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By A. Bak
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Extra resources for Algebraic K-Theory, Number Theory, Geometry, and Analysis: Proceedings
The chance of picking two letters that are A is (3/322) × (2/321). Similarly, the chance of picking two that are B is (14/322) × (13/321), and so on. 068. 066, so it’s a very good bet that we have a simple substitution cipher. Friedman called this test the phi test to distinguish it from other tests using the index of coincidence, which we will see later. 5. 046—not as low as random text, but much lower than a simple substitution cipher, even despite having more than 26 characters, which tends to raise the index.
After retiring from active duty, he wrote a short book that generally focuses on this particular technique. So what is the technique, now generally known as the Kasiski test? The central idea is that if the repetition of the key and a repetition in the plaintext happen to line up, they will cause a repetition in the ciphertext. Let’s consider again our previous example: 46 • Chapter 2 keyword: plaintext: ciphertext: keyword: plaintext: ciphertext: l t F e h M o e T n c Q l a M e t Y o o D n n B l t F e h M n a O l t F e t Y o e T n d R l a M e g L o n C n a O l t F o e T n m A l a M e t Y o b Q The plaintext letters at repeat 4 times.
Even before computers, this was considered quite feasible, and with a modern computer, it’s a snap. 5 shows the sums of the frequencies for each possible key. Eve sees that key letter l gives far and away the highest sum, so that’s probably the second key letter. Proceeding in this way gives all five key letters as glass, which makes her feel a lot better since she was wondering just what a gvehs was, anyway. Of course, the proof of the pudding is in the decrypting—try it and see if your answer makes sense!