# Developing a New Collision-Resistant Hashing Algorithm

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## Abstract

**:**

## 1. Introduction

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- Study the theory of modern hashing algorithms and collision attacks;
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- Build a mathematical model of a hash function resistant to collision attacks;
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- Perform an analysis of the developed hash function based on statistical methods;
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- Implement a data integrity system that is resistant to collision attacks and based on the developed hash function.

## 2. Materials and Methods

#### 2.1. Description of Hash Function and Collision Attack

#### 2.2. Review of Modern Hashing Algorithms and Collision Attacks

#### 2.3. Related Works

## 3. Results

#### 3.1. Development of the Collision-Resistant Hashing Algorithm

_{i}, the transformation is performed according to formula (7) (the indexes of the elements are taken modulo 16):

_{i}with indices 2 ≤ i ≤ 16, the transformation is performed according to the formula:

_{i}and B

_{i}, transformations are performed according to the formula

#### 3.2. Demonstration of the Implemented Data Integrity Checking System

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Hash Function | Absolute Difference between the Expected Value (256) and the Average Hamming Distance | Standard Deviation of the Hamming Distance |
---|---|---|

SHA512 | 0.3786 | 11.3647 |

SHA3-512 | 0.4921 | 11.3451 |

ΓOCT 34.11–2018 | 0.4515 | 11.2974 |

Nik-512 | 0.0467 | 11.2951 |

SHA-2 | SHA-3 | GOST 34.11-2018 | Whirlpool | Nik-512 | Vulnerable (SHA-1, MD-5) | |
---|---|---|---|---|---|---|

HashGenerator | + | + | − | − | − | + |

HashMyFiles | + | + | − | − | − | + |

HashTab | + | + | − | + | − | + |

QuickHash | + | − | − | − | − | + |

MultiHasher | + | − | − | − | − | + |

NikitaHasher | + | + | + | − | + | − |

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**MDPI and ACS Style**

Cherckesova, L.V.; Safaryan, O.A.; Lyashenko, N.G.; Korochentsev, D.A.
Developing a New Collision-Resistant Hashing Algorithm. *Mathematics* **2022**, *10*, 2769.
https://doi.org/10.3390/math10152769

**AMA Style**

Cherckesova LV, Safaryan OA, Lyashenko NG, Korochentsev DA.
Developing a New Collision-Resistant Hashing Algorithm. *Mathematics*. 2022; 10(15):2769.
https://doi.org/10.3390/math10152769

**Chicago/Turabian Style**

Cherckesova, Larissa V., Olga A. Safaryan, Nikita G. Lyashenko, and Denis A. Korochentsev.
2022. "Developing a New Collision-Resistant Hashing Algorithm" *Mathematics* 10, no. 15: 2769.
https://doi.org/10.3390/math10152769