RECTANGLE is a 64-bit block cipher with 80 and 128-bit key length proposed by Zhang et al(Lightweight Cryptography Workshop 2015). Integral attack is one of the typical evaluation tools of block cipher. The designers showed 7-round integral distinguisher. On the other hand, we find 8-round integral distinguisher which has balanced columns by our proposal search method of integral distinguisher. In this paper, we present the first integral attack on reduced-round RECTANGLE. Based on 8-round distinguisher, we can attack 12-round RECTANGLE-128 with computational complexity 2^109.98 with partial sum technique. Also, we can attack 10-round RECTANGLE-80 with computational complexity 270.08.

Integral distinguisher is the main factor of integral attack. In the conventional search strategy of integral distinguisher (ID), there are two steps. In the first step, first order ID is obtained. In the second step, first order ID is extended by increasing the order. We find it is problematic to apply the conventional strategy for Feistel ciphers whose number of sub blocks N is large such as TWINE and LBlock (N = 16). To solve the problem, we propose new search strategy which has large search scope and feasibility in realistic computational condition. By the reduction of the computational complexity, it is reduced from O((nN)×(2mn)) to O(N×2mn). And for the acceleration of the experiment, we use GPGPU (general-purpose computing on graphics processing units) platform. By using GPGPU platform, we can test substantially higher order ID than existing CPU platform. We execute computer experiment to discover the precise fifteenth order ID of TWINE and LBlock by proposal strategy. As a result, we find new fifteenth order ID which has 8 balanced sub blocks (32-bit) after 15-round encryption both in TWINE and LBlock. These results are the most precise evaluatiPon of TWINE and LBlock.