Search papers, labs, and topics across Lattice.
This paper introduces a novel bound on the total variation distance of random walks using equitable partitions to analyze the security of code-based cryptosystems. This approach offers an alternative to Fourier transform-based methods for bounding the smoothing parameter, a key metric for code security. The derived inequality generalizes existing results for finite abelian groups, potentially leading to tighter security analyses.
Random walks and equitable partitions offer a fresh perspective on bounding the smoothing parameter in code-based cryptography, potentially surpassing Fourier transform-based methods.
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.
