Generalization of the Self-Shrinking Generator in the Galois Field GF(𝑝^𝑛)

Table 6

Results from the NIST test suite for two sets of 100 keystreams of length 10⁶, generated by the pGSSG.

NIST Statistical Test	17GSSG		257GSSG
	𝑃-value	Pass rate	𝑃-value	Pass rate
Frequency	.798139	0.990000	.955835	1.000000
Block-frequency	.334538	0.990000	.834308	0.980000
Cumulative-sums 1	.637119	0.990000	.289667	1.000000
Cumulative-sums 2	.851383	0.990000	.595549	1.000000
Runs	.030806	1.000000	.867692	1.000000
Longest-run	.867692	0.970000	.162606	0.980000
Rank	.171867	1.000000	.437274	1.000000
FFT	.574903	1.000000	.191687	0.990000
Nonperiodic-templates*	.478512	0.988784	.504990	0.990676
Overlapping-templates	.096578	0.990000	.334538	0.990000
Universal	.213309	1.000000	.129620	1.000000
Apen	.000230	0.960000	.911413	1.000000
Random-excursions**	.246591	0.993663	.564158	0.993738
Random-excursions-variant***	.269248	0.992489	.479677	0.996289
Serial 1	.096578	1.000000	.437274	0.990000
Serial 2	.851383	1.000000	.574903	0.990000
Lempel-ziv	.012650	0.990000	.025193	0.980000
Linear-complexity	.739918	0.990000	.971699	0.970000

*The given values are average of the all 148 nonperiodic-templates NIST tests.
**The given values are average of the all 8 random-excursions NIST tests.
***The given values are average of the all 48 random-excursions-variant NIST tests.