One of Niven's Laws states that F×S=k or, to put it another way, the product of freedom and security is a constant (so the greater the security of a society, the lower the freedom within it).
I'm not sure I agree. By Ashby's Law of Requisite Variety, the control system must have sufficient states to absorb the number of possible states of the system being controlled. In more concrete language: a more complex control system (police, legal system and so on) allows more freedom of the society, in terms of allowed states, not less.
Note that this is discussing states of society as a whole, which doesn't correspond with individual freedom. For example: consider a society with 2 citizens. The first citizen has the freedom to occupy the states black/white, and the second to occupy red/green. There are 4 possible society states. But if both citizens have the freedom to occupy black/white, there are degenerate states at the society level: there are only 3 distinguishable society states.
(Also note that I'm equating security with having a more developed system of control, said system allowing feedback (such as locating and disarming a bomb) to occur.)
What this means, for freedom and control, is that increased control can buy us two different types of freedom: greater individual freedom, and greater freedom to be different from other people. Control (and decreasing personal freedom of the first type) allows us to have a more heterogeneous society.
(Implications? Individuals in a factory are freer than individuals in a conglomerate because they're all free in the same way and the factory-society can afford more of that for the same level of control. And a society comprised of a large number of similar villages can also afford more individual freedom than a society in which some individuals are allowed to express global freedom, via fame.)