# Why constrain the message lengths in indistinguishability in the presence of an eavesdropper?

I need your help with a very basic concept in cryptography which I can't understand/prove on my own.

I'm trying to prove and understand why, under "indistinguishability in the presence of an eavesdropper" encrpytion, it is required that the lengths of the messages output by the adversary satisfy $|m_0| = |m_1|$.

Just to make sure the reader understand exactly what's I'm talking about, the context of my question is page 6 of these lecture notes on Constructing a Computationally Secure Scheme Pseudorandomness (“Claim of indistinguishable encryptions in the presence of an eavesdropper”).

-

@SyndicatorBBB What is the size of the set of plaintexts of size $q(n)+2$? So, how large is the set of the corresponding ciphertexts? How large is the set of messages of size $\leq q(n)$? So a how big fraction of the "long plaintexts" can encrypt to a "short ciphertext"? So how big is the probability of getting a larger ciphertext? (You don't need exact numbers for each, often inequalities are enough.) – Paŭlo Ebermann Apr 5 '13 at 16:37