The ISC International Journal of Information Security

Abstract Given the rapid evolution of emerging technologies, such as the Internet of Things (IoT), there is a growing interest in lightweight block ciphers. This paper focuses on the security assessment of SAND-128, a newly proposed lightweight block cipher based on SIMON, recognized for its reliance on S-box-based security evaluation approaches. By employing Xiang’s MILP-aided method for integral distinguisher search, this study utilizes a MILP optimizer to identify a 16-round integral characteristic for SAND-128 with nine balanced bits. Furthermore, by extending the distinguisher to 17 rounds utilizing a novel idea without an increase in data complexity, we propose a comprehensive 20-round integral attack on SAND-128, including the key recovery step. This attack leverages the partial sums technique, resulting in a time complexity of 2119, memory complexity of 276 bytes, and data complexity of 2127. This cryptanalysis is, to the best of our knowledge, the best integral attack on reduced-round SAND-128 presented thus far.

Abstract Conventional Bit-based Division Property (CBDP), as a generalization of integral property, has been a powerful tool for integral cryptanalysis of many block ciphers. Exploiting a Mixed Integral Linear Programming (MILP) optimizer, an alternative approach to searching integral distinguishers was proposed, which has overcome the bottleneck of the cipher block length. The MILP-aided method starts by modeling CBDP propagation by a system of linear inequalities. Then by choosing an appropriate objective function, the problem of searching distinguisher transforms into an MILP problem. As an application of this technique, we focused on a newly proposed lightweight block cipher SAND. SAND is a family of two AND-RX block ciphers SAND-64 and SAND-128, which was designed to overcome the difficulty regarding security
evaluation. For SAND-64, we found a 12-round distinguisher with 23 balanced bits and a data complexity of 263, with the superiority of a higher number of balanced bits than the designers’ one. Furthermore, we applied an integral attack on a 15 and 16-round SAND-64, including the key recovery step which resulted in time complexity of 2105 and 2109.91 and memory complexity of 252 and 285 bytes, respectively.