AI 中文总结
该研究提出了适用于CKKS同态加密方案的SPRU自举算法，通过嵌入单位根降低乘法深度，借助OpenFHE实现少量槽位密文延迟最高降5倍，提升了自举效率。
AI 中文摘要
我们提出了稀疏单位根（SPRU）自举算法，这是一种针对近似算术的CKKS同态加密方案的新型自举算法。原始CKKS自举方法依赖于同态求值近似模q取余的多项式，而SPRU自举直接将模q的加法群嵌入到CKKS方案可原生求值的复单位根中。该方法大幅降低了自举所需的乘法深度，支持使用更小的环维度并提升效率。在实践中，借助OpenFHE C++库，当应用于少量槽位的密文时，SPRU自举的延迟最高可降低5倍。
英文摘要
We introduce Sparse Roots of Unity (SPRU) bootstrapping, a new bootstrapping algorithm for the CKKS homomorphic encryption scheme for approximate arithmetic. The original CKKS bootstrapping method relies on homomorphically evaluating a polynomial that approximates modular reduction modulo q. In contrast, SPRU bootstrapping directly embeds the additive group modulo q into the complex roots of unity, which can be evaluated natively in the CKKS scheme. This approach significantly reduces the multiplicative depth required for bootstrapping, enabling the use of a smaller ring dimension and improving efficiency. In practice, using the OpenFHE C++ library, SPRU bootstrapping achieves up to a 5x reduction in latency when applied to ciphertexts with a small number of slots.
