Abstract
In this paper we describe a new tool to search for boomerang distinguishers. One limitation of the MILP model of Liu et al. is that it handles only one round for the middle part while Song et al. have shown that dependencies could affect much more rounds, for instance up to 6 rounds for SKINNY. Thus we describe a new approach to turn an MILP model to search for truncated characteristics into an MILP model to search for truncated boomerang characteristics automatically handling the middle rounds. We then show a new CP model to search for the best possible instantiations to identify good boomerang distinguishers. Finally we systematized the method initiated by Song et al. to precisely compute the probability of a boomerang. As a result, we found many new boomerang distinguishers up to 24 rounds in the TK3 model. In particular, we improved by a factor 230 the probability of the best known distinguisher against 18-round SKINNY-128/256.
Highlights
Differential cryptanalysis is one of the most powerful cryptanalysis techniques
We propose a new Constraint Programming (CP) model to search for the best instantiation of a truncated boomerang characteristic
Assuming an MILP model to search for truncated differential characteristics on this cipher, we show how to turn it into an MILP model to search for truncated boomerang characteristics
Summary
Differential cryptanalysis is one of the most powerful cryptanalysis techniques. It was proposed by Biham and Shamir in [BS91] and has generated much attention since . The classical approach is to first search for two short characteristics with high probability and to combine them We believe this approach should be deprecated since the dependency in the middle rounds may hugely affect the probability of the distinguisher and it seems sub-optimal to search for both the lower and upper differentials independently. A more generic approach was proposed in [LS19], where Liu et al describe an MILP model to directly search for the best boomerang distinguisher against the block cipher GIFT. We propose a new Constraint Programming (CP) model to search for the best instantiation of a truncated boomerang characteristic.
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