一种公开参数长度固定的非零内积加密方案

Non-zero Inner Product Encryption Scheme with Constant-size Public Parameters

内积加密体制作为一种特殊的函数加密,被广泛应用于云计算领域.针对现有内积加密方案的公开参数随系统属性个数线性增长的缺陷,本文利用素数阶群上的双线性映射提出了一个公开参数长度固定且具有适应安全性的内积加密方案.在设计方案时,我们通过利用素数阶熵扩张引理给出的公开参数形式,实现了公开参数长度固定;方案的密钥生成算法,通过利用属性向量分量与随机向量结合的技巧,生成每个私钥分量,在素数阶熵扩张引理和MDDHk,k+1n困难假设成立条件下,利用Game序列的证明方法,证明了方案具有适应安全性.并且与现有内积加密方案相比,本文方案的公开参数长度仅有16个群元素,公开参数的选取不受属性个数影响,大大降低了公开参数选取量,使得方案的实用性和操作性更强.

As a special kind of functional encryption schemes,inner product encryption schemes are widely used in the field of cloud computing.The public parameters of the existing inner product encryption schemes increase linearly with the number of system attributes.In this study,a constantsize public parameters inner product encryption scheme with adaptive security is proposed based on bilinear maps on prime order groups.The proposed scheme achieves constant-size public parameters by using the public parameter form given by using the prime-order entropy expansion.In the proposed scheme,the key generation algorithm generates each private key component by using the combination of attribute vector components and random vectors.Under the conditions of the prime-order entropy expansion lemma and the MDDHk,k+1n difficulty assumption,the adaptive security of the scheme is proved by the method of proving the Game sequence.Compared with existing inner product encryption schemes,the length of public parameters of the proposed scheme is only 16 group elements,the selection of public parameters is not affected by the number of system attributes,greatly reducing the amount of public parameters,making the scheme more practical and operational.