Key size and vulnerability

In a pure mathematical attack (that is, lacking any other information to help break a cipher), three factors above all, count:

Mathematical advances that enable new attacks or weaknesses to be discovered and exploited.

Computational power available, that is, the computing power that can be brought to bear on the problem. Average performance/capacity of a single computer is not the only factor to consider. An adversary can use multiple computers at once, for instance, to increase the speed of exhaustive search for a key (such as “brute force” attack) substantially.

Key size (the size of key used to encrypt a message). As the key size increases, so does the complexity of exhaustive search to the point where it becomes infeasible to crack encryption directly.