ELECTROTECHNIC AND COMPUTER SYSTEMS, Odessa national polytechnic university

MATHEMATICAL METHODS FOR CONSTRUCTING HASH FUNCTIONS BASED ON THE THEORY OF FINITE FIELDS IN INFORMATION TECHNOLOGY SYSTEMS

Abstract:

In this paper a method for constructing hash functions based on irreducible polynomials in finite fields was considered. The problem of finding irreducible polynomials was considered. A computer simulation of hash functions was performed using irreducible polynomials. The results of using various irreducible polynomials and their analysis are given. The problem of the occurrence of collisions depending on the length of the hash, and the probability of collisions is estimated depending on the number of enumeration operations were considered.

Authors:

George Vostrov, ( vostrov@gmail.com,ORCID ID: 0000-0003-3856-5392 )
Olena Ponomarenko, ( ponomarenkoelena1997@gmail.com,ORCID ID: 0000-0003-1585-4706 )

Keywords

hash function, finite field, irreducible polynomial, collision, cyclic redundant code, polynomial arithmetic, “birthdays” paradox

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