结合格上的困难问题对基于身份的分层加密(HIBE)体制进行分析与研究.针对现存方案公钥长度大、密文扩展率高的缺陷,对理想格上的陷门产生函数算法进行改进,并以新的陷门作为私钥提取算法的输入,生成用户的私钥,实现消息的加解密,从而基于判定性R-LWE(learning with errors over ring)困难问题构造了一个高效安全的HIBE方案,对它的安全性以及效率进行了分析.分析表明,本文提出的方案效率较高,且能够实现较高的安全性.
With the development of quantum computer, multivariate public key cryptography withstanding quantum attack has became one of the research focus. The existed signcryption schemes from discrete logarithm and bilinear paring are facing the serious threats. Based on multivariate public key cryptography, a new certificateless multi-receiver hybrid signcryption scheme has been proposed. The proposal reduced the cipher text and could handle arbitrary length messages by employing randomness reusing and hybrid encryption, as well as keeping security. In the random oracle model, the scheme＇s confidentiality could withstand the IND-CCA2 adversary and its unforgeability could withstand the UF-CMA adversary under the hardness of multivariat quadratic （MQ） problem and isomorphism of polynomials （IP） assumption. It has less computation overhead and higher transmission efficiency than others. It reduced 33% cipher data compared with the existed similar scheme.
