ISSN 1000-1239 CN 11-1777/TP

• 信息安全 •

### 具有循环安全性的同态加密方案的设计

1. (武警工程大学网络与信息安全武警部队重点实验室 西安 710086) (武警工程大学电子技术系 西安 710086) (850301775@qq.com)
• 出版日期: 2015-06-01
• 基金资助:
基金项目：国家自然科学基金项目(61272492,61103230,61103231,61202492)

### Application of a Circular Secure Variant of LWE in the Homomorphic Encryption

Yang Xiaoyuan, Zhou Tanping, Zhang Wei, Wu Liqiang

1. (Network and Information Security Key Laboratory, Engineering University of the Armed Police Force, Xi’an 710086) (Electronics Department, Engineering University of the Armed Police Force, Xi’an 710086)
• Online: 2015-06-01

Abstract: Homomorphic encryption scheme is a powerful cryptographic system which allows for a variety of applications. Fully homomorphic encryption(FHE) permits arbitrary computations on encrypted data. The recent breakthrough work in 2009 by Craig Gentry has shown the possibility of FHE schemes, and has provided the first construction. Consequently, during the past five years, numerous FHE involving novel mathematical techniques and a number of application schemes have appeared. Indeed, the construction and application of homomorphic encryption schemes have great theoretic and practical meaning. Homomorphic encryption has important applications in cloud computing. However, almost all of the homomorphic encryption schemes share two common flaws that the multiplication depth must be set in advance and they all use secret keys of large scales. We construct a circularly secure re-linearization process based on the “special b” variant of the learning with errors problem(bLWE). Then, we present an efficient homomorphic encryption scheme. Compared with Brakerski et al’s scheme, our scheme reduces the L+1 secret keys to one and doesn’t need to know the multiplication depth in advance. Finally, we prove the chosen-plaintext attack(CPA) security of the homomorphic scheme and the circular security of the re-linearization process in standard model by reducing them into learning with errors problem(LWE) assumption.