# How to calculate entropy of a specific cryptosystem?

I want to calculate the entropy of a specific cryptosystem such as the Caesar cipher or Vernam cryptosystem etc but I don't quite understand how to do so. Any help?

• What does 'entropy of a specific cryptosystem' mean? Commented Jun 2, 2022 at 13:58
• Do you mean the entropy of the key? The entropy of the ciphertext (assuming a fixed plaintext)? Commented Jun 2, 2022 at 14:11
• Yes the entropy of the key of a cryptosystem Commented Jun 2, 2022 at 16:49
• Then I suggest that it's impossible to obtain a bitwise entropy value of a single key since they're derived from passwords like "secret". Commented Jun 2, 2022 at 18:39

The entropy of a cryptographic key $$K$$ cannot be computed in isolation for a single key. It is the property of the generation mechanism for the key.
Entropy is a function of a probability distribution. Assuming you mean the most common entropy measure, Shannon Entropy, given a key $$K\in \{0,1\}^b$$ which has been randomly generated from the set of $$b-$$bit strings according to some probability distribution $$P(x)=Prob\{K=x\},\quad x\in \{0,1\}^b$$ then the entropy of a key drawn from this distribution is $$H(X)=\sum_{x \in \{0,1\}^b} -P(x) \log_2 P(x)\quad\textrm{bits}.$$ If the distribution of $$K$$ is uniform then this entropy is $$b$$ bits.