Mathematical model of authentication of a transmitted message based on a McEliece scheme on shorted and extended modified elliptic codes using UMAC modified algorithm

Abstract

The subject of the research is a mathematical model of authentication of the transmitted message based on the McEliese scheme on shortened and elongated modified elliptic codes using the modified UMAC algorithm. The aim of this work is to develop such a scheme for the information exchange over Internet communication channels, which would ensure the proper level of verification and integrity of the transmitted information, taking into account the prevention of an increase in the costs of the actions taken. Tasks: analysis of existing ways to increase the resistance to hacking of transmitted messages over telecommunication networks; analysis of a message transfer scheme using blockchain technology; formalized description of a mathematical model for providing clear text authentication using a modified UMAC algorithm, as the formation of key data, a crypto-code construction (CCC) is used on the McEliese scheme on modified elliptic codes (MEС); development of data encryption and decryption algorithms using CCC based on McEliese on the MEC and UMAC algorithm. Аn approach was proposed to verify the authentication and verification of the information packet during transmission and reception via telecommunication channels, which allows using already known hashing methods to compare generated codegrams and transmitted messages for their correspondence, which increases the level of cryptographic stability of the transmitted data and the reliability of the received data. The developed schemes of algorithms for generating codеgrams and their decryption using the proposed approach make it possible to gradually demonstrate the implementation of procedures for generating codegrams and their hash codes using both shortening and lengthening the code. Further research should prove from a practical point of view the effectiveness of using this approach when transmitting a message regarding the preservation of its integrity and authenticity. Therefore, it is necessary to develop a test system that should implement the proposed approach, as well as evaluate the results obtained.