This paper introduces a cryptanalysis of image encryption techniques that are using chaotic scrambling and logic gates/circuits. Chaotic scrambling, as well as general permutations are considered together with reversible and irreversible gates, including XOR, Toffoli and Fredkin gates. We also investigate ciphers based on chaotic permutations and balanced logic circuits. Except for the implementation of Fredkin’s gate, these ciphers are insecure against chosen-plaintext attacks, no matter whether a permutation is applied globally on the image or via a block-by-block basis. We introduce a new cipher based on chaotic permutations, logic circuits and randomized Fourier-type transforms. The strength of the new cipher is statistically verified with standard statistical encryption measures.