In a one message communication. We are right after 2 DHKE (instead of one). Both users then have 2 secret numbers, J and K.
Is it a risk to replace the use of a Key Derivation Function with a multiplication of the form S=J**K, creating a big number and only use the bits we need to exchange the only message that conversation needs using a xor operation between S and the message?
After generating the arrays of solutions, that idea is definitely BAD for even values of J and if you don't truncate the first bits. Many numbers have a bias and large contiguous 0s are happening. Other than that, it really seems random.
"Other than that, it really seems random.". Let me rephrase it: if you are not using even values, no bias occur and the generated number really seems random and completely unrelated to previous values.