Improved related-tweakey rectangle attacks on round-reduced Deoxys-BC

Deoxys-BC is the internal tweakable block cipher of the authenticated encryption (AE) Deoxys family, in which Deoxys-II is the primary choice for the use case of 'Defence in depth' among the portfolio of CAESAR competition. Improvements of the related-tweakey rectangle attacks on round-reduced Deoxys-BC using the known distinguishers is focussed in this study. Under the new related-key rectangle attack framework proposed by Dong et al. in EUROCRYPT 2022, we present three kinds of precomputed tables to further reduce the time complexity in the key-recovery phase. In the related-tweakey rectangle attack, the invalid quartets are filtered or the subtweakey candidates are obtained by lookup the precomputed tables without more computation. Based on the precomputed table technique, we improved the related-tweakey rectangle attacks on 11-round Deoxys-BC-256, 13-round and 14-round Deoxys-BC-384. Furthermore, we reduce the time complexity of the 13-round related-tweakey rectangle attack on Deoxys AE scheme Deoxys-I-256-128 by a factor of 2(24) compared with the best previous attack.