Chaos-based encryption appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. While the first experimental realizations were made in Electronics, the Optics community rapidly showed a strong interest in this new scientific application due to the well-known feature of Optics in the area of nonlinear phenomena. Numerous optical demonstrations have been performed, involving chaotic dynamics with particularly interesting properties in terms of chaos complexity, and also in terms of bandwidth i.e., encryption speed. This special issue gives a review of most of the current works on optical chaos dedicated to encryption

Goedgebuer, Jp

Larger, L.

Laurent Larger

Jean-Pierre Goedgebuer

Comptes Rendus Physique

e chaotica strongumerouserms ofe currentrlinéaires entique s’estdepropriétésde codage.ptique.d fromtime, the. Securitytifying themn physicalC. R. Physique 5 (2004) 609–611Cryptography using optical chaos/Cryptographie par chaos optiqueEncryption using chaotic dynamicsfor optical telecommunicationsLaurent Largera,b,∗, Jean-Pierre Goedgebuera,ba GTL-CNRS Telecom/UMR FEMTO-ST 6174, 2–3, rue Marconi, 57070 Metz cedex, Franceb FEMTO/Optics Department, UMR CNRS 6174, université de Franche-Comté, 16, route de Gray, 25030 Besançon cedex, FrancePresented by Guy LavalAbstractChaos-based encryption appeared recently in the early 1990s as an original application of nonlinear dynamics in thregime. While the first experimental realizations were made in Electronics, the Optics community rapidly showedinterest in this new scientific application due to the well-known feature of Optics in the area of nonlinear phenomena. Noptical demonstrations have been performed, involving chaotic dynamics with particularly interesting properties in tchaos complexity, and also in terms of bandwidth i.e., encryption speed. This special issue gives a review of most of thworks on optical chaos dedicated to encryption.To cite this article: L. Larger, J.-P. Goedgebuer, C. R. Physique 5 (2004). 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.RésuméDynamiques Chaotiques Appliquées à la cryptographie pour les télécommunications optiques. La cryptographie pachaos est apparue récemment au début des années 90, comme une application originale des dynamiques nonrégime chaotique. Alors que les premières réalisations ont été mises en œuvre à partir de circuits électroniques, l’oprapidement intéressée au sujet. Grâce à des propriétés physiques particulières et familières dans le domaine de l’Optique,nombreux démonstrateurs originaux et variés ont été développés, fonctionnant avec des dynamiques chaotiques auxattractives, tant en terme de complexité des régimes chaotiques, qu’en terme de bande passante, et donc de vitesseCe numéro spécial passe en revue la plupart des travaux actuels sur les systèmes cryptographiques par chaos en oPourciter cet article : L. Larger, J.-P. Goedgebuer, C. R. Physique 5 (2004). 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.Keywords: Optical telecommunication; Chaos; EncryptionMots-clés : Télécommunications optiques ; Chaos ; CryptographieWith the advent of world wide networks and digital communication techniques, cryptography was brutally transferea very restricted area i.e., the military domain, diplomacy, state affairs, to a very broad area covering, at the sameprevious domains, but also private companies, medical and bank information, electronic payment on the internet, etcand secrecy are becoming fundamental requirements for everyone, in the present day communication society, thus jusnumber of current research activities on new and/or alternate encryption methods. Within this res arch domain, and apart frothe most general encryption techniques based on software algorithms, two original cryptographic methods based o* Corresponding author.E-mail address: laurent.larger@georgiatech-metz.fr (L. Larger).1631-0705/$ – see front matter 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.doi:10.1016/j.crhy.2004.05.004610 L. Larger, J.-P. Goedgebuer / C. R. Physique 5 (2004) 609–611aphy, andbe usedthe leveld (up tochaoticlly thateiveroperty ofdigitald for theach userithoutde secureld be usedo-randomjectories,that ofLorenzed evennamicscryptionof viewErbiumers; [9],systems,dght ande numberlectronice that theonlinearitythe otherd torom thecteristics.e in termsset-ups,nonlineardensity.ies: it ishowever,teaprinciples have appeared as physically and technologically feasible during the last two decades: quantum cryptogrchaos cryptography. The first is mainly dedicated to absolute security secret key distribution, in which the key can thento transmit securely information by conventional algorithm based encryption. The second method is also involved atof the physical layer in transmission systems, with the advantage of allowing potentially a very high encryption speeseveral tens of Gb/s, unlike algorithm-based encryption softwares that is typically limited to a few hundreds of Mb/s).The genesis of encryption using chaos started with the demonstration of the synchronization of two coupledtrajectories [1]. The synchronization property for such waveforms was thought initially to be nonrealistic, due to the intrinsicnatural tendency of two quasi-identical chaotic dynamics to diverge one from another, due to the so-called Sensitivity to InitialConditions, popularly called the ‘Butterfly effect’.In communication theory, the possibility of synchronization of a given waveform, sinusoidal or not, means generathe waveform can be used as an information carrier in a transmission system; the synchronization is then used at the recto retrieve the carried information. Moreover, when the waveform features a pseudo-random character, a privacy prthe communication can be expected, together with the carrier capability: this is typically the case for the well-knowntransmission technique, the Code Division Multiple Access or CDMA, used in the Global Positioning System (GPS), anthird mobile phone generation. Briefly, CDMA involves long pseudo-random bit sequences as a carrier waveform for echannel, whose carrier is consequently broadband due to the pseudo-random character. The sequence acts as a code, wwhich the decoding and the retrieving of the encoded information can not be performed, and the transmission is mathrough the use of this pseudo-random carrier. Similarly, it was assumed in the early 1990s that chaotic waveforms couas an information carrier signal, and at the same time as a means to protect the carried information due to its pseudand broadband character. The intrinsic determinism of the chaotic dynamics i.e., the mathematical law ruling their trais, of course, the milestone of the synchronization technique.The first experimental demonstration of information transmission using a chaotic carrier followed quite rapidlythe synchronization principle in 1993 [2]. The chaos generator of concern was an electronic circuit generating atype chaotic oscillation embedded in a 3-Dimensional phase space. The first cryptanalysis of such a system followfaster [3], highlighting that a low chaos complexity was definitively a weakness of the cryptosystem. Nonlinear dyin Optics (laser dynamics, large delay optical or optoelectronic cavities) were well knownfor their ability to produce highcomplexity dynamics. Different groups revisited independently various such optical systems for application to chaos ensystems, from the theoretical point of view [4] (external cavity semiconductor laser), and from the experimental pointas well [5] (synchronization of chaotic external cavity semiconductor lasers; [6], encryption/decryption with chaoticdoped fiber lasers; [7], encryption/decryption with chaotic laser wavelength; [8], synchronized chaos in microchip lasGHz synchronization between external cavity semiconductor lasers). All of these results were obtained with opticaldue to the following reasons:• these systems are, of course, intrinsically dedicated to modern communication systems using optical fibers;• the dynamical processes involved in optical systems can be fast, thusresulting in another interesting feature of chaos-baseoptical cryptosystems, their potentially very high encryption speed;• high complexity chaotic dynamics are obtained, whether due to intrinsic complex nonlinear coupling between limatter interactions in lasers, or due to the presence of a large delay feedback cavity enabling dynamics with largof degrees of freedom.Cryptanalysis of such optical chaos cryptosystems has been so far more difficult to implemente than that of the first eset-ups. Only Erbium fiber laser chaotic dynamics was shown to be analyzed with enough detail, with the disadvantagchaos thus generated can be broken and the message easily retrieved. The lack of complexity inherent to the weak nattached to the fiber laser dynamics is responsible for the success of the cryptanalysis attack [10]. Cryptanalysis ofchaos encryption systems are still under progress, but they aremuch more oriented towards techniques usually devotenonlinear dynamics analysis, the linear techniques being definitively not sufficient to retrieve enough information fchaotic time series masking the message.The optical chaos-based cryptosystems reported in this special issue exhibit most of the above mentioned charaHowever, the set-ups of interest are described by different nonlinear dynamical models, whose fundamental relevancof confidentiality and transmission quality is still one of the remaining open questions in the field. Among thesethe dynamics of the external cavity lasers (see Fig. 1, upper left) involve linear feedback delay terms, whereas theoperation consists in a coupling in the rate equations between the optical field amplitude and the inversion populationThe situation is different for optoelectronic encryption systems, for which the delayed feedback has two particularitnonlinear, and it is optical phase insensitive due to the electronic nature of the feedback. The latter situation is,explored in two distinct schemes. In the first one (Fig. 1, upper right), the differential process still originates from the laser raequations, in which the nonlinear coupling between the population inversion density and the optical field amplitude involvesL. Larger, J.-P. Goedgebuer / C. R. Physique 5 (2004) 609–611 611lectronicectronicpe opticalnizatione extremehighlyd,tecture,ricalFig. 1. Four sub-class of nonlinear dynamics in Optics mostlyinvolved in optical chaos generation for encryption.delay term originating from the feedback signal acting on the electronic pumping strength. In contrast, in the other optoefeedback scheme (Fig. 1, lower left), the differential process is determined by the linear filtering performed by the elpart of the oscillator feedback; this filteringis applied to a scalar nonlinear feedback transformation. Finally, the fourth setu(Fig. 1, lower right) involves nonlinear coupled rate equations in a solid state laser between population inversion and thelectric field, when the population inversion is driven by an externally modulated pump laser. The security (synchrocapability) of the chaos communication schemes using the previous optical chaos generators relies essentially on thsynchronization sensitivity with respect to the physical parameters and exact operating conditions, these latter constitutingthe key of the encryption method. Without the exact knowledge of the chaos generator set-up used at the emitter, it isdifficult for an unauthorized receiver to reproduce the right chaotic waveform which can synchronize with the one transmittethus enabling the message recovery.Such a diversity in the experimental optical chaos generator is very positive for the definition of the optimal archias well as for competition withinthe scientific community involved in chaos-based encryption systems. Work is still undeprogress to explore the best configuration, and also new configurations, that could be implemented in the future at the physlayer of a multi-Gbits/s fiber network.References[1] L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 64 (1990) 821.[2] K.M. Cuomo, A.V. Oppenheim, Phys. Rev. Lett. 71 (1993) 65.[3] Th. Beth, D.E. Lazic, A. Mathias, Lect. Notes in Comput. Sci. 839 (1993) 318.[4] C. Mirasso, P. Colet, P. Garcia-Fernandez, IEEE Phot. Techn. Lett. 8 (1996) 299.[5] V. Annovazzi-Lodi, S. Donati, A. Scire’, IEEE J. Quantum Electron. 33 (1997) 1449.[6] G.D. VanWiggeren, R. Roy, Science 279 (1998) 1198.[7] J.-P. Goedgebuer, L. Larger, H. Porte, Phys. Rev. Lett. 80 (1998) 2249.[8] A. Uchida, M. Shinozuka, T. Ogawa, F. Kannari, Opt. Lett. 24 (1999) 890–892.[9] I. Fischer, Y. Liu, P. Davis, Phys. Rev. A 62 (2000) 011801(R).[10] J.B. Geddes, K.M. Short, K. Black, Phys. Rev. Lett. 83 (1999) 5389.

Encryption using chaotic dynamics for optical telecommunications

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Encryption using chaotic dynamics for optical telecommunications

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