Fast public-key encryption scheme based on Chinese remainder theorem

Abstract

Traditional public-key cryptosystems suffer from a relatively low encryption/decryption speed, which hampers their applications in resource-constrained environments. A fast public-key cryptosystem is proposed to remedy this drawback. The new algorithm uses 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 matrixvector 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 difficult number-theoretic 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 lattice attack. The analysis shows that the encryption algorithm is a secure, fast and efficient public-key cryptosystem.