Pairing-based cryptography (PBC) is crucial in modern cryptographic applications.With the rapid advancement of adversarial research and the growing diversity of application requirements, PBC accelerators need regular updates in algorithms, parameter configurations, and hardware design.However, traditional design methodologies face significant challenges, including prolonged design cycles, difficulties in balancing performance and flexibility, and insufficient support for potential architectural exploration.To address these challenges, we introduce Finesse, an agile design framework based on co-design methodology.Finesse leverages a co-optimization cycle driven by a specialized compiler and a multi-granularity hardware simulator, enabling both optimized performance metrics and effective design space exploration.Furthermore, Finesse adopts a modular design flow to significantly shorten design cycles, while its versatile abstraction ensures flexibility across various curve families and hardware architectures.Finesse offers flexibility, efficiency, and rapid prototyping, comparing with previous frameworks.With compilation times reduced to minutes, Finesse enables faster iteration cycles and streamlined hardware-software co-design.Experiments on popular curves * Both authors contributed equally to this research.