Zero-knowledge proofs (ZKP) allows a prover to convince a verifier of computational correctness without revealing private data, ensuring both privacy and verifiability. However, proof generation is highly compute-intensive, dominated by polynomial (POLY) and elliptic-curve (EC) operations. These workloads pose two key challenges for hardware acceleration: (1) efficiently supporting diverse large-precision modular multiplications, and (2) maintaining high utilization across workloads that dynamically shift between POLY and EC stages. Existing reconfigurable accelerators address these issues only partially, remaining limited in precision scalability, algorithmic flexibility, and resource efficiency. To overcome these limitations, we propose ZK-Flex, a flexible and scalable software-hardware co-designed framework for accelerating ZKP proof generation. The software layer incorporates POLY and EC optimizers that reduce computation through hardware- and workload-aware algorithmic choices, while the hardware integrates TCore, a Toom-Cook-based multi-precision core with a flexible NoC and a linked-list memory mechanism that improves parallelism under limited memory capacity. Across representative ZKP benchmarks, ZK-Flex achieves 5 to 11 times speedup and up to 3.8 times higher area efficiency over the state of the art, establishing a new foundation for high-performance, reconfigurable ZKP acceleration.

翻译：零知识证明（ZKP）允许证明者在不泄露私有数据的情况下使验证者确信计算正确性，从而同时保障隐私性与可验证性。然而，证明生成过程高度计算密集，主要涉及多项式（POLY）和椭圆曲线（EC）两类运算。这些工作负载对硬件加速提出两大挑战：（1）高效支持多样化的高精度模乘运算；（2）在 POLY 与 EC 阶段动态切换的工作负载中保持高利用率。现有可重构加速器仅能部分解决上述问题，在精度可扩展性、算法灵活性和资源效率方面仍存在局限。为克服这些限制，我们提出 ZK-Flex——一种灵活可扩展的软硬件协同设计框架，用于加速 ZKP 证明生成。软件层集成了 POLY 和 EC 优化器，通过硬件与工作负载感知的算法选择降低计算量；硬件层集成 TCore——基于 Toom-Cook 的多精度核心，配备灵活片上网络（NoC）和链表式内存机制，在有限内存容量下提升并行性。在典型 ZKP 基准测试中，ZK-Flex 相比现有最优方案实现 5 至 11 倍加速比，面积效率提升最高达 3.8 倍，为高性能、可重构的 ZKP 加速奠定了新基础。