International Journal of Bifurcation and Chaos, Vol. 15, No. 2 (2005) 653–658 c  World Scientific Publishing Company CRYPTANALYSIS OF OBSERVER BASED DISCRETE-TIME CHAOTIC ENCRYPTION SCHEMES ERCAN SOLAK National Research Institute of Electronics and Cryptology, T¨ ubitak, Gebze 41470, Kocaeli, Turkey Received September 11, 2003; Revised February 20, 2004 This paper investigates the weaknesses of cryptosystems that use observer based synchronized chaotic systems. It is shown that known plaintext and chosen plaintext attacks can successfully be launched against such cryptosystems to recover the system parameters and subsequently eavesdrop on the message transmission. The methods employed rely only on the basic math- ematical relations that exist between the output sequence and the message sequence of the transmitter system and require very less computations. Keywords : Cryptanalysis; chaos synchronization; observers. 1. Introduction Starting with the observation that chaotic systems can be coupled to yield synchronized chaotic sig- nals, there has been an increasing research activity from various disciplines on chaos synchronization and its possible applications to secure communica- tions [Pecora & Caroll, 1990; Hasler, 1998]. Many different proposals have appeared in the literature on how to employ chaotic systems in secure communication schemes. This ranges from using chaotic systems as pseudorandom number generators to be used in a stream cipher to using chaotic signals as wide-band carriers modulated by the message [Kolumb´ an et al., 1998; Hasler, 1998]. Topological properties of chaotic systems make them promising candidates for pseudorandom num- ber generators. Basically the sensitive dependence of system trajectories on the initial state makes it possible to use the initial state as the seed and the (possibly quantized) trajectory as the pseudo- random sequence [Stojanovski & Kocarev, 2001]. Such a use is similar to a cryptosystem involving a one-time pad. Still, for a particular chaotic system employed in this manner, the statistical properties of the resulting sequence need to be verified against randomness tests [Menezes et al., 1996]. Another more common use of chaotic systems in encryption involves the modulation of some of the system signals by the message. Treating the system parameters as the secret key that is shared between the transmitter and the intended receiver, the security of the cryptosystem relies on the sen- sitive dependence of chaotic trajectories on the system parameters. It is generally assumed that an eavesdropper who does not know the system parameters cannot possibly construct a copy of the receiver system so as to decipher messages [Dachselt & Schwarz, 2001; Lian et al., 2000]. As Pecora’s seminal work [Pecora & Caroll, 1990], sparked a growing interest in chaos syn- chronization, a class of chaos synchronization prob- lems was shown to be equivalent to the problem of observer design for nonlinear systems [Morg¨ ul & Solak, 1996]. Basically, the synchronizing sig- nal is viewed as the transmitter system output and the receiver system is designed as an observer. This realization brought about the adoption of many classical observer design techniques to chaos 653