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Crown Ethers02:36

Crown Ethers

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Crown ethers are cyclic polyethers that contain multiple oxygen atoms, usually arranged in a regular pattern. The first crown ether was synthesized by Charles Pederson while working at DuPont in 1967. For this work, Pedersen was co-awarded the 1987 Nobel Prize in Chemistry. Crown ethers are named using the formula x-crown-y, where x is the total number of atoms in the ring and y is the number of ether oxygen atoms. The term 'crown' refers to the crown-like shape that these ether...
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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Ampere-Maxwell's Law: Problem-Solving01:17

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A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...
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Hybridization of Atomic Orbitals II03:35

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sp3d and sp3d 2 Hybridization
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Hybridization of Atomic Orbitals I03:24

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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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Related Experiment Video

Updated: Sep 18, 2025

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Efficient unified architecture for post-quantum cryptography: combining Dilithium and Kyber.

Patrik Dobias1, Lukas Malina1, Jan Hajny1

  • 1Department of Telecommunications, Brno University of Technology, Brno, Czech Republic.

Peerj. Computer Science
|June 26, 2025
PubMed
Summary

This study combines Dilithium and Kyber post-quantum cryptography schemes for efficient hardware implementation. The unified design offers superior performance and resource efficiency for secure communication in embedded systems and IoT devices.

Keywords:
DilithiumFPGAKyberPost-quantum cryptographyUnified architecture

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Area of Science:

  • Cryptography and Network Security
  • Post-Quantum Cryptography
  • Hardware Implementation

Background:

  • The ongoing standardization of post-quantum cryptography necessitates optimized implementations.
  • Combining multiple cryptographic schemes into unified architectures is crucial for efficiency.
  • NIST-selected schemes like Dilithium and Kyber are leading candidates for quantum-resistant security.

Purpose of the Study:

  • To investigate the combination of Dilithium and Kyber post-quantum schemes.
  • To propose novel optimization techniques for a unified hardware implementation.
  • To achieve a balanced approach between area efficiency and high performance in combined implementations.

Main Methods:

  • Developing novel optimization techniques for unified hardware architecture.
  • Implementing a combined hardware design for Dilithium and Kyber schemes.
  • Evaluating resource efficiency and performance against existing solutions.

Main Results:

  • The proposed unified architecture demonstrates superior resource efficiency and performance.
  • Achieved results are comparable or better than standalone implementations.
  • The design is more resource-efficient than previously reported unified architectures.

Conclusions:

  • Efficient and combined implementation of lattice-based digital signatures and key establishment is feasible.
  • The compact design is suitable for high-speed communication networks, servers, and gateways.
  • The design can be deployed on cost-effective FPGAs for embedded devices and IoT security co-processors.