Formally, an encryption scheme $($Gen$,$ Enc, Dec$)$ for message space $M$ and ciphertext

space $C$ is perfectly secure if:

$($a$)EE$ a message distribution $M$ such that, AAminM and AAcinC :

$Pr[M-m|C-c]-Pr[M-m]$

$($b$)AA$ message distributions $M,$ for any pair of messages $m,m^{\text{'}}$inM :

$Pr[M-m]-Pr[M-m^{\text{'}}]$

$($c$)$ none of the above is true

$($d$)$ both a and $b$ are true