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全同态加密能够在不解密的前提下直接对密文进行操作,是当前大数据和云安全背景下一个热门研究方向,但目前已有的全同态加密体制普遍存在公钥尺寸大、计算效率较低等问题.基于身份的全同态加密是近年来新兴的一种公钥加密体制,该加密体制既具有密文数据同态操作特性,又能有效管理密钥从而解决当前全同态密码公钥尺寸大的问题,因此具有更广阔的应用前景.CRYPTO 2013中,Gentry等构造了第一个真正意义上单身份的全同态加密体制,相比单身份的全同态加密体制,多身份的全同态加密体制实用性更强.本文利用不可区分混淆器和可穿孔伪随机函数,提出了身份转换算法.在身份转换算法的基础上,构造了支持多身份的全同态加密体制,该体制可支持属于不同身份密文间的同态运算和多次同态运算,同时体制的安全性在标准模型下可归约到LWE困难问题.与现有基于身份的全同态加密体制相比,我们构造的多身份的全同态加密体制、规模和效率上更优、解密操作更简洁、功能性更强、应用范围更广.
Fully isomorphic encryption can directly operate on ciphertext without decryption, which is a hot research direction under the background of current big data and cloud security. However, the existing universal homomorphic encryption system has a large public key size, Low efficiency and so on.Individual identity-based isomorphic encryption is a new public-key cryptosystem that has emerged in recent years. This cryptosystem not only has the characteristics of ciphertext data homomorphism but also effectively manages the key to solve the current homomorphism The public key cryptosystem has a large size of public key, so it has a broader application prospect.CRYPTO 2013, Gentry constructed the first truly single identity fully homomorphic encryption system, compared to the single identity of the total homomorphic encryption system, The multi-identity all-homomorphic encryption system is more practical.This paper proposes an identity conversion algorithm based on the indiscernible confusion device and puncturable pseudo-random function.According to the identity conversion algorithm, System, which can support homomorphic operations and multiple homomorphic operations that belong to different identity ciphertexts, and at the same time institutional security can be reduced to the LWE difficult problem under the standard model. Compared with identically homomorphic cryptosystems, the multi-identity homomorphic cryptosystem we construct is superior in scale and efficiency, and the decryption operations are more concise, more functional and more widely used.