The Number Theoretic Transform (NTT) is a powerful mathematical tool that has become increasingly important in developing Post Quantum Cryptography (PQC) and Homomorphic Encryption (HE). Its ability to efficiently calculate polynomial multiplication using the convolution theorem with a quasi-linear complexity O ( n log n ) has made it a key component in modern cryptography. NTT is particularly useful in lattice-based cryptography, which relies on the hardness of certain mathematical problems to ensure security. Its importance in these fields continues to grow as quantum computing technology advances and traditional encryption methods become vulnerable. In this report, we discuss the mathematical concepts of polynomial multiplications using NTT and provide a comprehensive review of the latest implementation and state-of-the-art of NTT in both PQC and HE schemes.

Dopamine (DA) is an important neurotransmitter in the kidney, cardiovascular system, and central nervous system, which abnormality is associated with many diseases. In this work, we synthesized a functionalized multi-walled carbon nanotube/silver nanoparticle (f-MWCNT/AgNP) nanocomposites as the biosensing material to detect DA. The SEM, EDS, and TEM characterizations indicated the success of the functionalization process with MWCNT as the base material. The values of the linear range, the limit of detection (LOD), and the selectivity of the nanocomposite were all obtained from the Differential Pulse Voltammetry (DPV) measurements. The obtained LOD value was 0.2778 µM in the linear range of 0–8 µM, which is lower than the required concentration value for detecting DA in human urine (0.3–3 µM). The biosensor’s high selectivity on DA with the presence of other human-related biofluids was also reported. These results show that f-MWCNT/AgNP nanocomposites are a promising biosensor material for the detection of DA. Graphical abstract

Dopamine concentration abnormalities in the body can cause various disorders and diseases such as Parkinson's, Tourette's syndrome, and depression. In this study, graphene oxide (GO) was combined with Fe₃O₄ to sensitively and selectively detect dopamine. The performance was evaluated by cyclic voltammetry (CV) and differential pulse voltammetry (DPV) methods. The results of testing with CV on the solution [Fe(CN)₆] showed that a modification with GO gave a maximum effective surface area value of 0.0127 cm², proving that GO can increase the effective area and conductivity of the sensor. DPV testing shows that dopamine detection using GO/Fe₃O₄ has a linear range at a concentration of 1–10 μM with a detection limit of 0.48 μM and a quantification limit of 1.6 μM. GO/Fe₃O₄ also shows good selectivity where the peak current is separated by 0.245 V with ascorbic acid, which is the closest interference compound. Graphical Abstract

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the virus identified as the cause of the Coronavirus Disease 2019 (COVID-19) outbreak. The gold standard for detecting this virus is polymerase chain reaction (PCR). The electrochemical biosensor method can be an alternative method for detecting several biomolecules, such as viruses, because it is proven to have several advantages, including portability, good sensitivity, high specificity, fast response, and ease of use. This study aims to optimize an electro­chemical aptasensor using an AuNP-modified screen-printed carbon electrode (SPCE) with an aptamer to detect RBD protein S SARS-CoV-2. Aptasensors with the streptavidin-biotin system were immobilized on the SPCE/AuNP surface via covalent bonding with linkers to 3-mercaptopropionic acid (MPA) and electrochemically characterized by the [Fe(CN)6]3-/4- redox system using differential pulse voltammetry. The results showed that the immobi­lized aptamer on the SPCE/AuNP electrode surface experienced a decrease in current from 11.388 to 4.623 µA. The experimental conditions were optimized using the Box-Behnken experimental design for the three factors that affect the current response. The results of the optimization of the three parameters are the concentration of aptamer, incubation time of aptamer, and incubation time of RBD protein S SARS-CoV-2, each of which is 0.5 µg/mL, 40 minutes, and 60 minutes, respectively. The RBD protein S SARS-CoV-2 with various concentrations was tested on an electrochemical aptasensor to determine the de­tection limit and quantification limit, and the respective results were 2.63 and 7.97 ng/mL. The electrochemical aptasensor that has been developed in this study can be applied to detect RBD protein S SARS-CoV-2 as a COVID-19 biomarker in a simple, practical, and sensitive way.

Research on the application of graphene (G) and graphene quantum dots (GQDs) for biomedical engineering has attracted much attention over the last decade. Graphene and its derivatives have shown great biocompatibility, solubility, selectivity, large surface area, high purity, biofunctionalization, high drug loading capacity, and cell membrane penetration capability potential to be applied in biomedical engineering areas. The unique physical and chemical properties of GQDs, including small size, chemical inertness, high photoluminescence stability, low cytotoxicity, and good biocompatibility, made them a promising candidate for biomedical engineering applications. The recent progress related to the development of G and GQDs toward biomedical engineering applications is presented in this work. This study reviews and discusses the development of G and GQDs, both top-down and bottom-up synthesis methods, for biomedical engineering applications, such as biosensing, tissue engineering, drug delivery, bioimaging, antibacterial, and antiviral.

Electrochemical method is often chosen to analyze various bio-chemical reactions due to its operation simplicity with versatile applications. Thus, for this purpose, the procurement of potentiostat, an electrochemical-based analysis instrument, also needs to focus on the low price, but maintaining its rich analysis features. In this paper, we designed a low-cost and portable potentiostat system based on the ESP32 microcontroller. Even with the low-cost system design, it supports various electrochemical measurement methods, i.e. cyclic voltammetry (CV), linear sweep voltammetry (LSV), square wave voltammetry (SWV), differential pulse voltammetry (DPV), normal pulse voltammetry (NPV), and the observation of electrochemical current against time based on chronoamperometry measurement method. The potentiostat performance was assessed by the electrochemical signal accuracy and errors. Furthermore, the measurements can also be carried out semi-parallelly within three measurement channels simultaneously. The results showed that it could produce voltammograms with an average accuracy of more than 90%, compared to the commercial Emstat Pico. Even though having this comprehensive and extensive electrochemical analysis, the cost of the total system realization could be downsized to only USD 21.4.