Expected security performance of random linear binary codes in syndrome coding

TL;DR: A code design method is presented which constructs a class of random codes, termed random permutation codes, which achieve high security levels and are easily generated, which has the practical advantage in syndrome coding of being able to use an ephemeral code for each communication session.

Abstract: In this study, random codes are applied to the classical syndrome coding scheme to achieve secrecy of communications. By analysing the effect of the values of the columns of the parity check matrix on the resulting security level of communications, a code design method is presented which constructs a class of random codes, termed random permutation codes, which achieve high security levels and are easily generated. A theoretical analysis method is presented which determines the security level achieved by randomly chosen, linear binary codes, and compared with simulation results obtained by Monte Carlo analysis. The results verify the theoretical approach. In particular, the theoretical method is also suitable for analysis of long codes having a large number of parity check bits which are beyond evaluation by computer simulation. The results show that the security performance of any randomly chosen permutation code is close to that of the best equivocation code having the same code parameters. This has the practical advantage in syndrome coding of being able to use an ephemeral code for each communication session, thereby providing forward secrecy, a desired feature of modern, secure communication systems.