Integral analysis of GRANULE and ESF block ciphers based on MILP

The lightweight block ciphers, which have the characteristics of lightweight structure and low power consumption, are especially suitable for resource-constrained environments. Bit-based division property with Mixed Integer Linear Programming (MILP) model is constructed according to the structural characteristics of the ciphers, which gives an automatic search method for the longest 10-round integral distinguisher of GRAN-ULE and the 9-round integral distinguisher of ESF, respectively. Based on the 8-round integral distinguisher, 12-round integral attack of GRANULE is obtained by extending backward 4-round. Employing the key equivalence relation to reduce the complexity, the time complexity is about 2
^58.17
and the data complexity is about 2
^62.17
chosen plaintexts of GRANULE. Compared with other attack methods of current GRANULE and ESF, this is the optimal analysis result of the two ciphers on the length of distinguisher and the number of attack rounds.