On 10/11/2013 11:22 AM, Jerry Leichter wrote: > 1. Brute force. No public key-stretching algorithm can help, since the > attacker > will brute-force the k's, computing the corresponding K's as he goes.

There is a completely impractical solution for this which is applicable in a very few ridiculously constrained situations. Brute force can be countered, in very limited circumstances, by brute bandwidth. You have to use random "salt" sufficient to ensure that all possible decryptions of messages transmitted using the insufficient key or insecure cipher are equally valid. Unfortunately, this requirement is cumulative for *ALL* messages that you encrypt using the key, and becomes flatly impossible if the total amount of ciphertext you're trying to protect with that key is greater than a very few bits. So, if you have a codebook that allows you to transmit one of 128 pre- selected messages (7 bits each) you could use a very short key or an insecure cipher about five times, attaching (2^35)/5 bits of salt to each message, to achieve security against brute-force attacks. At that point your opponent sees all possible decryptions as equally likely with at least one possible key that gives each of the possible total combinations of decryptions (approximately; about 1/(2^k) of the total number of possible decryptions will be left out, where k is the size of your actual too-short key). The bandwidth required is utterly ridiculous, but you can get security on a few very short messages, assuming there's no identifiable pattern in your salt. Unfortunately, you cannot use this to leverage secure transmission of keys, since whatever key larger than the initial key you transmit using this scheme, once your opponent has ciphertext transmitted using the longer key, the brute-force method against the possibilities for your initial short key becomes applicable to that ciphertext. Bear _______________________________________________ The cryptography mailing list cryptography@metzdowd.com http://www.metzdowd.com/mailman/listinfo/cryptography