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Frontiers in Optics/Laser Science 2015 Β© OSA 2015

Multi-Security Scheme Combining Chaotic Modulation and Masking using Acousto-Optic Feedback Devices Fares S. Almehmadi1 and Monish R. Chatterjee1 1

Department of Electrical & Computer Engineering University of Dayton, Dayton, Ohio 45469 E-mail: [email protected]

Abstract: An input signal is encrypted onto a chaotic carrier in a hybrid Bragg cell and added to a separately generated chaotic mask with independent encryption keys. Simulations indicate considerable enhancement in system performance vis-Γ -vis security. Keywords: acousto-optics, Bragg regime, scattering, security, chaos, encryption, decryption, masking.

1. Background Acousto-optic (AO) Bragg cells consist of a crystal that is vibrated by a piezoelectric oscillator, creating conditions that allow for the controllable diffraction of a laser. These acoustic vibrations effectively create a diffraction grating, and the laser deflection depends on the light and sound frequencies along with crystal properties. These parameters are summarized by the unitless Klein-Cook parameter (Q). If Q is larger than 8Ο€, the cell is in the Bragg regime of operation, and one diffracted order is created. Bragg cells are useful for signal-processing, including chaotic modulation of a signal if the cell is configured as a feedback loop. Such a loop is created by photo-detecting the diffracted beam, amplifying the resulting electrical signal and adding it to an offset, and then feeding it back to the piezoelectric driver. Appropriate amplification and offset values cause chaos in the photodetector output; such chaos has been shown to be useful for secure transmission of signals via encryption. 2. Chaotic modulation and recovery with profiled optical beams

Fig.1. Heterodyne scheme for modulation and recovery using A-O chaos.

A diagram illustrating this encryption process is shown in Fig.1, which shows a pair of hybrid closed-loop AO feedback (HAOF) systems, one for chaotic modulation (left) and recovery (right). An understanding of the HAOF is achieved by exploring the nonlinear dynamics of the photodetector current 𝐼(𝑑). The assumption of a uniform plane wave laser is often made, leading to a common equation for 𝐼(𝑑). However, to model realistic profiled beams, a modified version of this expression was developed and used to simulate the system for arbitrary profiles [1]. The modified expression is shown in Eq.1, where 𝑓 represents the observed output along the optical phase shift dimension for a non-uniform input profile, 𝛼̂0 is the peak phase delay, 𝛽̃ is the feedback gain, and 𝑇𝐷 is the feedback time delay [1]. 2

πΌπ‘β„Ž (𝑑) = |𝑓 [0.5 (𝛼̃0 (𝑑) + 𝛽̃ (πΌπ‘β„Ž (𝑑 βˆ’ 𝑇𝐷 )))]| .

(1)

Chaotic encryption of a signal 𝑠(𝑑) is achieved by adding this signal to the DC component of the phase delay, such that the peak phase delay applied to the bias driver has the form of 𝛼̂ = 𝛼̂0 + 𝑠(𝑑). The chaotic photodetector current produced can be viewed as a modulated version of 𝑠(𝑑). After transmission through a channel, 𝑠(𝑑) is recovered in the manner of standard heterodyne detection where a local chaos wave is generated using a second Bragg cell with parameters matched to the transmitter cell. The local chaos is multiplied with the modulated signal, and the product is low-pass filtered for recovery [2].

FW4A.4.pdf

Frontiers in Optics/Laser Science 2015 Β© OSA 2015

3. Chaotic masking combined with chaotic modulation Another way chaos is used for encryption is to directly add chaos to the information signal, and then perform a subtraction for recovery [3]. This requires the same synchronization between transmitter and receiver necessary for HAOF modulation. Masking is a relatively weak encryption method, because it is possible to approximate the carrier via matched parameters and subtract it from the encrypted signal, revealing the transmitted information. Figure 2 demonstrates a novel idea for strengthening the mask encryption described above. First, the information signal is chaotically encrypted using the HAOF. The resulting signal is added to a separately generated chaotic mask (with independent key parameters), with power matched to the encrypted signal prior to transmission. Decryption proceeds by first subtracting the mask, and then performing heterodyne demodulation, as previously described.

Fig.2: Block diagram illustration of combined AO chaotic modulation and AO chaotic masking, in order to increase encryption strength.

The left plot in Fig.3 contains a combined modulation and masking simulation. A (sinc) signal waveform is transmitted and recovered with matched parameters at the receiver relative to the modulation and masking HAOF. The signal is recovered accurately except for an initial transient time required for synchronization to occur at the receiver. The right plot in Fig.3 shows the results for a very slight mismatch in the gain parameter for the masking HAOFs, and the recovered signal is heavily distorted. This ultra-high gain sensitivity illustrates extreme encryption robustness beyond realizability; further examination with practical signals including images is currently ongoing. Encryption and Recovery Using Hybrid AO Feedback Chaos by Combining both Chaotic Modulation and Chaotic Masking

Encryption and Recovery Using Hybrid AO Feedback Chaos by Combining both Chaotic Modulation and Chaotic Masking

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Fig.3: Simulation result for combined modulation and masking, with matched parameters (left) and slight mismatch (right).

4. Conclusion The feasibility of combining chaotic modulation with additive chaotic masking is demonstrated. This scheme creates a complexity of encryption that is much greater than modulation or masking can achieve alone. 5. References [1] F.S. Almehmadi and M.R. Chatterjee, "Numerical examination of the nonlinear dynamics of a hybrid acousto-optic Bragg cell with positive feedback under profiled beam propagation," J. Opt. Soc. Am. B 31, 833-841 (2014). [2] F.S. Almehmadi and M.R. Chatterjee, β€œImproved Performance of Analog and Digital Acousto-Optic Modulation with Feedback under Profiled Beam Propagation for Secure Communication using Chaos,” Opt. Eng. 53, 126102 (2014). [3] O. Morgul and M. Feki, "A Chaotic Masking Scheme by Using Synchronized Chaotic Systems," Phys.Lett. A, vol. 251, 169 176, 1999.