Abstract Differential attack is one of the most important methods in cryptanalysis. When finding a high-probability differential trail, the effect of constant has long been ignored. In this paper, we focus on the effect of constants on the differential attack against $\mu ^2$. $\mu ^2$ is a newly proposed block cipher based on a Type-II generalized Feistel structure. Its 16-bit F function (denoted as F-box) is an ultra-lightweight permutation equipped with different constants. The designer applied the minimum number of active S-boxes to determine $\mu ^2$’ security margin in the design document. However, the F-boxes use different round constants in different rounds; the constants may lead to incompatibility of differential trails of F-boxes. Therefore, to provide a more precise differential attack on $\mu ^2$, we construct an model based on STP (Simple Theorem Prover) constraint solver to search for the valid differential trails with a more precise probability of $\mu ^2$ for different starting rounds. Finally, the related-key differential trail covers one more round than the existing methods. Analyzing the effect of constants on the validity and the probability of the differential trail reminds the designers and the attackers to have a more comprehensive analysis of specific ciphers.

WARP , an efficient lightweight block cipher presented by Banik et al., offers a viable alternative to AES with its 128‐bit block and a 128‐bit key. It adopts a 32‐nibble type‐II generalized Feistel network (GFN) structure, incorporating a nibble permutation optimized for both security and efficiency. Notably, WARP has achieved the lowest hardware implementation among 128‐bit block ciphers. Its bit‐serial encryption‐only circuit is only 763 gate equivalents (GEs). Consequently, WARP has received significant attention since its inception. The designers evaluated the number of active Sboxes for linear trails in WARP to establish its security. To further investigate WARP ’s resistance against linear attacks, we employed an automated model to analyze the optimal linear trails/hulls of WARP . To achieve this, the problem will be transformed into a Boolean satisfiability problem (SAT). The constraints in conjunctive normal form (CNF) are used to describe the mask propagation of WARP and invoke the SAT solver to find valid solutions. The results allowed us to obtain the optimal correlation of the initial 21‐round linear trails for WARP . Furthermore, by enumerating the linear trails within a linear hull, the distribution of linear trails is revealed, and the probability of the linear hull is improved to be more accurate. This work extends the linear distinguisher from 18 to 21 rounds. Additionally, the first independent analysis of WARP ’s linear properties is presented, offering a more precise evaluation of its resistance against linear cryptanalysis.

The morphological analysis of hippocampus is vital to various neurological studies including brain disorders and brain anatomy. To assist doctors in analyzing the shape and volume of the hippocampus, an accurate and automatic hippocampus segmentation method is highly demanded in the clinical practice. Given that fully convolutional networks (FCNs) have made significant contributions in biomedical image segmentation applications, we propose a notably discriminative feature network based on a hierarchical attention mechanism in hippocampal segmentation. First, considering the problem that the hippocampus is a rather small part in MR images, we design a context-aware high-level feature extraction module (CHFEM) to extract high-level features of scale invariance in the encoder stage. Further, we introduce a hierarchical attention mechanism into our segmentation framework. The mechanism is divided into three parts: a low-level feature spatial attention module (LFSAM) is developed to learn the spatial relationship between different pixels on each channel in the low-level stage of the encoder, a high-level feature channel attention module (HFCAM) is to model the semantic information relationship on different channel images in the high-level stage of the encoder, and a cross-connected attention module (CCAM) is designed in the decoder part to further suppress the noisy boundaries of hippocampus and simultaneously utilize the attentional low-level features from the encoder to better guide the high-level hippocampus edge segmentation in the decoder phase. The proposed approach achieves outstanding performance on the ADNI dataset and the Decathlon dataset compared with other semantic segmentation models and existing hippocampal segmentation approaches. Source code is available at https://github.com/LannyShi/Hippocampal-segmentation.