Secured polar code derived from random hopped frozen-bits

Abstract

The polar code is a unique coding approach that can achieve Shannon's capacity in modern communication systems' discrete memory-less channels with superior reliability, but it is not secure enough under modern attacks for such systems. This study aims to offer a comprehensive secured polar coding scheme that uses a combination of polar coding and the Mersenne-Twister pseudo-random number generator (MT-PRNG) to achieve a super secured encoding. The pre-shared crypto-system cyphering key initiates the starting state of the MT-PRNG as a seed. The randomly generated sequences govern the values of the frozen bits in polarized bit channels and their associated indices. A half-bit-error-rate probability system performance is calculated when the encoding ciphering keys at the receiver differ by a single bit from those utilized at the transmitter. Using calculated numerical analysis, the system is shown to be secure against brute force attacks, Rao-Nam attacks, and polar code reconstruction attacks.