基于格的属性签名方案

中文摘要: 基于格的属性密码体制具有许多优良特性，可迄今人们尚未提出基于格的属性签名方案。为此，首先构造了一个基于格的属性签名方案，其中根据Agrawal提出的格基扩展算法SampleBasisLeft生成用户的私钥，利用Agrawal提出的原像抽样算法SampleLeft产生消息的签名。并在标准模型下基于小整数解(SIS)问题的难解性严格证明了该方案的安全性，即其在选择性访问结构和消息攻击下满足存在性不可伪造性。所提出方案的签名长度不随用户的属性数量的变化而变化，且其支持在多值属性上的与门访问结构。
Abstract:Lattice attribute-based cryptography has several attractive and distinguishing features. However,a lattice attribute-based signature scheme has not yet been presented till now.Consequently,an attribute-based signature scheme from lattices was constructed firstly. In the proposed scheme,the user’s secret key was issued according to the lattice basis delegation algorithm of SampleBasisLeft, and the signature on a message was outputted by using the preimage sampling algorithm of SampleLeft.Furthermore,the proposed scheme was strictly proved to be secure under the intractability of the small integer solution (SIS) problem in the standard model,namely,it was existential unforgeable against selective access structure and message attacks. The proposed scheme achieved the constant signature length. And the access structure used in the proposed scheme was constructed by AND-gates on multi-valued attributes.