Abstract: In the industrial Internet that incorporates the Internet of things and 5G network technologies, end devices generate enormous amounts of data. The secure transmission of the data requires lightweight ciphers dedicated to such resource-constrained environments. Furthermore, the security evaluation of newly proposed lightweight ciphers is crucial to secure the industrial Internet. An improved integral property for ciphers with a particular structure is proposed by using the multivariate polynomial technique in this study. By using the proposed integral property, longer integral distinguishers are constructed, which improve the integral analysis from the algebraic structure perspective. A framework for constructing integral distinguishers of SPN and Feistel-SP block ciphers from the algebraic structure perspective is given. It is applied to the integral analysis of the lightweight block cipher WARP proposed by Banik et al. in SAC 2020. As a result, two 22-round integral distinguishers with data complexity 2¹¹⁶ are constructed, which are two rounds longer than the distinguishers given by the designers, with less complexity. Based on the 22-round distinguishers, a 26-round key-recovery attack is proposed, which is five rounds more than the one given by the designers. To the best of our knowledge, this is thus far the best known key-recovery attack on WARP in the single-key scenario. In addition, experimental verification of an 18-round integral distinguisher is carried out with the data complexity 2³².