Gb/s one-time-pad data encryption with synchronized ...

PRE-PRINT VERSION – J. LIGHTWAVE TECHNOLOGY 2016

Gb/s one-time-pad data encryption with synchronized chaos-based true random bit generators Apostolos Argyris, Evangelos Pikasis and Dimitris Syvridis

Abstract— Ultrafast physical random bit generators based on broadband optical signals have been presented lately at astounding speeds. Some of the most popular mechanisms to obtain such random sequences are through signals that emerge from the coherence collapse operation of semiconductor lasers or from the photodetection signal beating of amplified spontaneous emission optical noise. Especially in the first case, the potential of chaotic signals to synchronize offers a great potential for secure communications. In this work we combine two unique properties of semiconductor lasers that operate at a chaotic regime: their potential to become highly synchronized when optically coupled through appropriate configurations and their ability to seed ultrafast true random bit generators. The concurrent fulfillment of both conditions is shown in this work and is used to demonstrate experimentally the one-time-pad encryption communication protocol. We report an error-free operation of such an encryption system, exceeding for the first time the Gb/s rate. Forward error correction coding is applied on the encryption scheme, in order to drastically reduce the errors of the synchronized true random bit sequences and optimize the decoding performance of the system, while securing the distribution of the random seed. Index Terms— Semiconductor lasers, chaos, synchronization, true random number generator, one-time-pad encryption.

I. INTRODUCTION andom digital bit sequence generators have been recognized as significant building blocks in various security-oriented applications, as well as in numerical computations and simulations. Albeit computational algorithmic approaches can offer verified digital randomness

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The current work was supported by Greek General Secretariat for Research and Technology under the funding research action "ARISTEIA II" and the project "CONECT-4750" and was performed at the Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Panepistimiopolis, Ilisia, 15784, Greece. Apostolos Argyris is now with the Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (UIB-CSIC), Campus Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain (corresponding author’s e-mail: [email protected]). Evangelos Pikasis is now with the Institute for Digital Communications, School of Engineering, University of Edinburgh, EH9 3JL, UK. Dimitris Syvridis is with the Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Panepistimiopolis, Ilisia, 15784, Greece. Copyright (c) 2016 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected].

efficiently, only physical generators can be actually random with unclonable outputs. Truly random bit sequences (TRBSs) have been principally useful for secure digital communications and traditionally a prerequisite in the establishment of the undisputed one-time-pad (OTP) cryptographic protocol [1]. Nonetheless, the conditional requirements for the application of this protocol makes it deficient to secure transmission of large data volumes at high bit rates. Its implementation through the numerous quantum key distribution (QKD) approaches [2-14], albeit convincingly securing the key and data transmission, has been demonstrated at low rates up to the Mb/s range. A few years ago, the demonstration of semiconductor lasers (SLs) as sources of TRBS at Gb/s rates through their broadband, chaotic, optical emission was radical [15]. Since then, various architectures based on chaotic SLs [16-22] or optical noise sources [23-26] have evolved the random key generation at astonishing rates up to hundreds of Gb/s [18,22,25,26]. These two TRBS generation methodologies can offer various advantages, depending on the applications that may be used. A unique property that chaosbased TRBS generators can offer is their potential to synchronize under optimized hardware, coupling topologies and operational conditions. The concept of synchronization of two TRBS generators over a public channel using a classical mechanism and generation of identical keys has been theoretically studied in [27]. Lately, by exploiting nonconventional approaches with the use of SLs, secure key exchange has been shown through information theory concepts and also at low bit rates [28,29]. These works show the prospective of using statistical and not single-photon properties of light to surpass the limitations for securing modern communication lines at Gb/s rates. In this experimental work we demonstrate for the first time the one-time-pad encryption protocol between two communicating users at Gb/s rates, by exploiting chaos-based synchronized TRBSs. The users hold identical hardware equipment in order to generate highly-correlated chaotic analog signals through an optical channel. These signals are used locally by each user to seed individual TRBSs, which emerge after analog to digital (A/D) conversion and postprocessing. The latter are processes that induce errors in the synchronization of the digital sequences. Forward error correction (FEC) encoding is applied in these sequences, which are then used to encrypt / decrypt data sharing in a different communicating channel. The zero-lag synchronization mechanism [30] of the chaotic signals is not

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by definition a key-exchange protocol [31]. It is just the mechanism that provides the seed to the independently generated keys. The secure distribution of the chaotic seed is evaluated in this work by testing two eavesdropping scenarios. However, further considerations from QKD of information reconciliation and privacy amplification [32-34] could enhance the investigated protocol in terms of security.

transmission distances up to 100m the supported communication can be certainly at multi-Gb/s rates.

II. SYSTEM CONFIGURATION The proposed concept of the one-time-pad encryption system is analytically described in this work for two communicating users. These users access synchronized TRBSs for the pad (key) that emerge from the photodetected, chaotic, analog signals emitted by SLs and seed the TRBS generators, as shown in the experimental topology of Fig. 1. The generation and synchronization of these chaotic signals emerges from a mutual optical coupling system of SLs under strict operating conditions, as demonstrated by the recent authors’ work in [35]. In that system, an exceptional level of synchronization between two users has been achieved, with cross-correlation (CC) value of 0.9961, between chaotic signals of 5 GHz bandwidth. As shown in that analysis, the dependence of the CC level on signal bandwidth is significant [35]. This synchronized system of analog broadband signals sets a solid basis for preserving the synchronization after digitization of the signals. In this context, digitization should happen in a way that the emerging binary sequences conform to the criteria of randomness [36], in order to claim synchronized TRBSs. This is ensured by the post-processing (PP) methodology applied, as discussed later. The implementation of the OTP-encrypted communication system is presented in Fig. 2. User #1 and #2 get their encryption pads from the TRBS generators, which are seeded by the optical synchronization layer. User #1 encodes the data that wishes to send to user #2, with the appropriate FEC convolutional code and then applies a XOR operation with its locally generated TRBS. The encrypted data after transmission – in our work is an Ethernet electrical line of 10m – reaches user #2, where the decoding process takes place. User’s #2 locally generated TRBS – synchronized to the one at user’s #1 premises – participates also to a XOR operation in order to provide the initially encoded data to the decoder and obtain finally the initial data. Similarly, the opposite communication from user #2 to user #1 follows the same methodology and is supported by the same TRBS generators. The use of FEC coding minimizes (or even eliminates) synchronization errors that origin from the imperfect synchronization between analog chaotic signals and the digitization process. In the presented implementation of Fig. 2, it becomes clear that two independent links between users are needed. The first is a single mode fiber optical link (as shown in Fig. 1) and supports the transmission of chaotic signals in their analog form, generated by the bidirectional interaction of the SLs. This link is capable of supporting signals with large bandwidth; in our case the full spectral width of the chaotic signals is measured to be 6.8GHz at -10dB from maximum. The second link supports the encrypted data transmission and is an Ethernet cable. This electrical channel can support lower bandwidth signals in their digital form. However, for short

FIG. 1. Experimental setup of the fiber optic system that is analytically presented in [35] and used to seed the synchronized TRBSs generation between two users. POL: polarization controller, 1x2: optical splitter, ISO: optical isolator, PD: 10GHz photoreceiver, PP: post-processing stage including analog-to-digital convertion, EDFA: erbium-doped fiber amplifier, OF: optical filter, ATT: optical attenuator, PM: inline power monitor. Single (black) line connections are fiber-optic links. Double (red) line connections are electrical links.

FIG. 2. One-time-pad encryption system between two users. Both users access synchronized TRBSs, seeded by a backbone optical synchronization layer as presented in fig. 1.

FIG. 3. Histograms of user's #1 photodetected analog chaotic signal of (a) 5GHz bandwidth and (b) 8.5GHz bandwidth. Amplitude bins are expressed in Volts. The histograms emerge from timeseries of 524288 samples, at 40GSa/s rate. Equivalent histograms characterize the statistical properties of user's #2 analog emitted signals.

III. TRUE RANDOM BIT GENERATION METHODOLOGY The statistical properties of the synchronized chaotic signals are a primary indicator for their potential to seed TRBSs. It has been shown in [35] that there is a significant dependence on signals’ bandwidth. For the analog signals that we employ

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here and for the case of 5GHz signal bandwidth, the statistical properties fit suitably to the normal distribution profile. In Fig.’s 3a histogram, the adjusted R2 fitting value is over 0.995. On the contrary, larger signal bandwidths – e.g. at 8.5GHz – show significant deviation from the normal distribution statistics making them insufficient candidates for seeding a random sequence (Fig. 3a). A/D conversion of the above signals leads to digital streams that should fulfill the criteria of randomness in order to be used as random key generators. Digitization can be performed by a single-bit or a multi-bit representation of the A/D conversion. Here we examine the single-bit conversion by implementing a comparator that sets a binary decision threshold level around the median value of the analog signal. A fine tuning around the median voltage value – measured from -300μV to 600μV – is needed to provide each signal with the desired statistics that will pass the randomness tests. In our study, A/D conversion is performed through the oscilloscope's channels (model Agilent DSO81204B) that simultaneously monitor each user’s chaotic signal at a sampling rate of 40GSa/s. Sequentially to digital conversion, the TRBS generator mandates additional digital signal processing steps towards the desired route to randomness. The emitted chaotic signals inherently exhibit autocorrelation (AC) patterns related to characteristic times of the optical topology. These patterns are transferred after digitization to the digital sequence, causing annihilation of randomness. Time-delay concealment methods have been proposed in literature to eliminate this correlation [37-42]. Here, the use of a long transmission cavity in the bidirectionally-coupled optical system as presented in [35] shifts all high order AC-peaks beyond the single acquisition duration. Thus, no temporal signatures of cavity modes appear. Nevertheless, when studying the zero AC peak profile, significant correlation of neighboring samples is revealed. Annihilation of this type of correlation can be achieved by down sampling the recorded analog signals. This process, shown in Fig. 4a, considers only one out of every N samples and feeds the digital sequence. The higher the down sampling factor N is, the lower the bit generation rate will be, equal to R/N (where R=40Gb/s for the 1-bit digitization). Increasing values of N are considered and the emerging bit streams are evaluated in terms of randomness. As shown in Fig. 4b, de-correlation of samples ultimately leads to verified randomness as evaluated by NIST tests [36] (first maximum at N=14). For this N value, all 15 NIST tests pass the randomness criteria, as summarized in table I. 1000 sequences of 1Mb are evaluated with significance level a = 0.01 and desirable uniformity P-value should be larger than 0.0001, for successful tests. The proportion for success ratio should be in the range of 0.99 ± 0.0094392. Consequently, verified TRBSs are generated at bit rates equal to R/N ≈ 2.857Gb/s and this random key rate is available to be used in the OTP encryption protocol. If lower data bitrates are to be encrypted, only part of the generated TRBS can be used.

FIG. 4. (a) Digitization process of the analog chaotic signals, using a singlebit decision threshold and down sampling post-processing. The concept is shown here for a own sampling factor equal to N=3. (b) Number of the 15 NIST tests passed vs. the down sampling factor N. The variation bars indicate the lowest and highest number of NIST tests passed after testing the required repetitions of 1Mb sequences [36]. All tests must be successful in order to verify randomness. TABLE I RESULTS OF STATISTICAL NIST TESTS WITH a=0.01 AND BY USING A DOWN SAMPLING FACTOR OF N =14. Statistical test Tail probability Success ratio (P-value) Frequency Block frequency Runs Longest runs Rank DFT Non-overlapping template Overlapping template Universal Linear complexity Serial Approximate entropy Cumulative sum Random excursions Random excursions variant

0.5113 0.5459 0.871 0.2449 0.2991 0.6887 0.6213 0.65 0.8891 0.449 0.4521 0.5302 0.3799 0.5883 0.7122

0.991 0.991 0.988 0.991 0.986 0.987 0.985 0.984 0.986 0.991 0.992 0.990 0.988 0.983 0.983

IV. ONE-TIME-PAD ENCRYPTION AND BIT-ERROR-RATE PERFORMANCE

The synchronization error of the users’ analog signals at the optical synchronization level is directly translated as an error rate of the generated digital keys. The larger the CC value between two analog signals is, the smaller the error rate between the two emerging TRBSs will be. When considering

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the communication protocol presented in Fig. 2, but in absence of any convolutional code, the error rate of the key synchronization is measured to be too high for communication purposes (Fig. 5, black rectangles). For the maximum achieved CC value (0.9961) in the optical synchronization layer [35], the corresponding digital biterror-rate (BER) is as high as 4.6·10-2. Such a BER value indicates a significant mismatch in the digital key synchrony, regardless the remarkable level of analog signal correlation, and ultimately leads to a poor decryption performance. The introduction of an error correction stage changes dramatically the BER response. We employ FEC with a Viterbi encoder, at two different redundant code rates: 1/2 and 3/8 [43,44]. These rates express the ratio of actual data bits in a correcting scheme. Finally, we relate the improved BER with the level of synchrony of the available analog signals. For CC=0.9961, the FEC 1/2 code rate improves the communication performance, characterized by a BER value of 5·10-5 (Fig. 5, red circles). When considering the FEC 3/8 code rate, with an excess of redundant bits, data decoding becomes error free, after evaluating decrypted strings of 109 bits (Fig. 5, blue triangles).

FIG. 5. Interpretation of chaotic analog signals’ cross-correlation in terms of bit error rate of the synchronized TRBSs.

We subsequently exploit the error-free performance of the FEC 3/8 encoder in the OTP-encrypted communication platform. We generate random digital data at a personal computer at a bit rate of 2.8Gb/s. The encoded data stream is then ciphered with part of the generated TRBSs, at an equal rate (slightly lower than the one available at 2.857Gb/s), for one-to-one bit encryption. At the decoding stage, each user has to temporally align the generated key (TRBS) with the one used at the encoding stage of the counterpart user. This delay is determined by the delays induced by the encryption process (XOR operation) and the transmission time. In our implementation, each user compensates this delay at the optical layer, by using fiber transmission spools of appropriate length and tunable optical delay lines. Specifically, fiber spools and fiber patch-cords are used to compensate the delay at sub-ns level, while tunable optical delay lines (General Photonics model VDL-001) with 1200ps tuning range and 0.2ps resolution are used for fine tuning the temporal alignment of the digital samples. The tuning delay resolution is essential to be much shorter than the sampling duration of 25ps (40GSa/s) for efficient time alignment. In our case, the tuning resolution is over two orders of

magnitude. By scanning the time delay of the optical signal that is used at one user’s decoder, the BER between the TRBSs of the two users is minimized. Under the above settings, user #1 succeeds to establish an error-free communication through a short 10m-long Ethernet link with user #2 and vice-versa, at a bit rate of 2.8Gb/s. After discarding the redundant FEC 3/8 bits, the actual data recovery rate is 1.05Gb/s. This demonstrated test-bed validates for the first time the use of synchronized chaosbased TRBSs in an OTP-encrypted system at Gb/s rates. It is noted that in the demonstrated configuration, the optical system, including the optical to electrical conversion of the signals, their electrical filtering and sampling at 40GSa/s has been performed real-time. However, the acquisition of the multiple timetraces, the down sampling and the comparator used in decision threshold are performed offline, along with the FEC implementation that encrypts the information. The transmission of the encoded streams is performed online, through 10Gb/s identical Ethernet transceivers. Finally, decoding and retrieval of initial information at the receiver is performed offline. The complete implementation can be designed to operate fully online with state-off-the-art A/D conversion equipment that supports Gb/s sampling, acquisition and fast FPGA modules that support FEC encoding up to hundreds of Mb/s. Thus, communication at larger bit rates is currently limited, not by the TRBS key generation rate, but by the technology of the electronic modules to support fast acquisition and post-processing. Real-time operation at Gb/s rates could be obtained in more complex architectures than the one presented, including some parallel processing. In terms of transmission, communication at larger distances seems straightforward, since FEC encoders do not only assess the digital key synchronization error, but also the transmission impairments as they were originally proposed for. V. SECURITY ASPECTS OTP encryption is considered unconditionally secure in its theoretical definition. However, its practical implementation sets the actual security level. The prerequisites for the pad to be: (a) composed of truly random digits, (b) never be used more than once and (c) kept secret, must be preserved at any time. The first two conditions are genuinely met in the presented implementation. A further discussion on the secrecy condition for the key distribution is provided here, noting that the transmitted analog chaotic signal is not the key but the seed to generate the key. We discuss two attack scenarios that apply on the physical synchronization layer, the only one that an attacker can access, since brute-force attacks are not an effective approach for breaking the OTP protocol. The first scenario involves the attempt of a fraud user to access hardware matched devices and synchronize with the optical network. Hardware matching of each legitimate user’s TRBS generators – resembling the access of hardware keys – is critical for achieving synchronized randomness. Especially SL and photodetection modules are selectively matched to obtain optimal synchronization [35]. We substitute user’s #2 SL with another device from a different manufacturer - now named as user #2′. The new device has a tolerance mismatch

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in the operational characteristics less than 5% (e.g. threshold current, slope efficiency) and the same solitary wavelength emission.. By scanning the parameters of its operating conditions, it becomes clear that the synchronization level with user's #1 SL is not preserved: user #2′ cannot achieve a CC value higher than 0.97, as shown in Fig. 6. The fact that the best obtained CC value is not observed in zero mismatch conditions is due to a 0.2dB optical loss asymmetry between the optical paths of the two users. This results in a slightly smaller coupling in one laser, which is translated to lower injection strength from the system. The latter determines the final emission wavelength of the chaotic carrier, which is shifted compared to the solitary laser emission. Thus, a small mismatch is detected in user’s #2 SL operating conditions to achieve the optimal synchronization. The lower CC level is attributed to the possibility of mismatch in the internal parameters of the SLs (such as the device length, the gain coefficient, the linewidth enhancement factor, the photon lifetime, etc.). These not fully controllable parameters during the fabrication of the SL devices make difficult for an eavesdropper to access the appropriate device and achieve strict matching conditions that are needed for such an application. The obtained value of CC=0.97, however, may be rationally considered as evidence of efficient synchronization. In the specific implementation, nevertheless, it is too low to obtain synchronized TRBSs when translated in an error-rate estimation (Fig. 5); the obtained BER is higher than 10-2, regardless the applied FEC encoding method.

FIG. 6. Cross-correlation between two users (#1 and #2′) with non-identical lasers vs. various operational conditions of user's #2′ laser.

FIG. 7. Cross-correlation between: user #1 and user #2 emission without eavesdropping present, (black rectangles), user #1 and user #2 outputs in presence of 10% tapping of user's #2 optical power (red circles), and user #1 and eavesdropper's 10% tapped output (blue triangles).

The second security scenario considers the interception of an eavesdropper in the fiber-optic transmission line, through which TRBS synchronization emerges. We examine the case of an eavesdropper that taps 10% of the travelling optical power of user’s #2 emission and uses it to synchronize with user #1. A critical parameter for the users’ synchronization is the coupling conditions between them. By imposing different conditions of attenuation to the coupling level that lead initially to optimized synchrony, the eavesdropper’s efficiency to synchronize its analog emission with a legitimate user becomes dependent (Fig. 7). For an excess of 4dB attenuation, the legitimate users’ untapped synchrony (CC=0.996) is not affected. However, in presence of 10% optical power tapping, the 4dB attenuation leads to a signal correlation of CC=0.9937, rather than the respective value of 0.9948, for 0dB attenuation. This enhances the exposure of tapping to the legitimate users, through the increased rate of communication errors. At the same time, the eavesdropped signal correlates also at a lower value with user #1 (CC=0.9898) at 4dB attenuation, compared to the 0dB attenuation case (CC=0.9912). Even if we assume that the eavesdropper somehow knows and implements exactly the TRBS generation procedure which was agreed by the legitimate users, his obtained analog chaotic signal will lead to a communication bit-error-rate of the order of 10-4, when decoding with the FEC 3/8 code (see Fig. 5). VI. CONCLUSION Summarizing the concepts followed in the presented work, the following two conditions must be simultaneously fulfilled: (i) the chaotic analog signals emitted by the communicating users preserve high-quality synchronization, and (ii) these analog signals lead after digitization to verified synchronized TRBSs. Besides the matched hardware modules used by the users, the above prerequisites imply identical steps and parameterization of all post-processing procedures. In an actual implementation, the system’s synchrony and its security assessment can be supported by monitoring the CC level of the emitted signals among the users. This can be implemented following various approaches. For example, all users can submit a small part of their emitted analog time series (e.g. a short duration of μs, in time intervals of ms) that seed the TRBS generation in a common storage place. These data would not be sufficient to expose the overall seed; however they would define efficiently the CC statistical metric. In another possibility, a control unit with some intelligence could be used at the optical layer; its access to each SL’s optical emission before coupling with common transmission path, could monitor the CC metric among all users, even at real time. The presented concept can easily extend to support multiuser, OTP-secured communications. In the case that multiple users synchronize at the same wavelength and polarization condition at the optical layer, all of them will commonly access the same keys. Even if different data are sent from one user to the rest, they will all share a common key to decrypt all communications. This implements an encrypted broadcasting protocol from one-to-all users. Of course, all users will need to access matched devices for their optical configurations and

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their TRBS generation stages. In the case that the optical topology is used under multiplexing conditions (eg. different wavelengths between pairs of users or vertical polarization conditions) more bilateral communication links can be encrypted under the same configuration by sharing different random keys. The concept of generating ultrafast and real-time keys that can be distantly synchronized through analog chaotic signals gives a renewed impulse on the OTP cryptographic protocol. The limitations of key generation rates at Mb/s range imposed in secure key distribution approaches can be now surpassed. The verified TRBS generation rates at multi-Gb/s rates provide us with a powerful tool for implementing ultra-fast OTP protocols. Finally, at the security level, FEC coding that is explicitly engineered for the particular concept can further optimize the discrimination between a legitimate from a fraud user or the existence of an eavesdropper. Such engineering should target on interpreting very small differences of crosscorrelation of synchronized analog signals into huge error rate differences at the communication level. REFERENCES [1] [2] [3]

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Apostolos Argyris received the B.Sc. degree in physics (1999) from Aristotle University of Thessaloniki, Greece, the M.Sc. degree in microelectronics & optoelectronics (2001) from University of Crete, Greece and the Ph.D. degree in informatics and telecommunications (2006) from National and Kapodistrian University of Athens (NKUA), Greece. From 2006 to 2016 he was a senior researcher at the Optical Communications Laboratory at the Department of Informatics and Telecommunications, NKUA. During 2006-2009 and 2014-2015 he was appointed as a part-time adjunct lecturer in the University of Thessaly, Greece. Since 2016 he is a Marie-Skłodowska Curie Fellow at the Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC), Universitat de les Illes Balears (UIB), Spain. His research has been published in 80 works in international journals, conferences and book chapters. His research interests include optical communication systems, hardware security, non-linear dynamics in lasers, optical sensing, signal processing, reservoir computing and data analysis.

In 2006 he was distinguished as a "Top Young Innovator 2006 - TR35" by the Technology Review magazine published by M.I.T., U.S.A. The same year he was awarded the "Ericsson Award of Excellence in Telecommunications" for the South-East Europe region. Evangelos Pikasis received the B.S degree in electronic engineering (2005) from the Technological and Educational Institution of Athens, Greece, the M.S. degree in electronics and signal processing (2008) from Physics department of University of Patras, Greece, and the Ph.D. degree in informatics and telecommunications (2014) from NKUA, Greece, where he was a research associate until 2016. He is currently with the Institute for Digital Communications (IDCOM), School of Engineering at the University of Edinburgh, U.K. He has more than 20 publications in international journals and conference proceedings. His research interests include telecommunication systems, signal processing and embedded systems. Dimitris Syvridis has obtained the B.Sc. in Physics (1982), the M.Sc. in Telecommunications (1984) and the Ph.D. in Physics (1988) from NKUA, Greece. From 1988-1990 he was a Researcher at the Electronics Laboratory of the NKUA, Greece. During 1990-1993 he was Researcher at the Institute of Quantum Electronics, Swiss Federal Institute of Technology (ETH Zurich) and during 1993-1997 he was a senior researcher at the Department of Informatics, NKUA, Greece. He is currently a professor at the same department. He has more than 300 publications in scientific journals and conference proceedings. He is a reviewer for the IEEE and OSA organizations. He has participated in many European research projects in the fields of optical communications, photonic design and security. His research interests cover the areas of broadband, optical and secure communications and networks, photonic devices and subsystems, photonic integration and digital processing.