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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
11.4K
Electronic Structure of Atoms02:28

Electronic Structure of Atoms

28.0K

An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
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Atomic Nuclei: Larmor Precession Frequency01:11

Atomic Nuclei: Larmor Precession Frequency

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The earth's gravitational field produces a 'twisting force' perpendicular to the angular momentum of a spinning mass (such as a spinning top) that causes the mass to 'wobble' around the gravitational field axis in a phenomenon called precession. Similarly, the magnetic moment (μ) of a spinning nucleus precesses due to an external magnetic field directed along the z-axis. The precession of the magnetic moment vector about the magnetic field is called Larmor precession,...
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Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

2.4K
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
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Bewley Lattice Diagram01:12

Bewley Lattice Diagram

1.4K
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
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Related Experiment Video

Updated: Jan 17, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

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NTRU-MCF: A Chaos-Enhanced Multidimensional Lattice Signature Scheme for Post-Quantum Cryptography.

Rong Wang1, Bo Yuan2, Minfu Yuan1,3

  • 1Guangzhou Institute of Software, Guangzhou 510006, China.

Sensors (Basel, Switzerland)
|September 19, 2025
PubMed
Summary

This study presents NTRU-MCF, a quantum-resistant signature scheme using multidimensional lattices and chaotic systems. It offers enhanced security against quantum and physical attacks, suitable for high-security needs.

Keywords:
NTRU-MCFfractional-order chaosmultidimensional latticespost-quantum cryptographyquantum resistancesignature scheme

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Related Experiment Videos

Last Updated: Jan 17, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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Area of Science:

  • Cryptography
  • Applied Mathematics
  • Computer Science

Background:

  • Quantum computing poses a significant threat to current classical cryptographic methods.
  • Existing lattice-based cryptography requires further enhancements for robust security.

Purpose of the Study:

  • Introduce NTRU-MCF, a novel lattice-based signature scheme.
  • Enhance resistance against quantum computing and physical attacks.

Main Methods:

  • Extended NTRU framework to multidimensional polynomial rings.
  • Integrated fractional-order chaotic masks from a hyperchaotic Lü system.
  • Replaced conventional pseudorandom number generators (PRNGs) with chaotic masks.

Main Results:

  • Achieved a private key search space ≥2^256 for dimensions m≥2, rendering brute-force attacks infeasible.
  • Demonstrated robust resistance to physical attacks through nonlinear randomness.
  • Validated chaotic masks using NIST SP 800-22 randomness tests.
  • Security reduces to the Ring Learning with Errors (RLWE) problem, offering superior quantum resistance.

Conclusions:

  • NTRU-MCF provides robust quantum resistance and side-channel defense.
  • The scheme is suitable for high-security applications but less so for resource-constrained devices.
  • Advances post-quantum cryptography (PQC) for classical computing environments.