The Internet of Things (IoT) has become a necessary part of modern technology, enabling devices to connect and interact with each other. Unless applicable cryptographic components have adequate security protection, the IoT could easily leak private data. Impossible differential cryptanalysis (IDC) is one of the best-known techniques for cryptanalysis of block ciphers. Several papers are aimed at formalizing the IDC and constructing impossible differentials (IDs) automatically. In 2003, Kim et al. proposed a framework for searching IDs, namely the \(\mathcal {U}\) -method. Luo et al. improved it and presented the UID-method in 2009. The two methods target word-oriented block ciphers. In this paper, we present a framework for constructing impossible differential distinguishers without a matrix, called the \(\mathcal {K}\) 3.2 framework. This framework has a wider application on block ciphers than the \(\mathcal {U}\) -method, which works on the cipher with a certain property. In particular, the \(\mathcal {K}\) 3.2 framework employs fewer variables than the \(\mathcal {U}\) -method and the UID-method. Furthermore, we present 10 applications on block ciphers and structures. For an IoT cipher, ALLPC, we find the full-round IDs and two longer IDs with five more rounds than full rounds. We find some new results for two ISO standard ciphers. For SKINNY, considering single-key and single-tweakey, we discover the ID with one more round than the previous result. For CLEFIA, we find two new IDs with the length of the previous longest IDs. For LBlock, TWINE, Feistel, Gen-RC6, Gen-Skipjack, Gen-CAST256, and SMS4, we rediscover the known IDs.
