中文摘要：

传统公钥密码的加解密速度较慢，这就使得这些密码很难应用于一些资源受限的环境．针对这一缺陷，设计了一个快速公钥密码算法．该算法使用中国剩余定理来隐藏陷门信息，其加密算法使用了几个大模数的模乘法运算，而解密算法只使用了一个模乘法运算和一个低阶矩阵和向量的乘法运算，所以该密码具有很快的加解密速度．该算法的安全性同时基于两个数学困难问题，攻击者如果想从公钥求解私钥，就必须先分解一个大整数，然后再求解联立丢番图逼近问题．分析表明，该算法能够抵抗格规约攻击，是一个安全快速高效的公钥密码体制．

英文摘要：

Traditional public key cryptosystems suffer from a drawback that the encryption/decryption speed is relatively low, which hampers their applications in resource-constrained environments. A fast public-key cryptosystem is proposed to remedy this drawback. The new algorithm uses the Chinese remainder theorem to hide the trapdoor information. The encryption of the system only carries out several modular multiplication operations, and the decryption only needs a modular multiplication and a low-dimensional matrix-vector multiplication, which makes the speed of the encryption and the decryption of the scheme very high. The security of the system is based on two number-theoretic hard problems. The attacker has to solve the integer factorization problem and the simultaneous Diophantine approximation problem simultaneously to recover the secret key from the public key. The proposed cryptosystem is also shown to be secure against the lattice attack. Analysis shows that the encryption algorithm is a secure, fast and efficient public key cryptosystem.