DHCP was designed in the early 1990s, when the number of organizations on the Internet was relatively small. Furthermore, it was based on BOOTP, which was created in the 1980s when the Internet as we know it today barely even existed. In those days, Internet security wasn't a big issue, because it was mostly a small group of research and educational organizations using TCP/IP on the Internet. As a result, DHCP, like many protocols of that era, doesn't do much to address security concerns.
Actually, this is a bit understated. Not only does DHCP run over IP and UDP, which are inherently insecure, the DHCP protocol itself has in fact no security provisions whatsoever. This is a fairly serious issue in modern networks, because of the sheer power of DHCP: the protocol deals with critical configuration information. There are two different classes of potential security problems related to DHCP:
DHCP Authentication
To try to address some of the more specific security concerns within DHCP itself, in June 2001 the IETF published RFC 3118, Authentication for DHCP Messages. This standard describes an enhancement that replaces the normal DHCP messages with authenticated ones. Clients and servers check the authentication information and reject messages that come from invalid sources. The technology involves the use of a new DHCP option type, the Authentication option, and operating changes to several of the leasing processes to use this option.
Unfortunately, 2001 was pretty late in the DHCP game, and there are millions of DHCP clients and servers around that don't support this new standard. Both client and server must be programmed to use authentication for this method to have value. A DHCP server that supports authentication could use it for clients that support the feature and skip it for those that do not. However, the fact that this option is not universal means that it is not widely deployed, and most networks must rely on more conventional security measures.