# trying to identify the key of a vigenere cipher via brute force

I'm working on a bit of an ARG game type thing that uses the vigenere cipher. what im wondering is the chance a player could brute force said cipher by simply checking all possible key sequences of the right length, that being 41 characters, for deciphering a sequence of about 1000 characters. its also using more character types than the usual 26, it has 77 unique characters. so what are the chances they could stumble across the correct key by almost (or entirely) complete luck? additionally, could i possibly make the cipher more secure by applying a secondary layer of defense (like converting to a different base or something) and thus making it harder to tell what the alphabet of the cipher is. assume the players already know that it somehow relates to a vigenere cipher and they already know the character length of the key.

If you only think about Brute Force as an attack, then we first have to compute the number of possible keys: $$77^{41} = log_2(77^{41}) \approx 2^{260}$$. For Brute Force this would end up in 259-260 Bit security. Common sense is, that 128 - 256 Bit security is already save. Therefore your Cipher would be secure, if Brute Force is the only possible attack and the probability for someone guessing the correct key is negligible.