The RSA cryptosystem and elliptic curve cryptography (ECC) have been used practically and widely in public key cryptography. The security of RSA and ECC respectively relies on the computational hardness of the integer factorization problem (IFP) and the elliptic curve discrete logarithm problem (ECDLP). In this paper, we give an estimate of computing power required to solve each problem by state-of-the-art of theory and experiments. By comparing computing power required to solve the IFP and the ECDLP, we also estimate bit sizes of the two problems that can provide the same security level.