Strictly speaking, shift and xor alone will not net you a secure cipher, seeing that those are both linear GF(2) operations. You would need something else in the mix to generate some nonlinearity, like integer addition, multiplication, etc.
But on the subject of extremely simple constructions, you can compose many random permutations of a particular form---state[i] = state[i] xor F(state[j], state[k]), where state[i] is the ith bit of the state and F is a randomly chosen boolean function--- and obtain something asymptotically secure [1].