Cryptography

The History and Mathematics of Codes and Code Breaking

Author: scuddeam

Power of a Test

After the terrorist attack on San Francisco, the Department of Homeland Security ramps up security and surveillance in hopes of catching the people responsible, but instead only manage to inconvenience, detain, and even seriously harm innocent civilians. Marcus explains that the problem with the DHS system is that they're looking for something too rare in too large a population, resulting in a very large number of false positives.

What Marcus is describing is referred to in statistics as a Type I error - that is, we reject the null hypothesis (the assumption that nothing is abnormal) when the null hypothesis is actually true. In this case, the null hypothesis is "not a terrorist", and there's enough suspicious data, the null hypothesis is rejected in favor of flagging the person for investigation. Marcus claims that in order to look for rare things, you need a test that only rejects the null hypothesis at the same rate at which the thing we're testing for - in this case, terrorists - actually occur. The problem is, there's also Type II errors. While Type I errors are caused by being too cautious, Type II errors occur when our test "misses" the thing we are actually looking for. When determining how "tough" a test should be, we need to decide how to balance these two risks.

Marcus is advocating for making the system less broad, therefore reducing false positives. However, this increases the risk for false negatives as well. So, which is worse: a false positive or a false negative? That's a question of expected value, which is based off the probability of a result and its consequences. In this case, the result at one end of the spectrum is the terrorists are caught because of this system, but many innocent people are subject to surveillance and searching. On the other end is that no one is caught because they slip through a timid test, and more people are hurt as a result. Clearly, this can easily turn into a much more complicated debate on the values of time, trust, privacy, and life, so I won't try to determine what the correct balance is myself. Although it's easy to describe some aspects of this conflict with numbers, as Marcus did, it just isn't that simple.

Hindsight is 20/20

In his essay "Mining Student Data Could Save Lives", Morris suggests that by analyzing students digital activities, we could catch the oft-ignored signs of a future attack and take action before any lives are lost. At first glance, this seems like a perfect method to deter violence on campus. Sure, the students privacy is somewhat compromised, but the lives that could be saved are certainly worth the sacrifice, aren't they? However, even if we could justify the morality and ethics of such a system, there are some logical faults in this data-powered "crystal ball".

After a mass shooting, we often look at the evidence and wonder how no one noticed the signs - they seem so obvious. However, this is a classic example of hindsight bias, which refers to our tendency to see events that have already occurred as more predictable than they were. While some signs are indisputably concerning, such as outright threats and manifestos, many are not. Some may be subtle, and only stand out in context of the attack. Or, it may be difficult to gauge the severity and sincerity of a message, especially since people tend to be emboldened on the internet. Many indicators can have perfectly innocent, plausible explanations, and innocent behavior can seem sinister depending on one's perspective. Finally, there's a risk that those who design the system will build their personal biases into it, unfairly targeting certain groups.

How do we handle this ambiguity? Do we err on the side of false positives and discrimination, or should we lean towards giving the benefit of the doubt, even if we risk some attackers slipping through? If a student is identified as a threat, how do we intervene, discipline, or serve justice when no crime has been committed? Perhaps there are other ways we can prevent these violent acts, such as limiting students access to deadly weapons, building a strong community that prioritizes student care, and working to undo societal norms, standards, and pressures that contribute to violence. Since there are many other less inflammatory options, we ought to pursue them before turning to a faulty and unethical system of constant surveillance.

 

 

Inviting Suspicion

We generally don't bother to encrypt messages if we have nothing to hide. By using a code or cipher, it's implied that the contents are sensitive or illicit in nature. In fact, as Singh points out, they're likely to be more explicit because the encryption lulls the sender into a false sense of security and they write more openly about their plans. So by putting too much faith in an easily breakable cipher, you risk incriminating yourself further.

In addition, by using a cipher or code that is easily identifiable as such, you automatically invite suspicion.  In her trial, Mary claimed she knew nothing about the plot, but even without decrypting the message, it was clear she was corresponding with conspirators. Also, the fact that she didn't write her message in plain text implies she was concealing something. In situations like these, it may be better to stick to some sort of code that masks the message as something innocuous, or some sort of steganography that hides the secret message within another. By finding a way to hide a message in plain sight, it helps divert suspicion in the first place rather than relying on an imperfect cipher once you've drawn attention.

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