The average equivocation of random linear binary codes in syndrome coding

This paper studies the security performance of random codes in the syndrome coding scheme. We propose theoretical analysis using a putative (n, k) code having the same distribution of syndrome probabilities as the ensemble of all (n, k) random codes to calculate the average equivocation of random codes, and compare the theoretical results with the simulation results generated from Monte Carlo analysis which shows that the theoretical method is precise. Moreover the analysis works well for long codes having large values of n - k, which are not amenable to Monte Carlo analysis. We present results showing that the longer the length of the code the higher the value of the average equivocation and the lower the value of the standard deviation of the equivocation. For code lengths in excess of 150 bits or so almost any random code will produce high levels of secrecy.