Turnbull versus mathematics

In a press conference on Friday, normally intelligent and erudite Prime minister Malcolm Turnbull made a remarkable comment:

The laws of mathematics are very commendable but the only law that applies in Australia is the law of Australia.”

This is bizarre. Consider a simple law of mathematics. There is a number which we call one, the French call un, and people with their mouth full indicate by holding up one finger. It is a well known concept. The actual name is irrelevant – it is an abstract concept that existed before any humans could speak. If you multiply (another abstract concept) it by itself, you get itself back. One times one equals one. This property (another abstract concept) again exists independently of humanity, independently of the universe. Aliens in a five dimensional universe with no gravity would still be able to observe this same property.

I guess one could describe this as commendable. Bravo, one. You have bravely and tirelessly continued to equal yourself when squared. Jolly good show. Gilbert and Sullivan talked about cheery facts about the square of the hypotenuse, so if mathematical facts can be cheery they can surely be commendable too.

But this cross universe constancy apparently misses Australia, where Australian legislation could, we are told, change things. Maybe we could legislate that one times one should equal three and a half on pain of imprisonment (although it is not clear if it is the one that should be imprisoned or the three and a half). Possibly the prime minister was imagining some anthropomorphic personification of numbers like in Sesame Street, that one could then put behind bars until they behaved as he wished. It would be great. We could legislate that a small number minus a big number is actually a positive number, and solve the budget deficit.

I presume the prime minister has a more sophisticated understanding of mathematics than Sesame Street. But if so, it makes his statement utterly incomprehensible.

So what was the context of this uncharacteristic statement? Maybe he just had a temporary loss of oxygen to his brain. The prime minister was talking about how terrorists use food, and that food providers do not do an adequate job of stopping terrorists using the food they provide, and that the existence of food is a problem that something should be done about as it helps terrorists thrive. Oops. I meant cryptography, not food. Same principle, anyway. Food can come next.

Of course most people think that the world would be better if terrorists did not have access to cryptography. The trouble is that modern cryptography is mathematics. Mathematics works the same, regardless of whether you are naughty or nice. So we cannot make cryptography where nice people can intercept the nasty people’s communication, but nasty people can’t break nice people’s communications. This is where the laws of mathematics come in. No matter how commended they may be, mathematics is ethics free. Numbers do not behave differently for nice people or boogeymen. Even if it is legislated that they must. Even in Australia.

Of course most people don’t care if nasty people can intercept their communications. They have nothing to hide. Well, except they may not want cyber thieves breaking into their electronic banking and emptying their accounts, and while they are at it infecting their computers with ransom-ware. Or paedophiles having records of their children’s movements, photos, and conversations. Or their neighbours having their medical records. Or garden variety house thieves knowing their daily movements and how to open your nifty electronic lock. Or terrorists knowing the details of security arrangements. Or their competitors knowing their company secrets. Or their employer knowing who they voted for. Or a variety of other things, but apart from those things most people have nothing to hide.

So breaking cryptography helps the thieves, paedophiles, and spies. But that is not the government’s intention, surely. They just want it so that the good people and Senator Brandis can intercept people’s communications. Surely one could design a system that could only be used for good, or at least could only be accessed by people with some level of authority.

In some ways this is conceivable. One could, for instance, legislate that all telephones and other computers sold in Australia came with inbuilt security vulnerabilities that only a small number of people knew enough about to use. As these are generally made outside of Australia, these vulnerabilities would be under the control of a foreign government, and some method of international cooperation would be required (and that is what Senator Brandis and Prime Minister Turnbull are talking about), where presumably every government would have access. Not that any foreign government would ever spy on any Australian. Not that it would matter anyway, as we have nothing to hide, do we? Well, maybe Senator Brandis’ diary.

Even if every government in the world were a model of enlightenment, a secret that is used routinely in most police investigations around the world is not going to stay a secret for very long if history is any example. And once the secret is out, it is too late as everyone has compromised devices. Not that we would know that it was out, anyway.

Even if no one who had access to the secret lost it or sold it – and people would be willing to pay a fortune for it – history shows that the bad guys work out such secrets on their own, even ones that the originators were unaware of.

Companies are purposefully building communications systems that they are not able to intercept, partly as their customers don’t want their communications provider spying on them, but also because they know that that is the best way to keep it secure. Humans are ingenious at making wonderful complex applications, but we are lousy at making them secure. The fewer people who know a secret, the safer that secret is, regardless of intentions. In “end to end” encryption that Brandis and Turnbull are railing against, only the participants in the conversation know the key to decrypting it. That is the minimum number of people needed, and thus the most secure against terrorists, paedophiles, thieves, spies, and, of course, repressive governments. More complex (in the sense of wider secret sharing) systems are inherently more likely to have serious security holes.

I am sure that the police pushing this are hard working well meaning people frustrated at having a difficulty in one aspect of their jobs, and that is the part of the argument they see. But they don’t see the position from the people maintaining nuclear facilities who don’t want their cybersecurity weakened, nor hospitals that are disrupted by cybercrime. Remember too that the total amount of information the government has on its citizens is higher than at any time in the past, and rapidly growing.

This is not just me saying that I don’t see how to do it, and therefore we should not even try. This is the overwhelming consensus of cryptography experts who say the cure is worse than the disease. There are lots of other approaches for stopping the pathetic psychopathic murderers whom we dignify with the name terrorists without weakening our cybersecurity.

I should point out that the prime minister and Senator Brandis are explicit that they are not proposing a back door (a method of reading cryptographic conversations without breaking the cryptography). Presumably they were told by wise people that back doors were a bad idea, but not what back doors actually were. Since breaking the cryptography is not practical, this means that they just want a method of reading cryptographic conversations without having a method of reading cryptographic communications. But if you can change the laws of mathematics, then you can surely do the same to logic.

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