Key Size and Vulnerability
In a pure mathematical attack (i.e., lacking any other information to help break a cipher), three factors above all, count:
- Mathematical advances that allow new attacks or weaknesses to be discovered and exploited.
- Computational power available, i.e., the computing power which can be brought to bear on the problem. It is important to note that 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 (i.e., "brute force" attack) substantially.
- Key size, i.e., 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 impractable to crack encryption directly.
Since the desired effect is computational difficulty, in theory one would choose an algorithm and desired difficulty level, thus decide the key length accordingly.
An example of this process can be found at Key Length which uses multiple reports to suggest that a symmetric cipher with 128 bits, an asymmetric cipher with 3072 bit keys, and an elliptic curve cipher with 512 bits, all have similar difficulty at present.
Claude Shannon proved, using information theory considerations, that any theoretically unbreakable cipher must have keys which are at least as long as the plaintext, and used only once: one-time pad.
Read more about this topic: Cipher
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