Research Article

CFA: A New Family of Hybrid CA-Based PRNGs

Table 11

Selection process for the ruleset.

PrincipleChoice

Choose a nonlinear rule with good cryptographic properties for the first cellRule 30 selected [30]
In order to have a good compromise between the algebraic degree and the correlation immunity, an equal number of linear and nonlinear rules should be selected for the remaining cellsRules 60, 90, and 110 selected [30, 60, 110, 90]
To increase the algebraic degree, two or three nonlinear rules should be selected consecutivelyRule 30 followed by rule 110 [30, 60, 30, 110, 90]
To increase the order of correlation immunity, one nonlinear rule should be followed by more than one linear ruleRule 30 followed by rules 60 and 90 [30, 60, 90, 30, 110, 30, 60, 90]
To increase the period of the hybrid CA, rules with larger period should be chosenRules 90 and 150 selected [30, 90, 150, 30, 110, 30, 90, 150]

Input: the set of linear rules L = {60, 90, 102, 105, 150, 165, 195} and the set of nonlinear rules NL = {22, 30, 37, 41, 43, 45, 91, 110, 120, 135, 180, 210}. Output: a ruleset with rules having good cryptographic properties [30, 90, 150, 30, 110, 30, 90, 150].