利用RLWE构造基于身份的全同态加密体制

摘要

Fully homomorphic encryption provides a new idea on the solution of many problems,such as the whole life cycle of data privacy protection on cloud computing.Currently,the existing fully homomorphic encryption schemes share a common flaw of large size public keys.We construct an identity-based fully homomorphic encryption which compromises the merits of both kinds of encryption from ring learning with errors to work in arbitrary cyclotomic rings.To make user’s i-dentity as the unique public key,our scheme has advantage in computational efficiency and key management.The security of our scheme strictly reduces to hardness of decision ring learning with problem solving in the random oracle model.%全同态加密为云计算中数据全生命周期隐私保护等难题的解决都提供了新的思路。公钥尺寸较大是现有全同态加密体制普遍存在的问题。本文将基于身份加密的思想和全同态加密体制相结合，利用环上容错学习问题（Ring Learning With Errors，RLWE），其中将环的参数m扩展到任意正整数，提出了一种基于身份的全同态加密体制。体制以用户身份标识作为公钥，在计算效率和密钥管理方面都具有优势，安全性在随机喻示模型下可规约为判定性RLWE问题难解性假设。