At CRYPTO 2000, a new public-key encryption based on braid groups was introduced. This paper demonstrates how to solve its underlying problem using the Burau representation. By this method, we show that the private-key can be recovered from the public-key for several parameters with significant probability in a reasonable time. Our attack can be mounted directly on the revised scheme mentioned at ASIACRYPT 2001 as well. On the other hand, we give a new requirement for secure parameters against our attack, which more or less conflicts with that against brute force attack.