Recently, an identity-based quadratic exponentiation randomized cryptosystem scheme using the discrete logarithm problem and the integer factorization problem has been developed. Their contribution lies in that they initiated an idea to create the identity-based cryptographic scheme without bilinear pair. This scheme can achieve the security goal of protecting data and prevent the adversary from snooping the encrypted data, and finding the secrete keys. In this paper, we have proposed some modification in setup phase using floor function and super-increasing sequence, and modified the encryption and decryption process in the identity-based quadratic exponentiation randomized cryptographic scheme. We also discuss how to enhance the security of proposed scheme and processing cost of the proposed scheme.