Lock boxes enable limited access to premises so that authorized persons, such as repairmen, servicemen, or realtors, may enter the premises to perform their service when the occupant of the premises is not present.  Lock boxes are extensively used in the real estate industry in connection with the showing of real estate property to prospective purchasers.  It is impractical and undesirable to provide each real estate agent with a key to the listed property.  In addition, requiring an agent to obtain a key from the real estate sales office prior to showing each property is somewhat inconvenient.  Lock boxes provide a solution to these problems. 
A lock box generally includes a hollow box in which the key for a listed property may be placed.  Lock boxes are typically provided by a realtor entrusted with the sale of the property.  The realtor secures the lock box to the property so that a key to the home is always on the premises in a locked, safe place.  The local real estate board may then issue keys to the lock box to board-participating realtor.  Agents, having a lock box key, arrive at a home, open the lock box to access the homeowner's key, and then use the homeowner's key to open the door and show the home. 
Lock boxes have been designed to mount to the doorknob of an access door to the home.  This type of lock box generally comprises a hollow key receptacle mounted by a shackle to the shaft section of an exterior doorknob, or in some cases, a gate, fence or other secure mounting location that will accept a locking shackle.  Examples of such lock box assemblies are those disclosed in U.S. Pat.  Nos.  3,436,937; 4,532,783; 4,609,780; and 4,641,505.  However, these doorknob-mounted lock box assemblies often cause structural damage to the door.  As the door is closed, the centrifugal force of the closing door may swing the lock box into the door, marring the doorknob and denting or otherwise damaging the door and door jamb. 
In order to try to minimize the possible damage to doorknob-mounted lock boxes, shielding structures and stabilizing brackets for such lock boxes have been devised, for example, as shown in U.S. Pat.  Nos.  5,218,846 and 5,084,945, respectively.  Nevertheless, doorknob-mounted lock boxes frequently interfere with operation of the doorknob, causing the homeowner inconvenience. 
Another type of lock box assembly is disclosed in U.S. Pat.  No.  3,934,434.  This lock box includes a bracket which can be mounted on the top of a door.  Mounting the lock box over the top of the door, however, places the lock box above a convenient height for an average-sized person to reach.  In addition, lock boxes and other box structures are known which have been mounted on a door edge, either the knob edge or the hinge-edge between the door and door jamb.  Examples of such structures are the devices shown in U.S. Pat.  Nos.  2,023,826; 2,273,580; 4,494,690; 4,694,668; and 4,746,062. 
While these prior art structures have provided many advantages, the doorknob-mounted structures have interfered with door operation and/or marred the door.  The doortop brackets are awkward or impossible for short people to use, and the door edge bracket structures have had a common problem.  Once the door is opened, they can be removed and thrown away. 
One of the biggest security problems in connection with the use of lock boxes is the real estate agents themselves.  Agents can present the biggest exposures to burglaries.  Once the door is opened, the agent-burglar simply destroys or disposes of the lock box assembly and/or its memory.  In addition, conventional mounting assemblies provide easy access to the lock box shackle and/or the portion of the mounting assembly to which the lock box is attached.  As a result, tools such as bolt cutters, can be used to break the security of the connection.  Once removal of the lock box is achieved, the box can be taken to another location providing greater opportunity for forced entry into the key-containment chamber of the box. 
U.S. Pat.  No.  5,590,608 discloses a lock box mounting assembly for mounting on the door edge adjacent the door hinge.  This device includes a bracket which wraps around the edge of the door and an eye element extending from the exterior plate for receiving the lock box shackle.  In one embodiment, the bracket structure is mounted on the door by positioning the bracket in the reveal space when the door is in the open position and sliding the structure along the edge of the door to a resting position against the hinge.  In a second embodiment, the bracket is securely attached to the door by positioning the bracket between the door and the hinge portion normally directly attached to the door.  The hinge screws are then inserted through the hinge and the bracket, and into the door.  In yet a third embodiment, the bracket includes two separate plates removably positioned on opposite sides of the hinge.  Each plate includes a flange containing an opening for alignment with the opening in the other plate flange.  The lock box shackle extends through the flanges to connect the lock box to the assembly while also functioning to secure the plates to each other and, importantly, to the door.  However, undesirably, in the first embodiment, once the door is opened, the bracket mounting assembly can be easily removed.  In addition, in the second embodiment, the door hinge screws must be removed and replaced each time the mounting assembly is installed or removed thereby disadvantageously adding an unnecessary amount of time and effort to the installation process.  In the third embodiment, removal of the lock box will necessarily result in the separation of the plates creating a cumbersome disassembly process.  All of these embodiments also result in the shackle being vulnerable to cutting by bolt cutters, hacksaws and related burglary tools, etc.  Another related drawback of this assembly is the easy access to the portion of the assembly to which the shackle is attached.  These portions, i.e. flange or eye element, are equally easily accessible for cutting by tools thereby allowing removal of the device with the shackle still locked in place. 
Consequently, there is a need for a lock box mounting assembly which securely attaches to a door while effectively impeding unauthorized removal of the mounting assembly and/or lock box.