Unmasking Optical Chaotic Cryptosystems Based on Delayed Optoelectronic Feedback

Introduction

Chaotic signals typically have broadband spectrum. This property is desirable for applications that require robustness against interference, jamming and low detection probability. Those issues have been addressed by traditional communication systems by using spread spectrum and frequency hopping modulations. In chaos-based communications the broadband chaotic signal is generated at the physical layer instead of algorithmically. Additionally, chaotic carriers offer a certain degree of intrinsic privacy in the data transmission. In chaotic communication systems (Cuomo et al., 1993b; Colet & Roy, 1994) the masking of the message is performed at the physical layer by embedding the signal within a chaotic carrier in the emitter. The recovery of the message is based on the synchronization phenomenon (Ashwin, 2003) by which a receiver, quite similar to the transmitter, is able to reproduce the chaotic part of the transmitted signal. After synchronization occurs, the decoding of the message is straightforward by comparing the input and output of the receiver. Privacy in chaotic communication systems results from the fact that the eavesdropper must have the proper hardware and parameter settings in order to recover the message. The suitability of chaos-based optical communication systems for encrypting gigabit signals has been recently demonstrated in an installed optical network infrastructure of approximately 120 km that covers the metropolitan area of Athens (Argyris et al., 2005). However, the security of these systems remains the key issue to be addressed.

In conventional encryption techniques a key is used to alter the information symbols. The transmitter and the receiver share the key so that the information can be recovered. In a chaotic communication system the transmitter generates a time-evolving chaotic waveform that is used to mask the message. The cryptographic key relies on structural characteristics of the hardware as well as on the set of operating parameters chosen for the system. The message can be recovered with a receiver such that its configuration and parameter settings are matched to those of the transmitter. Encryption is achieved by encoding at the physical layer, providing full compatibility to conventional software encryption techniques. Dynamical encoding with a chaotic waveform can then be considered as an additional layer of encryption.

Chaos cryptography is a recent encryption technique (the idea was proposed in the early 90s), and it will take some time for its security analysis to mature. Some rules have been suggested to achieve a reasonable degree of security (Alvarez & Li, 2006). Methods to quantify the cryptanalysis of chaotic encryption schemes have been also proposed (Tenny & Tsimring, 2004). However, more research needs to be done to develop a systematic cryptographic approach for the analysis of the security of different chaotic communication systems. Many chaos-based encryption schemes have been proposed, and many of those schemes have been broken later on.

Some chaotic encryption systems were broken even without reconstructing the transmitter’s chaotic dynamics, that is, without searching for the secret key that was used to encrypt the message. This kind of attack is usually applicable if the statistical properties of the ciphertext change as a result of changing the transmitted plaintext. Return maps (Perez & Cerdeira, 1995) and spectral analysis (Yang et al., 1998a) of the transmitted ciphertext have been used to decode the message eliminating the need to reconstruct the secret dynamics.