Integral Attack with Bit-Based Division Property on Block Cipher LBC-3

The block cipher LBC-3, which was proposed by Nyssanbayeva et al. in 2022, has a 64-bit block size, an 80-bit secret key size, and the number of rounds is 20. The designer investigated the avalanche effect of LBC-3, and Yasushi et al. evaluated the security against differential and linear cryptanalysis. On the other hand, it has not been evaluated the security against integral cryptanalysis, which is one of the most powerful cryptanalysis techniques on block cipher. In this paper, we apply integral cryptanalysis to LBC-3. By establishing the Mixed Integer Linear Programming (MILP) model based on bit-based division property, we discovered the 18-round integral characteristic, the longest integral characteristic of LBC-3. Then, based on the 16-round characteristic newly found, we show that the integral attack on full-round LBC-3 is more efficiently possible with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2^{50.8}$</tex> data and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2^{51.4}$</tex> times of encryption.