Cloud storage usually adopt client-based deduplication, which can achieve considerable savings in both storage and bandwidth. However, an attacker can carry out a steal-file-content (SFC) attack, exposing data privacy. In this paper, a simple yet effective scheme, called double bytes transport protocol (DBTP), is proposed. In this scheme, the client-side requests deduplication checks of the double chunks simultaneously, and the server-side receives the deduplication request and response with a reasonable value. The result demonstrates that DBTP can significantly mitigate the side channel's risk while maintaining the high bandwidth efficiency of deduplication.