nope! you can reduce the size. trivial example is just XOR: Enc(A) xor Enc(B) = Enc(A^B).. 2 bits in, one bit out. what you can't do is implement variable-size

nope! you can reduce the size. trivial example is just XOR: Enc(A) xor Enc(B) = Enc(A^B).. 2 bits in, one bit out. what you can't do is implement variable-size compression like Huffman trees. if you think about implementing Huffman as a circuit, you have a fixed length output - the worst-case length. you can't read the output any more than you can read the input, so you don't know how much padding you can throw away. therefore it's useless. the same principle applies to running any algorithm that has a dynamic computational complexity. so you can run a Turing machine in FHE, but you won't know when it halts.