Computer-implemented method for generating a shared secret

Abstract

The invention relates to a computer-implemented method for generating a shared secret based on the use of a tree parity machine (1). The computer-implemented method according to the invention is characterized in that neurons (3) of two artificial neural networks operate according to the leaky-integrate-and-fire principle and the following steps are performed for synchronization: - for each input neuron (3E) of the artificial neural networks: generating an input vector (4), whereby corresponding input neurons (3E) of the artificial neural networks receive the same input vector (4); - Initializing the weights (2) of the neurons (3); - Supplying the input vectors (4) to the input neurons (3E); - Calculation of an output vector (6); - For each neuron (3): Determine the iteration step at which the neuron (3) fires for the first time; - for each neuron (3): Determine an iteration step difference (7); - if the output vectors (6) of the first and second artificial neural networks match: adjust the weights (2) of the neurons (3); and - Repeated adjustment of the weights (2) of the neurons (3) until synchronization between the first and second artificial neural networks is achieved.

Description

[0001] The invention relates to a computer-implemented method for generating a shared secret of the type defined in more detail in the preamble of claim 1, and to an information technology system comprising a vehicle.

[0002] With increasing digitalization, the proportion of computer systems in vehicles is also growing. To ensure the vehicle's operational functionality and to provide various assistance functions, a wide range of information is processed by computing units within the vehicle. Information can be transmitted between these computing units, or between computing units and sensors or actuators, via a communication network, such as one or more Ethernet data lines or a CAN bus. Using a telecommunications unit, the vehicle's onboard network can also be connected to the internet, for example, via mobile network or Wi-Fi. This enables the exchange of information with a central computing facility, such as a server or server cluster.

[0003] This interconnectedness also increases the risk of cyberattacks on communication networks in vehicles. To prevent the risk of unwanted manipulation, encrypted data transmission and authentication of the respective communication partners are preferred. Proven cryptographic encryption mechanisms, such as symmetric and / or asymmetric encryption, can be used for this purpose, especially in the context of signature-based authentication.

[0004] Appropriate cryptographic security measures can be integrated into the transmission of a key for unlocking a vehicle's doors. Authorization information can be stored, for example, on a key fob or a mobile device such as a smartphone. This information can be transmitted wirelessly to the vehicle, for example, via radio frequency. This can be initiated manually, for example, by pressing a button, or automatically as soon as the respective device and the vehicle are within communication range. This occurs, for example, in so-called keyless entry systems. Communication between the device and the vehicle is typically cryptographically secured using established encryption technologies. However, these methods are vulnerable to various types of attacks, particularly replay attacks and man-in-the-middle attacks.

[0005] Furthermore, established cryptographic encryption mechanisms, such as the Advanced Encryption Standard (AES) or Rivest-Shamir-Adleman (RSA), are based on specific number-theoretical algorithms and are therefore vulnerable to being cracked by quantum computers. This jeopardizes cybersecurity during vehicle operation.

[0006] Currently, the spread and acceptance of artificial intelligence is increasing. One subfield of machine learning involves processing information using artificial neural networks. Building on this, so-called "neural cryptography" has developed. For example, cryptographic keys can be generated using a so-called "tree parity machine" (TPM), which is a special type of multi-layered feedforward neural network. These keys also exhibit inherent security against decryption by quantum computers. Such generated keys are not based on known number theories, but rather on the unidirectional or bidirectional synchronization between two neural networks. These tree parity machines are used in the context of the Neural Key Exchange (NKX) protocol. The synchronization between two tree parity machines...The underlying artificial neural networks operate similarly to the synchronization between two chaotic oscillators in so-called chaos communication. The two artificial neural networks to be synchronized have the same structure, meaning the same number of layers and the same number of neurons per layer. From iteration to iteration, the weighting factors assigned to the neurons are adjusted between the neural networks so that, in the synchronized state, a corresponding pair of neurons in the first and second artificial neural networks has the same weighting factor. This results in both TPMs calculating the same result from the same input data in the synchronized state.

[0007] The first and second artificial neural networks, or the first and second TPMs, are executed on systems that communicate with each other; these can be dedicated hardware. The weighting factors can be used to create a shared secret in the form of a cryptographic key. Since the weighting factors are identical on both TPMs, both systems also possess the same key.

[0008] More in-depth information can be found in: Neural cryptography, Wikipedia The Free Encyclopedia, https: / / en.wikipedia.org / wiki / Neural_cryptography;

[0009] Plesa, Mihail-lulian et al., A key agreement protocol based on spiking neural P systems with anti-spikes, Journal of membrane computing, Vol. 4, 2022, No. 4, pp. 341-351, ISSN 2523-8914; sowie: Sooyong Jeong et al., Neural Cryptography Based on Generalized Tree Parity Machine for Real-Life Systems, Security and Communication Networks, 4. Februar 2021, https: / / doi.org / 10.1155 / 2021 / 6680782.

[0010] Furthermore, US patent 2016 / 0277189 A1 discloses a method and a device for performing mutual authentication based on confidential information. This involves the mutual authentication of a vehicle's electronic control unit (ECU) with an external device. The external device submits an authentication request, to which a random number is generated in response. Based on this random number, a variable i is generated using an equation. A session key is then generated based on this variable i and an existing secret key. Applying a function to a first response key received from the external device, the vehicle's ECU generates a second response key. The random number, the variable i, and the session key are taken as parameters in this function. The external device is authenticated if the first response key matches the second response key.

[0011] Document US 11,791,997 B2 describes in a similar context a method and device for generating a secret key for encrypted communication using a synchronized neural network.

[0012] The present invention is based on the objective of providing an improved method for generating shared secrets, which is particularly secure and involves low technical effort.

[0013] According to the invention, this problem is solved by a computer-implemented method for generating a shared secret with the features of claim 1. Advantageous embodiments and further developments, as well as an information technology system for carrying out the method, are described in the dependent claims.

[0014] A generic computer-implemented method for generating a shared secret based on the use of a tree parity machine, wherein a first artificial neural network on an A-machine and a second artificial neural network on a B-machine are synchronized, wherein the first and second artificial neural networks have the same structure, wherein in the synchronized state the weighting factor of each neuron of the first artificial neural network is identical to its corresponding neuron in the second artificial neural network, and wherein the shared secret represents a mathematical recombination of the weighting factors assigned to the individual neurons, is further developed according to the invention in that the neurons of the artificial neural networks operate according to the leaky-integrate-and-fire principle and the following steps are carried out for synchronization: - for each input neuron of the artificial neural networks: generating an input vector with a fixed number of vector elements, containing random numbers from a defined initial range of values; - Initializing the weights of the neurons of the first and second artificial neural networks with random numbers from a defined second range of values; - Supplying the input vectors to the input neurons; - Computation of an output vector by the first and second artificial neural networks based on the input vectors, whereby the vector elements are processed iteratively to represent a time iteration step; - for each neuron: Determine the iteration step at which the neuron fires for the first time; - for each neuron: Determine an iteration step difference at which the neuron fires for the first time between the corresponding neuron in the first and second artificial neural network; - if the output vectors of the first and second artificial neural networks are the same: adjust the weights of the neurons of the first and second artificial neural networks depending on the respective iteration step difference of the respective pair of neurons; and - repeated adjustment of the neuron weights until synchronization between the first and second artificial neural networks was achieved.

[0015] The method presented here is a special form of the so-called spiking tree parity machine (STPM). Using the spiking tree parity machine according to the invention, particularly secure and efficient key generation is possible, incorporating communication via public communication channels. In contrast to conventional tree parity machines, the inclusion of the leaky integrate-and-fire principle provides an additional degree of obfuscation, thus improving cybersecurity. Instead of static learning rules, a temporal weight adjustment is implemented, as the input vectors are processed iteratively by the artificial neural networks, with each entry of the corresponding vectors being considered a time step.

[0016] As with conventional tree parity machines, the first and second artificial neural networks have the same structure. This means that both artificial neural networks have the same number of neuron layers, typically an input layer, an intermediate layer (also called a hidden layer), and an output layer. Furthermore, both artificial neural networks have the same number of neurons in each neuron layer. Typically, there is a single output neuron on the last layer. In this paper, the neurons on the input layer are referred to as input neurons, the neurons on the intermediate layer as intermediate neurons (also called "hidden neurons"), and the neuron on the output layer as the output neuron. The first artificial neural network and the second artificial neural network are typically referred to as "A-Machine" and "B-Machine," respectively.In the context of this text, however, the terms “A-machine” and “B-machine” refer to the underlying system that executes the respective artificial neural network, for example in the form of two logical or even physical computer systems.

[0017] The shared secret represents a number, that is, a sequence of digits. The individual weights or weighting factors of the neurons form the digits. The digits can be arranged in any order. Furthermore, mathematical operations can be applied to the digits or the resulting number. For example, a digital root can be calculated, or a hash value can be generated from the number using a suitable hash function. This number, or the hash value derived from it, can then be used as a shared secret, for example, as a symmetric key in a symmetric encryption algorithm. Such a key can be used for mutual authentication in a signature-based authentication process.

[0018] In a typical tree parity machine, each input neuron receives a randomly chosen input value of -1, 0, or +1. These input factors are then multiplied by the respective weight of the input neuron and fed to the neuron on the intermediate layer. For the sake of simplicity, the term "weight" is used in this text instead of "weighting factor." The result output by each intermediate neuron is based on the sum of the input factor-weight products fed by the respective input neurons. The signum function is applied to this intermediate result, so that the intermediate neuron outputs -1 if the intermediate result is less than 0, 0 if the result is 0, or +1 if the intermediate result is greater than 0. -1 can also be output instead of 0.The result of the tree parity machine, that is, the output of the output neuron, is the product of the results supplied to the output neuron by the intermediate neurons. It is therefore an output value of -1 or +1. The result of the tree parity machine is thus binary.

[0019] According to the invention, the neurons of the first and second artificial neural networks operate using the leaky-integrate-and-fire principle, or based on the leaky-integrate-and-fire model. The input neurons each receive an input vector with a fixed number of vector elements. The number of vector elements can be interpreted as a fixed time duration.

[0020] For example, if ten vector elements are used, each vector element can correspond to a time step of 0.1 seconds. Thus, the time duration is one second. It is particularly advantageous for the vector elements to be equidistantly distributed over the defined time duration. Each time step is therefore of equal length. The size of the time step can be chosen arbitrarily large, such as a few milliseconds, seconds, minutes, or the like. A suitable number of vector elements can be used, which can be determined by the developer. Each input neuron receives its own input vector, with corresponding neurons from the first and second artificial neural networks receiving the same input vector. These input vectors are communicated between the first and second artificial neural networks, or rather, between the underlying A-machine and B-machine.The output of the neurons on the intermediate layer also represents a vector. Such an intermediate vector has the same length as the respective input vectors, thus comprising the same number of vector elements, or time steps. The vector elements of the intermediate vector can take the values ​​0 or +1. The intermediate vector for a given time step contains the value 0 if the intermediate neuron does not fire, and the value 1 if the neuron fires during that time step. The output neuron on the last layer multiplies the intermediate vectors accordingly, so that the output vector from the output neuron also comprises the same number of vector elements, which take the values ​​0 or +1. In contrast to the familiar tree parity machine, a vector, rather than a single number, is output.

[0021] According to the invention, a proprietary synchronization method for STPMs is described. For TPMs, synchronization is usually performed using one of the following learning rules: Hebbian Learning Rule, Anti-Hebbian Learning Rule, or Random Walk. According to the invention, however, synchronization is based on the iteration step difference between corresponding neurons. This iteration step difference can also be understood as a time difference due to the analogy of time. Thus, for example, if a neuron in the first artificial neural network fires for the first time at the second iteration step, and the corresponding neuron in the second artificial neural network fires for the fourth iteration step, the iteration step difference is "2". If the duration of a time step is, for example, 0.1 seconds, then the time difference is accordingly 0.2 seconds. The iteration step difference, or...The time difference can now be incorporated into a suitable mathematical equation to adjust the individual weights. Ideally, the weights of the neurons in the first and second artificial neural networks are adjusted simultaneously so that they approach a common value. The respective weights can be increased or decreased. Once the first and second artificial neural networks reach a state of synchronization, both weights assume the same value. It is not necessary for both corresponding neurons to reach the common weight value in the same synchronization step.

[0022] Learning and synchronization only occur if the output vectors of the first and second artificial neural networks match. This is the same process used in conventional tree parity machines. If a matching output vector is not generated in a synchronization step, the weights of the neurons in both artificial neural networks are not adjusted, as is typical. Instead, new input data is generated, and the respective output vectors are recalculated.

[0023] An advantageous further development of the method according to the invention provides that the second value range comprises real numbers. The weights of conventional TPMs consist only of integers. According to the invention, however, weights can also be formed using rational numbers or "decimal numbers." This further increases the degree of obfuscation, thus inherently increasing cybersecurity. The weights of the artificial neural networks can therefore also be described as "real-valued."

[0024] According to a further advantageous embodiment of the method according to the invention, the membrane potential of the neurons is multiplied from iteration to iteration by a decay factor from the open interval of 0 to 1, wherein, in particular, the same decay factor is used for all neurons and is kept constant during the calculation of the respective output vectors. Preferably, the decay factor of the neurons remains constant during a synchronization step. The respective neurons on the intermediate layer in the first and second artificial neural networks fire as soon as the membrane potential exceeds a critical threshold. This critical threshold can be defined by the developer. After such an intermediate neuron has fired, the membrane potential drops to a defined value. This value can be 0 or correspond to a positive or negative number.Additionally, the membrane potential can be reduced from iteration to iteration, i.e., from time step to time step, using the decay factor. This allows the firing time of the corresponding neuron to be shifted back to later vector entries. By incorporating the decay factor, a further degree of obfuscation can be achieved, which consequently enhances cybersecurity even further.

[0025] A further advantageous embodiment of the method according to the invention provides that the first and second artificial neural networks each have more than one intermediate layer, or hidden layer. This increases the complexity of the artificial neural networks, thereby further enhancing obfuscation. For example, the structure of the artificial neural networks can be extended by an additional hidden layer. The second hidden layer, i.e., the second intermediate layer, can function like the single intermediate layer. The first intermediate layer, however, can function like the input layer. This means that the outputs from the input neurons supplied to the neurons on the first intermediate layer are added together, and the neurons on the first intermediate layer fire accordingly when a corresponding threshold is exceeded.Each neuron on the first intermediate layer can also be assigned a weight, so that the output signal of 0 or 1 is multiplied accordingly. In general, including further intermediate layers in the structure would be a possibility.

[0026] According to a further advantageous embodiment of the method according to the invention, it is further provided that the A-machine and the B-machine generate a symmetric key for a symmetric encryption method based on the shared secret. This enables the use of further deep encryption mechanisms.

[0027] Preferably, machine A and machine B generate further symmetric keys iteratively based on the generated symmetric key. This further enhances cybersecurity. As previously described, the shared secret, or the symmetric keys derived from it, can be used for cryptographic encryption of messages exchanged between machine A and machine B.

[0028] Accordingly, new symmetric keys can be generated for each message to be exchanged, so that even if an attacker were to intercept a corresponding message and derive the symmetric key used from it, subsequent messages could not be decrypted.

[0029] Symmetric keys are particularly preferred when generated using the logistic equation. The logistic equation is also known as the logistic map and is: xn+1=r xn(1−xn).

[0030] With each successful authentication of the A and B machines, or with the transmission of a new message, the formula is iterated further to generate new keys X. n+1 to generate. Subsequent keys are therefore based on the previously generated keys X. n Using the logistic equation, chaotic and complex behavior can be generated based on a simple, non-linear equation. This allows the degree of obfuscation to be increased even further, enabling the generation of particularly secure symmetric keys.

[0031] A further advantageous embodiment of the method according to the invention provides that the factor r of the logistic equation is selected from the chaotic range, in particular from the open interval of 3.57 to 4.0. The selection of the parameter r is crucial to ensure a high degree of unpredictability and thus security. If the parameter r is selected from the chaotic range, the equation becomes extremely sensitive to the initial value. This means that even slight differences in the initial value x0 (i.e., the shared secret or a quantity derived from it) lead to drastically different results. This allows for a further improvement in cybersecurity.

[0032] According to a further advantageous embodiment of the method according to the invention, the initial value of the logistic equation is determined by applying mathematical operations to the shared secret, wherein, in particular, the initial value is not 0 or 1. Thus, mathematical operations can be applied to the shared secret to determine the initial value for the logistic equation. As already described, the shared secret represents a number generated from the weights of the synchronized first and second artificial neural networks. Mathematical operations can then be applied to this number, or the shared secret can be inserted into a suitable formula, such as a hash function. This allows the degree of obfuscation to be increased even further.A formula is particularly preferred such that the result calculated from the shared secret does not correspond to a trivial value, specifically not to 0 or 1, or a number close to zero or one. For example, the normalized last valid output value of the spiking tree parity machine can be chosen, or a derivative value calculated from the final synchronized weights. This linkage directly binds x0 to the context and state of the spiking tree parity machine, ensuring that each key is unique and difficult to predict.

[0033] A further advantageous embodiment of the method according to the invention provides that at least one of the following key figures is used: - a learning rate of 0.5; - a time constant of 10; - a number of input neurons of 25; - a number of intermediate neurons of 5; - a threshold for neuronal firing of 4.5; and / or - a second range of values ​​from the closed interval of -0.5 to +0.5.

[0034] Using the metrics described above, a spiking tree parity machine was developed that reliably generates highly secure keys with minimal technical effort. Effective synchronization was achieved within 1000 time steps. Simulations of attacks on the generated keys were successful at 10 7 The passes did not cause the keys to crack.

[0035] According to a further advantageous embodiment of the method according to the invention, it is further provided that the shared secret and / or a symmetric key calculated from the shared secret is used for the cryptographically secured transmission of information in a communication network in a vehicle, in particular within the framework of signature-based authentication, and / or for the cryptographically secured transmission of an unlocking command from a vehicle key to the vehicle. As already described, the method according to the invention for generating cryptographic keys can be used to secure communication during the operation of a vehicle. The cybersecurity of the vehicle can thus be increased. Since the method according to the invention for generating corresponding keys requires little technical effort, it can also be executed easily and reliably even on less powerful hardware.It is therefore particularly suitable for integration and application in a vehicle. For example, the control unit of a vehicle subsystem or a key fob can be used as an A or B machine. Due to its outstanding security against conventional attacks as well as cracking by quantum computers, an unprecedented level of cybersecurity can be achieved.

[0036] An information technology system according to the invention, comprising a vehicle, is characterized in that - a computing unit of the vehicle forms an A-machine and a B-machine; - a first computing unit of the vehicle forms an A-machine and a second computing unit of the vehicle forms a B-machine, wherein the first and second computing units are connected to each other via a communication network of the vehicle; or - a first computing unit of the vehicle forms an A-machine and a mobile terminal form a B-machine, wherein the vehicle is in communication connection with the mobile terminal, in particular via a UWB communication connection; wherein the A-machine and the B-machine are designed as an A-machine and B-machine that can be used in a method described above.

[0037] Thus, various possibilities exist for applying the inventive method for generating shared secrets in the automotive context. According to a first embodiment, machine A and machine B can run on the same computing unit. This allows the processes running within a single computing unit to be protected. The respective computing units can be any computer systems in a vehicle, such as, in particular, a central on-board computer, the control unit of a vehicle subsystem, a telecommunications unit, and the like. For example, it could be an embedded system, such as a system-on-a-chip (SoC).

[0038] Machine A and machine B can each be configured with their own processing unit. This can be used to cryptographically secure communication between two processing units in the vehicle, for example, between two control units, a control unit and a central on-board computer, or a telecommunications unit.

[0039] Furthermore, it is also possible for one of the machines to be controlled by a computing unit in the vehicle and the other by an external device, such as a smartphone, laptop, diagnostic tester, or the like. The external device or mobile terminal can preferably be a key fob. Such a key fob can also be provided by an application running on a mobile terminal, such as the aforementioned smartphone. In particular, the key fob or smartphone can perform ultra-wideband (UWB) communication. Thus, the method according to the invention is suitable for the secure transmission of an unlocking command to the vehicle. Man-in-the-middle attacks or replay attacks described above can therefore be reliably prevented. The risk of a vehicle being stolen can thus be reduced.

[0040] Further advantageous embodiments of the computer-implemented method according to the invention for generating a shared secret also result from the exemplary embodiments which are described in more detail below with reference to the figures.

[0041] This shows: Fig. 1 a schematic representation of the operating principle of an adapted tree parity machine used within the framework of a method according to the invention; Fig. 2 a schematic representation of an alternative firing mechanism of neurons; Fig. 3 an equation usable for adjusting the weights of the artificial neural networks used to form the tree parity machine; Fig. 4 an equation usable for key generation from a shared secret generated by the Tree Parity Machine; Fig. 5 an advantageous structure of the artificial neural networks used to form the tree parity machine; Fig. 6 a flowchart of the method according to the invention; and Fig. 7 an exemplary application of the method according to the invention in the automotive context.

[0042] A computer-implemented method according to the invention for generating a shared secret is based on the use of a so-called, in Fig. The Tree Parity Machine 1 shown in Figure 1 is an artificial neural network (ANN) in the form of a multi-layer feedforward neural network. The one in Figure 1 is a multi-layer feedforward neural network. Fig. Figure 1 of the artificial neural network (ANN) depicted has the following structure: an input layer LE, an intermediate layer LH (also called a hidden layer), and an output layer LA. A single output neuron 3A is located on the output layer LA, which in turn receives information from three intermediate neurons 3H located on the intermediate layer LH. The intermediate neurons 3H, in turn, receive information from three input neurons 3E each located on the input layer LE.

[0043] Each input neuron 3E is supplied with its own input vector 4. Fig. Figure 1 shows the corresponding input vectors 4 in the form of x for the first branch of the Tree Parity Machine 1. 11 , x 12 and x 13The input vectors 4 contain a fixed number of vector elements 5, which correspond to random numbers from a defined initial range of values. This initial range of values ​​can, for example, extend from 0 to 1. In particular, the numbers are evenly distributed along this range. Four vector elements 5, corresponding to four time steps of equal length, are shown as an example.

[0044] The input vectors 4 or the respective vector elements 5 are then multiplied by the weights or weighting factors 2 of the individual neurons 3, which are denoted here as W KN (w 11 , w 12 , w 13 ) are denoted. The resulting result vectors 17 are in Fig. 1 is shown in the center right. The result for the first iteration or the first time step is highlighted by a dotted border. Thus, for x 11Multiplying "1" by "0.2" results in "0.2", and so on. The Tree Parity Machine 1 thus iterates through the individual vector elements 5. Each iteration can be considered a time step. In the illustrated example, there are four vector elements 5, where, for example, the time step size can be 0.25 seconds, so that the total time duration is one second. These are purely illustrative values.

[0045] Initially, the weights 2 of the neurons 3 were initialized. For this purpose, a random number from a defined second range of values ​​is assigned to each neuron 3 as its weight 2. Preferably, this second range of values ​​comprises real numbers. For example, as in Fig. 5 is shown, the second range of values ​​comes from the closed interval from -0.5 to 0.5.

[0046] According to the invention, the neurons 3 operate according to the so-called leaky-integrate-and-fire principle. The process is illustrated in diagram 18 in Fig. Figure 18 shows the membrane potential 8 of the first intermediate neuron 3H1 across a synchronization step. The quantity "U" was chosen as an example to describe the membrane potential 8. The first intermediate neuron 3H1 is supplied with the input vectors 4: x 11 , x 12 and x 13The first iteration step, as indicated by the dotted outline, involves adding the first vector elements 5, each multiplied by a weight of 2. A threshold value 13 for the membrane potential 8 to fire, here denoted as "θ", is not yet exceeded. In the next iteration step, the membrane potential 8 decreases before subsequently increasing again. In the second iteration step, the result of the sum of the products of weight 2 and the second vector elements of the input vectors 4 is added to the result of the first iteration. In the third iteration step, the membrane potential 8 exceeds the threshold value 13 for firing, so the corresponding vector element in the intermediate vector 19 assumes the value 1. The intermediate vectors 19 for the further intermediate neurons 3H are also shown as examples. Multiplying the intermediate vectors 19 yields the output vector 6 for the artificial neural network ANN.the Tree Parity Machine 1.

[0047] After firing, the membrane potential drops to an initial value of 20. This initial value of 20 can be any predetermined level, such as 0. Fig. Example 1 is chosen as the starting value 20: "0.1". The starting value 20 could also be negative. In the fourth iteration step, the value 0.09 is added, so that the membrane potential 8 increases to 0.19.

[0048] According to Fig. 2. The membrane potential 8 can also be multiplied by a so-called decay factor 9, denoted here by the symbol δ, from iteration to iteration. For example, the decay factor 9 is set to "0.9" or 90%. Thus, the membrane potential 8 decreases by 10% from iteration to iteration. At the in Fig. In the embodiment shown in Figure 2, the sum of the products supplied by the input neurons, consisting of the respective vector element multiplied by its weight, is "10" in the first iteration. Taking into account the decay factor of 9, this results in a value of "9". In the second iteration, the sum is also "9", which is added. The result, "18", exceeds the firing threshold of 13, so the value "1" is written as the second entry in the intermediate vector. The membrane potential drops to the initial value of 20, here "0". In the third iteration, the sum of the products is "15" and, taking into account the decay factor of 9, drops to "13.5". Since the threshold of 13, "16", was not exceeded, the intermediate vector receives the value "0" as its third entry. In the fourth iteration, the sum of the products is "2", which is added to "13.5".Since "15.5" is still smaller than "16", the intermediate vector also receives the value "0" as its fourth entry. Therefore, the intermediate neuron only fires in the second iteration step.

[0049] Fig. Figure 3 shows an advantageous equation used by the applicant to adjust the weights 2. The parameter η represents the learning rate 11. How Fig. As shown in Figure 5, the value η = 0.5 can be advantageously used for the learning rate 11. The value of the constant is fixed by the developer. The developer also specifies the time constant 12 with the symbol τ. The iteration difference 7, which can also be interpreted as a time difference, enters the equation as a variable. Therefore, the iteration difference 7 is denoted as "t" in the formula. diff“Explained out. For this purpose, for each neuron 3 of a first and second artificial neural network to be synchronized, the iteration step at which the respective neuron 3 first fires is determined. This iteration step, or the corresponding time, is then compared for the corresponding neurons, and the corresponding difference is calculated. The factor Δw can be positive or negative. If the factor is positive, the corresponding weight 2 is increased; if it is negative, the weight 2 is reduced. This process is repeated until all weights 2 of corresponding neurons 3 in the first and second artificial neural networks are identical. This state is referred to as synchronous.

[0050] Fig. Figure 4 shows the logistic equation 10. Logistic equation 10 can be advantageously used to generate symmetric keys from the shared secret, which is generated based on the weights 2 of the synchronized artificial neural networks. The shared secret, or a quantity calculated from it, can already be used as a symmetric key. The initial value x0 can be the shared secret or the aforementioned quantity calculated from the shared secret. It is particularly advantageous that this value is not equal to or close to 0 or 1. Specifically, a value in the chaotic range, i.e., between 3.57 and 4, is chosen as the parameter r. The in Fig. The logistic equation shown in Figure 4 illustrates how new keys can be calculated from previously used shared secrets or symmetric keys. It becomes advantageous how Fig. Figure 7 shows the inventive method for cryptographically securing communication in the context of a vehicle 15. For example, each message exchanged between computing units can be encrypted or decrypted with a correspondingly newly generated key.

[0051] Fig. Figure 5 shows an alternative structure of the artificial neural networks (ANNs) used to form the Tree Parity Machine 1 and Spiking Tree Parity Machines. Particularly advantageous is the inclusion of exactly one output layer (LA), one intermediate layer (LH), and one input layer (LE). The artificial neural network (ANN) comprises a single output neuron (3A), five intermediate neurons (3H), and for each intermediate neuron (3H), five input neurons (3E), for a total of 25 input neurons (3E). The following are particularly advantageous: Fig. The parameters shown in the upper box are used. Here, K corresponds to the number of intermediate neurons 3H and N to the number of input neurons 3E per intermediate neuron 3H. θ denotes the threshold value 13 for firing the intermediate neurons 3H. W specifies the range of values ​​for the weights 2.

[0052] The process of the inventive method is described again using the following examples: Fig. Section 6 explains this. In step 601, synchronization between the first and second artificial neural networks begins. In step 602, random input vectors 4 are generated and processed by the first and second artificial neural networks in steps 603 and 604, respectively. The sequence of steps is shown sequentially, but they could also run in parallel. The respective artificial neural networks are usually referred to as "A-machine" and "B-machine," respectively. By analogy, the respective computer systems on which these machines run are referred to as... Fig. 7. These are referred to as machine A and machine B. However, it would also be possible for the first and second artificial neural networks, i.e., machine A and machine B, to run on one and the same computer system.

[0053] The two output vectors 6 generated by the artificial neural networks are exchanged in step 605, as are the input vectors 4, via a public communication channel. This communication channel can be secured using established cryptographic encryption mechanisms.

[0054] In step 606, it is checked whether the two output vectors 6 match. If this is not the case, the procedure jumps back to step 602, so that newly generated input vectors 4 are supplied to the input neurons 3E. If, on the other hand, the results match, the weights 2 are adjusted in step 607 based on the values ​​in Fig. The equation shown in Figure 3 is used. The procedure continues iteratively. In step 608, it is checked whether convergence has occurred, i.e., whether the weights 2 between the first and second artificial neural networks are identical, so that they can be considered synchronous. This is verified in step 609. If synchronization has not yet occurred, the procedure jumps back to step 602. If, however, synchronization has occurred, the procedure ends in step 610. Accordingly, the weights 2 are used as a shared secret. Based on this, the aforementioned symmetric keys can be generated using the equation shown in Figure 3. Fig. The logistic equation 10 shown in section 4 can be generated.

[0055] Fig.Figure 7 illustrates the application of the method according to the invention in an automotive context. For example, machine A is integrated into a computing unit in the vehicle 15, and machine B is integrated into a vehicle key 16. A transmitter-receiver 21 can be integrated to mediate the communication between the computing unit and the vehicle key 16. The transmitter-receiver 21 communicates with the computing unit via the communication network 14 of the vehicle 15. By pressing a button on the vehicle key 16, a user can send a door unlocking command to the vehicle 15. This command is encrypted with the shared secret or one of the iteratively generated symmetric keys and decrypted on machine A using the same symmetric key.

Claims

[1] Computer-implemented method for generating a shared secret based on the use of a tree parity machine (1), wherein a first artificial neural network on an A-machine (A) and a second artificial neural network on a B-machine (B) are synchronized, wherein the first and second artificial neural networks have the same structure, wherein in the synchronized state the weight factor (2) of each neuron (3) of the first artificial neural network is identical to its corresponding neuron (3) in the second artificial neural network, and wherein the shared secret is a mathematical recombination of the weight factors (2) assigned to the individual neurons (3), characterized by , that the neurons (3) of the artificial neural networks operate according to the leaky-integrate-and-fire principle and the following steps are performed for synchronization: - For each input neuron (3E) of the artificial neural networks: Generating an input vector (4) with a fixed number of vector elements (5) containing random numbers from a fixed first range of values, wherein corresponding input neurons (3E) from the first and second artificial neural networks receive the same input vector (4); - Initializing the weights (2) of the neurons (3) of the first and second artificial neural networks with random numbers from a defined second range of values; - Supplying the input vectors (4) to the input neurons (3E); - Computation of an output vector (6) by the first and second artificial neural networks based on the input vectors (4), wherein the vector elements (5) are processed iteratively to represent a time iteration step; - For each neuron (3): Determine the iteration step at which the neuron (3) fires for the first time; - For each neuron (3): Determine an iteration step difference (7) at which the neuron (3) fires for the first time between the corresponding neuron (3) in the first and second artificial neural network; - If the output vectors (6) of the first and second artificial neural networks are the same: Adjust the weights (2) of the neurons (3) of the first and second artificial neural networks depending on the respective iteration step difference (7) of the respective pair of neurons; and - Repeated adjustment of the weights (2) of the neurons (3) until synchronization between the first and second artificial neural networks is achieved. [2] Method according to claim 1, characterized by , that the second range of values ​​includes real numbers. [3] Method according to claim 1 or 2, characterized by, that the membrane potential (8) of the neurons (3) is multiplied from iteration to iteration by a decay factor (9) from the open interval of 0 to 1, in particular using the same decay factor (9) for all neurons (3) and keeping it constant during the calculation of the respective output vectors (6). [4] Method according to any one of claims 1 to 3, characterized by that the first and second artificial neural networks each have more than one hidden layer. [5] Method according to any one of claims 1 to 4, characterized by , that the A machine (A) and the B machine (B) generate a symmetric key for a symmetric encryption algorithm based on the shared secret. [6] Method according to claim 5, characterized by , that the A-machine (A) and the B-machine (B) iteratively generate further symmetric keys based on the generated symmetric key. [7] Method according to claim 5 or 6, characterized by , that symmetric keys are generated using the logistic equation (10). [8] Method according to claim 7, characterized by , that the factor r of the logistic equation (10) is chosen from the chaotic range, in particular from the open interval from 3.57 to 4.

0. [9] Method according to claim 7 or 8, characterized by , that the initial value of the logistic equation (10) is determined by applying mathematical operations to the shared secret, in particular the initial value is not 0 or 1. [10] Method according to any one of claims 1 to 9, characterized by that at least one of the following key figures is used: - a learning rate (11) of 0.5; - a time constant (12) of 10; - a number of input neurons (3E) of 25; - a number of interneurons (3H) of 5; - a threshold (13) for the firing of the neurons (3) of 4.5; and / or - a second range of values ​​from the closed interval of -0.5 to 0.

5. [11] Method according to any one of claims 1 to 10, characterized by , that the shared secret and / or a symmetric key calculated from the shared secret is used for the cryptographically secure transmission of information in a communication network (14) in a vehicle (15), in particular in the context of signature-based authentication, and / or for the cryptographically secure transmission of an unlock command from a vehicle key (16) to the vehicle (15).

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