Some years ago I wrote a subsection in my thesis (sec 8.4.3, p. 154), entitled “How Many Security Officers are Best?”, where I reviewed over the various operating procedures I’d seen for Hardware Security Modules, and pondered why some people chose to use two separate parties to oversee a critical action and some chose to use three. Occasionally a single person is even deliberately entrusted with great power and responsibility, because there can be no question where to lay the blame if something goes wrong. So, “one, two, or three?”, I said to myself.

In the end I plumped for three… with some logic excerpted from my thesis below:

But three security officers does tighten security: a corrupt officer will be outnumbered, and deceiving two people in different locations simultaneously is next to impossible. The politics of negotiating a three-way collusion is also much harder: the two bad officers will have to agree on their perceptions of the third before approaching him. Forging agreement on character judgements when the stakes are high is very difficult. So while it may be unrealistic to have three people sitting in on a long-haul reconfiguration of the system, where the officers duties are short and clearly defined, three keyholders provides that extra protection.

Some time later, I mentioned the subject with Ross, and he berated me for my over-complicated logic. His general line of argument was along these lines “The real threat for Security Officers is not that they blackmail, bribe or coerce one another, it’s that they help! Here, Bob, you go home early mate; I know you’ve got to pack for your business trip, and I’ll finish off installing the software on the key loading PC. That sort of thing. Having three key custodians makes ‘helping’ and such friendly tactics much harder – the bent officer must co-ordinate on two fronts.”

But recently my new job has exposed me to a number of real dual control and split knowledge systems. I was looking over some source code for a key loading HSM command in fact, and I spotted code that took a byte array of key material, and split it into three components each with odd parity. It generates two fresh totally random components with odd parity, and then XORs these onto the third. Hmmm, I thought, so the third component would contain the parity information of the original key, dangerous — a leakage of information preferentially to the third key component holder! But wrong… because the parity of the original key is known anyway in the case of a DES key… it’s always odd.

I chatted to our chief technical bod about this, and he casually dropped a bombshell — that shed new light on why three is best, an argument so simple and elegant that it must be true, yet faintly depressing to now believe that no-one agonised over the human psychology of the security officer numbers issue as I did. When keys are exchanged a Key Check Value (KCV) is calculated for each component, by encrypting a string of binary zeroes with the component value. Old-fashioned DES implementations only accepted keys with odd parity, so to calculate KCVs on these components, each must have odd parity as well as the final key itself. For the final key to retain odd parity from odd parity components, there must be an odd number of components (the parity of keys could be adjusted, but this takes more lines of code, and is less elegant than just tweaking a counter in the ‘for’ loop). Now the smallest odd integer greater than one is three. This is why the most valuable keys are exchanged in three components, and not in two!

So, the motto of the story for me is to make sure to apply Occam’s Razor more thoroughly when I try to deduce the logic behind the status quo, but I still think there are some interesting questions raised about how we share responsibility for critical actions. There still seems to be to me a very marked and qualitative difference in the dynamics of how three people interact versus two, whatever the situation: be it security officers entering keys, pilots flying an aircraft, or even a ménage à trois! Just like the magnitude of the difference between 2D and 3D space.

If one, two and three are all magical numbers, qualitatively different, are there any other qualitative boundaries higher in the cardinal numbers, and if so, what are they? In a security-critical process such as an election, can ten people adjudicate effectively in a way that thirty could not? Is there underlying logic or just mysticism behind the jury of twelve? Or, to take the jury example, and my own tendency to over-complicate, was it simply that in the first proper court room built back a few hundred years ago, there happened only to be space for twelve men on the benches on the right hand side!