Design and Analysis of a Provable Secure Multi-Recipient Public Key Encryption Scheme

针对现有安全广播协议密钥分发效率较低的问题,提出了一种通过多接收者公钥加密实现安全广播的方法.以Shamir的门限秘密共享方案为设计基础,首先提出了一个基于椭圆曲线上双线性变换的具有抗不可区分选择明文攻击(IND-CPA)安全性的多接收者公钥加密方案,然后对所提方案进行安全扩展,在此基础上最终提出了一个具有抗不可区分自适应选择密文攻击(IND-CCA2)安全性的多接收者公钥加密方案.基于双线性判定Diffie- Hellman假设和双线性间隙Diffie-Hellman假设,对上述所声称的IND-CPA安全性和IND-CCA2安全性进行了证明.同时,对方案的正确性及性能等进行了分析和证明.分析发现,该方案是一个安全、有效的公钥加密方案.由一个加密密钥所加密的密文可以被多个解密密钥解密而得到其所对应的明文,这使得该方案具有非常重要的应用,尤其是可以用来实现安全广播,以便在不安全的、开放的网络环境中安全地广播敏感信息.;To improve the inefficiency of the existing key distribution protocols in the secure broadcasting, an ideal multi-recipient public key encryption scheme to achieve the secret broadcasting is proposed. Based on Shamir’s threshold secret sharing scheme, a multi-recipient public key encryption scheme of the IND-CPA security is proposed on bilinear pairing on elliptic curve. And then, extension is made on the proposed scheme to construct a new multi-recipient public key encryption scheme with the IND-CCA2 security. Based on the Bilinear Decisional Diffie-Hellman assumption and the Gap Bilinear Diffie-Hellman assumption, their security claimed above is proved. At the same time, analyses are made on the correctness and performance of the scheme. Analyses show that the proposed scheme is a efficient and secure public-key encryption scheme, in which, a ciphertext encrypted by an encryption key can be decrypted by a number of decryption keys. This makes it play an important role in many applications. Especially in the secure broadcasting, it can be applied to securely broadcast sensitive information in an unsafe and open network situation.