CHAOS BASED ENCRYPTION
NEIL PARMAR
DEPARTMENT OF COMPUTER SCIENCE
ENCRYPTION
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Medical systems
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In this paper, Electroencephalograms (EEGs)
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brain waves and can be used to detect epilepsy and other diseases
Mood Swings
Cognitive functions of the patients
16-Channel EEG Visual User Environment Scheme
Goal: To create a robust and real-time chaos-based image encryption functionality.
Figure 1.
16- Channel EEG Vue Signals
Chaos Based Encryption System for Encrypting
Electroencephalogram Signals
1. Purpose
a) Encrypt the medical EEG 16-channel EEG Vue Signals.
b) Generate robust and real-time encryption
c) Electroencephalograms Visual User Environment Signals are encrypted
2. Unique Approach
a) Microsoft Visual development kit and C# Programming language
b) Three Level Approach
3. Overview
a)
b)
c)
d)
C# based Level I, II, III chaos-based encryption algorithm.
Level I uses bifurcation parameters, chaotic map and initial value to achieve highspeed, real-time encryption.
Threshold parameters were added in Level II to enhance level of robustness.
In Level III, moreover to all the above parameters, a bit stream address index
assignment strategy is incorporated in order to achieve the most robust level encryption.
Algorithm
LEVEL I
STEP 1: Enter the starting point x, and bifurcation parameter r
STEP 2: Generate a chaotic sequence of (Length of the clinical EEG Vue
signal bit stream (EEGS)) length LF
cn+1 = CMT (cn);
c0 = x; n = {1,2,…..LF}
(1)
i.e., cn+1 = rcn(1-cn)
STEP 3: The A Chaos-based encryption bit streams (CBEBS) are generated as
follows
CBEBS = {yn}
n = {1,2,…..LF}
yn = {1 cn >= 0.5}
yn = {0 cn< 0.5}
STEP 4: Deliver Electroencephalograms Visual User Environment Signal Bit
Stream of Length LF
EEGS = {eeg1, eeg2, eeg3,……eegLF}
STEP 5: Generate encrypted Generated encrypted clinical Electroencephalogram
Visual User Environment Signal Bit Streams (GEEG)
GEEG = EEGS
+
CBEBS
Limitation of Level I
The starting point and the chaotic map can be easily tracked.
LEVEL II
STEP 1: Enter the starting point x, bifurcation parameter r, CMT, bit stream length LF,
number of discarded initial chaotic index points nF(10<=nF<=1000000),
and level of security dF(0.01<=dF<=0.99).
STEP 2: (a) c0 = x
(b) Generate nF chaotic points
cn+1 = CMT(cn)
then discard them.
STEP 3: (a) cnF + 1 = CMTF(cnF)
(b) If cn>dF then discard this point and go to step 3 (a);
otherwise perform step 3(c).
(c) Generate a chaotic sequence of length LF.
cn; n = {1,2,3,…..LF}
STEP 4: The A Chaos based encryption bit streams (CBEBS) is generated as follows:
CBEBS = {yn}
n = {1,2,…..LF}
yn = {1 cn >= 0.5}
yn = {0 cn< 0.5}
STEP 5: Deliver Electroencephalograms Visual User Environment Signal Bit
Stream of Length LF
EEGS = {eeg1, eeg2, eeg3,……eegLF}
STEP 5: Generate encrypted Generated encrypted clinical Electroencephalogram
Visual User Environment Signal Bit Streams (GEEG)
GEEG = EEGS
+
CBEBS
Scope for Level III
In Order to enhance the security, the paper introduces the Level III security.
LEVEL III
C#- based Level III encryption algorithm, which is described as follows:
A chaotic logistic map was employed in the chaotic maps CMTF and CMT.
CMT is the chaotic map of GCCS, the chaotic candidate point generator process.
CMTF is the chaotic map of FCIA, the chaotic address index assignment process
STEP 1: Enter the starting points x, and x2, length LF, number of discarded initial chaotic
index points nF, and the level of security dF.
STEP 2: Generate nF chaotic points
cn+1 = CMT(cn)
and then discard them.
STEP 3: (a) cn+1 = CMT(Cn)
(b) The initial value of index j is 1, and j=j+1
mj =
1
cn+1
Step 4: [compare mj and the previous mk, 1<=k<=j-1 ]
If mj ϵ {mk, 1<=k<=j-1}, then discard this point and go to step 3;
otherwise proceed to the next step.
Step 5: If j>= LF, terminate the procedure, output mj, 1<=j<=LF, and perform the next
step;
Otherwise, go to step 3.
Step 6: [ FCIA: generate the chaotic index address assignment ]
(a) 1<=j<=LF, mj ϵ N
FCIA: M = {m1, m2, m3,…. mLF}
(b) mC* = maximum index address = max1<=j<=LF mj
Step 7: Input x2, the starting point for CMTG.
yn+1 = CMTG(yn), y0 = x2;
Step 8: If yn>dF then discard this point and go to step 7; otherwise, perform the next
step.
STEP 9: Generate a chaotic sequence with a finite length mc* by performing the
following iterative algorithm:
Y = {y0, y1, y2,…. Ymc*}
STEP 10: Generate a chaotic sequence of length LF.
Zn = {z0, z1, z2,…. zLF} = {ym0, ym1, ym2,…. YmLF};
STEP 11: The A Chaos based encryption bit streams (CBEBS) of W is generated as follows:
CBEBSW = {wn}
n = {1,2,…..LF}
wn = {1 zn >= 0.5}
wn = {0 zn< 0.5}
STEP 12: Deliver Electroencephalograms Visual User Environment Signal Bit
Stream of Length LF
EEGS = {eeg1, eeg2, eeg3,……eegLF}
STEP 13: Generate encrypted Generated encrypted clinical Electroencephalogram
Visual User Environment Signal Bit Streams (GEEG)
GEEG = EEGS
+
CBEBSW
Limitations of the Paper
• Microsoft-based operating system.
• Speed, is it necessary for encryption?
Thank You
Any Questions?
References
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