Vassil S. Dimitrov

D. F. G. Coelho, R. J. Cintra, F. M. Bayer et al.

This paper introduced a matrix parametrization method based on the Loeffler discrete cosine transform (DCT) algorithm. As a result, a new class of eight-point DCT approximations was proposed, capable of unifying the mathematical formalism of several eight-point DCT approximations archived in the literature. Pareto-efficient DCT approximations are obtained through multicriteria optimization, where computational complexity, proximity, and coding performance are considered. Efficient approximations and their scaled 16- and 32-point versions are embedded into image and video encoders, including a JPEG-like codec and H.264/AVC and H.265/HEVC standards. Results are compared to the unmodified standard codecs. Efficient approximations are mapped and implemented on a Xilinx VLX240T FPGA and evaluated for area, speed, and power consumption.

Vidal Attias, Luigi Vigneri, Vassil Dimitrov

RSA cryptography is still widely used. Some of its applications (e.g., distributed signature schemes, cryptosystems) do not allow the RSA modulus to be generated by a centralized trusted entity. Instead, the factorization must remain unknown to all the network participants. To this date, the existing algorithms are either computationally expensive, or limited to two-party settings. In this work, we design a decentralized multi-party computation algorithm able to generate efficiently the RSA modulus.

J. Adikari, V. S. Dimitrov, R. J. Cintra

Koblitz curves are a special set of elliptic curves and have improved performance in computing scalar multiplication in elliptic curve cryptography due to the Frobenius endomorphism. Double-base number system approach for Frobenius expansion has improved the performance in single scalar multiplication. In this paper, we present a new algorithm to generate a sparse and joint $τ$-adic representation for a pair of scalars and its application in double scalar multiplication. The new algorithm is inspired from double-base number system. We achieve 12% improvement in speed against state-of-the-art $τ$-adic joint sparse form.

A. Edirisuriya, A. Madanayake, R. J. Cintra et al.

An area efficient row-parallel architecture is proposed for the real-time implementation of bivariate algebraic integer (AI) encoded 2-D discrete cosine transform (DCT) for image and video processing. The proposed architecture computes 8$\times$8 2-D DCT transform based on the Arai DCT algorithm. An improved fast algorithm for AI based 1-D DCT computation is proposed along with a single channel 2-D DCT architecture. The design improves on the 4-channel AI DCT architecture that was published recently by reducing the number of integer channels to one and the number of 8-point 1-D DCT cores from 5 down to 2. The architecture offers exact computation of 8$\times$8 blocks of the 2-D DCT coefficients up to the FRS, which converts the coefficients from the AI representation to fixed-point format using the method of expansion factors. Prototype circuits corresponding to FRS blocks based on two expansion factors are realized, tested, and verified on FPGA-chip, using a Xilinx Virtex-6 XC6VLX240T device. Post place-and-route results show a 20% reduction in terms of area compared to the 2-D DCT architecture requiring five 1-D AI cores. The area-time and area-time${}^2$ complexity metrics are also reduced by 23% and 22% respectively for designs with 8-bit input word length. The digital realizations are simulated up to place and route for ASICs using 45 nm CMOS standard cells. The maximum estimated clock rate is 951 MHz for the CMOS realizations indicating 7.608$\cdot$10$^9$ pixels/seconds and a 8$\times$8 block rate of 118.875 MHz.

Vassil Dimitrov, Diego Coelho

This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis for factorizations other than the well-known binary and ternary basis. We show that is possible to reduce the overall complexity for the usual binary decomposition from 2log2(N)-2 multiplications to around 1.72log2(N)-2 using a basis of size five. Merging different basis we can demonstrate that we can build fast algorithms for particular sizes. We also show the asymptotic case where one can reduce the number of multiplications to around 1.70log2(N)-2. Simulations are performed for applications in the context of wireless communications and image rendering, where is necessary perform large sized matrices inversion.

R. J. Cintra, V. S. Dimitrov, H. M. de Oliveira et al.

Fragile digital watermarking has been applied for authentication and alteration detection in images. Utilizing the cosine and Hartley transforms over finite fields, a new transform domain fragile watermarking scheme is introduced. A watermark is embedded into a host image via a blockwise application of two-dimensional finite field cosine or Hartley transforms. Additionally, the considered finite field transforms are adjusted to be number theoretic transforms, appropriate for error-free calculation. The employed technique can provide invisible fragile watermarking for authentication systems with tamper location capability. It is shown that the choice of the finite field characteristic is pivotal to obtain perceptually invisible watermarked images. It is also shown that the generated watermarked images can be used as publicly available signature data for authentication purposes.