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Secure computational geometry (SCG) is an important type of secure multi-party computation (SMC) problem, which studies how to calculate the relationship of several geometric objects securely. Quantum SCG (QSCG) can achieve higher security than classical SCG protocols, but the achievements of QSCG are still limited at present. In this paper, we define a new SCG problem: the secure clockwise sorting (SCS) problem, and propose a quantum protocol to solve it. We first propose a quantum secure clockwise comparison subprotocol, where the cross and scalar products of two vectors are calculated by using a quantum secure two-party scalar product protocol, and then the relative clockwise order of two points is determined. Based on the subprotocol, we then give a quantum SCS protocol to determine the clockwise order of a series of points. Finally, we show the correctness, security, and efficiency of our protocol through detailed performance analysis. [ABSTRACT FROM AUTHOR]

Density functional theory calculation is used to investigate the oxidation of cyclo-olefin (cyclobutene, cyclopentene, cyclohexene, cycloheptene, and cyclo-octene) by the complex [FeIV(O)(TQA)(NCMe)]2+, which has S = 2 ground state, and the effect of electronic factors and steric hindrance on reaction barriers. Our results suggest that the oxo–iron(IV) complex can oxidise C–H and C = C bonds via a single-state mechanism, and two different ways of electron transport exist. The energy barriers initially decrease with increasing substrate size, and the trend then reverses. Comparison of the energy barrier in different systems reveals that except for the reaction between [FeIV(O)(TQA)(NCMe)]2+ and cycloheptene, oxo–iron(IV) complexes prefer epoxidation to hydroxylation. However, the hydroxylated product is more stable than the corresponding epoxidated product. This result indicates that the products of epoxidation tend to decompose first. The energy barrier of hydroxylation and epoxidation originates from the balance of orbital interaction and Pauli repulsion from the equatorial ligand and protons on the approaching substrate. In this regard, we calculate the weak interaction between two fragments (oxo–iron complex and substrates) using the independent gradient model and drawn the corresponding 3D isosurface representations of reactants. [ABSTRACT FROM AUTHOR]

Exploiting quantum mechanisms, quantum attacks have the potential ability to break the cipher structure. Recently, Ito et al. proposed a quantum attack on Feistel-2* structure (Ito et al.'s attack) based on the Q2 model. However, it is not realistic since the quantum oracle needs to be accessed by the adversary, and the data complexity is high. To solve this problem, a quantum all-subkeys-recovery (ASR) attack based on multi-equations quantum claw-finding is proposed, which takes a more realistic model, the Q1 model, as the scenario, and only requires 3 plain-ciphertext pairs to quickly crack the 6-round Feistel-2* structure. First, we proposed a multi-equations quantum claw-finding algorithm to solve the claw problem of finding multiple equations. In addition, Grover's algorithm is used to speedup the rest subkeys recovery. Compared with Ito et al.'s attack, the data complexity of our attack is reduced from O (2 n) to O(1), while the time complexity and memory complexity are also significantly reduced. [ABSTRACT FROM AUTHOR]

Mesoporous SiO 2 of SBA-15 is reported to modify carbon paste electrodes for detecting epinephrine (EP). Carbon paste electrodes modified with synthesized SBA-15 show high sensitivity for voltammetric determination of EP, which is attributed to the strong adsorption ability of SBA-15 to EP and large surface area of the working electrode resulted from SBA-15 modification. The effects of pH value, amount of SBA-15 and scan rate were investigated. Under optimum conditions, the anodic peak current of EP was proportional to its concentration over the range from 1.0 × 10 −6 to 6.0 × 10 −5 mol L −1 and the limit of detection was 6.0 × 10 −7 mol L −1. The results show mesoporous SiO 2-modified carbon paste electrodes, particularly SBA-15-modificd electrodes, create new opportunities for sensitive, simple and suitable method in the electrochemical analysis of EP. [ABSTRACT FROM AUTHOR]