Construction of hash functions based on theory of finite fields with the use of irreducible polynomials

Abstract

With an increase in the amount of information, the problems associated with large amounts of data are aggravated, which in the future require the implementation of storage, transfer or processing processes. Working with large volumes of files significantly complicates these processes, and therefore there is a need for the existence of algorithms that allow compressing the volumes of files to the required size, acceptable for their efficient processing.

Hash functions play an important role in the process of interacting with files. The use of hash functions implies the transformation of the original data according to a certain algorithm into a sequence of fixed length. This allows you to significantly speed up the search among a large number of files to view, modify or delete, to compare files, to verify immutability in cases where the data should not be changed by unauthorized persons. Thus, hashing is used in all areas where the question of storing, transmitting or processing data in the form of files arises, namely in cryptography, computer graphics, when organizing data on a computer and on the Internet.