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Automated Truncation of Differential Trails and Trail Clustering in ARX
Biryukov, Alexei; Cardoso Dos Santos, Luan; Feher, Daniel et al.
2022In Selected Areas in Cryptography - 28th International Conference, Revised Selected Papers
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Keywords :
secret-key cryptography; Symmetric-key; Block Ciphers; Differential Cryptanalysis; Truncated Differentials; ARX; Speck
Abstract :
[en] 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.
Research center :
Interdisciplinary Centre for Security, Reliability and Trust (SnT) > CryptoLUX – Cryptography
Disciplines :
Computer science
Author, co-author :
Biryukov, Alexei ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
Cardoso Dos Santos, Luan ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
Feher, Daniel ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Cryptolux
Velichkov, Vesselin;  University of Edinburgh
Vitto, Giuseppe ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > Cryptolux
External co-authors :
yes
Language :
English
Title :
Automated Truncation of Differential Trails and Trail Clustering in ARX
Publication date :
2022
Event name :
Selected Areas in Cryptography - 28th International Conference
Event place :
Canada
Event date :
September 29 - October 1, 2021
Audience :
International
Main work title :
Selected Areas in Cryptography - 28th International Conference, Revised Selected Papers
Publisher :
Springer
Peer reviewed :
Peer reviewed
Focus Area :
Security, Reliability and Trust
FnR Project :
FNR11684537 - Security, Scalability, And Privacy In Blockchain Applications And Smart Contracts, 2017 (01/08/2018-31/07/2021) - Alex Biryukov
Name of the research project :
R-AGR-3125 - PRIDE15/1062187/SPsquared (01/01/2017 - 30/06/2023) - MAUW Sjouke
FNR11684537 - Security, Scalability, And Privacy In Blockchain Applications And Smart Contracts, 2017 (01/08/2018-31/07/2021) - Alex Biryukov
Funders :
FNR - Fonds National de la Recherche [LU]
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since 19 January 2022

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