## 2 Related Work  
The algorithms in cryptography uses various types of cryptographic functions and transformations; these possess different factors which are important for designing such functions [6]. For example, algebraic, random and heuristic constructions of functions are important in this case. In paper [7], the authors have discussed the propagation properties of Boolean functions. New properties are also identified which have the high strict avalanche criterion. The research work in [8] analyses the inverse permutation on the field component functions. The weights of derivatives of the component functions also use Kloosterman sums. The authors in the paper [9] show the property of aperiodic autocorrelation in Boolean function aspect and define the Aperiodic Propagation Criteria (APC). The work also shows the relation between aperiodic autocorrelation and the first derivative of the function.  
The concept of correlation immunity in Boolean functions was introduced by [PERSON] [10]. Furthermore, this feature of Boolean functions has been considered to be an important characteristics for strong cryptographic algorithms and has been researched with concern as shown in [11; 12; 13; 14]. Some of the contemporary research has been done to provide immunity to the functions both as correlation aspect and algebraic aspect. High algebraic immunity is a required factor for cryptographic algorithms to prevent algebraic attacks. Algebraic immunity must have a lower bound failing which functions must not be used in cryptography. Such a lower bound in evaluated in [15]. The relation of algebraic immunity and extended algebraic immunity is researched in [16; 17]. The bent functions are also in use for construction of a class of functions in infinity [18]. The authors have considered only odd number of variables. Decomposition of the first-order correlation-immune Boolean functions is researched significantly [19]. Following this, an enumerative encoded Boolean function is designed [20]. In the paper [21], optimal algebraic immunity construction strategy has been shown using vector spaces and m-sequences. Boolean functions can be presented into two hybrid classes [22]. The magnitude of the inter-class algebraic immunity is maximum. It also prohibits resistance against algebraic attacks with high non-linearity. 1-resilient functions are also in existence. Algebraic immunity on balanced functions has been shown in the papers [23; 24]. Vector valued functions over finite field has also experimented for maximum algebraic immunity in [25].  
Some of the recent developments in field of random and pseudo-random number generators have been reviewed. For example, the random number generation in [26; 27] show the applications in BIST and IoT Applications. The later one is based on chaos and is validated by statistical tests. A pseudo random generator for cryptographic applications has been shown in [28]. Several studies were carried out in this domain for validation of random numbers and generation of random numbers as shown in [29; 30; 31; 32; 33]. Such studies show that random numbers are in real need for various applications and their design factors are also very important.  
Symmetric Random Function Generator (SRFG) is random bit generator that produces the symmetric and balanced outputs [34]. The authors have analysed the nonlinearity, resiliency, balancedness properties of SRFG. In our present work, we have extended the feature analsyis of SRFG with the explanation for propagation and immunity characteristics, security analysis and statistical testing. The main contribution of the presented research work are:  
1. The analysis of propagation and immunity characteristics of SRFG.
2. Statistical testing on SRFG output-based NIST recommendations.
3. Security analysis for SRFG as a random number generator.