中文摘要：

函数加密是公钥密码中一新的研究方向.不同于传统的公钥加密,它允许用户细粒度访问控制加密信息,利用私钥对密文进行解密,但得不到关于明文的任何信息.利用一般函数构造简单加密方案对函数加密的研究至关重要.现有的具体函数加密方案大多是基于椭圆曲线上双线性对来构造的,满足较高的安全性,但是双线性群上的乘法以及指数运算较慢,参数选择复杂,导致计算效率不高,且得不到关于明文的函数或者得到的函数依然是基于离散对数这一困难问题.文章提出了一种利用可逆矩阵作为主私钥的内积函数加密方案,即解密者利用一个关于向量的私钥解密一个消息x的密文,结果得到〈x,y〉却得不到关于x的任何信息,并证明方案的安全性.

英文摘要：

Functional encryption is a new research field in public-key encryption.Different from traditional public-key cryptosystem,functional encryption allows users to access to a large number of finely controued information that is revealed by a ciphertext,and to decrypt the encrypted data with the secret key,but can not achieve anything about the data.It is important to employ general functionalities for constructing simple encryption schemes.Existed concrete functional encryption schemes are usually constructed by bilinear pairing on elliptic curve and have higher security,but the multiplication and exponential operations based on bilinear group calculate fairly slowly,the parameters are relatively complicated,and computation efficiency is lower.They can not achieve the functionality for the message,or achieved the functionality is still based on the discrete log problem.This paper proposes an inner product encryption scheme by using invertible matrix as the master secret key,which indicate that decrypting an encrypted vector x with a key for a vector y will reveal only x,y and nothing else,in addition,this scheme is secure under only ciphertext attack.