The field of post-quantum cryptography (PQC) is continuously evolving. Many researchers are exploring efficient PQC implementation on various platforms, including x86, ARM, FPGA, GPU, etc. In this paper, we present an Efficient CryptOgraphy CRYSTALS (ECO-CRYSTALS) implementation on standard 64-bit RISC-V Instruction Set Architecture (ISA). The target schemes are two winners of the National Institute of Standards and Technology (NIST) PQC competition: CRYSTALS-Kyber and CRYSTALS-Dilithium, where the two most time-consuming operations are Keccak and polynomial multiplication. Notably, this paper is the first highly-optimized assembly software implementation to deploy Kyber and Dilithium on the 64-bit RISC-V ISA. Firstly, we propose a better scheduling strategy for Keccak, which is specifically tailored for the 64-bit dual-issue RISC-V architecture. Our 24-round Keccak permutation (Keccak-$p$[1600,24]) achieves a 59.18% speed-up compared to the reference implementation. Secondly, we apply two modular arithmetic (Montgomery arithmetic and Plantard arithmetic) in the polynomial multiplication of Kyber and Dilithium to get a better lazy reduction. Then, we propose a flexible dual-instruction-issue scheme of Number Theoretic Transform (NTT). As for the matrix-vector multiplication, we introduce a row-to-column processing methodology to minimize the expensive memory access operations. Compared to the reference implementation, we obtain a speedup of 53.85%$\thicksim$85.57% for NTT, matrix-vector multiplication, and INTT in our ECO-CRYSTALS. Finally, the ECO-CRYSTALS implementation for key generation, encapsulation, and decapsulation in Kyber achieves 399k, 448k, and 479k cycles respectively, achieving speedups of 60.82%, 63.93%, and 65.56% compared to the NIST reference implementation. Similarly, the ECO-CRYSTALS implementation for key generation, sign, and verify in Dilithium reaches 1 364k, 3 191k, and 1 369k cycles, showcasing speedups of 54.84%, 64.98%, and 57.20%, respectively.

Burst detection is an inherent problem for data streams, so it has attracted extensive attention in research community due to its broad applications. One of the basic problems in burst detection is how to count frequencies of all elements in data stream. This paper presents a novel solution based on Improved Counting Bloom Filter, which is also called BCBF+HSet. Comparing with intuitionistic approach such as array and list, our solution significantly reduces space complexity though it introduces few error rates. Further, we discuss space/time complexity and error rate of our solution, and compare it with two classic Counting Bloom Filters, CBF and DCF. Theoretical analysis and simulation results demonstrate the efficiency of the proposed solution.

We propose a new variant of Non-negative Matrix Factorization (NMF), including its model and two optimization rules. Our method is based on positively constrained projections and is related to the conventional SVD or PCA decomposition. The new model can potentially be applied to image compression and feature extraction problems. Of the latter, we consider processing of facial images, where each image consists of several parts and for each part the observations with different lighting mainly distribute along a straight line through the origin. No regularization terms are required in the objective functions and both suggested optimization rules can easily be implemented by matrix manipulations. The experiments show that the derived base vectors are spatially more localized than those of NMF. In turn, the better part-based representations improve the recognition rate of semantic classes such as the gender or existence of mustache in the facial images.

The fast independent component analysis (FastICA) algorithm is one of the most popular methods to solve problems in ICA and blind source separation. It has been shown experimentally that it outperforms most of the commonly used ICA algorithms in convergence speed. A rigorous local convergence analysis has been presented only for the so-called one-unit case, in which just one of the rows of the separating matrix is considered. However, in the FastICA algorithm, there is also an explicit normalization step, and it may be questioned whether the extra rotation caused by the normalization will affect the convergence speed. The purpose of this paper is to show that this is not the case and the good convergence properties of the one-unit case are also shared by the full algorithm with symmetrical normalization. A local convergence analysis is given for the general case, and the global behavior is illustrated numerically for two sources and two mixtures in several typical cases.