The inter-domain routing protocol, Border Gateway Protocol (BGP), plays a critical role in the reliability of the Internet routing system, but forged routes generated by malicious attacks or mis-configurations may devastate the system. The security problem of BGP has attracted considerable attention, and although several solutions have been proposed, none of them have been widely deployed due to weaknesses such as high computational cost or potential security compromise. This paper proposes Fast Secure BGP (FS-BGP), an efficient mechanism for securing AS paths and preventing prefix hijacking by signing critical AS path segments. We prove that FS-BGP can achieve a similar level of security as S-BGP, but with much higher efficiency. Our experiments use BGP UPDATE data collected from real backbone routers. Compared with S-BGP, FS-BGP only requires a very small cache, and can reduce the cost of signing and verification by orders of magnitude. Indeed, the signing and verification can be accomplished as fast as the most bursty BGP UPDATE arrivals, which implies that FS-BGP will hardly delay the propagation of routing information.