Data encryption of optical fibre communication using pseudo-random spatial light modulation

1. Introduction

Optical communication systems have become a common medium of transferring information due to great efficiency, as well as high accessibility. They found variety of applications for personal, commercial and military use. Due to great popularity and variety of applications, it is important that optical network is properly secured. Security refers to all the layers [1] of the network. Therefore, providing the highest level of security of all the layers is required. A very common and risky practice is employing security procedures at higher levels of the network without securing the lowest ones. In order to build a complex solution, it is required to secure the physical layer of an optical system against various kinds of dangers. The physical layer of a network based on optical fibres is vulnerable to a variety of attacks [2], ranging from attacks on physical infrastructure, interception to eavesdropping.

Because of high and constantly increasing data rates, achieving high level of optical networks’ security is very challenging as all the mechanisms, required to operate at real-time, have to process significant amount of data.

By now, a variety of kinds of techniques for information encryption, both hardware and software are known. Software techniques are converting the original data by computer processing. In the case of hardware techniques the hardware unit performs encryption that uses specific physical phenomenon to replace the original data. Several approaches have been proposed including quantum cryptography [3,4], secure chaotic communications [5,6], and optical code division multiple access (OCDMA) [7,8]. All of these techniques increase security level but also have limitations. Quantum communication systems are considered as low-speed and expensive, chaotic communication is very challenging in practical applications [9] and OCDMA systems are very demanding from technological point of view [10].

Our research efforts have focused on improving security of the optical network low level by applying hardware conversion of transmitted information. The paper presents a method of encryption of data transmitted through an optical fibre at the wavelength of 1550 nm. However, the presented method may be used for other wavelengths, as well. We propose to spatially modulate input light pulses in order to encrypt the transmitted information. The method uses a spatial light modulator to convert light pulses into pseudo-random binary patterns. The input data are modulated according to the pattern. Both processes of data encryption and decryption are based on the Compressed Sensing (CS) framework which is known as a good and reliable encryption method. The presented method does not require to introduce any changes in the telecommunication line.

The paper presents theoretical fundamentals of encryption and principles of encryptor’s operation in Sect. II. Decryption process is described in Sect. III. Results of numerical analysis are shown in Sect. IV.

2. Theory

2.1. Encryption

Encryption is often defined as a process of encoding information in such a way that only authorized parties can read it [11]. This raises the important implication that encryption does not of itself prevent interception. The presented method does not strengthen physical resistance against interception or eaves-dropping.

Generally, encryption techniques are usually based on a particular encryption key. The encryption key plays a role of a pattern used to transform the information. It is not likely to restore the original data from the encrypted data without knowing the key. The presented approach follows this practice, however it uses several encryption keys in various sequences instead of using a single key. The key is reflected in current configuration of a spatial light modulator which converts light pulses into an encrypted message.

The presented encryption method is performed by optical conversion of an optical signal in which each pulse represents a binary value. The optical conversion can be treated as performing a series of mathematical operations (operations processing optical laser pulse). In practice, mathematical operations are executed by an optical element that converts the light pulse – a spatial light modulator (SLM) [12,13]. Brief description of the encryption process is shown in Fig. 1.

Fig. 1

Block diagram of the encryptor

Figure 1 shows a block diagram of the encryption process. The encryption process starts with generating the data. In our approach we do not intend to change the original structure of telecommunication system, therefore the method uses laser to generate light pulses. The original data are typically generated in the form of laser pulses forming a string of binary symbols. Information we want to send is read by N_s-bit word buffer, which gathers subsequent packages of N_s-bits of the original data.

After reading the information, the laser generates a single pulse which uniformly illuminates a spatial light modulator (SLM). Main difference between regular telecommunication systems is the mode of transmitting information. Entire information in form of a bit string is divided into N_s-bit words in order to send word after word, in contrast to sending bit-by--bit. The laser power is modulated according to the value of the N_s-bit word. For example, laser power can be set to an upper limit (i.e., 100% of the nominal power) for a word consisting only of binary ‘1’ and at the lower limit (i.e., 0%, 1%, 10%, 25% or 50% of the nominal power) for a word consisting only of binary ‘0’. The remaining words correspond to a value between the lower and upper limits, depending on the word value.

While a laser pulse is illuminating the SLM, the modulator is set according to the encryption key (an array of binary values). The spatial light modulator consists of a sufficient number of cells (at least N_s), where each cell can be controlled separately. In order to reflect binary values on the SLM, each individual cell of the modulator can be set in one of two states – transmit light into the optical fibre or do not pass/guide in other direction. As an effect, the amount of light introduced to the fibre depends on the SLM configured according to the encryption key.

In order to encrypt the N_s-bits of the original data, the encryption key has to be changed M-times (where N s ≥ M ) while M pulses need to be generated.

During the transmission of these M pulses a buffer reads bits of the word to be encrypted. The encryption key is provided by an encryption driver which also controls the SLM. The light beam transmitted by the SLM is focused on the second beam shaping element and introduced to the optical fibre which transmits the encrypted data to the receiver. The receiver reads and collects information sent through the fibre. Since a light pulse introduced into the fibre has modulated amplitude, in order to decrypt the information, amplitude of a received signal is required. The received signal can be decrypted according to the input conditions. We assume that the encryption keys can be the same for all words, or may vary for consecutive words.

2.2. Physical model

The paper presents the method which may be applied in several different ways depending on the communication link architecture. We assume to apply the method for optical communication systems based on multi-fibre cables, as well as single-fibres. The main components necessary for the method to operate are presented in Fig. 1. However, the configuration may vary between particular realizations.

The basic configuration is intended to be applied with single-fibres. The SLM which converts the original data can be realized in the form of an array of micro-mirrors (digital micro-mirror device – DMD) or an array of liquid crystals cells.

The method was initially tested using an array of polarizing liquid crystal cells operating at the wavelength of 1550 nm. The modulator (SLM) consists of a layer of molecules aligned between two transparent electrodes, and two polarizing filters (parallel and perpendicular), the axes of transmission of which are (in most of the cases) perpendicular to each other. The SLM has the size of 4 by 4 cells. The array has specific alignment of the contact electrodes that allows to control each single cell of the array separately. The cells have wide spectral range and the value of transmission at the wavelength of 1550 nm is 41.3%. In order to maximize the efficiency of light modulation, the array will be optimized for the specific wavelength. Therefore, another liquid crystal array, optimized for the wavelength of 1550 nm is developed.

The SLM used for the initial experiments is a twisted nematic liquid crystal array. The twisted nematic effect is based on the precisely controlled realignment of liquid crystal molecules between different ordered molecular configurations under the action of an applied electric field [14]. In this kind of device, before an electric field is applied, the orientation of the liquid-crystal molecules is determined by the alignment of electrodes. By controlling voltage applied across the liquid crystal layer in each cell, light can pass through in varying amounts, thus constituting different levels of gray. The method we propose is most effective when each pixel represents one of two binary states – ‘0’ or ‘1’ which correspond to no transmission and maximum transmission of each cell.

Without liquid crystal between the polarizing filters, light passing through the first filter would be blocked by the second (crossed) polarizer. As an effect each individual pixel of the array blocks the radiation or transmits it to the fibre. Therefore, the amount of light introduced to the fibre depends on the current configuration of the liquid crystal cells. SLM modulates the amplitude of the laser pulse according to the encryption key as presented in Fig. 2.

Fig. 2

Diagram of the encryption process

The amplitude of a modulated pulse is given the following equation

(1)Im1 = I0⋅μp⋅np⋅cp,

where I₀ is the amplitude of the laser pulse illuminating the array of liquid crystals, μ_p is the attenuation introduced by the single cell of the spatial light modulator, n_p is the number of pixels transmitting light and c_p is the fraction of the entire SLM transmitting light.

The output amplitude at the end of the fibre is following

(2)Im = I0⋅μp⋅np⋅cp⋅μf(l) =  Im1⋅μf(l).

Where μ_f (l) is the attenuation introduced by the fibre over the optical path. The modulation of the amplitude is schematically presented in Fig. 3. The initial amplitude of the signal I₀ is modulated by the SLM (I_m1) and decreases as a result of propagation in the optical fiber (I_m).

Fig. 3

Modulation of a signal amplitude

The performance of the encryptor depends on several factors. One of the most influential factors is performance of the SLM. Dimensions of a single liquid crystal cell, number of cells in an array and switching time of a single cell is crucial for the performance of hardware part of the encryptor. The performance of the decryption process mainly depends on the algorithm applied for the decryption.

3. Mathematical fundamentals

Decryption is the reverse process to encryption, and its effect is reconstruction of original data from encrypted data. The method we present is Compressed Sensing based, however we do intend to encrypt the signal instead of compressing it. In this section a brief description of the mathematical fundamentals will be presented and described.

The Compressed Sensing (CS) was initially proposed by Emmanuel Candès, Terence Tao, and David Donoho [15–18] in 2004 as a signal processing technique for efficient signal acquisition and reconstruction by finding solutions to underdetermined linear systems. The CS does not follow the Nyquist-Shannon sampling theorem which specifies that in order to avoid losing information when capturing a signal, one must sample at least two times faster than the signal bandwidth [19]. This method employs non-adaptive linear projections that preserve the structure of the signal. The original signal is then reconstructed from these projections using an optimization process. CS is based on two ideas: natural signals can be compressed in certain basis and the compressed signal can be reconstructed from small number of linear non-adaptive random measurements. The signal can be reconstructed perfectly or with small or zero errors [20].

The CS approach is introduced into presented encryption method. The theory of compressed sensing was basically described in Refs. 20–23. We consider a bit stream x as a real-valued, one dimensional, discrete signal. The signal is an N × 1 column vector in ℝ^N with elements n = 1, 2, …, N. The idea of a compressive signal means that any signal can be compressed in certain basis of N × 1 vectors {Ψi}i=1N We assume the basis is orthonormal in the basis ψ = [ψ₁|ψ₂|ψ₃|…|ψ_N], and the signal (bit stream) can be expressed as

where s is the N × 1 column vector of weighting coefficients si=〈x, Ψi〉= ΨiT x (T denotes transposition). In this terminology, s is the representation of x in the domain. Another assumption is that the signal x is K-sparse. It means that only K coefficients of s_i are nonzero and (N – K) are zero.

In CS, the measurement process generates M < N samples and collection of vectors {ϕi}j=1M. In the presented method, the output signal is described as y_i = ⟨x, ϕ_j⟩, and is an M × 1 vector. The representation of the y in the certain basis can be presented in the following form

where y denotes the obtained measurement values M × 1 vector, is a M × N measurement matrix (encryption key), x is a real-value, discrete time signal with finite dimension N, s the signal (key) to be reconstructed, and the signal sparse representation.

The matrix is non-adaptive which means that it does not depend on the signal x. However, it has to fulfill two conditions. The first one is sparsity which requires the signal to be sparse in some domain. The second one is the incoherence between the sensing matrix and the sparse operator that is applied through the isometric property which is sufficient for sparse signals

where y, are the column vector of and, respectively, and N is the length of the column vector.

In order to recover the signal, the reconstruction algorithm must take the input arguments. The list of the arguments contains the vector y, the sensing matrix and the basis . An ideal recovery is achievable from a small number of measurements if both, the sensing matrix and the sparse operator, are highly uncorrelated, i.e.,

The signal x can be recovered (decrypted) using various algorithms, one of which is the l₁ norm reconstruction. In order to recover x the following equation should be solved

The minimization can be practically realized using, e.g., the conjugate gradient algorithm [24] or gradient projection method [25–28], or Orthogonal Matching Pursuit (OMP) [29–31]. The algorithms differ in efficiency and speed.

4. Experiments

This section illustrates the results of sample signals’ recovery. It also presents that the theoretical considerations proposed in the previous section are correct. We use the terminology recovery in order to refer to decrypting and reconstructing the original signal from the measurement data. In order to recover the original data, the encryption key is required to be available to the recipient.

The decryption process is required to provide us with the exactly the same data as original. The CS method was basically invented to acquire less data instead of compressing after acquisition process. However, it is possible to recover the original signal perfectly. The case of a perfect signal recovery is presented in Fig. 4.

Fig. 4

Reconstruction of a signal (a) original signal x with 50 samples and its (b) reconstruction x’

The simulation of a perfect recovery was not aimed at compression. In order to perfectly reconstruct a 50-bit signal, 50 measurement samples should be acquired.

The effectiveness of signal reconstruction is determined by number of iterations and signal sparsity. The number of iterations refers to the number of signal measurements – it means that the signal can be reconstructed from incomplete data with some probability. The plot presented in Fig. 5 shows what percentage of signals was recovered correctly as a function of the number of measurements and sparsity. Each curve in the plot represents the different sparsity level K. Theoretical assumptions are fulfilled while the results indicate that more measurements are necessary to guarantee signal recovery when the number of nonzero components increases.

Fig. 5

Probability of exact reconstruction for various number of iterations

The proposed method and architecture were simulated in order to verify their validity. In order to recover the original signal x, the measurement data y together with encryption matrix are required. Due to the eventuality to eavesdrop the measurement data, the encryption key should guarantee the security. We assume, that during the attack, an attacker knows everything except the encryption key. The key may be obtained by a brute-force attack, therefore in order to resist this type of attack, the encryption key is required to be sufficiently large. The size of the key space defines computational requirements for the brute-force attack.

For simulation purposes we performed several numerical experiments. The test signal x used to simulate the encryption process had 1 Mb and was divided into 64-bit messages. In order to encrypt that signal the SLM with 64 cells is required. We used the same key to encrypt every message. For simulation purposes we generated the encryption key which consisted of 64 pseudo-random arrays (sub-keys) of size 8 × 8 cells (64 cells). Each cell represents one bit of information. This gives a 4096-bit key which requires 2⁴⁰⁹⁶ combinations to guess it. Taking into account currently used processing units, the 4096-bit key can provide sufficient security level against brute force attacks. However, the method is flexible and allows to change the key size.

Each single measurement of the output signal has its sub-key assigned, as presented in Fig. 6. It is highly important to assign measured bits with the encryption sub-key in a proper order, because it is not possible to recover the signal properly when the order of sub-keys is changed. This introduces another level of security. If an attacker knows the order of sub-keys, then he may want to guess 64-bit sub-keys instead of the entire key at once. It should also be outlined that the signal is possible to be recovered only when the number of bits of measured data and original data are the same. We consider the attack to require very high computational complexity which makes it practically infeasible. However, further studies in this field are required to define its constraints.

Fig. 6

Assignment of sub-keys and measurement data.

There is a great number of reconstruction algorithms to enumerate here. However, the results of our investigations show that OMP and gradient algorithms are reliable. Still, there is a room for an improvement of performance in the field of computation time and required storage space.

During the reconstruction process, we used the OMP algorithm. All the algorithms and results reported here are based on implementation using MATLAB environment. All the routines have been implemented as without any bias towards encryption and decryption speed.

We employed the algorithm to reconstruct 15625 messages. Due to every 64-bit message was encrypted with the same key, the reconstruction process is sequential and recurrent. During the experiments all the messages were decrypted/reconstructed with the same key with correct, as well as incorrect order of sub-keys. The reconstructed data was compared with a cipher text in order to check correctness of the reconstruction. The experiment showed that when using correct ordered sub-keys, all of the messages were reconstructed perfectly. The swap of two sub-keys resulted with incorrect reconstruction. The mean number of changed bits was 22 which means about 34%.

During the experiments, we focused on reconstruction efficiency without investigating time consumption of the overall process. Computation time, as well as storage space, are the field for improvement and further investigations.

5. Conclusions

We proposed the method for optical encryption of fiber transmission. The presented method can be applied with various kinds of architectures. It takes benefit of hardware conversion of the optical wave using spatial modulation and pseudo random encryption keys. The linear combination of light pulses with pseudo-random patterns provides required encryption performance. The method uses multiple encryption keys to spatially modulate the light beam. The decryption process is based on Compressed Sensing. The method combines computational decompression with possible optical reduction of data amount. The theoretical and empirical work in this paper demonstrates that this method is an effective solution for data encryption. We considered the attack scheme that consisted of eavesdropping and brute force attack to estimate the encryption key. While the first part of the scheme is possible, the second part, depending on the key size may be computationally infeasible. The simulation results proved the required security level.