Score:3

Why Pr[C = 1∣M = a] = 1 ≠ 0 = Pr[C = 1∣M = b]?

gi flag

The statement is false. We show this by providing a counter-example.

Define

  • M = {a, b},
  • K = {k1, k2},
  • C = {0, 1}.

Let Enc(k, a) = 0 and Enc(k, b) = 1 for k = k1, k2.

Dec algorithm will return an on input ciphertext 0 and b on input ciphertext 1. Clearly, the scheme is correct.

Pr[C = 1∣M = a] = 1 ≠ 0 = Pr[C = 1∣M = b],
thus showing that the scheme is not perfectly secret.

Why Pr[C = 1∣M = a] = 1 and Pr[C = 1∣M = b] = 0?
I think it should be Pr[C = 1∣M = a] = 0 ≠ 1 = Pr[C = 1∣M = b].

cn flag
@fgrieu the vertical bar is generally used to denote conditional probabilities.
fgrieu avatar
ng flag
@Maeher: Ah,eclipse of the mind, because recently I've been seeing a lot of [conditional probabilities](https://en.wikipedia.org/wiki/Conditional_probability) with the assumption in subscript, as in $(\Pr_{M=a}[C=1]=1)≠(0=\Pr_{M=b}[C=1])$. I'm still not sure about the parsing of the center.
cn flag
Where does this statement come from? Yes, for the example you provide it's obviously incorrect. Most likely someone somewhere accidentally swallowed zero and one.
cn flag
That was supposed to read "swapped", I do not recommend swallowing bits.
I sit in a Tesla and translated this thread with Ai:

mangohost

Post an answer

Most people don’t grasp that asking a lot of questions unlocks learning and improves interpersonal bonding. In Alison’s studies, for example, though people could accurately recall how many questions had been asked in their conversations, they didn’t intuit the link between questions and liking. Across four studies, in which participants were engaged in conversations themselves or read transcripts of others’ conversations, people tended not to realize that question asking would influence—or had influenced—the level of amity between the conversationalists.