At present, the RSA cryptosystem is most widely used in public key cryptography. On the other hand, elliptic curve cryptography (ECC) has recently received much attention since smaller ECC key sizes provide the same security level as RSA. Although there are a lot of previous works that analyze the security of ECC and RSA, the comparison of strengths varies depending on analysis. The aim of this paper is once again to compare the security strengths, considering state-of-the-art of theory and experiments. The security of RSA is closely related to the hardness of the integer factorization problem (IFP), while the security of ECC is closely related to the elliptic curve discrete logarithm problem (ECDLP). In this paper, we compare the computing power required to solve the ECDLP and the IFP, respectively, and estimate the sizes of the problems that provide the same level of security.