentiality of the digital key being maintained. The development of computers with greater processing power, and in particular quantum computers, presents a serious risk to the security of such devices. In particular such computers have the processing power required to crack the encryption protocols used to encrypt the digital keys. This means that there is a very tangible risk that existing digital keys may be cloned by malicious users and used to gain unauthorized access to secure devices and services.

[0008] Another shortcoming is that existing solutions were designed for fixed computers under human control. In addition to the shift to portable and mobile devices there are now wireless sensor networks and other devices which have their own IP address - generally known as the Internet of Things (loT). By 2020 the estimated number of high-value loT devices is between 20 billion (Gartner) and 50 billion (Cisco). Traditional security using classical cryptography is not designed to provide robust security for physically unprotected devices, most of which have limited resources e.g. memory and computational power.

[0009] We can summarize the shortcomings to secure an loT device as follows:

• The loT device has insufficient memory

• The power consumption required to authenticate is too high

• The cost is too high to be commercially viable

• With the right tools the security of an electronic device can be compromised [0010] A physical unclonable function (PUF) is one response to this challenge. A physical unclonable function, or PUF, is a "digital fingerprint" that serves as a unique identity for a semiconductor device such as a microprocessor. PUFs depend on the uniqueness of their physical microstructure. This microstructure depends on random physical factors introduced during manufacturing. These factors are unpredictable and uncontrollable, which makes it virtually impossible to duplicate or clone the structure. Rather than embodying a single cryptographic key, PUFs implement challenge-response authentication to evaluate this microstructure. When a physical stimulus is applied to the structure, it reacts in an unpredictable (but repeatable) way due to the complex interaction of the stimulus with the physical microstructure of the device. This exact microstructure depends on physical factors introduced during manufacture which are unpredictable. The applied stimulus is called the challenge, and the reaction of the PUF is called the response. A specific challenge and its corresponding response together form a challenge-response pair or CRP. The device's identity is established by the properties of the microstructure itself. As this structure is not directly revealed by the challenge-response

mechanism, such a device is resistant to spoofing attacks. Source: Wikipedia.

[0011] While this definition of a PUF relates to the manufacturing variations of a semiconductor device such as an SRAM, the principle applies to other materials. There are two types of PUF. A Weak PUF is akin to a secret key, whereas a Strong PUF is more like a physical hash function. The two big differences are:

1 ) A weak PUF has only a few, sometimes only one, challenge response pair. A strong PUF has many. 2) One must restrict access to a Weak PUF to prevent a third-party being able to view the responses. That is not necessary with a strong PUF.

[0012] The most common form of commercially available weak PUF is called an SRAM PUF.

[0013] Many loT devices exist in unprotected and hostile environments. Many will never be inspected throughout their lifetime. With the right tools and sufficient time, it is a realistic assumption that any piece of software can be hacked, any password cracked, and any piece of hardware reverse engineered, cloned and modified.

[0014] If the digital responses arising from a Weak PUF are read out by invasive means, the security of the system is compromised. This is in principle comparable to the security of a secret key stored in NVM (non-volatile memory), even though the PUF-response exists in the system only for a short time. Still, this inherent attack point of Weak PUFs has been successfully exploited in recent publications by Nedospasov et al. Even if care is taken to prevent SRAM PUF values from ever being read over standard on-chip channels, attacks using laser stimulation can reveal cell states in a powered SRAM PUF. Source:

PUFS at a Glance https://scholar. google. co.uk/citations?user=Jok8C54AAAAJ

[0015] Can strong PUF’s be cracked? That depends on the number of challenge response pairs. If a hacker could get hold of a PUF device and have enough time to generate billions of challenge response pairs and use machine learning techniques, they might be able to interpolate the whole set. [0016] Gassend et al. successfully attacked arbiter PUF, which is a type of strong PUF using standard machine learning (ML) methods, such as the support vector machine (SVM) and perceptrons method, after collecting a number of CRPs. They used the collected CRPs of the PUF to train the ML algorithm, then predicted the key based on the responses. The prediction accuracy can be significantly improved when the number of training CRPs is sufficiently large. Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6022205/.

[0017] To date only Optical PUF’s are known to have resisted Machine Learning. [0018] The invention disclosed here can perform as a strong PUF. Like an

Optical PUF, the set of challenge response pairs is so large that it will be impractical to create because it will take years. In one embodiment with 6 inputs and 52 frequency variations the domain space (i.e. the theoretical potential challenge- response pairs) is 52 ^L 6. Currently the highest security requires 10 ^L 256. However, the reason that the highest level of security requires such a high number is to counter extremely powerful computers. The present invention takes approximately half a second to perform a challenge-response and this cannot be sped up. With 52 ^L 6 combinations it would take a computer approximately 313 years to characterize all permutations in a single volume. [0019] The excel formula to calculate the time is:

DATED I F(0,((52 ^A 6)/120/60/24), "y")&" years " DATEDIF(0,((52 ^A 6)/120/60/24), "ym")&" months "&DATEDIF(0,((52 ^A 6)/120/60/24), "md")&" days" [0020] Optical PUF’s require a laser and an optical medium, so are more expensive to manufacture, may fail after a period and are more prone to variations in environment such as temperature affecting the optical medium and optical line drift for the laser.

[0021] Another important distinction between the invention disclosed here is when operating as a PUF. Most PUFs need to have some error correction software. The responses are noisy; they cannot be directly used as cryptographic keys. The reason is that often they are being forced to do a task that they weren’t really designed to do. They are operating at the boundaries. Reliability is a common issue. Changes in environment may affect performance.

[0022] In contrast the invention disclosed when performing as a PUF is ‘clean’. It is doing what it is designed to do, and it is therefore highly stable, and the signal does not require to be‘cleaned up’.

BACKGROUND OF PIEZOELECTRIC MATERIALS FOR COMPUTATION

[0023] It is well known that polyvinylidene fluoride (PVDF), polyvinyl alcohol (PVA), and lead zirconate titanate (PZT) contain mobile dipoles. The mobility of the dipoles in the polymers is related to the molecular weight and the degree of crystallization. PVA is not a particularly crystalline polymer; PVDF is highly crystalline; and of course, in the PZT ceramic, the dipoles have even less mobility. All three of these materials have piezoelectric properties. PVDF is used in

manufacturing of small microphone and buzzer applications. PZT is used in almost all major ultrasonic applications from medical to undersea communication. PVA is typically not used for piezoelectric applications because it is highly hydroscopic. [0024] The crystallites in PVDF and the poly-crystals in the ceramic PZT act as supramolecular-scale capacitors (Yamagami and Fukada, 1973). The dipoles in these materials come about because of asymmetry of the positive and negative charge density in the material. The negative pole of a dipole arises because of free or unbound electrons. For example, water molecules are polar because of free electrons on the oxygen atom.

[0025] The total dipole moment of a molecule is given by:

[1 ] where _£, [r] and ^jr) are the electron and nuclear charge densities. For a polymer, it is a little more difficult because we need to consider the average molecular conformation and the degree of polymerization, N. In this case the square average is

[2] where is the moment for one monomer (e.g. Eq. [1 ]) and F is a constant representing the folded polymer conformation. Polyvinylidene fluoride (PVDF) has the highest dipole moment of 2.1 D (debye) of any polymer. Further, because PVDF and PVA are crystalline polymers, we can orient the dipoles.

[0026] This invention relates to using piezoelectric materials as programmable matter. Critical background information is that electrical pulses sent into the piezoelectric material results in electrical signals coming out of the material. Often the output signals are lower amplitude, phase shifted, and pulse-width modulated. We can exploit this for computation. [0027] Computation is a dynamical process. Wolfram (2002) has developed the principle of computational equivalence in which he shows that computation is simply a question of translating inputs and outputs from one system to another. It is important to remember that the computers on our desktops are extensively designed systems for deterministic input-output relations. It is we humans who have designed them with specific interpretations for the I/O relations. A CPU is essentially a glorified reconfigurable lookup table. With piezoelectric materials as programmable matter we are interpreting the input/output relations as the computation.

[0028] A simple example of an application of this would be for a physically unclonable function. We attach electrodes, say a 3 X 3 grid, to two opposite faces of a 1.5 cm cube of the piezoelectric material. We send and receive challenge- response pairs for authentication. An input set of signals is sent into the piezoelectric material and an output set is received. One then matches the output with the expected output to verify the security. Multiple challenge-response pairs may be sent for complex verification. Each piezoelectric sample will have a different set of challenge-response pairs.

[0029] To program the piezoelectric material for more extensive

computational applications, consider the following. Given a 1.5 cm cube of the material with 3 X 3 grid of electrodes on all six faces. We assign one face (9 wires) as input and the opposite face (9 wires) as output. We then assign the 9 wires on each of the other four faces (36 wires total) as programming signals. When we send an input vector (9 pulse-trains, i.e. time-domain signals) to the input wires, we will observe 9 outputs on the output lines, again as time-domain signals. Sending other pulse-trains (up to 36) into the wires on the perpendicular faces will result in constructive and destructive interference of pulses between these programming and input signals. This will result in a modulation of the output signals. These input and programming signals with unique output signals constitute a computation, wherein the computation is a result of the complex dynamics that takes place within the piezoelectric material.

[0030] One could use a genetic algorithm for the actual“discovery” of the program control signals. We’ll briefly describe the genetic algorithm for this application. Details are found in Goldberg (1989).

[0031] The present invention allows us to find a mapping relation between (for example) one 9-element set of pulses (input) and another 9-element set of pulses (output). This could be, for example, a time-domain, pattern matching task.

To map the input to the output we dither with the programming signals (36 of them) until we have a good match between the input and output. The details of this dithering process are the genetic algorithm. The end result is we have a 36-element set of pulse signals that allow us to map the 9 inputs to the 9 outputs.

[0032] What makes this a secure computation is that when the power driving the signals is turned off, the dipoles in the piezoelectric material relax. If we want to match a particular input pattern to a particular output pattern in which we have already developed the programming pattern (36 signals), we simply set the input and programming signals to the appropriate values and read out the answer on the output wires.

[0033] The piezoelectric material is said to be programmable matter. When pulses of varying frequency are sent into the piezoelectric material they interact in complex ways and produce complex pulse streams at the outputs. The input pulses, say N time-streams, interact to produce M output pulse time-streams. There is a unique relationship between these, inputs and outputs, given by the relation M = f(N), where M and N are multi-dimensional vectors in time. When the power driving the input pulses is disconnected, the“stored” interacting pulse patterns dissipate. This immediately suggests three applications: 1 ) physical unclonable function (PUF), 2) reservoir computing neural network and, 3) a system that can“compute” complex secure functions that were previously programmed using a genetic algorithm.

3. Description of the Related Technology

[0034] It is an object of the present invention to address at least some of the shortcomings associated with the prior art solutions shown or mentioned below in date order.

SUMMARY OF THE INVENTION

[0035] The method for performing secure computation using a solid volume of material to which a number of electrodes are attached described herein may be used as a capacitor network, a physical unclonable function, a neuromorphic computer including reservoir computation and pattern/audio/image recognition, a genetic algorithm reader, and/or a method of authentication.

[0036] Certain materials, such as PVDF, PVA and PZT may be exploited for computation. Basically, blocks of these substrates become programmable matter. One key feature of the programmable matter introduced here is that each instance of it, each sample, can be configured to behave as a capacitor network at low

frequencies (for example below a threshold of 10 kHz using PZT), but quite similar to one another at higher frequencies. This suggests a new type of secure computing. Taking advantage of the unique behaviour below the threshold, first a low frequency challenge response is performed, and the individual device authenticated. Then a set of higher frequencies are sent to perform the computation. If the device fails the authentication test then the computation can be stopped.

[0037] Secure computing first suggests a physically unclonable function (PUF). These are devices for computer-user authentication. The most secure versions are called strong PUFs and involve multiple“challenge-response” pairs. A simpler version is as a lock dongle with the potential to immobilize a computer.

[0038] A strong PUF that is essentially unique, and programmable, suggests using the device for secure function evaluation after programming it (pinning the dipoles into place at specific frequencies) with a genetic algorithm. [0039] This also suggests several types of neural networks, reservoir computing architecture, including one-view content addressable memory,

convolution computation chip, long/short term memory recurrent network and a more advanced device known as a transformatron (US Patent 6,735,336).

[0040] In accordance with an aspect of the invention there is provided a solid volume of piezoelectric material having a plurality of faces. The piezoelectric material comprises at least one input configured on a first face and arranged to input a first signal in the piezoelectric material; and at least one output configured on a second face, which may the opposite face, of the piezoelectric material different to the first face and arranged to output a second signal from the piezoelectric material, the second signal having characteristics dependent at least in part on a

characteristic of the first signal and a molecular characteristic of the piezoelectric material. The molecular characteristic of the piezoelectric material may relate to a molecular dipole moment within the piezoelectric material. In this way, as the input signal interacts with the molecular dipole moment within the piezoelectric material, a second signal having characteristics different to the input signal is output from the piezoelectric material. By varying the characteristics of the programming signal, it is possible to vary the characteristics of the output second signal for any given first input signal. This behaviour is exploitable for increasing the versatility of the computational circuit.

[0041] In this way the piezoelectric material may be used as a

computational circuit.

[0042] Alternatively, if the dielectric material used is constructed to be a network of capacitors, irrespective of whether it includes piezoelectric material, this embodiment of the invention may still be used to access a restricted device. [0043] The piezoelectric material may comprise any one of the polymers: a) Polyvinylidene fluoride (PVDF);

b) Polyvinyl alcohol (PVA);

c) Polyvinylidene fluoride blended with polymethylmethacrylate;

d) Polyvinyl alcohol blended with polymethylmethacrylate.

[0044] In certain embodiments the piezoelectric material may comprises Lead zirconate titanate (PZT) and other piezoelectric ceramics such as Aluminium nitride, Barium titanate, Bismuth titanate, Lead scandium tantalite, the perovskites Lithium tantalite, and Sodium bismuth titanate.

[0045] Other compound-piezoelectric materials may also be used including:

a) Apatite

b) Gallium phosphate

c) Lanthanum gallium silicate

d) Potassium sodium tartrate

[0046] The programming signal may be modulated in dependence on a genetic algorithm.

[0047] In accordance with a further aspect of the invention there is provided a method of controlling access to an operatively coupled device using a solid volume of piezoelectric material, the solid volume of piezoelectric material having a characteristic threshold frequency below which it exhibits physical behaviour unique to it.

[0048] The method may comprise: receiving a first signal at a first face of the solid volume of piezoelectric material, the first signal having a frequency less than the threshold frequency; receiving a second signal output from a second face of the solid volume of piezoelectric material; enabling access to the operatively coupled device in dependence on the second signal having a characteristic substantially consistent with an expected signal. Inputting a signal having a frequency below a characteristic threshold frequency of the solid volume of piezoelectric material results in a second signal being output from the piezoelectric material having physical characteristics (e.g. frequency and/or amplitude) unique to the specific specimen of piezoelectric material. In this way it is possible to use the solid volume of

piezoelectric material as a security device.

[0049] For example, the solid volume of piezoelectric material may be effectively used as a secure key to access a computer terminal. In order to access the computer terminal, a user would need to be in possession of the specific solid volume of piezoelectric material. A different yet identically shaped solid volume of the same piezoelectric material would not display identical behavioural characteristics, and would not output a second signal having the same characteristics as the genuine volume of piezoelectric material. This is due to slight differences in the material that cannot be replicated even by the manufacturer.

[0050] In certain embodiments the threshold frequency may be

approximately 10 kHz. In this way the unique behaviour of the solid volume of piezoelectric material is displayed for input first signals having frequencies lower than 10 kHz. In this frequency range the embodiment acts as a network of capacitors which share a common output. The second signal may comprise one or more physical characteristics at least partly dependent from the frequency of the first signal, the number of capacitors in the network, the type of material used, the size and shape of the material used and environmental factors such as temperature, vibration, humidity, the age of the material, the number of previous challenge responses performed and the length of the resting state interval between each challenge response pair.

[0051] In some embodiments the ability to distinguish one output signal from another is possible by increasing or reducing an input signal by 10 mHz.

[0052] In accordance with a further aspect of the invention there is provided a method of controlling access to an operatively coupled device using a network of two or more capacitors made from a dielectric material acting as a physical unclonable function (the capacitor network).

[0053] The method may comprise: receiving a first signal to the capacitor network, the first signal having a frequency less than the threshold frequency;

receiving a second signal output from the capacitor network; enabling access to the operatively coupled device in dependence on the second signal having a

characteristic substantially consistent with an expected signal. Inputting a signal having a frequency below a characteristic threshold frequency of the capacitor network results in a second signal being output from the capacitor network having physical characteristics (e.g. frequency and/or amplitude) unique to the specific capacitor network. In this way it is possible to use the capacitor network as a security device.

[0054] For example, the capacitor network may be effectively used as a secure key to access a computer terminal. In order to access the computer terminal, a user would need to be in possession of the capacitor network. A different yet identically shaped the capacitor network material would not display identical behavioural characteristics, and would not output a second signal having the same characteristics as the genuine capacitor network. This is due to slight differences in the dielectric material that cannot be replicated even by the manufacturer. [0055] In certain embodiments the threshold frequency may be approximately 10 kHz. In this way the unique behaviour of the capacitor network is displayed for input first signals having frequencies lower than 10 kHz. The second signal may comprise one or more physical characteristics at least partly dependent from the frequency of the first signal, the number of capacitors in the network, the type of dielectric material used, the size and shape of the material used and environmental factors such as temperature, vibration, humidity, the age of the material, the number of previous challenge responses performed and the length of the resting state interval between each challenge response pair.

[0056] In some embodiments the ability to distinguish one output signal from another is possible by increasing or reducing an input signal by 10 mHz

[0057] In some embodiments the capacitor network may only perform authentication and not computation. This may be because the dielectric material used in the capacitor network does not have piezoelectric qualities or because the shape of the material is such that it is not possible to modulate any given input to change the output.

[0058] In some embodiments the capacitor network may perform authentication and limited computation. This may be because the dielectric material used in the capacitor network does not have piezoelectric qualities or because the shape of the material is such that the ability to modulate any given input to change the output is limited.

[0059] Irrespective of the material used the characteristic of the

programming signal may comprise any one of:

a) an amplitude of the programming signal;

b) a frequency of the programming signal; c) and/or frequency or amplitude modulated programming signal.

[0060] The method may comprise varying a characteristic of the

programming signal in order to vary the characteristic of the output second signal.

[0061] The method may comprise modulating the programming signal using a genetic algorithm, in order to vary the characteristic of the output second signal.

[0062] Genetic algorithms (GA) are typically used for complex

optimizations (Goldberg, 1989). Suppose we want to program a FPGA to output a pulse train of 1 MHz, 50% duty cycle on pin number 9. An FPGA is a 2-dimensional array of logic blocks that may be arranged in an almost unlimited number of possibilities. The goal for the GA is to wire the insides of the FPGA so as to produce consistent 50% duty cycle, 0 to 5 volt pulses at 1 MHz. So, our fitness function, that is how we evaluate the goodness of the wiring of the insides of the FPGA, can be directly measured by digital pulse counting techniques.

[0063] We start with a population of, say 10-bit strings that represent all possible connections within the FPGA. We sequentially download each of the bit strings and evaluate the output at pin 9. This evaluation may result the following outputs for 10-bit strings: string 1 , nothing; string 2, nothing; string 3, 1 Hz; string 4, nothing; string 5, 100 Hz; string 6, nothing; string 7, 10 Hz; string 8, nothing; string 9, nothing; string 10, 1 Hz. We now have a direct relationship between the bit strings, as circuits in the FPGA, and their performance as oscillators. The bit strings that resulted in some oscillations (numbers, 3, 5, 7, 10), we will combine by simply swapping pieces of bit strings. This is called crossover. We will take the remaining bit strings and mutate them, i.e. we flip, say 50% of the bits. This completes the first generation. We repeat this for, say 1000 generations or until we get a good bit string producing the desired oscillations.

[0064] The operations we just described can also be done with the present invention. Other machine learning applications where there is an obvious goodness metric e.g. pulse counting, are also possible. As an example, consider, image recognition where we have a measure of the goodness of fit of the image, from an initially sloppy preforming member of a population, and the final desired result.

[0065] Once the bit string representing the oscillation at pin 9 is

discovered, or the image recognition bit string has been found, we just apply this bit string to the piezoelectric material, send in the input string in the case of the image, and read out the results on the appropriate output pins. When the pulses

representing the input and control bit strings are removed, the piezoelectric material relaxes to its initial state and there is no trace of what the piezoelectric material was used for.

[0066] Yet a further aspect of the invention relates to a method of reservoir computing, comprising: using the aforementioned computational circuit to generate an output signal in dependence on an input signal.

[0067] A reservoir computing system takes an input vector and“computes” an output vector. The“computation” is done by a randomly connected matrix of neurons. So, the computation is a vector matrix multiplication of the input and this random matrix. The output is a vector. Because we are not changing anything on the inside of the piezoelectric material, each input vector will map to a unique output vector. To now make use of this for, an image recognition task, for example, we take these output vectors and map them to a desired output by multiplying this output vector from the piezoelectric material with another matrix of random weights in the digital computer controlling the system. We use a gradient descent to adjust these weights in the piezoelectric material in the computer to give the final output. Naturally we can change the random piezoelectric material dynamically from control bits and this increases the usefulness of the piezoelectric material as a reservoir computer.

[0068] Various objects, features, aspects, and advantages of the present invention will become more apparent from the following detailed description of preferred embodiments of the invention, along with the accompanying drawings in which like numerals represent like components.

[0069] Moreover, the above objects and advantages of the invention are illustrative, and not exhaustive, of those that can be achieved by the invention. Thus, these and other objects and advantages of the invention will be apparent from the description herein, both as embodied herein and as modified in view of any variations which will be apparent to those skilled in the art.

BRIEF DESCRIPTION OF THE DRAWINGS

[0070] One or more embodiments of the invention will now be described, by way of example only, with reference to the accompanying diagrams, in which:

[0071] Figure 1 is a schematic system diagram illustrating a security device in operative communication with a restricted device, in order to access the restricted device, in accordance with an embodiment of the invention;

[0072] Figure 2 is a process flow chart outlining a method carried out by the restricted device to verify the authenticity of the security device illustrated in Figure 1 ;

[0073] Figure 3 is an optional process flow chart outlining a method to record that a challenge-response pair has been used before and therefore should not be re-used. [0074] Figure 4 is a schematic diagram of a security device comprising a coin shaped piece of PZT material upon which one face has six pie-shaped silver electrodes printed for inputs and the reverse face is covered by a single electrode used as an output.

[0075] Figure 5 shows two schematic diagrams of a PUF security device.

[0076] Figure 6 shows how increasing the number of capacitors in the input network causes the error rate to drop to zero.

[0077] Figure 7 is a schematic of piezoelectric material at a

supramolecular level.

[0078] Figure 8 demonstrates four separate volumes of piezoelectric material producing the same output signal.

[0079] In Figure 9 there are five histograms. Each histogram is the output value from all 2 ^L 15 inputs. Each histogram is a separate experiment of the 2 ^L 15 inputs at different frequencies.

[0080] Figure 10 shows impedance spikes at resonance frequencies associated with an applied 3V square wave.

[0081] Figure 11 describes computation from a physics perspective.

[0082] In Figure 12 a cube of piezoelectric material has three inputs and one output.

[0083] Figure 13 is a schematic of a system to perform computing using a volume of piezoelectric material.

[0084] Figure 14 is a schematic of the invention used as a reservoir computer.

[0085] Figure 15 is a schematic of the invention used as a genetic algorithm reader. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0086] Before the present invention is described in further detail, it is to be understood that the invention is not limited to the particular embodiments described, as such may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting, since the scope of the present invention will be limited only by the appended claims.

[0087] Where a range of values is provided, it is understood that each intervening value, to the tenth of the unit of the lower limit unless the context clearly dictates otherwise, between the upper and lower limit of that range and any other stated or intervening value in that stated range is encompassed within the invention. The upper and lower limits of these smaller ranges may independently be included in the smaller ranges is also encompassed within the invention, subject to any specifically excluded limit in the stated range. Where the stated range includes one or both of the limits, ranges excluding either or both of those included limits are also included in the invention.

[0088] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Although any methods and materials similar or equivalent to those described herein can also be used in the practice or testing of the present invention, a limited number of the exemplary methods and materials are described herein.

[0089] It must be noted that as used herein and in the appended claims, the singular forms "a", "an", and "the" include plural referents unless the context clearly dictates otherwise. [0090] All publications mentioned herein are incorporated herein by reference to disclose and describe the methods and/or materials in connection with which the publications are cited. The publications discussed herein are provided solely for their disclosure prior to the filing date of the present application. Nothing herein is to be construed as an admission that the present invention is not entitled to antedate such publication by virtue of prior invention. Further, the dates of publication provided may be different from the actual publication dates, which may need to be independently confirmed.

[0091] Figure 1 is a schematic system diagram that illustrates how the security device (101 ) may be used to access a restricted device (103) by comparing the challenge responses stored on the Authentication server (102). In the illustrated example, the restricted device (103) relates to an electronic device having a processor (105) and an input (107). The authentication server (102) has a database (111 ) and sends an output (119) to the security device (101 ). The security device (101 ) illustrated comprises a capacitor network which may or may not be

piezoelectric material (113). Operatively coupled to the capacitor network (113) are one or more inputs (115), and at least one output (117). For illustrative, non-limiting purposes, the security device (101 ) of Figure 1 is shown as comprising four different inputs (115) to the capacitor network (113). It is however to be appreciated that the security device may have a different number of inputs in other embodiments. While the output (119) and the database (111 ) are illustrated as being an authentication server, it is understood that these may be local and connected to the processor (105). [0092] In practice, to access the restricted device (103), a user brings the security device (101 ) into operative communication with the authentication server (102), via a shared communications channel (114). The communications channel (114) may relate to a physical channel, or to a contactless channel. In certain embodiments the security device (101 ) may comprise a dongle, and the

communications channel (114) may comprise a Universal Serial Bus (USB) channel. This is particularly useful where the restricted device (103) relates to a computer terminal, for example. In other embodiments the security device (101 ) may comprise a self-contained unit, and the communications channel (114) may be wireless or wired. This is particularly useful where the restricted device (103) relates to an loT device, for example.

[0093] Once the security device (101 ) has been brought into operative communication with the authentication server (102), the communications channel (114) is used to execute a verification protocol, in which the authentication server (102) verifies that the security device (101 ) is an authentic device associated with the restricted device (103). This is achieved by the authentication server (102) and the security device (101 ) exchanging one or multiple challenge-response messages. Specifically, the authentication server (102) is configured to output a challenge signal, which is input to the capacitor network (113) via the one or more inputs (115). The signal output from the capacitor network (113) (interchangeably referred to as the response signal) is forwarded to the authentication server (102) via the security device’s output (117). Upon receipt of the response signal via a communication channel (118), the authentication server (102) verifies the authenticity of the received response signal by cross-referencing it with the contents of a database (111 ). To this end, the database (111 ) is configured with a list of valid response signals associated with the given security device (101 ).

[0094] In accordance with aspects of the invention, the frequency of the output challenge signals is selected in dependence on the material of the capacitor network (113). In particular, it is noted that each type of capacitor network will have an associated threshold frequency which will depend on factors such as thickness and density. Below this threshold frequency each volume of material will exhibit unique behavior. In other words, when the challenge signal has a frequency that is below the capacitor network’s associated threshold frequency, then the response signal output from the volume of network capacitor (113) will be unique to that specific volume of material. This unique behavior arises because of the molecular variations specific to each volume of material used. When the material is stimulated with a signal having a frequency below its threshold frequency, the molecules within the material are able to relax back to their ground state between stimulations, which ensures that the output response signal is unique to the specific specimen of material comprised in the security device.

[0095] In certain embodiments the volume of piezoelectric material may comprise polyvinylidene fluoride (PVDF), polyvinyl alcohol (PVA), or lead zirconate titanate (PZT). In embodiments where PZT is used, the threshold frequency varies depending on the size and shape of the embodiment. For example, where a poled disk is used whose dimensions are 25mm x 2mm the threshold is 1 kHz, and accordingly the one or more challenge signals output by restricted device (103) have frequencies that are below this threshold frequency. [0096] Below the threshold input voltage changes of as little as 10 mHz result in changes in the output that are distinctive and measurable. Therefore, an embodiment with 4 inputs and one output would have a theoretical delta f of 4 ^L 100,000 permutations, while an embodiment with 6 inputs and one output would have a theoretical 6 ^L 100,000 permutations.

[0097] In certain embodiments, the authentication server (102) is configured with copies of valid response signals output by the security device (101 ). Copies of the valid response signals may be securely stored within the database (111 ) connected to the authentication server (102). This may be achieved via an initial configuration process. Once this process has been completed, the security device (101 ) may effectively be used as a secure, unique digital key for

authenticating the restricted device (103). Because the response signal output by the security device (101 ) is unique to the specific device, and specifically because it is unique to the capacitor network (113) comprised in the security device (101 ), only the security device (101 ) that has been specifically configured to be associated with the restricted device (103) may be authenticated. Even if an attempt was made to clone the security device (101 ), this would fail, because it is simply not practically possible to exactly reproduce a volume of material having the exact same molecular variations as the volume of material comprised in the genuine security device (101 ). The security of the security device (101 ) resides in the practical inability to exactly reproduce a volume of material sharing the same molecular variations as the genuine version.

[0098] While a weak PUF has a few, sometimes only one, challenge- response pairs, the invention disclosed has trillions. When the invention disclosed is set up, a random sub-set of the total domain space (for example 100,000) is recorded in the database (111 ). For each PUF device a different random set can be selected.

[0099] At run-time the challenger selects one challenge from the database (111 ) and compares the response received. This process may be repeated multiple times, if two or more PUF security devices have the same or similar response. Each time the process is repeated the number of PUF security devices that are candidates reduces, until there is only one left. Typically, where multiple responses are used no more than ten challenge-response pairs are required.

[0100] Figure 2 is a process flow chart illustrating the method (200) carried out by the authentication server (102) to verify the authenticity of the operatively coupled security device (101 ). The database (111 ) in Figure is referred to as 211 in Figure 2.

[0101] The method commences once a communication channel (114 and 118) has been established between the security device (101 ) and the authentication server (102) as shown in Figure 1 , and upon receipt of a request to access the secure device, at step (201 ). The authentication server (102) then outputs a verification signal to the security device (101 ), at step (202). In certain embodiments the authentication server (102) may select the frequency characteristics of the challenge signal. As previously described this task may be performed remotely. The challenge signal is then received by the security device (101 ) as described

previously. The authentication server (102) awaits receipt of the response signal from the security device (101 ) and it is compared with a set of known responses stored in a database (211 ), which is received at step (202). The authentication server (102) then determines, at step (204), if the received response signal is consistent with an expected response signal. This is carried out by the authentication server (102), consulting the database (211 ). To authenticate may require multiple challenge responses. If so then each time a response is received the result is stored in memory at step (206) and the process repeated from step (201 ). Step (207) increments a counter. If after n iterations it is determined that the received response signals are not consistent with an expected response signal to characterize one specific volume of the material, as determined by consulting the database (211 ), then access to the restricted device is refused, at step (208), and the method is ended. If instead it is determined that the received response signals are consistent with the expected response signals unique to one specific volume of the material, then access to the restricted device (103) shown in Figure 1 is enabled, at step (205), and the method is ended. In this way it is possible for the restricted device (103) via the authentication server (102) shown in Figure 1 to determine if the provided security device (101 ) is associated with it.

[0102] The method of Figure 2 may equally be used to access restricted services. Such embodiments are substantially like the above described embodiment, albeit now the restricted device (103) shown in Figure 1 is replaced with a generic computer terminal comprising a secure service. Again, access to the secure service is achieved by exchanging one or multiple challenge-response pairs and determining if the received response signals are consistent with expected responses signal.

[0103] Figure 3 describes one method by which the security device is protected against machine learning and replay man-in-the-middle attacks.

[0104] In one embodiment, once a challenge-response pair is used in (300), it is marked accordingly at (301 ) and the database (311 ) is updated. The process then concludes at (303). Thus, each challenge-response pair is only used one time. This adds a further level of security by preventing replay attacks where a previous challenge-response pair is used by a third party attempting to emulate a genuine challenge-response pair.

[0105] The physical location, size and material used for the inputs have an impact on the characteristics of the output signal. For example, where using PZT one huge electrode next to a small electrode will result in different response than two electrodes the same size because different volumes of the material are being activated.

[0106] To create a very large domain of challenge response pairs, more than one input signal is required. In one embodiment there are six inputs and fifty- two variations in the frequency. Each input signal is sent simultaneously and in parallel to the other inputs to ensure a consistent and repeatable output.

[0107] At run-time the output signal must match an output signal previously stored in the database (311 ). As several volumes of the material might have the same or sufficiently similar outputs, it may be necessary to perform multiple challenge-responses.

[0108] The threshold frequency varies according to the material, size and shape of the material. For example, when using PZT the threshold is 1 kFIz for a ‘coin’ shape with a diameter of 25mm and a thickness of 2mm. The threshold increases to 10 kFIz when using a cube whose sides are 50mm. The Delta f is the change in input frequency that is enough to observe a variation in the output frequency. Below the Delta f the two outputs are too similar. The Delta f may also vary based on the material used. For the PZT coin with a diameter of 25mm and a thickness of 2mm it is 10 mFIz.

[0109] In one embodiment shown in Figure 4 the device comprises a PZT ceramic‘coin’ with dimensions 2 mm x 25 mm. [0110] The front face (401 ) comprises six‘pie’ shaped fired-on electrodes (411 ) separated by a one-mm insulation gap (402). There is also a one-mm insulation gap (407) from outer circumference so that the electrode does not touch the side of the coin.

[0111] The rear face (400) has a single fired-on silver electrode (410).

There is also a 1 mm insulation gap (407) from the outer circumference so that the electrode (410) does not touch the side of the coin. An optional unique ID serial number (408) may be printed on the surface for identification purposes.

[0112] Electrical 22-24-gauge multi-strand wire minimum length 30 mm (403) can be soldered (404) to the center of the front face (400) and soldered (404) to the center of the six pie slice electrodes (411 ) on the rear face (401 ).

[0113] The other end of the electrical wires (403) are connected to the electrical circuit shown in Figure 5 which controls the input frequencies sent to the wires on the rear face (403) and reads the output frequency from the wire (403) connected to the front face (400).

[0114] Figure 5 shows two schematics of the electrical circuit that control the capacitor network. In the left-hand diagram, a Tiny Micro-controller Circuit (501 ) is connected via (for example) six inputs (503) and one output on the reverse face (502). The capacitor network is a volume of piezoelectric material.

[0115] In the right-hand diagram, a Tiny Micro-controller Circuit (511 ) is connected via (for example) six inputs (513) and one output (512). The capacitor network is a set of connected capacitors.

[0116] In Figure 6 for each PUF security device a registration process records the responses for a set of challenges in a database. The number of capacitors in the network of the PUF security device can be increased from (for example) one to six. Each time an additional capacitor is added to the network the number of errors dropped. With one capacitor the number of recorded errors is 5,565. This reduces to 4,598 with two capacitors. With three capacitors the error is 174, with four, 162, with five, 77. With six capacitors the PUF device is correctly identified with no errors. The number of capacitors in the network required is a function of the population size. One method to reduce errors to an acceptable level is just to perform multiple challenge responses and pick the winner i.e. the PUF security device that is uniquely identified the most times. Another method is to increase the number of capacitors in the network. Both methods can be combined if required to provide redundancy.

[0117] Figure 7 is a schematic of piezoelectric material at a

supramolecular level. The polymer crystallites, or ceramic crystallites, can be thought of as rigid supramolecular structures separated by regions of higher mobility. The structure is random and unpredictable making it suitable as a physical unclonable function. Over a certain threshold the input signals are powerful enough to overcome these variations and produce a consistent output.

[0118] The tiny crystal regions are essentially supramolecular structures separated by tangled polymer regions. These tangled regions have a higher mobility than the crystal regions. Though we have no nano-scale imaging, it is easy to imagine that in an electric field these crystallites align. With a square pulse of 5V and > 100Flz frequency, the relaxation time of these crystallites is measured to be about 400 microseconds. This means, in even small fields of a few volts the crystallites will align and relax. This dipole modulation changes the dielectric constant over the length scale of the attached electrodes. This change in the dielectric constant is a key parameter of capacitors. [0119] Four cubes of piezoelectric material each have five electrodes attached, one to each of their five faces. Four of the electrodes are then connected to oscillators which send pulses at 100 kHz, 200 kHz, 500 khlz and 500 MFIz respectively.

[0120] In Figure 8 the plot shows four upper oscillations (701 -704) which represent the inputs at 100 khlz, 200 khlz, 500 MFIz, 500 khlz respectively. The four lower oscillations (705-708) are the outputs from four different volumes of PZT material. While there are very minor variations it is apparent that the outputs are largely identical. This demonstrates that over a certain threshold all volumes of the piezoelectric material behave the same.

[0121] In Figure 9 there are five histograms.

[0122] In this experiment five wires on three faces are connected as inputs (15 wires). A fourth face has 5 wires as outputs. The input square wave 5-volt frequencies may be picked at random from 240 khlz down to 1 khlz. This is computing the average value of the output signal on one output for a period of one minute. This is a time-variant signal. Each histogram is the output value from all 2 ^L 15 inputs. Each histogram is a separate demonstration of the 2 ^L 15 inputs at different frequencies.

[0123] HP 4192A impedance analyzer may be used to analyze the impedance of PVDF material. For a four-probe measurement, 4 embedded electrodes are connected to the impedance analyzer. One electrode is connected to an auxiliary function generator. A second electrode is connected common (to ground). Eight experiments were conducted starting at no input signal and then in one MFIz intervals from 1 MFIz up to 7 MFIz. The bottom scale shows a scale from

1 MHz to 10 MHz. [0124] Figure 10 shows impedance spikes at resonance frequencies associated with an applied 3V square wave. The impedance spikes show that it is possible to modulate the impedance of a volume of material (in this case PVDF) using an external source.

[0125] Figure 11 describes computation from a physics perspective. The

“system” gives a reproducible response to the same inputs. Depending on the complexity of the“system” each input will give a unique output. Compilers may be written to interpret the input/output dynamics.

[0126] From a simple physics perspective computation is an input-output relation. For some given input signal, a unique output signal is produced. To demonstrate the programmability of a sample of piezoelectric material several prototype devices were constructed.

[0127] In one embodiment a cube of piezoelectric material has three inputs and one output. In Figure 12 the bottom trace is a representative input and the top trace is the output is 500 millivolts scaled. The bottom trace is a combination of three input signals, 4 kHz, 1 kFIz and 400 Flz on a 5-volt scale.

[0128] This demonstrates conclusively that a repeatable computation is taking place. The output is not the same as the input.

[0129] Figure 13 is a schematic of a system to perform computing using a volume of piezoelectric material.

[0130] A computer (1301 ) is connected by way of example to a Micro Controller Unit (1303) through a Universal Serial Bus (1302). The Micro Controller Unit (1303) is connected to a Field Programmable Gate Array (1304). The surface of a cube of piezoelectric material (1308) is coated in an electrode which has been printed so that on each surface there are (for example) nine distinct pads (1309). [0131] The 54 pads (9 x 6) are connected to the FPGA. In one embodiment on one face 9 electrodes are configured as inputs, on the opposite face 9 electrodes are configured as outputs and the four remaining faces with 36 electrodes act as control lines to modulate the input signals. Dynamic RAM (1305) is used to store inputs and outputs as required. The FPGA (1304) controls the inputs and control lines through inputs (1306) and outputs (1307).

[0132] Fig 14 is a schematic of the invention used as a reservoir computer.

[0133] Reservoir computers are a type of neural network with only one layer of weights to train, via a gradient descent algorithm.

[0134] Input data as modulations is passed from the computer (1401 ) into the volume of piezoelectric material (1402) acting as a reservoir, "processed" by the network of connections embedded in the reservoir, and then the output signals from the reservoir are fed as signals into a layer of weights (1403) for gradient descent. The weight layer is in the training code for the reservoir.

[0135] The only thing that changes during the training process are the strength of the connections between the reservoir and the readout.

[0136] Figure 15 is a schematic of the invention used as a genetic algorithm reader.

[0137] The Genetic Algorithm runs on the computer (1501 ). Each iteration passes a bit stream (1503) through, by way of example, a cube of piezoelectric material (1502) and back. The process is equivalent to tuning a violin. Once 'tuned' the final bit stream can be sent insecurely over the Internet to anyone with the same embodiment of the invention. All the recipient needs are a similar volume of material configured the same as the original, the Genetic Algorithm, the final bit stream and the correct frequency to readout the Genetic Algorithm results. As there is only real- time computation on an input to output functional basis the results are available nearly instantaneously.

[0138] The techniques, processes and methods described may be utilized to control operation of any device and conserve use of resources based on conditions detected or applicable to the device.

[0139] The invention is described in detail with respect to preferred embodiments, and it will now be apparent from the foregoing to those skilled in the art that changes and modifications may be made without departing from the invention in its broader aspects, and the invention, therefore, as defined in the claims, is intended to cover all such changes and modifications that fall within the true spirit of the invention.

[0140] Thus, specific methods for secure programmable matter have been disclosed. It should be apparent, however, to those skilled in the art that many more modifications besides those already described are possible without departing from the inventive concepts herein. The inventive subject matter, therefore, is not to be restricted except in the spirit of the disclosure. Moreover, in interpreting the disclosure, all terms should be interpreted in the broadest possible manner consistent with the context. In particular, the terms "comprises" and "comprising" should be interpreted as referring to elements, components, or steps in a non- exclusive manner, indicating that the referenced elements, components, or steps may be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced.