Medical image segmentation, as a crucial component of computer-aided diagnosis, has witnessed remarkable progress in recent years under the "prompt-segmentation" paradigm based on large models. MedSAM has demonstrated excellent performance in medical scenarios but requires substantial computational resources. LiteMedSAM, a lightweight version, is suitable for resource-constrained environments, yet it does not fully utilize diverse mask information during the prompt encoding stage, making it difficult to achieve ideal segmentation results under conditions of sparse annotations. To address this issue, a lightweight medical image segmentation algorithm based on random diverse scribble prompts is proposed. This algorithm maintains the lightweight nature of LiteMedSAM while incorporating three modules: random diverse scribble generation, adaptive prompt weight based on Gumbel-Softmax, and multi-level gate fusion, which are well-suited to the prompt encoder structure. Specifically, it first uses the global representation of sparse prompts to pre-select the most discriminative scribble patterns at the logical level, then randomly generates multiple binary masks with diverse geometric shapes based on adaptive weights, and finally fuses the mask prompts with maskless prior information through a spatial-channel-level gating mechanism with dynamic weighting. Experimental results show that, without significantly increasing computational costs, the proposed method achieves higher Dice similarity coefficients (DSC) and normalized surface distances (NSD) on multiple medical image segmentation datasets compared to LiteMedSAM. Currently, this method has been successfully applied in the scenario of medical image radiation dose assessment, confirming its clinical application value.