中文摘要：

在弱的安全假设下构造可证明安全的密码体制原型可以有效提高密码体制的安全性,该文对用Lucas序列构造公钥密码体制做进一步研究,给出一种新的可证明安全的密码体制原型,该密码体制的加、解密效率比现有的LUC密码体制效率高,并证明它的安全性等价于分解RSA模数,最后给出该体制在签名方面的应用,伪造签名等价于分解RSA模数。

英文摘要：

Constructing provably secure cryptographic primitives under weak assumptions can improve the security of cryptographic schemes efficiently. Further research on the construction of public-key cryptosystem is provided, and a new public-key encryption primitive is investigated. This scheme is more efficient than that of existing LUC cryptosystems. More over, the proposed scheme is provable secure and its security is proved to be equivalent to the factorization of RSA modulus. At last, an application in signature is suggested; forgery of signature is also equivalent to the factorization of RSA modulus.