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Assume that there is a protocol $(A,B)$ such that receives no input and satisfies:

$A$ - outputs two random bits $x_0, x_1 \in \{0,1\}$

$B$ - outputs a random bit $b \in \{0,1\}$ and also outputs $x_b$

$A$ is supposed to learn what is $b$, and $B$ isn't supposed to learn what is $x_{\lnot b}$

I want to formally define the security of $(A,B)$.

Intuitively, I think I understand how to define the security of $(A,B)$, but I'm having problem how to formally write it.

For example, about the security of $A$ (the sender), I thought about this:

A is secure, if for every adversary $B^*$ of time complexity at most $T$, $B^*$ can guess correctly the value of $x_{\lnot b}$ with probability of at most $\frac{1}{2} + \epsilon$

Now, I want to write this as a math statement using probabilities, but I am not sure exactly how.

The same goes about the security of $B$.

Help would be appreciated.

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  • $\begingroup$ Your description of ROT is incorrect. $\endgroup$
    – Myath
    Commented Jan 5, 2021 at 8:59
  • $\begingroup$ Your third criteria should be "$A$ is not supposed to learn what $b$ is and $B$ isn't supposed to learn what is $x_{\neg b}$". To write your statement using math formalism, have $B^*$ output a guess for $x_{\neg b}$ and describe the probability that this guess is correct. $\endgroup$
    – lamontap
    Commented Jan 8, 2021 at 22:57

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