### Abstract

In the present paper we define a new hash function, based on inhomogeneous polynomials. First we define a large family of polynomials over finite fields and we prove that the members of this family are nearly permutational polynomials. Then we define a subfamily of the above family, such that the elements in the subfamily are easy to evaluate. We prove that (working in a large enough finite field) finding a preimage by chance of such a function is computationally infeasible, and we mention that methods for solving the equation corresponding to the preimage problem for such polynomials are also out of reach.

Original language | English |
---|---|

Pages (from-to) | 1-13 |

Number of pages | 13 |

Journal | Tatra Mountains Mathematical Publications |

Volume | 47 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2010 |

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### Keywords

- collision
- hash function
- polynomials

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Tatra Mountains Mathematical Publications*,

*47*(1), 1-13. https://doi.org/10.2478/v10127-010-0028-3

**On a family of preimage-resistant functions.** / Bérczes, Attila; Folláth, János; Pethő, A.

Research output: Contribution to journal › Article

*Tatra Mountains Mathematical Publications*, vol. 47, no. 1, pp. 1-13. https://doi.org/10.2478/v10127-010-0028-3

}

TY - JOUR

T1 - On a family of preimage-resistant functions

AU - Bérczes, Attila

AU - Folláth, János

AU - Pethő, A.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - In the present paper we define a new hash function, based on inhomogeneous polynomials. First we define a large family of polynomials over finite fields and we prove that the members of this family are nearly permutational polynomials. Then we define a subfamily of the above family, such that the elements in the subfamily are easy to evaluate. We prove that (working in a large enough finite field) finding a preimage by chance of such a function is computationally infeasible, and we mention that methods for solving the equation corresponding to the preimage problem for such polynomials are also out of reach.

AB - In the present paper we define a new hash function, based on inhomogeneous polynomials. First we define a large family of polynomials over finite fields and we prove that the members of this family are nearly permutational polynomials. Then we define a subfamily of the above family, such that the elements in the subfamily are easy to evaluate. We prove that (working in a large enough finite field) finding a preimage by chance of such a function is computationally infeasible, and we mention that methods for solving the equation corresponding to the preimage problem for such polynomials are also out of reach.

KW - collision

KW - hash function

KW - polynomials

UR - http://www.scopus.com/inward/record.url?scp=85026123927&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85026123927&partnerID=8YFLogxK

U2 - 10.2478/v10127-010-0028-3

DO - 10.2478/v10127-010-0028-3

M3 - Article

AN - SCOPUS:85026123927

VL - 47

SP - 1

EP - 13

JO - Tatra Mountains Mathematical Publications

JF - Tatra Mountains Mathematical Publications

SN - 1210-3195

IS - 1

ER -