# A Secure Random Number Generator with Immunity and Propagation Characteristics for Cryptography Functions

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

- The analysis of propagation and immunity characteristics of SRFG.
- Statistical testing on SRFG output-based NIST recommendations.
- Security analysis for SRFG as a random number generator.

## 3. Symmetric Random Function Generator (SRFG)

## 4. Propagation Criterion of SRFG

## 5. Immunity Feature of SRFG

## 6. Results

#### 6.1. Performance of SRFG

#### 6.2. Comparative Analysis

#### 6.3. Statistical Analysis

**Hypothesis**

**1.**

**Hypothesis**

**2.**

#### 6.4. Security Analysis

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Propagation criterion. (

**a**) Varying number of bits and variables; (

**b**) Varying number of bits and expression length.

**Figure 5.**Correlation Immunity. (

**a**) Correlation immunity with varying bits and input variables; (

**b**) Correlation immunity with varying bits and expression length%.

Metrics | Values |
---|---|

No. of variables (N) | 2 to 5 |

No. of bits (n) | 16, 32, 64, 128, 256, 512, 1024 and 2048 |

No. of Expressions (L) | 2 to 10 |

Boolean functions | AND, XOR, NOT, OR |

Sample size | 800 |

Sample technique | Random |

Propagation Criterion | Correlation Immunity | Algebraic Immunity | |
---|---|---|---|

SRFG | $\frac{n}{2}$ | 100% | $\frac{n}{2}$ |

Wang et al. [18] | $\sqrt{\frac{n}{2}}-1$ | 57.63% | 0 |

Kumar et al. [26] | $\frac{n}{4}$ | 87.50% | 0 |

Hsueh et al. [27] | $\frac{n}{4}$ | 85.33% | 0 |

Vigna [29] | logn | 76.67% | 0 |

Kaya [31] | $\frac{n}{2}$ | 92.30% | $\frac{n}{2}$ |

Stanchieri et al. [32] | logn | 76.67% | 0 |

Martirosyan et al. [33] | $\frac{n}{2}$ | 94.33% | 0 |

Monobit Test | Frequency Test within a Block | Runs Test | Test for Longest Run in the Block | Binary Matrix Rank Test | |
---|---|---|---|---|---|

Test on SRFG and their p-values | 1.00 | 1.00 | 0.723 | 0.1933 | 0.5320 |

Spectral test | Non overlapping template matching test | Overlapping template matching test | Maurer’s test | Linear complexity test | |

0.300 | 0.300 | 0.280 | 0.777 | Applicable only for LFSR | |

Serial test | Approximate entropy test | Cumulative sum test | Random excursions test | Random excursions variant test | |

NA as per NIST recommendation | 0.2770 | 0.433 | 0.777 | 0.777 |

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**MDPI and ACS Style**

Saha, R.; Geetha, G.; Kumar, G.; Buchanan, W.J.; Kim, T.-h.
A Secure Random Number Generator with Immunity and Propagation Characteristics for Cryptography Functions. *Appl. Sci.* **2021**, *11*, 8073.
https://doi.org/10.3390/app11178073

**AMA Style**

Saha R, Geetha G, Kumar G, Buchanan WJ, Kim T-h.
A Secure Random Number Generator with Immunity and Propagation Characteristics for Cryptography Functions. *Applied Sciences*. 2021; 11(17):8073.
https://doi.org/10.3390/app11178073

**Chicago/Turabian Style**

Saha, Rahul, Ganesan Geetha, Gulshan Kumar, William J. Buchanan, and Tai-hoon Kim.
2021. "A Secure Random Number Generator with Immunity and Propagation Characteristics for Cryptography Functions" *Applied Sciences* 11, no. 17: 8073.
https://doi.org/10.3390/app11178073