理想格上高效的身份基加密方案

Efficient Identity-based Encryption Scheme over Ideal Lattice

基于格的身份基加密方案是近年来密码学研究的热点之一,但是标准格上的身份基方案密钥大且密文扩张率高。为此,基于理想格构造一个密钥较小且密文扩展率较低的身份基加密方案。采用基于NTRU的数字签名与理想格上的对偶加密相结合的方法,在随机预言机模型下证明其安全性。分析结果表明,密钥生成中心的公钥和私钥分别只含有1个和4个环元素,用户的解密密钥只含有2个环元素,密文只含有2个环元素且密文扩张率较小,加密和解密分别只需要4次和2次多项式环上的乘法。与基于传统数论的身份基加密方案相比,提出方法的计算效率更高。

Recently, Identity-based Encryption （IBE） scheme based on lattices becomes one of the focuses of cryptographic research. But the IBE scheme based on standard lattice have large key size and high ciphertext expansion rate. So based on ideal lattices,this paper presents an efficient identity-based encryption scheme with small key size and low ciphertext expansion rate. The proposed scheme uses a method that combines the NTRU digital signature and the dual encryption based on ideal lattices. It is provably secure in the random oracle model. Analysis results show that the public key and the private key of key generation center contain one ring element and four ring elements respectively. The decryption key of each user is comprised of two ring elements. The ciphertext contains only two ring elements and the ciphertext expansion rate is a small constant. The encryption and decryption require four and two multiplications in the polynomial ring. Hence,the IBE scheme is more computationally efficient than that of traditional number theory based IBE scheme.