One uses a cryptosystem with encryption function $E_{a, b, c}\colon \Z_p \to (\Z_p)^2$ defined as
$$E_{a, b, c}(x) = (a + x \bmod p, b x + c \bmod p),$$
where $p=101$.
Alice encrypts each plaintext $x \in \Z_p$ with a random key
and sends cipher text $(c_i)_{i=0}^3$ to Bob.
Tomas wants to mess with Bob, so
he intercepts the messages and changes some of them.
Bob has the following keys that Alices used
- $k_1 = (27, 44, 78)$
- $k_2 = (48, 12, 75)$
- $k_3 = (29, 77, 34)$
For which of the following received ciphertexts will Bob detect tempering?
- $c_1 = (77, 56)$
- $c_2 = (60, 34)$
- $c_3 = (23, 77)$
What is the probability of undetectable tampering? Round to 4 decimal places.
Submit the answer as a sequence of numbers, eg. 2 3 0.1234.