基于非交互零知识证明的可验证全同态加密算法  

Verifiable Fully Homomorphic Encryption Based on Zero‑Knowledge Succinct Non‑interactive Arguments of Knowledge

作　　者：孙劲桐 周福才[1] 王强 边澈[2] SUN Jin-tong;ZHOU Fu-cai;WANG Qiang;BIAN Che(School of Software,Northeastern University,Shenyang 110169,China;The Fourth Affiliated Hospital,China Medical University,Shenyang 110165,China)

机构地区：[1]东北大学软件学院,辽宁沈阳110169 [2]中国医科大学附属第四医院,辽宁沈阳110165

出　　处：《东北大学学报(自然科学版)》2024年第11期1537-1546,共10页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(62072090,62202090,62173101);辽宁省自然科学基金医工交叉联合基金资助项目(2022-YGJC-24);辽宁省博士科研基金资助项目(2022-BS-077);中央高校基本科研业务费专项资金资助项目(N2217009)。

摘　　要：同态加密(homomorphic encryption,HE)由于低执行效率和无法保护数据完整性的问题严重限制了其在实际应用中的部署,尤其是在对延迟有严格要求的场景中,为此,提出了一种新的HE来解决这些问题并增强通用性.为了解决执行效率低的问题,设计了多线程矩阵乘法(multithreaded matrix multiplication,MMM)算法.利用MMM算法,可以将加密任务拆解分配给多个线程并行执行,达到加速的目的.针对恶意服务器场景下的数据篡改问题,设计了一个可验证加密机制,利用非交互零知识证明(zk-SNARK)技术保护外包计算中密文的完整性.结合MMM算法,设计了一种高效的基于零知识证明的可验证全同态加密算法(verifiable fully homomorphic encryption based on zk-SNARKs,zk-VFHE).理论分析和实验结果表明,zk-VFHE比同类协议具有更快的执行速度和更高的安全性.Homomorphic encryption(HE)is severely limited in its practical deployment due to low execution efficiency and the inability to ensure data integrity,particularly in scenarios with strict latency requirements.To address such issues and enhance general applicability,a new HE scheme is proposed.To improve execution efficiency,a multithreaded matrix multiplication(MMM)algorithm is designed.With the MMM algorithm,encryption tasks can be decomposed and distributed across multiple threads for parallel execution,thus achieving acceleration.To tackle data tampering in malicious server environments,a verifiable encryption mechanism is designed using zk-SNARK techniques to protect the integrity of ciphertext in outsourced computations.By combining MMM,an efficient verifiable fully homomorphic encryption based on zk-SNARK(zk-VFHE)was developed.Theoretical analysis and experimental results demonstrate that zk-VFHE outperforms similar protocols in terms of both execution speed and security.

关 键 词：全同态加密 误差学习 非交互零知识证明 可验证计算 矩阵编码 

分 类 号：TP309.2[自动化与计算机技术—计算机系统结构]