implication of tweak on bruteforcing a block cipher Consider a KPA attack, where the attacker gets known plain text and the corresponding cipher text. Since the encryption algorithm is known, he can brute force all possibilities of key bits. What is the implication of having additional tweak on brute forcing the algorithm?

Is this correct to say that now the attacker must try $2^k * 2^t$ possibilities, thus increasing the effort required to break the algorithm and so making it more secure?
(where k is number of bits in key and t is number of bits in tweak).

Edit: Assuming tweak is kept secret . And also that my application prepends the tweak string to the plain text while encrypting it , $AES_K(Tweak || plain ) $. Is my above assumption correct ? 

Edit 2 : The AES in above is being used as a PRF in Luby Rackoff Construction like any other Format Preserving Encryption mode. So the AES is not exactly an encryption of the plain text but right half of the Feistel Network .(Honestly apologize for multiple edits)
The tweak is generally not secret, i.e. the adversary knows it (perhaps even chooses it, depending on the attack model) and thus doesn't have to try to guess it.  So no, tweaks don't increase the effort to brute force a cipher ... unless of course the tweak is kept secret, in which case it may or may not increase the required effort, depending on how the tweak is mixed into the cipher state.