function. If yes, prove it; if not, show a distinguisher that succeeds with non- negligible probability. Hint: to prove that some of these candidates are not PRFS, it may be useful to assume the existence of MACS or PRFS with input and output of arbitrary size. Feel free to assume that such PRFS and MACs do exist, and pick the parameter sizes that are the most suitable to prove your result. (a) F' (k, x) def - MAC ([k],[x]). def (b) F" (k,x) = F(k, x)||AND(x). (c) F" (k, x) def MAC ([F(k, 1")]}³, [x]}). = 3. (MACs and PRFs) Let II = (Gen, MAC, Verify) be a secure MAC scheme with Gen (1) Є {0, 1} and MAC: {0, 1} × {0, 1} → {0,1}" (i.e., the MAC scheme works with keys and messages of size n/2 and returns a tag represented by a bit-string of size n). Let F {0, 1}"{0, 1}" → {0, 1}" be a length-preserving pseudorandom function. State whether each of the following PRF candidates is or is not a pseudorandom

Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.

 

Very very grateful!