Welcome to the resource topic for 2021/1194
Title:
Automated Truncation of Differential Trails and Trail Clustering in ARX
Authors: Alex Biryukov, Luan Cardoso dos Santos, Daniel Feher, Vesselin Velichkov, Giuseppe Vitto
Abstract:We propose a tool for automated truncation of differential trails in ciphers using modular addition, bitwise rotation, and XOR (ARX). The tool takes as input a differential trail and produces as output a set of truncated differential trails. The set represents all possible truncations of the input trail according to certain predefined rules. A linear-time algorithm for the exact computation of the differential probability of a truncated trail that follows the truncation rules is proposed. We further describe a method to merge the set of truncated trails into a compact set of non-overlapping truncated trails with associated probability and we demonstrate the application of the tool on block cipher Speck64. We have also investigated the effect of clustering of differential trails around a fixed input trail. The best cluster that we have found for 15 rounds has probability 2^{-55.03} (consisting of 389 unique output differences) which allows us to build a distinguisher using 128 times less data than the one based on just the single best trail, which has probability 2^{-62}. Moreover, we show examples for Speck64 where a cluster of trails around a suboptimal (in terms of probability) input trail results in higher overall probability compared to a cluster obtained around the best differential trail.
ePrint: https://eprint.iacr.org/2021/1194
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