•A permutation based non-chaotic image encryption technique.•Have used properties of cyclic group to define a sequence (or permutation of a sequence) which is used to perform pixel and bit level permutation.•Experimental results against different statistical and differential attacks prove the immunity of the proposed method.•Comparative analysis with some state of the art methods provides the scheme a strong base in the field of image encryption. Image encryption using permutation is gaining its popularity over general encryption schemes like AES, DES, RSA etc., due to its high security, less time complexity using reasonable computational overheads. Mainly chaotic functions are employed in permutation based techniques to define a sequence, based on which the pixels or bits of an image are permuted. In parallel, researches are also carried out to define permutation using non chaotic techniques. In this paper, a novel non-chaotic image encryption technique is proposed. The properties of cyclic group are used as the backbone of the proposed method and using these properties some sequences/permutations are defined. These permutations are used for row/column level permutation of pixels and bit-level permutation. Iterative pixel addition operation with bit shifting using a ‘Transform array’ transforms the pixel value of the bit permuted image. Experimental results show that the proposed scheme is secure against statistical and differential attacks and provide a secure and efficient way for digital image encryption.