A New Approach to Code Smoothing Bounds
This work addresses a specific problem in cryptography for analyzing code-based cryptosystems, but it appears incremental as it generalizes prior results.
The paper tackles the problem of bounding the smoothing parameter for code-based cryptosystems by deriving an inequality for the total variation distance of random walks using equitable partitions, showing that this bound generalizes existing results for finite abelian groups.
To analyze the security of code-based cryptosystems, the smoothing parameter, which is closely related to the total variation distance of codes, has been investigated. While previous studies have bounded this distance using the Fourier transform on locally compact abelian groups, we take an alternative approach based on random walks. In this paper, we derive an inequality for the total variation distance of random walks using equitable partitions, and we show that our proposed bound generalizes existing results for finite abelian groups.