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Synchronization Attack to Chaotic Communication Systems

Profile image of JUAN HUGO GARCIA LOPEZJUAN HUGO GARCIA LOPEZ

2013, The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity

https://doi.org/10.5890/DNC.2013.11.003
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11 pages

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Abstract

ABSTRACT Synchronization of chaotic oscillators has an important application in cryptography. When two identical oscillators are coupled, they can be completely synchronized and the chaotic output of the transmit- ter oscillator can be used to mask a message. Although the oscilla- tor parameters are usually used as secret keys, the sensitivity of such cryptosystems to parameter changes has never been systematically an- alyzed. To cryptanalyze a communication system based on synchro- nization of chaotic oscillators, we use a synchronization attack that allows estimating all unknown parameters by minimizing the synchro- nization error. Using this attack we cryptanalyze popular communica- tion systems based on the Ro ̈ssler and Chua chaotic electronic circuits. We suggest to include this attack as a standard security test for crypt- analysis of chaotic communication systems.

Figures (10)
where x;, yj, and z; are the Rossler system variables associated with output voltages X, Y, and Z (Fig. 1). The piecewise linear function g(x;) is determined by the diode in the operational amplifier U5, which is switched on when the voltage X exceeds 3 v. The oscillator presents a chaotic behavior for the following parameters [18,19]: a = =a = = gto = = rates =10'5 T= Re = 0.05, B Re 05,A=1,7 Rk — eRe = 0.236, and p = #2 = 15. "The Chua decwanic. circuit (Fig. 2) consists of a linear inductor 1), a linear resistor R7, two linear ca- pacitors C;, Cz and a nonlinear resistor Np, built with the arrangement of operational amplifiers MC34084P and recictare RP, - The carrecnoandino eanationge are oiven hy [90 91]
where x;, yj, and z; are the Rossler system variables associated with output voltages X, Y, and Z (Fig. 1). The piecewise linear function g(x;) is determined by the diode in the operational amplifier U5, which is switched on when the voltage X exceeds 3 v. The oscillator presents a chaotic behavior for the following parameters [18,19]: a = =a = = gto = = rates =10'5 T= Re = 0.05, B Re 05,A=1,7 Rk — eRe = 0.236, and p = #2 = 15. "The Chua decwanic. circuit (Fig. 2) consists of a linear inductor 1), a linear resistor R7, two linear ca- pacitors C;, Cz and a nonlinear resistor Np, built with the arrangement of operational amplifiers MC34084P and recictare RP, - The carrecnoandino eanationge are oiven hy [90 91]
where v,, and v,, are the voltages at VC1, VC2 and iz, is the electrical current through L1. The function f (vp) describes the electrical response of the nonlinear resistor Nr:
where v,, and v,, are the voltages at VC1, VC2 and iz, is the electrical current through L1. The function f (vp) describes the electrical response of the nonlinear resistor Nr:
Fig. 3 Schematic of a two-channel virtual communication system based on chaos synchronization using chaotic masking. The channel variables correspond to the Réssler oscillators. M. Zanin et al. / Discontinuity, Nonlinearity, and Complexity 2(4) (2013) 333-343
Fig. 3 Schematic of a two-channel virtual communication system based on chaos synchronization using chaotic masking. The channel variables correspond to the Réssler oscillators. M. Zanin et al. / Discontinuity, Nonlinearity, and Complexity 2(4) (2013) 333-343
Fig. 4 (Upper graph). Recorded time series from X (solid black), Y (dashed blue), and Z (dotted red) outputs from the Rossler electronic circuit in the transmitter. (Lower graph). Time series of the X output with transmitted encrypted message (solid black), original binary message (dashed blue), and recovered message (dotted red).
Fig. 4 (Upper graph). Recorded time series from X (solid black), Y (dashed blue), and Z (dotted red) outputs from the Rossler electronic circuit in the transmitter. (Lower graph). Time series of the X output with transmitted encrypted message (solid black), original binary message (dashed blue), and recovered message (dotted red).
Fig. 5 Synchronization sensitivity (in units of Hamming distances) of Réssler oscillators to the parameter mismatch in the receiver. The dotted lines indicate the standard deviation. M. Zanin et al. / Discontinuity, Nonlinearity, and Complexity 2(4) (2013) 333-343
Fig. 5 Synchronization sensitivity (in units of Hamming distances) of Réssler oscillators to the parameter mismatch in the receiver. The dotted lines indicate the standard deviation. M. Zanin et al. / Discontinuity, Nonlinearity, and Complexity 2(4) (2013) 333-343
Fig. 6 Hamming distance of the Rossler communication system when two parameters are simultaneously varied.
Fig. 6 Hamming distance of the Rossler communication system when two parameters are simultaneously varied.
Fig. 7 Hamming distance of the Chua communication system as a function of ‘¥ parameter mismatch. The dotted lines indicate the standard deviation. Fig. 8 Evolution of the decryption error (Hamming distance) as a function of the signal amplitude (in % of carrier voltage) for the Réssler (left) and Chua (right) oscillators. The dotted lines indicate the standard deviation.
Fig. 7 Hamming distance of the Chua communication system as a function of ‘¥ parameter mismatch. The dotted lines indicate the standard deviation. Fig. 8 Evolution of the decryption error (Hamming distance) as a function of the signal amplitude (in % of carrier voltage) for the Réssler (left) and Chua (right) oscillators. The dotted lines indicate the standard deviation.
M. Zanin et al. / Discontinuity, Nonlinearity, and Complexity 2(4) (2013) 333-343
M. Zanin et al. / Discontinuity, Nonlinearity, and Complexity 2(4) (2013) 333-343
Table 1 Parameter ranges used in the brute-force attack to the Réssler communication system. The first stage corre- sponds to an exhaustive search in the parameter space, whereas the second and third stages are local optimizations.
Table 1 Parameter ranges used in the brute-force attack to the Réssler communication system. The first stage corre- sponds to an exhaustive search in the parameter space, whereas the second and third stages are local optimizations.
Table 2 Results of two attack strategies for 10% (Réssler) and 1.66% (Chua) message (2.6 kbit/s) intensity. Mean and standard deviations are calculated over 60 (R6ssler) and 70 (Chua) different experimental time series. 4 Brute-force attack
Table 2 Results of two attack strategies for 10% (Réssler) and 1.66% (Chua) message (2.6 kbit/s) intensity. Mean and standard deviations are calculated over 60 (R6ssler) and 70 (Chua) different experimental time series. 4 Brute-force attack

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