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[Download eBook] A Droga Da Obedincia Coleo Os Karas - PDFFormat at resourceone.info Book file PDF easily for everyone and every device. Download this. THE MYSTERY OF MOVEMENT AND IMMOBILITY IN THE POETRY OF OSKARAS MILA-ŠIUS AND VYTAUTAS PETRAS BLOŽĖ. Jonathan Garde. Salomėja Zaksaitė Unmasking the aggression in the works of Oskaras Korsunovas and Lars von Trier Translated from: Agresijos demaskavimas Oskaro .

Therefore, the two-dimensional method is superior to the one-dimensional method for this problem. Chapter 4 Physical Layer Security in the Presence of Interference In this chapter, the effect of interference on the secrecy performance of a wireless communications system is investigated.

In Section 4. The system model that will be used in this chapter is described in Section 4. Afterwards, the theoretical analysis and derivation of the SOP for this system model is given in Section 4. Finally, in Section 4.

The results presented in this chapter have been published in [50]. A scenario where two independent confidential messages are trans- mitted to their respective receivers was examined in [52], and the equivocation rate at the eavesdropper was used as a metric to ensure mutual information-theoretic secrecy, taking into consideration the inter- ference between the receivers.

The problem of security with interference was examined from a similar standpoint in [53], where two transmitters were assumed to sent two messages to a cognitive receiver, who should be able to decode both messages, and a noncognitive receiver, who should only be able to decode one message while the other is kept secret.

Again, secrecy was measured in terms of equivocation rate. The effect of interference on secrecy capacity was also investigated in the literature. In more de- tail, in [54], a system that consisted of a primary transmitter-receiver pair, as well as a number of secondary transmitters and receivers, and a single eavesdropper, was examined.

It was considered that the secondary users and the eavesdropper were distributed according to a PPP. However, the impact of multipath fading was not taken into consideration.

Physical Layer Security in the Presence of Interference eavesdropper. Based on 4. A closed-form expression for the SOP was not derived, but numerical and simulation results were presented. In [55], the secrecy capacity was examined for a cognitive radio system based on artificial noise, which was proposed in order to deal with the eavesdropper.

The transmitter was equipped with M antennas, whereas the receivers and eavesdroppers were single- antenna. There was also a single-antenna secondary transmitter who was treated as an interferer. Also, hpp and hsp were the fading channel matrices. The SOP was not studied in [55], and the expressions derived are in the form of approximations.

Game theory has also been used to tackle the problem of security with interference. In [56], the two- user Gaussian interference channel was investigated, where each user attempted to transmit a confidential message to a different receiver, while each user aimed to maximize the difference between its secrecy rate and the secrecy rate of the other transmitter. Through a game-theoretic approach, it is concluded that an optimum solution is achievable. Also, achievable rate regions were studied for the multiple- input multiple-output MIMO interference channel in [57], where a multiple-antenna transmitter sent a different message to two receivers, and each receiver was assumed to be an eavesdropper for the other receiver.

As before, a game-theoretic approach was followed, and an operating point that balances network performance and fairness was found. There had been several other works in the literature that deal with the problem with interference in security. In [58], the exact sum secure degrees of freedom for the K-user Gaussian interference channel were determined, under several constraints. Cooperative jamming was employed in order to obtain an optimal solution.

The problem was also examined from the perspective of secure degrees of freedom in [59], where lattice codes and layered coding are also employed to provide secrecy. Interference alignment was suggested in the literature for interference management in wireless networks. In this context, in [60], an anti-jamming technique was proposed, in order to deal with interference from a malicious jammer.

Also, an artificial noise scheme was proposed, for disrupting the eavesdropper without affecting the legitimate network. In [61], it was shown that the use of interference alignment can achieve non-zero secure degrees of freedom in a K-user Gaussian interference channel with secrecy constraints. In [62], maximization of the secure degrees of freedom was examined, by exploiting co-channel interference, with a cooperative secrecy transmission scheme. Moreover, the channel between Alice and Bob is denoted by hB , that between Alice and Eve by hE , that between the i-th interferer and Bob by hBi , and that between the i-th interferer and Eve by hEi.

By using 4. Physical Layer Security in the Presence of Interference 4. Recall that the SOP is defined as the probability that the secrecy capacity is lower than an target secrecy rate rs , i. Theorem 4. Please refer to Appendix D. Please note that these distances were selected, so that it will always be geometrically possible to find locations for Alice, Bob and the interfering BSs that that satisfy these values.

Moreover, it is assumed that the signals transmitted by the interferers have equal energy, denoted by EsI. Also, higher transmission rates lead to higher values of the SOP.

This can be explained because the impact of the interferers is dependent on their location, i. In Fig. We observe that, in all cases, as rs increases, the SOP also increases. As in Fig. In all cases, it can be seen that as rs increases, the SOP also increases.

Again, these results show the importance of taking into consideration the location of the interfering BSs and user terminals in the design and deployment of a wireless communications system with PHY security. Another approach that was taken to evaluate the impact of interference on PHY security is examining different positions of Eve.

Moreover, we observe that higher values rs lead to a higher SOP. Again, note that these results are dependent on the specific locations of all the BSs and users, and have to be examined individually for each practical system. This information can be used in order to produce a cryptographic key. Afterwards, an encryption algorithm can be used in order to encrypt the message by using the cryptographic key. PHY key exchange, as well as the methods and algorithms proposed in this thesis, will be presented in detail in Chapter 6.

However, in this chapter, in order to illustrate some of the fundamental concepts of key exchange, we present the Diffie-Hellman algorithm [12] and the RSA algorithm [13]. Also, we analyze two categories of encryption algorithms, namely stream ciphers and block ciphers. Consider, for example, that Alice aims to transmit a message P to Bob.

The key K is transmitted to Bob through a secure chan- nel. The key K is selected from the keyspace, i. The message P may not be transmitted through the secure channel, due to limitations in time and capacity.

The main weakness of this approach is that the key has to be transmitted over a secure channel, which is not always available or practical. Such an encryption scheme can be seen in Fig.

This is referred to as public key cryptography. These elements should have the following properties: The third property allows the process EK to be made available to the public without compromising the security of DK. Therefore, if we consider EK to be the encryption algorithm and DK to be the decryption algorithm, knowledge of the encryption algorithm does not allow a potential eavesdropper to decipher the message.

Given such a system, it is easy to see that the encryption process is vastly simplified. Specifically, Bob can generate an enciphering key KE , which is made public. Afterwards, Alice can use KE to encrypt the message and transmit it to Bob, who deciphers the message by using a private key KD. Such an encryption scheme is shown in Fig. In , based on the research by Diffie and Hellman, Ralph Merkle published an algorithm that satisfies these requirements in [65].

This is referred to as the Diffie-Hellman algorithm, and is outlined as follows: Alice and Bob agree to a prime number p and a base g. Alice chooses a secret number A, and sends g A mod p to Bob. Bob chooses a secret number B, and sends g B mod p to Alice. Alice computes g B mod p A mod p. Bob computes g A mod p B mod p. In the above, mod denotes the remainder of integer division.

After this process, the number calculated by both Bob and Eve is identical. Also, note that p and g are not needed to be protected; therefore, the pair p, g is the public key.

On the other hand, the pair A, B needs to be secret; therefore it is the private key. The Diffie-Hellman protocol is shown in Fig. Regarding the security of the scheme, it is considered that in order to crack the Diffie-Hellman algorithm, the Diffie-Hellman problem DHP should be solved.

The definition of this problem was provided in [66, 67] and is given as follows. Definition 5. Given an element g, and the values of g x and g y , where x and y are two randomly generated integers, what is the value of g xy?

As of today, no easy solution to this problem has been published. The most efficient ways to solve the DHP is by solving the discrete logarithm problem DLP , which is to find x given x and gx [68, 69]. Even though its computational complexity is rather high, it is however considered secure, for sufficiently large key lengths. The algorithm is described as follows. Alice picks two sufficiently large prime numbers, p and q, which are kept secret.

The pair e, N is made public, and is considered as the public key. Bob transmits C to Alice. It has been proven [71] that the problem of prime factorization is NP-hard, i. To this end, Alice employs a symmetric cipher, i. According to [5, 73], symmetric ciphers can be split into two categories: Each bit of the message is encrypted individually. A bit from a key stream is added to a plaintext bit. An entire block of plaintext bits is encrypted at a time with the same key.

Next, we provide an analysis for both categories of ciphers. They can be either synchronous, where the key stream only depends on the key, or asynchronous, where the key stream depends on the key and the ciphertext. Historically, stream ciphers were more efficient from a computational and hardware standpoint, however modern block ciphers approach the efficiency that used to only be attainable by stream ciphers.

A stream cipher model is shown in Fig. The encryption and decryption process of a bit stream with a stream cipher is described as follows [5]. Observe that the encryption and decryption functions are the same.

From the above, it is evident that encryption and decryption are simple and straightforward processes. Therefore, the nature of a stream cipher depends entirely on the key stream and how it is generated. It should be noted that the key stream itself is not the key, but it is generated based on the key.

Intuitively, we assume that a requirement for the key stream is that it divulges as little information as possible about the key to Eve. A truly random sequence can be generated by exploiting real-world random events, such as, for example, the noise and instability in the electronic circuitry of the encryption device.

This is an ideal case for generating the key stream of a stream cipher, since it is impossible for an eavesdropper to reproduce the output of the key stream generator. This is referred to as a true random number generator TRNG [76, 77]. Unfortunately, TRNGs cannot be used as key stream generators in practice. Therefore, we have to resort to other solutions. Pseudorandom sequences can be produced by using pseudorandom number generators PRNGs , which use a seed, s0 , in order to generate a sequence that appears to have the statistical properties of a random sequence.

However, a specific value of the seed will always produce the same sequence, which means that these methods do not produce true randomness. For example, one such function can be the following: However, not any PRNG can be used for cryptographic purposes. Other than the appearance of randomness, another characteristic that is required is unpredictability.

In order to be considered unpre- dictable, a PRNG should pass the next-bit test. It has been proven in [79] that any CSPRNG that passes the next-bit test will also pass any other polynomial-time statistical test for randomness. According to [80], the next-bit test is defined as follows.

For any function family, Gk: In a stream cipher, the cryptographic key would be used as the seed. Also, p and q should be congruent to 3 mod 4 , which guarantees that each quadratic residue has one square root, which is also a quadratic residue. If the primes p and q are large enough, then the computational hardness of reversing the BBS generator is appropriate for cryptographic applications. The data encryption standard DES [82], first published in , was selected by the National Institute of Standards and Technology NIST and approved in November as a federal standard in order to encrypt unclassified, sensitive information by the US government.

It remained so until , when it was replaced by the advanced encryption standard AES [17]. By that time, DES was not considered to be sufficiently secure, due to the improvement of the hardware available to the eavesdropper, which significantly increased the speed of cryptanalytic attacks.

A block cipher model is shown in Fig. Next, we give a description of the DES cipher, as shown in [82], which encrypts bit blocks with a bit key. It is also a symmetric cipher, meaning that the same key is used for encryption and decryption. The operation of the DES cipher is based on a Feistel network [83], which is commonly used in block ciphers. One basic characteristic of Feistel networks is that encryption and decryption are very similar processes.

The operation of the Feistel network is outlined as follows: Consider a bit plaintext message x. It is put through a bitwise permutation, namely IP x. The result is split into two bit parts, namely L0 and R0 , which are referred to as the left half and the right half, respectively. A round key k1 is generated from the main bit key by using a key schedule.

The right and left half are swapped. Steps are repeated 15 more times by using the result of the previous permutation as input. The structure of a Feistel network is graphically illustrated in Fig. It has been determined that the permutation operation does not impact the security of the Feistel network, however it was included in the DES standard in order to facilitate some aspects of the hardware implementation of the encryption scheme.

The output of the expasion function is XORed with the bit round key ki. The result of this operation is split into eight 6-bit parts. Each of these parts is fed into a substitution box S-box. Note that each substitution box gives a 4-bit output. The outputs of all the S-boxes form a bit word. The S-boxes are the most important part of the DES, because they introduce a nonlinearity aspect to the encryption operation that makes mathematical attacks, such as differential cryptanalysis, very difficult to perform.

Also, the scheme is designed, so that, after the fifth iteration of the Feistel algorithm, every bit of the output is a function of every plaintext bit and every key bit. This property is generally considered to make cryptanalytic attacks significantly more difficult. Moreover, Bob can easily perform decryption with knowledge of the key, since the decryption function is the same with the encryption function, the only difference being that the key schedule is reversed.

Eventually, DES became far too unreliable for secure communications, since the improvement of the available hardware made it more vulnerable to cryptanalytic attacks. This algorithm is adequately secure for modern applications, and is still used today.

It has a fixed block size of bits, and a key size of , or bits. Depending on the size of the key, the number of repetitions, referred to as rounds, is different. Specifically, there can be 10, 12 or 14 cycles for each of the key sizes mentioned above. The operation of the AES cipher is outlined below. Consider 16 bits, denoted as b0 , b1 , Encryption Algorithms 47 Key expansions: Initial round: A bitwise XOR is performed on each byte of the state with a block of the round key.

Intermediate rounds: The specific construction of this operator can be found in [17], but similarly to DES, the purpose of the S-box is to provide a nonlinear component to the cipher.

The last 3 rows of the state are shifted cyclically in a certain number of steps, while the first row is left unchanged. Specifically, each byte of the second row is shifted one place to the left, the third row is shifted two places to the left, and the fourth row is shifted three places to the left. This way, each column of the state consists of bytes from each of the columns of the original state.

The purpose of this step is to prevent the colums from being linearly dependent, which would facilitate cryptanalytic attacks. A mixing operation, that operates on the columns on the state and combines the four bytes in each column, is applied. Specifically, a fixed matrix is multiplied with each column of the state. A bitwise XOR is performed on each byte, ai,j , with a block of the round key. Final round: The same as the intermediate rounds, but without step 3 of the process described above.

Over the years, there have been several attempts to find efficient cryptanalytic attacks on the Rijndael cipher, see for example [85—91]. However, none of them has been particularly successful.

In the following chapter, we will describe the PHY key exchange methods proposed in this thesis. After key exchange and agreement has been performed, the key can be used in an encryption cipher, such as the ones described in this chapter.

Chapter 6 Physical Layer Key Exchange In this chapter, a category of key exchange protocols is investigated, where Alice and Bob extract two highly correlated channel magnitude envelopes by exploiting the principle of reciprocity.

The motivation for this approach is that Alice and Bob can utilize information that is only known to them, and not to Eve. As pointed out in [93], the channel magnitude envelopes are normally not known to Eve.

However, due to the existence of noise and various sources of interference, there will generally be discrepancies between the two generated bit strings. Symmetric key cryptography requires that both transceivers possess identical cryptographic keys. Therefore, a method should be used, which allows the two transceivers to generate identical keys, from similar bit strings with some discrepancies.

This process is referred to as error reconciliation. The rest of the chapter is organized as follows. In Section 6. Related works from the literature are presented in 6.

A new channel thresholding method is proposed in Section 6. Simulation results are provided in Section 6. The results presented in this chapter have been published in [94, 95].

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These methods are referred to as PHY key exchange algorithms in the literature. Traditional key exchange schemes provide security through computational complexity, meaning that their effectiveness is dependent on the computational capability of the eavesdropper. PHY key exchange is a concept that addresses some of these concerns.

In fact, PHY security may become a part of a multi-layered security scheme where each layer achieves a specific security goal. The concept of combining key exchange with PHY characteristics was first presented in in [96], where the use of channel reciprocity in multipath fading channels for key generation was proposed.

This means that, if both transceivers transmit a signal of equal strength to each other, the channel amplitude envelope received will be the same for both. However, an eavesdropper at a different location will observe a different, uncorrelated channel amplitude envelope, when receiving the signal from either one of the two transceivers.

In order to generate a similar bit sequence, Alice and Bob transmit a signal of equal strength to each other, and perform this thresholding process on the channel amplitude envelope, over the same time frame. This expression can only be computed numerically. In practice, when a PHY key exchange scheme is used, we first aim to upper bound the probability of error, and afterwards to maximize the rate of generation of secure bits s-bits.

For a Rayleigh fading channel, the level-crossing rate LCR , i. Related Literature 51 fd s-bits per second. In practice, the channel probing rate fs also affects the s-bit generation rate. Specifically, it increases as fs increases, and saturates to a value in the order of fd.

Since then, several PHY key exchange methods have been proposed in the literature. In [99], factors such as noise and interference were taken into consideration, and a key exchange protocol was presented and tested in a real-world setting.

Three such schemes are constructed. The length of these bit strings is n, and the number of deep fades in the sampled envelope is t. Each deep fade translates to a run of continuous ones in the generated bit string, and k is the maximum length of the runs of ones.

Each value of il uniquely defines a position for jl , since the duration of each run of ones is considered to be constant. However, Bob will also need some verification information, so that he can identify which one of the bit strings searched is correct. The bit string with an identical hash to the one received from Alice, is the correct bit string. A shortcoming of the first method is that it requires a brute force check to perform reconciliation, which can be computationally intensive for Bob.

Therefore, the event of 6.

It's a Nonlinear World

This method is shown to be both more accurate, and much more computationally efficient than the first method. Physical Layer Key Exchange 3. The third method uses a block error correction code, in order to perform error reconciliation. The event of 6. Therefore, we use a block error correction code that can correct up to 2st errors. Consider that we use a systematic block error correction code, i. Transmitter authentication in wireless channels was also explored in [] and [], while in [] and [] several key exchange methods were proposed with emphasis on the design of a high bit rate implementation.

In [], the concept of using multiple-antenna diversity for key generation purposes was investigated. Also, the use of an adaptive quantization algorithm for key exchange was proposed in [], and error reconciliation based on randomness extractors was examined in [].

A practical implementation of a key sharing platform at 60 GHz was presented in [], while the performance of several key exchange methods and their practical feasibility are discussed in [93, , ].

This research area continues to attract a considerable amount of attention in the open technical literature [—], based on the principle of channel reciprocity, as well as other channel characteristics.

Further information and recent research efforts about PHY key exchange techniques can be found in [2, 3, ] and references therein. A comprehensive analysis of neural networks can be found in [].

In general, a neural network is a massively parallel distributed processor that consists of simple processing units, namely neurons, which are connected between them with certain synaptic weights. The network receives an input and produces an output, and its behavior depends on previous inputs, which have been stored through a learning algorithm. The main goal of the learning algorithm is to modify the synaptic weights in order to achieve a certain goal regarding the output of the network.

The model of a neuron, which is the basic processing unit of the neural network, is shown in Fig. We observe that the neuron consists of 3 basic parts. A set of connections or synapses, each one of which is characterized by a synaptic weight.

Specifi- cally, a signal xj in the input of the j-th synapse connected to the k-th neuron is multiplied with the weight wkj. A summing junction, which calculates the sum of all the input signals, multiplied with the corre- sponding weights for each synapse.

There may also be a bias parameter, which is shown as a fixed input in Fig. There are three basic types of activation functions: Thresholding function: Piecewise linear function: Sigmoid function: As a tends to infinity, the sigmoid function tends to the thresholding function.

Next, we examine the connection of the neurons between them in order to form the neural network. Usually, neurons are categorized into levels, where each neuron has neurons of the previous level as inputs. Generally, there are three categories of neural networks: Single level neural networks: There is only one layer of neurons, which receives data as inputs and produces the corresponding outputs.

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Multilevel neural networks: There are more layers of neurons, which are referred to as hidden layers. Here, the output of each layer is the input of the next one, which means that each neuron takes as input the outputs of the neurons of the previous layer.

If each neuron is connected with all neurons of the previous layer, then it is called fully connected, otherwise it is partially connected. Feedback neural networks: Similar to the previous categories, but there is also a connection from the output to the input of the neural network. Training is the process that causes the neural network to exhibit the desired behavior.

The motivation behind training is that, knowledge of the expected output by the neural network given a specific input, modifies the synaptic weights of the network appropriately. In order to achieve that, we use a set of known input-output pairs.

This set is referred to as the training set. Regarding the formation of the training set, some similar inputs are selected, for which the same output is expected. There are various metrics to evaluate the similarity of the inputs, such as the Hamming distance and the Mahalanobis distance [].

After the training process is completed, the behavior of the trained neural network is verified by using inputs that do not belong to the training set, and by checking if they give the desired output.

This verification process is called generalization. Specifically, the key exchange scheme should: Nevertheless, the methods presented in this chapter are also applicable to other channel models, such as Rician or Nakagami-m fading.

Also, we assume that Eve is located at such a distance from both communicating nodes, that the envelope of the signal received by Eve is uncorrelated with the signals received by Alice and Bob. This assumption is valid for most practical scenarios. Specifically, an eavesdropper who is more than half a wavelength away from both Alice and Bob, will experience two independent fading channels towards Alice and Bob.

According to [93], these channels are uncorrelated with the channel between the two legitimate nodes. We further assume that the number of deep fades in a specific time interval might be known to Eve, but not their duration or their time location.

It is also assumed that the hardware is such, that the principle of reciprocity holds, as it has been documented in the open literature [96, 99]. A channel sampling procedure is proposed in [2], which takes into account the principle of reciprocity. Specifically, assuming that a transmitter sends a signal to a receiver, due to the principle of reciprocity, if it sends a signal back to the original transmitter, it will experience the same realization of fading at that instant.

In order to take advantage of this property, we assume that the Alice and Bob exchange L pilot signals. Specifically, when Alice transmits a signal, Bob measures the received signal strength, sends a signal back to Alice, who also measures the received signal strength, and so forth. Note, that the time between two consecutive transmissions from the same transceiver, Ts , must be less than the channel coherence time, in order to assume an identical impulse response between two consecutive channel samplings by Alice and Bob.

Following this process, Alice and Bob each construct an estimate of the channel magnitude envelope, that consists of L samples. Then, Alice and Bob apply a thresholding process to their respective sampled magnitude envelopes, so that they each generate a bit string of equal length.

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However, in practice, the principle of reciprocity holds only approximately, due to the presence of noise, various sources of interference, the characteristics of the specific hardware, and synchronization issues between Alice and Bob in the sampling process.

Thus, there are discrep- ancies between the bit strings generated by each transceiver, so they cannot be immediately used as a cryptographic key. In order to resolve this problem, a novel neural network based error reconciliation scheme is proposed and described in Section 6. Here, we present an alternative thresholding method which is more efficient especially in environments where deep fades do not occur, e. The motivation behind the proposed method is to detect fades of smaller depth, in order to increase the security of the system.

Specifically, a larger number of fades in a smaller time interval increases the time required for Eve to perform a brute force check. Also, the proposed method can cause uncertainty to Eve about the number of fades, if he is unaware of the existence of fades of smaller depth.

Let gA and gB be the sampled sequences of length L that both transceivers, Alice and Bob, denoted by A and B, have generated by sampling the channel magnitude envelope. A a Magn. B Thres. A 0,1 Thres. The degree of the polynomial can be selected depending on the length of the sampling time frame and the maximum Doppler shift. Afterwards, a sequence of length L, sK , is formed by both Alice and Bob, by sampling their respective least-square curves at L equally spaced time intervals.

Otherwise, it is set equal to 1. An example of the proposed thresholding method for a simulated channel magnitude envelope is shown in Fig. Specifically, Fig. The main advantage of the above proposed thresholding technique is its ability to detect fades of smaller depth, compared to the constant threshold method. Also, the ability of Alice and Bob to detect fades of small depth might cause Eve to miscalculate the number of fades, by ignoring or not being aware of fades with a smaller depth.

The correlation between the channels perceived by Alice and Bob will always be less than 1. This means that there will be discrepancies between the bit strings generated by the thresholding process. This is clearly shown in Fig. The method presented in this section uses these two bit strings in order to generate a cryptographic key, which will be known to both Alice and Bob. The neural network that will be used handles binary inputs and outputs, and consists of an input layer of L nodes, a hidden layer of N nodes, and an output layer of Lt nodes.

The value of N is selected, taking into account that higher values increase the complexity, but also the error reconciliation capability of the key exchange scheme. A model of the neural network used in the proposed scheme is shown in Figure 6. Next, we give an overview of the proposed scheme.

Alice creates a binary neural network with the parameters as mentioned above and randomly initializes its synaptic weights. This is described in more detail in Section 6. The synaptic weights of the neural network are transmitted to Bob. Physical Layer Key Exchange 5. In step 2, the cryptographic key is randomly generated.

Also, in step 4, to ensure the correct transmission of the required information, the use of an error correction scheme is recommended. The motivation behind the construction of the training set is that it should contain bit strings, that simulate the kind of errors that appear in practice.

In [2], an efficient bit string representation was proposed, where each bit string is represented by a set of pairs. The first element of each pair denotes the position of the beginning of a fade, and its second element denotes the end of the fade.

Bit discrepancies usually occur due to miscalculations of the position of the beginning or the end of a fade. The motivation behind this formation of the training set is that, as can be seen in Fig. Hence, the training set is formed, so that the neural network can detect and correct this kind of discrepancies. There are two layers of neurons, i.

This can refer to either the hidden or the outer layer. The synaptic weight for the j-th input of the i-th neuron of this layer is denoted by wij. It follows from 6. This process is performed m times. The training set T is formed as in 6. Each element of T is used m times. The security of the proposed method is based on the fact that, in order to deduce the value of the cryptographic key, Eve would have to somehow perform a completely accurate reversal of the training process.

As previously mentioned, there is no such documented method, and if it were attempted to develop such a method, it would be impeded by the randomization of the initial synaptic weights. Therefore, there is no way for Eve to fully reproduce the original key. As outlined in Section 6. In the first stage, only the output layer is trained. Here, two layers of neurons output and hidden are trained, with Lt N and LN weights to be updated, respectively.

However, in Section 6. Physical Layer Key Exchange Table 6. Key Length Lt Ntotal 50 1. Error reconciliation based on BCH coding has been examined in [2], and has been applied in quantum key distribution in []. However, the proposed method adds a layer of protection, in order to strengthen the security of the method against an eavesdropper attack.

Furthermore, we consider a systematic linear block coding scheme, such as a BCH code. We also assume that this code can correct up to t errors. This function will ultimately produce the cryptographic key. We introduce this function because, for security purposes, we require that the key is uniformly distributed.

Given a seed s, the generator outputs a bit sequence of length L.

However, it is possible if the appropriate computational power is available. The key exchange algorithm consists of the following steps: The selection of the linear block code used in this algorithm is not examined in this work, since the description of the method does not depend on the specific code used.

This is also true for the PRSG. For example, a Blum Blum Shub generator [81] could be used for this purpose. It should be noted that the exact computational complexity cannot be calculated in this case, since it depends on the selection of the linear block code and the PRSG. Next, we provide a justification why this method provides stronger security compared to unmasked linear block code based error reconciliation.

However, in [99] it is assumed that the number t of deep fades might be known to Eve, but not their location or length. Therefore, under these assumptions, Eve would only need to check for bit strings that fit this criterion, specifically strings that consist of t runs of ones. Therefore, our method provides a significant improvement in security.

We first consider the neural network based error reconciliation method. We also assume that the synaptic weights are equal at Alice and Bob, meaning that there are no transmission errors.

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The simulations were performed for two maximum Doppler shift frequencies, i. Rayleigh and Rician fading channels were simulated for each of these frequencies. It should be noted that a zero degree polynomial represents a constant threshold. We observe that in all cases, a polynomial with a degree greater than zero can lead to an increase of the LCR. This applies even to the line-of-sight scenarios, modeled here by Rician fading.

We can thus conclude that the proposed thresholding technique has better fade detection capabilities than the one, which uses a constant threshold. As previously mentioned, this leads to an increase of the security level against eavesdropper attacks. The simulations were performed for three key lengths, i. We observe that in all cases, the success rate drops as the number of errors increases. This indicates that smaller key lengths lead to better error reconciliation capabilities. The corresponding key agreement percentages are also depicted in Fig.

We observe that the proposed neural network-based method offers much higher agreement rates in all cases. In this case, a retransmission scheme can be implemented, so that the key exchange process is repeated. Three key lengths were tested in order to examine the security of the scheme in relation to the key length i. If, however, we have to minimize the probability that the neural network, intercepted by Eve, will generate the actual key as an output, it is best to choose a large key length.

This means that the Hamming distance of 0 is relatively farther from the center of the distribution for larger key lengths. One of the most important advantages of the proposed neural network based key exchange method is its customizability. The simulations performed also revealed some interesting observations about the key length. Specifically, an increase in the key length is more secure, but might reduce the key agreement probability. A trade-off can also be made between these two factors.

Simulations were also conducted for the linear block coding based error reconciliation method. Specif- ically, for 3 key lengths, i. The linear block code used was a n, k BCH code, and a Blum-Blum-Shub generator was used in order to generate the bit masks. We observe that the average difference between the values of ARD perceived by Alice and Bob increases, as the number of bit discrepancies increases.

Also, as the key length increases, the average ARD difference decreases. This way, errors can be detected and corrected without retransmission. In , FEC was pioneered by Richard Hamming, who invented the first error correcting code, the Hamming 7, 4 code [19].

As outlined in Part I, several other codes have been proposed in the literature. Polar codes, first introduced by Erdal Arikan in his pioneering work [23], are a class of block error correction codes based on the phenomenon of channel polarization.

This refers to the fact that, by using a set of N independent copies of a binary-input discrete memoryless channel B-DMC W , it is possible to synthesize a new set of N binary-input channels such that, as N tends to infinity, the fraction of channels whose symmetric capacity is near 1 approaches the symmetric capacity of W.

Polar codes have attracted considerable attention in the literature, because they are, as of the writing of this thesis, the only provably capacity-achieving codes to have been proposed in the open technical literature. This chapter is devoted to describing the principles behind polar coding, a detailed description of their construction, as well as the encoding and decoding algorithms.

The output alphabet Y is considered to be arbitrary. Next, we define two parameters of the channel W that will be particularly useful for the description of polar codes. On the other hand, Z W is an upper bound on the probability of maximum-likelihood ML decision error, when W is used to transmit a 0 or a 1. Both I W and Z W take values in [0, 1]. Intuitively, we expect that when the achievable transmission rate increases, the probability of decision error decreases.

This intuition is confirmed in the following inequalities. Please refer to [23] for the proof of 7. This process consists of two phases: Channel combining is a recursive process where, by using W , we can construct a combined channel WN: The first step of the recursion is the construction of W2: From Fig. Specifically, the recursive transformation process is shown in Fig. Introduction to Polar Codes 7. In the following, the transformation process from two independent copies of a binary-input channel W: It is proven in [23, Prop.

Consider the transformation of a binary-input channel W: Channel Polarization 71 Also, as proven in [23, Prop. Also, from 7. This result shows that the single-input channel transformation operation leads to channel polarization. This can also be observed for the Bhattacharyya parameters of the transformed 2 1 channels in 7.

The results of 7. Also, compared to the N independent copies of W , the preservation of total symmetric capacity and the total reliability improvement are valid for the set of N transformed channels, i.

The polarization result of 7. From 7. All these concepts give an intuitive understanding of the polarization phenomenon. However, the construction of capacity achieving codes by taking advantage of channel polarization is formalized in Theorem 7.

Theorem 7. Specifically, we describe the construction of the encoder, as well as a decoding algorithm referred to as successive cancellation SC. This code is characterized by a generator matrix GN. Then, it follows from 7. The vector uA represents the information vector, i. Also, uAc is the frozen vector, and it is a fixed vector selected arbitrarily. Note that it has not been proven that any particular value of uAc will yield better code performance than any other possible choices, so there are no criteria for its selection.

The vector uAc can be seen as the overhead of the code, and K N is the coding rate. Also, a polar code with the parameters mentioned above is denoted as N, K, A, uAc. In order to determine the size of the sets A and Ac , we take into consideration the result of Theorem 7.

Based on this, as N tends to infinity, the size of the information vector K can be such, that the coding rate K N tends to the symmetric channel capacity I W. Therefore, polar codes are proven to be capacity achieving. Next, we examine how A can be split into A and Ac , in order to ensure that the information vector will be placed in the positions of the most reliable channels. However, the calculation of these parameters is not straightforward. There have been several works in the literature that propose construction methods for polar codes that can provide estimations and approximations for i i I WN or Z WN , see for example [—].

Next, we examine the formulation of the generator matrix GN. To do that, we will express the process described in Section 7. Recall the three components of the transformation process, as outlined in Section 7. These can be expressed in matrix form as follows. For the transformation of sN N 1 into v1 , RN is modeled as a N -by-N transposition matrix that performs the permutation operation of 7.

Taking this into consideration, 2 2 7. Consider that uN N 1 is encoded into a codeword x1 , which is N N transmitted through the channel W , and the receiver gets the channel output y1. This means that, after an estimate for each bit of the information vector is produced, it is considered known in the following iterations of the decoding algorithm.

The functions of 7. Note that the values of the decision functions can be computed recursively by using 7. An Example of Successive Cancellation Decoding Here, we present an example of SC decoding, in order to better illustrate its means of operation. The BSC model is shown in Fig. Consider a polar code 8, 4, A, uAc , i. Therefore, based on 7. Next, we will follow the decoding process through a series of diagrams that demonstrate the operation of the SC decoder, as implemented in [].

First, observe Fig. The received vector y18 is placed on the right side of the diagram, i. Using the information available to us, we attempt to reconstruct the encoding process by performing estimates of the bits at each step, which can be seen as a reverse engineering of the encoding process. Starting at the right side of the diagram, we calculate the channel transition probabilities for the inputs of the four W2 modules, which can be calculated by using 7.

Afterwards, we do the same for the two W4 channels and the W8 channel by using 7. Afterwards, by using 7. Note that, when bits at any point of the diagram are known, either thanks to the frozen bits or the estimates of the previously computed bits, these are considered known and fixed for each subsequent iteration. Note that, in Figs. The complexity of the encoding and decoding process is quantified in [23, Th. Introduction to Polar Codes 0 0 1 0 0 0 1 0.

It has been proven [23, Prop. Proposition 7. Related Work 77 Theorem 7. In addition to the works mentioned above, the performance of polar codes under various assumptions has been investigated in the literature. For instance, many of the results analyzed in this chapter refer to infinite length polar codes. The performance of finite length polar codes has been investigated in [—] under belief propagation BP decoding.

Performance is evaluated in terms of stopping sets, since they contribute to decoding failure, and they play an important role in bit error rate and error performance of the code.

Also, simuation results show that, while finite length polar codes do not perform as well as LDPC codes in terms of error performance, they perform better in terms of error floor. An improved version of BP decoding is employed in order to improve the BER performance of polar codes. In this section, we will outline some of these works. Specifically, polar coding structures have been developed, for which it has been proven that polar codes achieve the secrecy capacity of the wiretap channel [—].

The corresponding channel outputs are denoted by Y and Z. Next, recall the notions of secrecy presented in Section 2. These sets denote the channels whose Bhattacharyya parameters are close to 0 and 1, respectively. Based on all the above, the weak security coding scheme is defined by the following three subsets of [n]. In the encoding process, the channels of R are filled with uniformy random bits that might become available to Eve and are transmitted securely.

The information vector is placed in the channels of A, and the frozen vector is placed in the channels of B. It was proven in [, Th. In order to satisfy the strong security condition of 7. Next, we re-define the sets R, A and B as follows: It has been proven in [, Th. Comparisons with Turbo and LDPC codes have shown significant room for improvement in the available decoding algorithms for polar codes [].

Some research works build upon the SC decoder and propose improved decoder structures. For example, in [], a decoding algorithm was proposed, which considered all the possible decoding paths, i. A pruning process was applied, in order to reduce complexity by keeping only the best decoding paths, and the best overall decoding path was selected. Simulation results showed improvement over the performance of the original SC decoding algorithm.

Two other improved versions of SC decoding were presented in [], i.

Based on these techniques, a new decoding algorithm was proposed, which is referred to as SC hybrid SCH decoding, which can achieve a better trade-off between computational complexity and space complexity.

Also, pruning techniques were applied to avoid unneccessary path searching operations. In [], a SC list decoder with cyclic redundancy check CRC was proposed, which significantly reduced the decoding complexity, compared to the original SC algorithm.

Also, simulation results showed that increasing the size of the list reduces the frame error rate FER , thus improving decoding performance. The suitability of polar codes for data storage applications, taking into consideration the decoding techniques mentione above, has been investigated in [], where it was concluded that polar codes do not exhibit an error floor in the error-rate region of interest.

A legal perspective could fill the silence and bring a little bit of clarity. It would be purposeful to image a hypothetical situation that may arise from S.

Similarly, P. Zimbardo experiment raises some doubts as to whether real police offers legally arrested the experiment participant at their homes sometimes in the presence of curious neighbours before putting them into the assumed prison Frommas a; 94— And if the artist M. Accordingly, who would be responsible, if the plate chips, broken during The Depths, hit the eye of an actor actress or viewer?

Moreover, the sound of a real shot in The Seagull can seriously frighten the more sensitive audience, if not make them deaf. The philosopher Nerijus Milerius was right to observe that by his performances O. A surprisingly similar idea was expressed by aforementioned historian Y. Harari, arguing that the real is only what can be felt. In other words, the fictions of people — money, banks, states, nations, corporations — are not real because they do not feel pain.

According to. During the press conference of the film Antichrist, the actress Charlotte Gainsbourg also spoke about extraordinary scenes of suffering— precisely these scenes and not those, where the actress was naked were the hardest to act for her press conference of the film Antichrist a; 4 min.

Referring back to the question of who would be responsible for errors, harm, or pain within the meaning of criminal responsibility, we would probably fall into the category of the so-called casus accident , where, paradoxically, nobody would be guilty.

However, in terms of discipline or civil responsibility, the standard of proof is lower, and the limits of responsibility are wider. Milgram, and the participant of the experiment, who administered the electroshock, would be found liable.

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Furthermore, it might be considered that the arrest in P. Zimbardo experiment potentially violates at least a few interrelated rights, established in Articles 3 and 8 of the European Convention for the Protection of Human Rights and Fundamental Freedoms: While speaking about the limits of M. It is more likely that under the current standards of protection of human rights, the person, responsible for murder, would not avoid criminal liability and would be convinced, following the general procedure.

Meanwhile, the situation, related with health damage, is not so clear — perhaps, the court of both then and now times would interpret the violent acts of the experiment as permissible, similar to tolerated injuries in a boxing ring or an ice hockey rink. However, the legal perspective is useful not only for hypothetical imagination of possibility of error and interpretation of experimentation limits.

In terms of application of law, the works of art could be considered as the means for prevention of crime and other destructive behaviour. The aforementioned performances could be played for certain marginal groups of audience — prisoners, pupils of socialization centres, for sportsmen, who are constantly facing aggression, or residents of hostels. Selection to play for marginal social groups is in line with the methodology of Brazilian director and human rights advocate 4 It should be noted that having in mind an absurdly playful style of O.

Korsunovas, it is highly doubtful whether the director would seriously consider similar legal issues. It is likely that due to pain measuring he would respond with the words of D. Another old woman poked her head out of a window to look at the one who had broken into pieces, but excessive curiosity made her too fall out of the window, plummet to the ground and break into pieces. Then a third old woman fell out of a window, then a fourth, then a fifth. Charms D.

Old Women Falling Out. Online access: Boal said that imprisoned people are not free in space, but free in time, differently from us, who are free in space, but usually pressed in time. Thus, having in mind that prisoners have plenty of free time, A. Meanwhile O. Korsunovas, as it might be implied, has his own vision of who should play in the performances like The Lower Depths or Hamlet. His selection to play not for certain addressees, but for all viewers, and at the same time, for anyone Bergmann Festival video ; 38—40 min.

The key idea of H. The origins of H. This was analysed by aforementioned philosopher M. Buber, who makes a surprisingly similar conclusion about banality of the evil: Envy or anger is not enough to explain the monstrous act of Cain. Cain even did not know about existence of the act as murder — he was the firstborn and the first, who killed. Thus, the decisive factor in committing a crime was a simple opportunity rather than a motive.

Thus, both the analysed trilogy and the religious themes, examined by the philosophers, discussed in this article, presuppose that a murderer is not only the one, who externally kills another human being, but also the one, who kills a human being in himself. According to H. Arendt and in the words of murderer A. No matter what the source of this blind 5 A.

Boal used theatre as the measure to promote social and political changes. In the Theatre of the Oppressed, the audience becomes active, the viewers analyse and transform the reality, which they live in.

Bauman and L. The struggle between the good and the evil promotes to analyse Hamlet from a theoretical perspective. One of the most obvious moments, referring to the religious themes, is when Hamlet despite the existing opportunity does not kill Claudius while praying because is afraid of God — he does not want that Claudius would go to heaven, while himself — to hell. It is interesting to note than Hamlet continuously doubts and hesitates, and one of the most important reasons of this indecisiveness is of metaphysical nature: The scene of trap or mousetrap is one of the key scenes in the play Hamlet, which also can be understood in a broader sense: In this view, one can turn to St.

The blood of Jesus is bait, and the cross is the mousetrap. Satan believed that he had won when Christ was crucified. However, on Easter morning, the devil realized that he had been deceived Scott-Macnab ; 6—7. A rat in the works of art or folklore may symbolize the devil. For example, L. Donskis notes that in the medieval legend, the charismatic rat-catcher of Hamelin was actually the masked Bauman, Donskis, ; For example, in Shutter Island by M.

In the performance, directed by O. Korsunovas, the boundaries of the aforementioned lake are presented in even a more pronounced manner, as if it was exaggerated, i. In this respect, theological interpretation is close to the Gospel of Judas, found in Egypt in s. It says that Judas was the closest friend, a trustee of Jesus Christ — he was entrusted with a special mission to deceive Satan by pretending to be a traitor, who hands Christ over to be arrested and then murdered.

Several details of The Lower Depths unwittingly refer to the discussed gnostic studies: However, a rhetorical question remains: Thus, in the works of Korsunovas, deception might be used to reveal the truth.

A similar technique is observed in S. In this way, the characters of the film overlap with the actors as individuals, thus, revealing their own fictitiousness Koutsurakis ; For reasons of objectivity, it should be noted that other trilogies or even individual films of L. Dogville , which is technically more similar to the ascetic theatre than the usual film, deserves special attention. Persistently trying to justify and love the people of the town, Grace eventually fails and at the end of the film, upon acquiring unlimited authority, she orders to shoot down all the inhabitants of the town, except for the dog Moses, who, according to her, was the only one with the right to be angry with her because once she took his bone.

The work is described as a social experiment, which seeks to find out how solidarity and common sense mutually beneficial exchanges transform into animosity, punishment and grand revenge Koutsurakis ; It is important to mention the press news, announcing that Dogville was one of the favourite films of the prisoner Anders Breivik. In response to this, L. Breivik to kill people in Utoya, he is sorry for this, but the film itself was intended to educate the public by giving it the opportunity to separate from revenge rather than encourage violence The Hollywood Reporter, It seems that the most obvious metaphor for utopia in the trilogy in question is the Antichrist Eden — the forest cabin.

The other utopian element is the planet Melancholia, which is sentimentally fetishized before colliding with the Earth it is especially true in case of depressive Justine , attributing to it the symbols of longing, expectation and faith.

According to L. It tells the story of a couple, trying to survive their grief after their son died later, it turns out that the woman intentionally allowed their son to die without noticing how he approaches the opened window. It seems that the man successfully copes with the stressful situation, while the woman suffers from anxiety and fear attacks — she is afraid of nature, believing that evil comes from nature, that evil comes from all women, who are the tool of the devil.

On the other hand, perhaps, the man really did not understand the inner world of his wife, and instead of helping her, he only aggravated her misery, made her angry, and eventually became destructive himself.

However, in my opinion, this interpretation is limited. It rather seems that the devil or evil has really incarnated itself in the woman later, it also succeeded to incarnate itself in the man , and when the man showed the mirror — the photo of their child with shoes on the wrong feet — to devil Her , the women became furious and attacked the man. Precisely this moment resembles the Shakespeare scene, where L. In this way, the rational origin of the man appeared as no less evil than the unexplainable fears of the woman — taking on a form of moral blindness at the end of the film, when there was no particular reason to kill the woman it is doubtful whether the man was still at risk of death , but she was killed.

The film seems to warn that an attempt to curtail aggression by means of artistic, scientific or therapeutic means can go far beyond what a person can imagine. In general, the Danish director does not tend to emphasize the results: Melancholia tells the story of two sisters — Justine and Claire — one of whom is preparing to get married, and another one organizes the wedding.

Justine is sick, and it is hard for her to hide this from her future husband. Furthermore, Justine finds it hard to eat, wash, and do any body movements.

Over time, frustration overwhelms her so that she becomes aggressive even to her beloved horse. The end of the film coincides with the end of the world — the planet Melancholia collides with the Earth, making a macabre death dance.

Justine remains stoically calm in the face of apocalypse, while Claire finds it hard to make it up. This question is visually responded by Claire, who seems to be able to understand and accept the end of everything, but her maternal nature cannot accept that her son Leo will also die.

Referring back to the recurring Korsunovas-like themes, the child, as the symbol of purity and hope, is not so obvious in Hamlet, The Lower Depths and The Seagull, however, at the end of Cathedral, the child acquires precisely that sense of hope and faith, which L. On one of the most painful scenes, Claire and the housekeeper are trying to put Justine in the bath, but in vain — Justine is not even able to put her leg in the water.

After that, they attempt to attract Justine at the dinner table by making her a favourite meat steak, but Justine simply shouts out that food tastes ash. This place requires deeper examination, since it strangely reminds of the previously discussed theological themes. As it has already been mentioned, the devil was deceived by seducing him with the blood of Christ.

However, in L. Thus, it turns out that Justine, from the theological perspective in question, was a tool of the devil in the whole film, a warning to mankind that everything will end quickly, that it is not worth the efforts, and that life itself is evil. This plotting technique is based on the principle of irony and contrast: This is an art — and this is where the strength of L. The film ends in an absurdly logical way: Seligman tries to have intercourse with the sleeping Joe saying himself that it is nothing bad about it, since she has done it with thousands of men.

This part begins with a broken mirror and Joe, looking at her image. She also sees her injured genitalia on the mirror and a week-old baby on the computer screen, whom she avoids looking at and demands abortion.

The doctor refuses to perform surgery without first consulting a psychologist, but Joe does not want to talk to a psychologist and decides to abort at home. The moment when Joe kills her baby is probably the most shocking thing in the whole movie. Having done everything with her own hands and knowing how the abortion is really performed, she seems disarm Seligman like an inexperienced child, who tells about the right to abortion as the student, who have read too many brainy books.

The naked brutality, seen during this surgery, echoes on the last scene, where Joe kills one more person, i. The seventh part of the film ends with manifesto of nymphomaniac, where Joe laughs at addiction therapy, proudly declaring that she cannot be compared with other female patients and with the therapist, that she loves herself, her genital organs, and her dirty scary lust.

Conclusions and recommendations While paraphrasing J. Gilligan, it might be argued that there is a lot of violence in the play of Hamlet, however, there is no doubt about the depth of sufferings. Thus, it would probably not be desirable to reproduce the relevant violence in reality. Consequently, the performance or the film, where violence is played in a real, persuasive, and vital situation, should discourage from being violent.

When there is no de facto acting. On the other hand, from the historical-philosophical point of view, according to Y. Harari, humanity is constantly acting with the help of its imagination — it essentially defines and separates people from remaining animals: In this sense, theatre and cinema lose their autonomy.

Thus, theatre or cinema is a kind of a more sincere, archetypal fiction. This insight leads to a reasonable idea — to combine one fiction with another, for example, combine theatre with criminological education, focusing on specific addressees.

Performances, where violence is acted, could be played to the targeted audiences, tended to destructive behaviour: Within the meaning of the Criminal Code of the Republic of Lithuania, the target group is defined even more specifically — inter alia the persons, imposed with the penal measure, established in clause 9 of paragraph 2 of article 27, i.

After performance, the audience together with the actors and director, could discuss the characters, their actions and the work itself. Accordingly, it should be possible to avoid what might have happened with Dogville and A.

Breivik, or with other films that ostensibly promote aggression: At the same time, it should be noted that despite being natural, the proposed idea should be implemented with great caution: Accordingly, some legal issued would emerge, if acted violence turned into real aggression. So, what figurative price would be paid by the artists, in order the acted violence and the resulting pain becomes vital and real?

On the other hand, one should not speak about the direct or figurative price, but paraphrase the question in the way similar to the director A. Tarkovsky L. Arendt, Hannah. Augustinas, Aurelijus. Bauman, Zygmund; Donskis, Leonidas. Takusis blogis. Versus aureus. Birrel, Susan; Donnelly, Peter. Sport and Modern Social Theorists.

Basinstoke, UK: Palgrave Macmillan. Boal, Augusto. Games for Actors and Non-actors. Buber, Martin. Good and Evil. New York: Charms, Daniil. Demaria, Cristina. Provocation as Art 2: Fine, Gary Alan; Manning, Philip. Blackwell Reference Online.

Frommas, Erichas. I tomas. II tomas. Gilligan, James. Smurto prevencija. Goffman, Erving. Gorkis, Maksimas. Apsakymai, dramos. Harari, Yuval. Kitos knygos. The Hollywood Reporter. Koutsourakis, Angelos. Daktaro disertacija, University of Sussex. Maceina, Antanas. Didysis inkvizitorius. Marsh, Cynthia. Meyer, Marvin. The Gospel of Judas. Second edition. Washington, DC: National Geographic Society. Milgram, Stanley. Provocation as art No 2: Scott-Macnab, David.Hurtig Oskaras Polska.

Anot K. Alexandros Apostolos Boulogeorgos. Obok kursow instruktorskich i spoiecznych Instytut przeprowadzal takze kursy or- ganizacyjno-propagandowe. This was an early form of a substitution cipher, since each letter of the message was replaced with a different one by using a specific, easily reversible rule.