摘要：

针对传统公钥加密模式多数只能由单发送方将消息发送给单接收方的限制,基于整数全同态加密方案,设计一种基于整数多项式环的一对一全同态加密算法。在此基础上,通过修改一对一全同态加密算法的密钥生成方式,扩展加密方个数,提出基于整数多项式环的多方加密一方解密的全同态加密算法。给出该算法的正确性和同态性证明,并在随机预言机模型下,基于离散子集求和问题和近似最大公因子问题证明该算法的安全性。性能比较结果表明,该算法可扩展加密方个数,提高解密方效率。

关键词: 整数多项式环, 多对一全同态加密方案, 离散子集求和问题, 近似最大公因子问题, 随机预言机模型

Abstract:

Aiming at the limitation that most traditional public key encryption mode can only send messages from a single sender to a single receiver,a one to one homomorphic encryption algorithm based on integer polynomial ring is designed based on integer homomorphic encryption scheme.On this basis,by modifying the key generation method of one to one homomorphic encryption algorithm and expanding the number of encryption parties,a fullly homomorphic encryption algorithm based on integer polynomial ring for multi-party encryption and one-party decryption is proposed.The correctness and homomorphism of the algorithm are proved,and the security of the algorithm is proved based on Sparse Subset Sum Problem(SSSP) and Approximate Greatest Common Divisor(AGCD) problem under the random oracle model.Performance comparison results show that this algorithm extends the number of encryption parties and improves the efficiency of decryption.

Key words: integer polynomial ring, multiple to one fully homomorphic encryption scheme, Sparse Subset Sum Problem(SSSP), Approximate Greatest Common Divisor(AGCD) problem, random oracle model

中图分类号: 

• TP309.7