A chaos-based visual encryption mechanism for clinical EEG signals

Abstract

In this study, we have developed a chaos-based visual encryption mechanism that can be applied for clinical electroencephalography (EEG) signals. In comparison with other types of random sequences, chaos sequences were mainly used to increase unpredictability. We used a 1D chaotic scrambler and a permutation scheme to achieve EEG visual encryption. One approach of realizing the visual encryption mechanism is to scramble the signal values of the input EEG signal by multiplying a 1D chaotic signal to randomize the EEG signal values. We then applied a chaotic address scanning order encryption to the randomized reference values. Simulation results show that when the correct deciphering parameters are entered, the signal is completely recovered, and the percent root-mean-square difference (PRD) values for control and alcoholic clinical EEG signals are 4.33 × 10⁻¹⁵ and 4.11 × 10⁻¹⁵%, respectively. As long as there is an input parameter error, with an initial point error of 0.00000001% as an example, thereby making these clinical EEG signals unrecoverable.

Appendices

Appendix 1

The encryption process shown in Fig. 1 is given as follows:

• Step 1: Select a chaotic logistic map type CMT _F of F _CIA, the starting point SP _F of CMT _F , the length L _F for an encrypted clinical EEG signal, and the parameters n _F and δ _F for the security level.

• Step 2: Generate a chaotic sequence with length n _F .

  $$ x_{n + 1} = {\text{CMT}}\left( {x_{n} } \right); \quad x_{0} = {\text{SP}}_{F}; \quad n = \left\{ { 1, 2, \ldots , n_{F} } \right\} $$

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• Step 3: Discard the previous n _F chaotic sequence.

• Step 4: Generate a chaotic sequence

  $$ x_{n} = {\text {CMT}}(x_{{n_{F} + 1}} ); \quad n = \left\{ {n_{F} + 1, \ldots } \right\} $$

• Step 5: If x _n  > δ _F ; discard x _n ; and go to step 4. else; go to step 6; end.

• Step 6:

  $$ m_{k} = \left\lceil {\frac{1}{{x_{n} }}} \right\rceil $$

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  $if\,m_{k} \notin \{ m_{1} , \ldots ,m_{k - 1} \}; M = \{ m_{1} , \ldots ,m_{k - 1} ,m_{k} \} ;$ go to step 7. else; go to step 4; end.

• Step 7: If k = L _F

  $$ M = \{ m_{1} ,m_{2} , \ldots ,m_{{L_{F} }} \}; \quad m_{C}^{*} = \max \{ m_{1} ,m_{2} , \ldots ,m_{{L_{F} }} \} $$

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  else; go to step 4; end.

• Step 8: Deliver $m_{C}^{*}$ to the chaotic candidate point generator process G _CCS.

• Step 9: Deliver a chaotic logistic map type CMT _G of G _CCS, which is the starting point SP _G of CMT _G .

• Step 10: Generate a chaotic sequence with length $m_{C}^{*}$.

  $$ g_{n + 1} = {\text {CMT}}_{G} (g_{n} ); \quad g_{0} = {\text {SP}}_{G} ; \quad n = \{ 1,2, \ldots ,m_{C}^{*} \}; \quad G = \{ g_{1} , \ldots ,g_{{m_{C}^{*} }} \} $$

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• Step 11: Deliver M to the chaotic candidate point generator process G _CCS.

• Step 12: Generate encrypted chaotic signal CE.

  $$ M = \{ m_{1} ,m_{2} , \ldots ,m_{{L_{F} }} \}; \quad G = \{ g_{1} , \ldots ,g_{{m_{C}^{*} }} \}; \quad {\text {CE}} = \{ g_{{m_{1} }} ,g_{m2} , \ldots ,g_{{m_{{L_{F} }} }} \} $$

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• Step 13: Deliver EEG medical signal EEGS with length L _F to G _CCS

  $$ {\text {EEGS}} = \{ {\text {eeg}}_{1} , \ldots ,{\text {eeg}}_{{L_{F} }} \} $$

• Step 14: Generate encrypted clinical EEG signal GEEG.

  $$ \begin{array}{l} {EEGS = \left\{ {eeg_{1} , \ldots ,eeg_{{L_{F} }} } \right\}; \quad CE = \left\{ {g_{{m_{1} }} ,g_{{m_{2} }} , \ldots ,g_{{m_{{L_{F} }} }} } \right\}} \hfill \\ {GEEG = EEGS \cdot CE = \left\{ {eeg_{1} \cdot g_{{m_{1} }} ,eeg_{2} \cdot g_{{m_{2} }} , \ldots ,eeg_{{L_{F} }} \cdot g_{{m_{{L_{F} }} }} } \right\}} \hfill \\ { = \left\{ {geeg_{1} , \ldots ,geeg_{{L_{F} }} } \right\}} \hfill \\ \end{array} $$

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Appendix 2

The chaotic scanning encryption mechanism S _csem that we developed is given as follows:

• Steps 1–5 are the same as those given in Appendix 1.

• Step 6:

  $$ m_{k} = \left\lceil {\frac{1}{{x_{n} }}} \right\rceil $$

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  $if\,m_{k} \le L_{F} ;m_{k} \notin \{ m_{1} , \ldots ,m_{k - 1} \} ;M = \{ m_{1} , \ldots ,m_{k - 1} ,m_{k} \} ;$ go to step 7. else; go to step 4; end.

• Step 7: If k = L _F $M = \{ m_{1} ,m_{2} , \ldots ,m_{{L_{F} }} \} ;$ else; go to step 4; end.

• Step 8: Deliver M to the output encrypted signal process.

• Step 9: Deliver the encrypted clinical EEG signal GEEG to output encrypted signal process.

• Step 10: Generate chaotic scanning of the encrypted clinical EEG signal SGEEG.

  $$ \begin{array}{l} {GEEG = \left\{ {geeg_{1} , \ldots ,geeg_{{L_{F} }} } \right\}; \quad M = \left\{ {m_{1} ,m_{2} , \ldots ,m_{{L_{F} }} } \right\}} \hfill \\ {SGEEG = \left\{ {geeg_{{m_{1} }} ,geeg_{{m_{2} }} , \ldots ,geeg_{{m_{{L_{F} }} }} } \right\} = \left\{ {sgeeg_{1} ,sgeeg_{2} , \ldots ,sgeeg_{{L_{F} }} } \right\}} \hfill \\ \end{array} $$

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