Paper 2024/1217

A Compact and Parallel Swap-Based Shuffler based on butterfly Network and its complexity against Side Channel Analysis

Abstract

A prominent countermeasure against side channel attacks, the hiding countermeasure, typically involves shuffling operations using a permutation algorithm. Especially in the era of Post-Quantum Cryptography, the importance of the hiding coun- termeasure is emphasized due to computational characteristics like those of lattice and code-based cryptography. In this context, swiftly and securely generating permutations has a critical impact on an algorithm’s security and efficiency. The widely adopted Fisher-Yates shuffle, because of its high security and ease of implementation, is prevalent. However, it has a limitation of complexity O(𝑁) due to its sequential nature. In response, we propose a time-area trade-off swap algorithm, FSS, based on the Butterfly Network with only log(𝑁) depth, log(𝑁) works and O(1) operation time in parallel. We will calculate the maximum gain that an attacker can achieve through butterfly operations with only log(𝑁) depth from side channel analysis perspective. In particular, we will show that it is possible to derive a generalized formula of the attack complexity with higher-order side channel attacks for arbitrary input sizes through a fractal structure of the butterfly network. Furthermore, our research highlights the possibility of generating efficient and secure permutations utilizing a minimal amount of randomness.