Let frequency = (double)characterCounts/entropyString.Length Similar to zngu's answer, I think better than just counting the number of characters would be calculating the character-entropy of the message: public double CalculateEntropy(string entropyString)ĭictionary characterCounts = new Dictionary() įoreach(char c in entropyString.ToLower())ĬharacterCounts.TryGetValue(c, out currentCount) If the string is long enough the no brainer approach is: try to compress it, and calculate the ratio between the compression output and the input. so what you actually want here is to take the absolute value. ? this will appear to have a better distribution, since the derivative is 1,-1,1,-1. It is as trivial as subtracting the second char from the first, the thrid from the second, so in our example string this turns into: "abcdefg" => 1,1,1,1,1,1 So what you want here is to take also the first derivative, and check the distribution of the first derivative. Given a string of length N, how many A chars should I expect in average, given my model (that can be the english distribution, or natural distribution)?īut then what about "abcdefg"? No repetition here, but this is not random at all. Comparing characters that are the same is exactly this in some way, but the generalization is to build a frequency table and check the distribution. But I want to suggest to you a few things that can make a very simple but practical model. I'll not dig further in the math side, since I'm not an expert in the field. For instance the PI digits are well distributed, but actually is the entropy high? Not at all since the infinite sequence can be compressed into a small program calculating all the digits. In theory you can measure entropy only from the point of view of a given model. Result -= frequency * (Math.Log(frequency) / Math.Log(2)) Var frequency = (double)item.Value / len Public static double ShannonEntropy(string s) / returns bits of entropy represented in a given string, per It is a more "formal" calculation of entropy than simply counting letters: /// In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits. In information theory, entropy is a measure of the uncertainty associated with a random variable. I also came up with this, based on Shannon entropy.
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