Novel Image Encryption Scheme Based on Chebyshev Polynomial and Duffing Map

Table 1

NIST statistical test suite results for 2×1000 sequences of size 10⁶-bit each generated by the proposed Chebyshev polynomial based pseudorandom bit generator and Duffing map based pseudorandom bit generator.

NIST statistical test	Chebyshev PRBG		Duffing PRBG
	𝑃-value	Pass rate	𝑃-value	Pass rate
Frequency (monobit)	0.649612	990/1000	0.490483	989/1000
Block-frequency	0.455937	991/1000	0.777265	992/1000
Cumulative sums (forward)	0.877083	990/1000	0.660012	988/1000
Cumulative sums (reverse)	0.983938	992/1000	0.284024	987/1000
Runs	0.062427	995/1000	0.490983	993/1000
Longest run of ones	0.215574	993/1000	0.612147	992/1000
Rank	0.848027	991/1000	0.212184	988/1000
FFT	0.194813	993/1000	0.013474	993/1000
Nonoverlapping templates	0.504571	990/1000	0.458442	990/1000
Overlapping templates	0.219006	992/1000	0.279844	988/1000
Universal	0.660012	986/1000	0.278461	991/1000
Approximate entropy	0.000478	990/1000	0.363593	991/1000
Random excursions	0.508738	597/603	0.671829	612/618
Random excursions variant	0.614825	596/603	0.490932	612/618
Serial 1	0.585209	991/1000	0.779188	990/1000
Serial 2	0.767582	989/1000	0.713641	993/1000
Linear complexity	0.711601	986/1000	0.699313	991/1000