A Chaos Robustness Criterion for 2D Piecewise Smooth Map with Applications in Pseudorandom Number Generator and Image Encryption with Avalanche Effect

Table 1

The required intervals of the FIPS 140-2 Monobit Test, Porker Tests, Runs Test. Here, MT, PT, and LT represent the Monobit Test, the Porker Test, and the Long Runs Test, respectively. represents the length of the run of a tested sequence. DT represents distribution.

Test item	FIPS 140-2		Golomb’s postulates
	Required intervals	Accepted intervals
MT	9,725~10,275	9,725~10,275	10000
PT	2.16~46.17	2.16~46.17	DT
LT	26	<26	—
	Run Test	Run Test	Run Test
1	2,315~2,685	2,362~2,638	2,500
2	1,114~1,386	1,153~1,347	1,250
3	527~723	556~694	625
4	240~384	264~361	313
5	103~209	122~191	156
6+	103~209	122~191	156