基于格的全同态加密方案设计  

Design of Lattice-based Fully Homomorphic Encryption Scheme

作　　者：韩鹏 唐春明[1] HAN Peng;TANG Chun-ming(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2022年第1期33-39,共7页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11871058);大学生创新创业训练计划项目(cxcy2021308)。

摘　　要：由于量子计算机的攻击,许多经典意义下的密码方案不再安全。全同态加密(FHE)被认为是维护机器学习系统隐私安全最重要的解决方案,但同态加密方案的备用方案较少,效率低下,运算成本过高导致不能投入实际应用市场。本文研究了安全性基于MLWE困难问题的抗量子计算密码CRYSTALS-Kyber,解析了Kyber加密方案同态过程中的私钥设计理念并且进行了相应的推广,同时应用新私钥设计它的全同态加密方案。通过设计新私钥巧妙地约减了同态计算的过程,降低了成本并且提高全同态加密的效率。Many classical cryptography schemes are lack of safety as a result of quantum computer attack.Although fully homomorphic encryption is considered as the most improtant solution to maintain the privacy of machine learn-ing systems,it fails to be put into the practical application market because of fewer alternatives of homomorphic encryption schemes,low efficiency and high homomorphic computing cost.This paper talks about the opst-quautum computing crptography of scheme CRYSTALS-Kyber based on diffcult problems no MLWE and analyzes the design cioncept of private key over CRYSRTALS-Kyber in the homomorphic process of encryption scheme.In addition,the corresponding promotion is carried out and the homomorphic encryption scheme is designed by a new private key.The design of a new private key has not only ingeniously reduced the homomorphic computing process,but also reduced the cost and improved the efficiency of homomorphic encryption.

关 键 词：CRYSTALS-Kyber 量子计算 MLWE 机器学习 FHE 

分 类 号：O236[理学—运筹学与控制论]