Rabin encryption and a secure ownership transfer protocol based on the difficulty of factorization of a public key use a small public exponent. Such encryption requires random number padding. The Coppersmith's shortpad attack works effectively on short padding, thereby allowing an adversary to extract the secret message. However, the criteria for determining the appropriate padding size remains unclear. In this paper, we derived the processing-time formula for the shortpad attack and determined the optimal random-padding size in order to achieve the desired security.