With the rapid development of intelligent education, Computerized Adaptive Testing(CAT) has garnered significant attention for its ability to tailor exercises to individual examinees. The adaptability of CAT is primarily achieved through the alternating optimization of two core components: the cognitive diagnosis model and the exercise selection module. However, existing CAT approaches, despite their remarkable achievements, often come at the expense of high time costs. Statistical-based approaches incur increased time overhead due to complex computations, while data-driven approaches further exacerbate time inefficiency because of the iterative processes in reinforcement learning, making it challenging to balance evaluation effectiveness and time efficiency. To this end, in this paper, we propose HashCAT, an efficient CAT approach based on learning to hash, aiming to balance efficiency and evaluation effectiveness. Our approach comprises two stages: the hash representation generation and the exercise selection. In the first stage, we design an information alignment module and a novel cognitive diagnosis function to model the interaction between examinees and exercises, generating hash representations with clear physical significance. In the second stage, we propose an uncertainty reduction-based algorithm that utilize information entropy to quantify the uncertainty in student ability estimation and selects exercises that most effectively reduce this uncertainty. Experimental results on four real-world datasets demonstrate that the proposed method significantly improves question selection efficiency while maintaining competitive evaluation performance. The code exists anonymously in https://github.com/sherklock/Intelligent-Education/tree/main/HashCAT-main.