As pervasive computing environments become popular, RFID devices, such as contactless smart cards and RFID tags, are introduced into our daily life. However, there exists a privacy problem that a third party can trace user's behavior by linking device's ID. The concept of unlinkability, that a third party cannot recognize whether some outputs are from the same user, is important to solve the privacy problem. A scheme using hash function satisfies unlinkability against a third party by changing the outputs of RFID devices every time. However, the schemes are not scalable since the server needs O(N) hash calculations for every ID matching, where N is the number of RFID devices. In this paper, we propose the K-steps ID matching scheme, which can reduce the number of the hash calculations on the server to O(log N). Secondly, we propose a quantification of unlinkability using conditional entropy and mutual information. Finally, we analyze the K-steps ID matching scheme using the proposed quantification, and show the relation between the time complexity and unlinkability. Copyright 2005 ACM.