A switched chaotic encryption scheme using multi-mode generalized modified transition map

Abstract

This paper presents a multi-mode generalized modified transition chaotic map and a switched chaotic encryption scheme based on it. Eight different modes of operation can be selected based on the map graph (concave or convex), the range modification procedure (shrinking or widening) and the sign of one of its independent parameters. The generalization and modification preserve the controllability and continuous chaotic behavior properties, respectively. For the same encryption key and map equation, multi-mode operation occurs through switching between four alternatives of the dependent parameters. Switching between various modes is shown to overpass single modes in randomness by investigating the frequency distribution, autocorrelation function, histograms and 0-1 test. In addition, most bits, 75%, of the scaled and quantized chaotic output are shown to be suitable for pseudo-random number generation based on National Institute of Standards & Technology (NIST) statistical test suite. The performance of the proposed scheme is validated for several speech, grayscale and RGB images through various evaluation criteria, where good results are achieved. These criteria include basic perceptual and statistical aspects, the more advanced NIST tests, key sensitivity and robustness against brute force and differential attacks. The efficiency of the scheme is improved by up to three or six times faster than encrypting one sample or one channel of a pixel at a time for speech and image inputs, respectively. The proposed scheme demonstrates good security and efficiency with more applied evaluation criteria compared to similar recent works.

Appendix: List of Abbreviations and Symbols

List of Abbreviations

NIST:

National Institute of Standards & Technology

DES:

Data Encryption Standard

AES:

Advanced Encryption Standard

PRNG:

Pseudo-Random Number Generator

LSB:

Least Significant Bit

PV:

P-value distribution

PP:

Proportion of passing sequences

MSB:

Most Significant Bit

MSE:

Mean Squared Error

NSCR:

Number of Samples Change Rate

UACI:

Unified Average Changing Intensity

NPCR:

Number of Pixels Change Rate

FPGA:

Field Programmable Gate Array

List of Symbols

x, x_n:

Iterated map variable

f(.):

Map equation

λ :

Main parameter

μ :

Shifting parameter

a :

Scaling parameter

c :

Shaping parameter

x _max+ :

Maximum value of x for generalized concave map

x_max− (x_min−):

Maximum (Minimum) value of x for generalized convex map

β :

Range modification parameter

R_min (R_max):

Lower (Upper) bound on the map domain

M(n):

Mean square displacement

K :

Growth rate (0-1 test)

z _n :

Chaotic output after scaling and quantization

hex2dec(.):

Converts a hexadecimal number to a decimal number

K₁, K₂, K₃, K₄:

Sub-key values in hexadecimal format

x_fix, a_fix, β_fix, c_fix:

Pre-defined fixed values of the parameter that guarantee chaotic behavior

x_key, a_key, β_key, c_key:

Key dependent perturbations

P _{s u m} :

Input dependent perturbation

mod(m, 10):

Remainder after dividing m by 10

r _{x y} :

Correlation coefficient

P(S_i):

Probability of the sample value S_i

p :

Number of bits per sample

P(i, j):

Pixel value