Neural Space-filling Curves

We present Neural Space-filling Curves (SFCs), a data-driven approach to infer a context-based scan order for a set of images. Linear ordering of pixels forms the basis for many applications such as video scrambling, compression, and auto-regressive models that are used in generative modeling for images. Existing algorithms resort to a fixed scanning algorithm such as Raster scan or Hilbert scan. Instead, our work learns a spatially coherent linear ordering of pixels from the dataset of images using a graph-based neural network. The resulting Neural SFC is optimized for an objective suitable for the downstream task when the image is traversed along with the scan line order. We show the advantage of using Neural SFCs in downstream applications such as image compression. Code and additional results will be made available at https://hywang66.github.io/publication/neuralsfc

A Lower Bound On Proximity Preservation by Space Filling Curves

Abstract: A space filling curve (SFC) is a proximity preserving mapping from a high dimensional space to a single dimensional space. SFCs have been used extensively in dealing with multi-dimensional data in parallel computing, scientific computing, and databases. The general goal of an SFC is that points that are close to each other in high-dimensional space are also close to each other in the single dimensional space. While SFCs have been used widely, the extent to which proximity can be preserved by an SFC is not precisely understood yet. We consider natural metrics, including the nearest-neighbor stretch of an SFC, which measure the extent to which an SFC preserves proximity. We first show a powerful negative result, that there is an inherent lower bound on the stretch of any SFC. We then show that the stretch of the commonly used Z curve is within a factor of 1.5 from the optimal, irrespective of the number of dimensions. Further we show that a very simple SFC also achieves the same stretch as the Z curve. Our results apply to SFCs in any dimension d such that d is a constant

Processor allocation on Cplant: Achieving general processor locality using one-dimensional allocation strategies.

Abstract Follows 3 Abstract The Computational Plant or Cplant is a commodity-based supercomputer under development at Sandia National Laboratories. This paper describes resource-allocation strategies to achieve processor locality for parallel jobs in Cplant and other supercomputers. Users of Cplant and other Sandia supercomputers submit parallel jobs to a job queue. When a job is scheduled to run, it is assigned to a set of processors. To obtain maximum throughput, jobs should be allocated to localized clusters of processors to minimize communication costs and to avoid bandwidth contention caused by overlapping jobs. This paper introduces new allocation strategies and performance metrics based on space-filling curves and one dimensional allocation strategies. These algorithms are general and simple. Preliminary simulations and Cplant experiments indicate that both space-filling curves and one-dimensional packing improve processor locality compared to the sorted free list strategy previously used on Cplant. These new allocation strategies are implemented in the new release of the Cplant System Software, Version 2.0, phased into th

On the security of permutation-only image encryption schemes

Permutation is a commonly used primitive in multimedia (image/video) encryption schemes, and many permutation-only algorithms have been proposed in recent years for the protection of multimedia data. In permutation-only image ciphers, the entries of the image matrix are scrambled using a permutation mapping matrix which is built by a pseudo-random number generator. The literature on the cryptanalysis of image ciphers indicates that the permutation-only image ciphers are insecure against ciphertext-only attacks and/or known/chosenplaintext attacks. However, the previous studies have not been able to ensure the correct retrieval of the complete plaintext elements. In this paper, we revisited the previous works on cryptanalysis of permutation-only image encryption schemes and made the cryptanalysis work on chosen-plaintext attacks complete and more efficient. We proved that in all permutationonly image ciphers, regardless of the cipher structure, the correct permutation mapping is recovered completely by a chosenplaintext attack. To the best of our knowledge, for the first time, this paper gives a chosen-plaintext attack that completely determines the correct plaintext elements using a deterministic method. When the plain-images are of size M × N and with L different color intensities, the number n of required chosen plain-images to break the permutation-only image encryption algorithm is n = logL(MN). The complexity of the proposed attack is O (n · M N) which indicates its feasibility in a polynomial amount of computation time. To validate the performance of the proposed chosen-plaintext attack, numerous experiments were performed on two recently proposed permutation-only image/video ciphers. Both theoretical and experimental results showed that the proposed attack outperforms the state-of-theart cryptanalytic methods

A NOVEL JOINT PERCEPTUAL ENCRYPTION AND WATERMARKING SCHEME (JPEW) WITHIN JPEG FRAMEWORK

Due to the rapid growth in internet and multimedia technologies, many new commercial applications like video on demand (VOD), pay-per-view and real-time multimedia broadcast etc, have emerged. To ensure the integrity and confidentiality of the multimedia content, the content is usually watermarked and then encrypted or vice versa. If the multimedia content needs to be watermarked and encrypted at the same time, the watermarking function needs to be performed first followed by encryption function. Hence, if the watermark needs to be extracted then the multimedia data needs to be decrypted first followed by extraction of the watermark. This results in large computational overhead. The solution provided in the literature for this problem is by using what is called partial encryption, in which media data are partitioned into two parts - one to be watermarked and the other is encrypted. In addition, some multimedia applications i.e. video on demand (VOD), Pay-TV, pay-per-view etc, allow multimedia content preview which involves „perceptual‟ encryption wherein all or some selected part of the content is, perceptually speaking, distorted with an encryption key. Up till now no joint perceptual encryption and watermarking scheme has been proposed in the literature. In this thesis, a novel Joint Perceptual Encryption and Watermarking (JPEW) scheme is proposed that is integrated within JPEG standard. The design of JPEW involves the design and development of both perceptual encryption and watermarking schemes that are integrated in JPEG and feasible within the „partial‟ encryption framework. The perceptual encryption scheme exploits the energy distribution of AC components and DC components bitplanes of continuous-tone images and is carried out by selectively encrypting these AC coefficients and DC components bitplanes. The encryption itself is based on a chaos-based permutation reported in an earlier work. Similarly, in contrast to the traditional watermarking schemes, the proposed watermarking scheme makes use of DC component of the image and it is carried out by selectively substituting certain bitplanes of DC components with watermark bits. vi ii Apart from the aforesaid JPEW, additional perceptual encryption scheme, integrated in JPEG, has also been proposed. The scheme is outside of joint framework and implements perceptual encryption on region of interest (ROI) by scrambling the DCT blocks of the chosen ROI. The performances of both, perceptual encryption and watermarking schemes are evaluated and compared with Quantization Index modulation (QIM) based watermarking scheme and reversible Histogram Spreading (RHS) based perceptual encryption scheme. The results show that the proposed watermarking scheme is imperceptible and robust, and suitable for authentication. Similarly, the proposed perceptual encryption scheme outperforms the RHS based scheme in terms of number of operations required to achieve a given level of perceptual encryption and provides control over the amount of perceptual encryption. The overall security of the JPEW has also been evaluated. Additionally, the performance of proposed separate perceptual encryption scheme has been thoroughly evaluated in terms of security and compression efficiency. The scheme is found to be simpler in implementation, have insignificant effect on compression ratios and provide more options for the selection of control factor

A NOVEL JOINT PERCEPTUAL ENCRYPTION AND WATERMARKING SCHEME (JPEW) WITHIN JPEG FRAMEWORK

Due to the rapid growth in internet and multimedia technologies, many new commercial applications like video on demand (VOD), pay-per-view and real-time multimedia broadcast etc, have emerged. To ensure the integrity and confidentiality of the multimedia content, the content is usually watermarked and then encrypted or vice versa. If the multimedia content needs to be watermarked and encrypted at the same time, the watermarking function needs to be performed first followed by encryption function. Hence, if the watermark needs to be extracted then the multimedia data needs to be decrypted first followed by extraction of the watermark. This results in large computational overhead. The solution provided in the literature for this problem is by using what is called partial encryption, in which media data are partitioned into two parts - one to be watermarked and the other is encrypted. In addition, some multimedia applications i.e. video on demand (VOD), Pay-TV, pay-per-view etc, allow multimedia content preview which involves „perceptual‟ encryption wherein all or some selected part of the content is, perceptually speaking, distorted with an encryption key. Up till now no joint perceptual encryption and watermarking scheme has been proposed in the literature. In this thesis, a novel Joint Perceptual Encryption and Watermarking (JPEW) scheme is proposed that is integrated within JPEG standard. The design of JPEW involves the design and development of both perceptual encryption and watermarking schemes that are integrated in JPEG and feasible within the „partial‟ encryption framework. The perceptual encryption scheme exploits the energy distribution of AC components and DC components bitplanes of continuous-tone images and is carried out by selectively encrypting these AC coefficients and DC components bitplanes. The encryption itself is based on a chaos-based permutation reported in an earlier work. Similarly, in contrast to the traditional watermarking schemes, the proposed watermarking scheme makes use of DC component of the image and it is carried out by selectively substituting certain bitplanes of DC components with watermark bits. vi ii Apart from the aforesaid JPEW, additional perceptual encryption scheme, integrated in JPEG, has also been proposed. The scheme is outside of joint framework and implements perceptual encryption on region of interest (ROI) by scrambling the DCT blocks of the chosen ROI. The performances of both, perceptual encryption and watermarking schemes are evaluated and compared with Quantization Index modulation (QIM) based watermarking scheme and reversible Histogram Spreading (RHS) based perceptual encryption scheme. The results show that the proposed watermarking scheme is imperceptible and robust, and suitable for authentication. Similarly, the proposed perceptual encryption scheme outperforms the RHS based scheme in terms of number of operations required to achieve a given level of perceptual encryption and provides control over the amount of perceptual encryption. The overall security of the JPEW has also been evaluated. Additionally, the performance of proposed separate perceptual encryption scheme has been thoroughly evaluated in terms of security and compression efficiency. The scheme is found to be simpler in implementation, have insignificant effect on compression ratios and provide more options for the selection of control factor