The difficulty of brute forcing an encryption system is based on the degree of randomness produced by the key.  When a key is less than the length of a file, there has to be some type of reuse, and this means less than perfect randomness and thus some small susceptibility to being brute forced.

Thus, in order to make something truly brute force proof against an attacker with unlimited resources and time, the only option is a truly random key that is the same length as the input and that has never been used as a key on another message.  This technique is actually very, very old and is known as a one time pad (or OTP).  An OTP is completely future secure as long as the key remains secret.  Since the key is random and only used once, the input bears no resemblance to the output and "jfeidj" could just as easily be "attack" as it could be "dinner".

That said, attackers don't have unlimited time or resources, so practically speaking, almost any modern symmetric algorithm will provide more than enough security even at key lengths as low as 128 bits or lower.  128 bit AES, for example, while "technically" able to be brute forced would take so long trying to brute force that chances are good that if every computer on the planet worked on nothing but cracking the message, the sun would die and the solar system get sucked in to a black hole before they finished cracking the message.  (Provided there aren't any unknown flaws in the algorithm and that the key is properly generated.)  If you make it 256bit, the heat death of the universe will come before you successfully brute force it.

So practically speaking, just about any modern algorithm is secure against brute forcing with sufficient key length.

Is it possible to encrypt a file so that it can not be brute forced?
For any professors out there, do you feel that there are any differences in how you selected and recruited students from the time when you were newly hired, to a well-established stage (i.e. after getting tenure)? I'm asking this out of curiosity. There are oftentimes questions about whether students should choose a new/old advisor, but I haven't seen any that asked about this from the prof's perspective.

I would assume there are since the challenges and priorities for the two groups are normally somewhat different, but I'm not sure exactly how it would differ. For instance, it might be more difficult for the new PI to recruit students (especially good ones) when they have to "compete" with older, better funded peers. This would lead one to think that new PIs might be more likely to take on students they might not necessarily love, but just need bodies in the lab. However, on the other hand, new PIs are more likely to have limited funding, and if they are on the tenure-track, would need their few students to succeed in order to establish a name for themselves in the industry. In this case, it would be detrimental if they chose the wrong student(s) in the beginning, especially if they are limited to the number of students they can afford due to funding issues. I realize that this is field and situation specific, but I'm looking to hear stories/insights from people who have gone through/know about the process.

Thanks!
