This paper presents a new public-key encryption with security based on the two-sided digital circulant matrix action problem defined over the semiring proposed by Huang et al. ^[14]. The performance evaluation of the proposed encryption scheme shows its robustness and efficiency compared to state-of-art encryption schema. We also provide a security analysis of the proposed encryption. It is suitable for post-quantum cryptography and IoT platforms.

Let $N=\left\{n_1,n_2,\dots ,n_k\right\}$ be a finite set of positive numbers. The problem of finding the minimal number of additions required to compute all elements of N starting from 1 (called the addition sequence problem) is NP-complete. It is equivalent to finding the minimum number of multiplications needed to compute a group exponentiation $g^{n_1},g^{n_2},\dots ,g^{n_k}$, where g is an element in a group. This paper aims to propose a new metaheuristic algorithm using a simulated annealing strategy to generate a short addition sequence. The performance of the proposed algorithm is measured by considering two parameters: The size of N and the domain of $n_{\mathrm{i}},1\le i\le k$. The proposed algorithm is a new trade-off between the length of the generated addition sequence and the average running time of generating addition sequences. It sometimes produces longer addition sequences than exact algorithms that are slower, and it is slower than suboptimal algorithms that produce longer addition sequences.

Ribonucleic acid (RNA) structure alignment is an important problem in computational biology to identify structural similarity of RNAs. Obtaining an efficient method for this problem is challenging due to the high computational time for the optimal solution and the low accuracy of a heuristic solution. In this paper, an efficient algorithm is proposed based on a mathematical model called longest arc-preserving common subsequence. The proposed algorithm uses a heuristic technique and high-performance computing to optimize the solution of RNA structure alignment, both in terms of the running time and the accuracy of the output. Extensive experimental studies on a multicore system are conducted to show the effectiveness of the proposed algorithm on two types of data. The first is simulated data that consists of 450 comparisons of RNA structures, while the second is real biological data that consists of 357 comparisons of RNA structures. The results show that the proposed algorithm outperforms the best-known heuristic algorithm in terms of execution time, with a percentage improvement of 71% and increasing the length of the output, i.e., accuracy, by approximately 45% in all studied cases. Finally, future approaches are discussed.