Differential and Linear Cryptanalysis of ARX with Partitioning - Application to FEAL and Chaskey

In this work, we refine a partitioning technique recently proposed by Biham and Carmeli to improve the linear cryptanalysis of addition operations, and we propose an analogue improvement of differential cryptanalysis of addition operations. These two technique can reduce the data complexity of linear and differential attacks, at the cost of more processing time. Our technique can be seen of the analogue for ARX ciphers of partial key guess and partial decryption for SPN ciphers. We show a first application of the generalized linear partitioning technique on FEAL-8X, revisiting the attack of Biham and Carmeli. We manage to reduce the data complexity from 2 to 2 known plaintexts, while the time complexity increases from 2 to 2. Then, we use these technique to analyze Chaskey, a recent MAC proposal by Mouha et al., that is being studied for standardisation by ISO and ITU-T. Chaskey uses an ARX structure very similar to SipHash. We use a differential-linear attack with improvements from the partitioning technique, combined with a convolution-based method to reduce the time complexity. This leads to an attack on 6 rounds with 2 data and 2 time (verified experimentally), and an attack on 7 rounds with 2 data and 2 time. These results show that the full version of Chaskey with 8 rounds has a rather small security margin.