Yamaguchi, Okayama, and Miyahara proposed a simple but efficient authentication system, SPLICE/AS. In this article, we show that their method is vulnerable to the guessing attack. An attacker can obtain the password, private-key, and public-key of the user. To overcome the vulnerability of SPLICE/AS to the guessing attack, we propose an improvement of their system. In our scheme, we not only prevent the guessing attack to obtain secret messages but also enhance the security of the SPLICE/AS authentication system in WIDE.