<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

On a family of preimage-resistant functions

Institute of Mathematics University of Debrecen Number Theory Research Group Hungarian Academy of Sciences and University of Debrecen P.O. Box 12 H–4010 Debrecen HUNGARY

Faculty of Informatics University of Debrecen P.O. Box 12 H–4010 Debrecen HUNGARY

Tatra Mountains Mathematical Publications

{"article-title":"On a family of preimage-resistant functions"}

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...

On a family of preimage-resistant functions

Data publikacji: 13 lis 2012

Zakres stron: 1 - 13

DOI: https://doi.org/10.2478/v10127-010-0028-3

Słowa kluczowe
hash function, collision, polynomials.

This content is open access.

On a family of preimage-resistant functions

Data publikacji: 13 lis 2012

Zakres stron: 1 - 13

DOI: https://doi.org/10.2478/v10127-010-0028-3

Słowa kluczowehash function, collision, polynomials.

This content is open access.

Słowa kluczowe
hash function, collision, polynomials.