A cipher (E, D) over (K, M, C) that is OTP if
K = M = C = {0, 1}^n
c = E(k, m) = k xor m
m = D(k, c) = k xor c
where c in C, k in K, m in M
OTP has perfect secrecy because |k| = |m|.
How do we understand the statement?
We can give a simple example.
K = M = C = {0, 1}^2
Below is the table of the OTP cipher.
We focus on c = 11 to guess the probability of m where k is a uniform random variable.
Pr[E(k, 00) = 11] = 1/4
Pr[E(k, 01) = 11] = 1/4
Pr[E(k, 10) = 11] = 1/4
Pr[E(k, 11) = 11] = 1/4
It describes that the OTP is perfect secrecy because
Pr[E(k, m) = c] = 1/4, for all c in C,
where k is a uniform random variable.
-Count
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