Acceptable condition for dictionary search
In a chosen plaintext attack, the expected ciphertext length required to conclude that a decryption is correct was derived by Claude Shannon and is called the unicity distance. It depends on the distributions of the plaintext and the key and is infinite for the one time pad.

So if $K$ is the random variable describing the key with a known distribution, and the message has $N$ symbols, say $(M_1,\ldots,M_N)$ with the message distribution known, let the encryption map be $$(C_1,\ldots,C_N)=E(M_1,\ldots,M_N;K).$$

Then the unicity distance is defined as
$$D:=\min\{ N: H(K|(C_1,\ldots,C_N))=0\},$$
where $H(\cdot|\cdot)$ is the conditional Shannon entropy.

See, e.g., wikipedia or van der Lubbe's Information Theory text.