JPEG Image Encryption Using Combined Reversed And Normal Direction-Distorted Dc Permutation With Key Scheduling Algorithm-Based Permutation

This thesis work studied on digital image encryption algorithms performed towards JPEG images. With image encryption algorithms, JPEG images can be securely scrambled or encrypted prior to distribution. The intended recipient will be given a decryption key in which only with this key the receiver can received and decrypt the media for viewing. The proposed approach uses a frequency domain combinational framework of coefficients scrambling with Key Scheduling Algorithm based (KSA-based) permutation. This novel algorithm applies coefficients scrambling using Combined-Reverse-and-Normal-Direction (CRND) scanning together with Distorted DC permutation (DDP). This encryption algorithm involved the manipulation of JPEG zigzag scanning table according to 10 different scanning tables which was derived by reversing the existing zigzag scanning directions. With the same compression properties, this encryption algorithm was shown to be able to produce average file size smaller than baseline JPEG and other encryption. It was also shown that the average decoding speed for this technique outperform most of other existing techniques and the same time able to maintain image quality (PSNR) as other techniques. It terms of security, with the combination of Distorted DC permutation (DDP), it was considered to be having medium security based on some basic attack analysis that was carried out. It is also shown that this technique is fully format compliance as most of other techniques do. Based on the simple nature of CRND, this technique is easy to be implemented on existing system and thus should be able reduce the cost of implementing a new encryption system

Multidimensional continued fractions and a Minkowski function

The Minkowski Question Mark function can be characterized as the unique homeomorphism of the real unit interval that conjugates the Farey map with the tent map. We construct an n-dimensional analogue of the Minkowski function as the only homeomorphism of an n-simplex that conjugates the piecewise-fractional map associated to the Monkemeyer continued fraction algorithm with an appropriate tent map.Comment: 17 pages, 3 figures. Revised version according to the referee's suggestions. Proof of Lemma 2.3 more detailed, other minor modifications. To appear in Monatshefte fur Mathemati