Elementary Analysis of the Communication Complexity of Divide-and-Conquer Diffie-Hellman Key Agreement Protocol

We present a rigorous elementary analysis of the communication complexity of the Divide-and-Conquer Diffie-Hellman Key Agreement Protocol (DC-DHKA). The analysis is conducted by first determining the number of transmissions in DC-DHKA and then comparing the resulting communication complexity of this protocol with other variants of Diffie-Hellman key agreement protocols that utilize regular Diffie-Hellman key, namely the ING, GDH.1, GDH.2, and GDH.3 protocols. The mathematical and numerical analyses show that the total number of bits transmitted in the DC-DHKA protocol is always fewer than those of ING, GDH.1, and GDH.2 protocols for a group of N >= 19 participants. In addition, we also prove that the total number of bits required for the entire messages’ transmissions in DC-DHKA protocol for N participants that uses the multiplicative group Fq* is log2(q) 2^(log2(N)) (log2(N) + 1) - 2

Secure and Space Efficient Accounts Storage System Using Three-Dimensional Bloom Filter

This paper investigates the application of a three dimensional Bloom Filter (3DBF) to accomplish a secure and efficient accounts storage system by exploiting hashes of usernames and their corresponding passwords. We conducted numerical experiments and mathematical analysis to study the efficiency level of several 3DBF schemes. Our experimental results and analysis show that the level of occupancy for 3DBF is positively correlated to the value of its false positive rate, viz., if the occupancy level increases then so does the value of the false positive rate. Moreover, we also derive a formula for determining the minimum number of bits for storing some data in a 3DBF scheme given the value of its acceptable false positive rate and its occupancy level. We infer that the product of the dimensional parameter of a 3DBF scheme is inversely proportional to the false positive rate and occupancy level used in the scheme

Solving Yin-Yang Puzzles Using Exhaustive Search and Prune-and-Search Algorithms

We investigate some algorithmic and mathematical aspects of Yin-Yang/Shiromaru-Kuromaru puzzles. Specifically, we discuss two algorithms for solving arbitrary Yin-Yang puzzles, namely the exhaustive search approach and the prune-and-search technique. We show that both algorithms have an identical asymptotic running time of O(max{mn, 2^(mn−h)}) for finding all solutions of a Yin-Yang instance with h hints of size m x n. Nevertheless, our experiments show that the practical running time of the prune-and-search technique outperforms the conventional exhaustive search approach

Pelatihan Berpikir Komputasional untuk Peningkatan Kompetensi Guru Telkom Schools sebagai Bagian dari Gerakan PANDAI

Berpikir komputasional (BK) atau computational thinking (CT) merupakan salah satu keahlian esensial yang diperlukan sumber daya manusia Indonesia dalam rangka menghadapi revolusi industri 4.0 dan masyarakat 5.0. Gerakan PANDAI (Pengajar Era Digital Indonesia) merupakan suatu gerakan nasional yang merupakan kolaborasi nirlaba antara komunitas Bebras Indonesia, Kementerian Pendidikan dan Kebudayaan Indonesia, dan Google Indonesia dalam rangka meningkatkan kompetensi BK yang dimiliki oleh guru sekolah dasar dan menengah. Pada tahun 2022, Biro Bebras Universitas Telkom mengadakan pelatihan BK kepada lebih dari 60 guru Telkom Schools sebagai bagian dari gerakan ini. Pelatihan ini terdiri dari lima tahapan besar yang meliputi lokakarya luring, pembelajaran mandiri, lokakarya daring, dan dua kegiatan microteaching. Hasil analisis kuantitatif menunjukkan peningkatan kemampuan konseptual peserta terkait BK, meskipun masih banyak hal yang perlu dibenahi dari sisi kemampuan teknis dalam pengerjaan soal-soal BK

A Backtracking Approach for Solving Path Puzzles

We study algorithmic aspects of the Path Puzzles---a logic puzzle created in 2013 and confirmed NP-complete in 2020. This paper proposes a polynomial time algorithm for verifying an arbitrary path puzzle solution and a backtracking-based method for finding a solution to an arbitrary path puzzle instance. We prove that the asymptotic running time of our proposed method in solving an arbitrary Path puzzle instance of size $m \times n$ is $O(3^{mn}$. Despite this exponential upper bound, experimental results imply that a C++ implementation of our algorithm can quickly solve $6 \times 6$ Path puzzle instances in less than $30$ milliseconds with an average of $3.02$ milliseconds for $26$ test cases