To be seriously considered "strong", any cryptographic method has to fulfill two requirments:
- The algorithm must guarantee an exponential relation
between key size and the computational effort for decoding the message without the key. There must be no back doors in the algorithm itself.
- The key size that is used must be large enough to ensure that (through the above-mentioned exponential relation) decoding without the key takes so long that it is infeasible on even the most advanced hardware, now and in the foreseeable future.
For example,
DES cannot be considered strong cryptography anymore because it uses a fixed, relatively small key size which eventually made it impossible to fulfill the second requirement.
Note that I have not used the expression brute force, since the fastest algorithms for e.g. prime factoring (which is necessary for cracking RSA) are quite sophisticated and achieve far better results than the "brute" try all keys method that has to be used on the likes of RSA and IDEA.
However, the first requirement is still fulfilled since the relation is still exponential (though the base is smaller).
Something that has to be considered when deciding whether a cryptographic method fulfills the first requirement is how vulnerable to differential cryptanalysis it is.