Full-round impossible differential attack on shadow block cipher

Lightweight block ciphers are the essential encryption algorithm for devices with limited resources. Its goal is to ensure the security of data transmission through resource-constrained devices. Impossible differential cryptanalysis is one of the most effective cryptanalysis on block ciphers, and assessing the ability of resisting this attack is a basic design criterion. Shadow is a lightweight block cipher proposed by Guo et al. (IEEE Internet Things J 8(16):13014–13023, 2021). It utilizes a combination of ARX operations and generalized Feistel structure to overcome the weakness of the traditional Feistel structure that only diffuses half in one round. In this paper, we focus on the differential property of Shadow and its security against impossible differential cryptanalysis. First, we use the SAT method to automatically search for a full-round impossible differential distinguisher of Shadow-32. Then, based on the experimental results, we prove that Shadow has a differential property with probability 1 based on the propagation of the state. Further, we can obtain an impossible differential distinguisher for an arbitrary number of rounds of Shadow. Finally, we perform a full key recovery attack on the full-round Shadow-32 and Shadow-64. Both experimentally and theoretically, our results indicate that Shadow is critically flawed, and regardless of the security strength of the internal components and the number of rounds applied, the overall cipher remains vulnerable to impossible differential cryptanalysis.