<p>Integral attacks are among the most effective techniques for analyzing block ciphers. At FSE 2016, Todo introduced the bit-based division property, reformulating integral properties through division property. Proving security bounds against such attacks is critical for modern ciphers, as it provides a guarantee of resistance to potential vulnerabilities. In this paper, we propose a general framework for evaluating the upper bounds of integral distinguishers based on the division property. Specifically, we formalize the necessary and sufficient conditions for determining whether integral distinguishers can be constructed. Technically, we address the exponential difficulty of constraints in the ZR’s method when applied to linear layers exceeding 16 dimensions. This challenge is overcome using dynamic constraint techniques, which are utilized in linear layers of dimensions 16, 32, and 64. Furthermore, we employ two-stage division property propagation methods to reduce the complexity of the MILP model, significantly improving the solving efficiency. By applying these techniques, we demonstrate the absence of integral distinguishers constructed via division property for 5-round ARIA, 14-round SM4, 10/13-round uBlock-128/256, 5-round AES, 13-round Ascon, 11-round GIFT-64, 13-round SKINNY-64, 10-round PRESENT, and 14-round CRAFT, further advancing the understanding of ciphers’ resistance to integral attacks.</p>