Unlike traditional methods, such as RSA or ECC, that rely on hard problems. Laue's predictions were confirmed when two researchers: Friedrich and Knipping, successfully photographed the diffraction pattern associated with the x-ray radiation of crystalline \(CuSO_4 \cdot 5H_2O\). Lattice-based cryptography is a promising approach to secure data and communications in the era of quantum computing. His postulate was based on the following assumptions: the atomic lattice of a crystal is periodic, x- rays are electromagnetic radiation, and the interatomic distance of a crystal is on the same order of magnitude as x-ray light. Without having any evidence to support his claim on the periodic arrangements of atoms in a lattice, he further postulated that the crystalline structure could be used to diffract x-rays, much like a grating in an infrared spectrometer can diffract infrared light. In 1912, Max von Laue, at the University of Munich in Germany, postulated that atoms in a crystal lattice had a regular, periodic structure with interatomic distances on the order of 1 Å. Diffraction and measurement of such small wavelengths would require a grating with spacing on the same order of magnitude as the light. If the wave idea was correct, researchers knew that the wavelength of this light would need to be on the order of 1 Angstrom (Å) (10 -8 cm). The nature of x- rays, whether they were particles or electromagnetic radiation, was a topic of debate until 1912. In 1895, Wilhelm Rontgen discovered x- rays. This technique takes advantage of the interatomic spacing of most crystalline solids by employing them as a diffraction grating for x-ray light, which has wavelengths on the order of 1 angstrom (10 -8 cm). X-ray crystallography is an instrumental technique used to determine the arrangement of atoms of a crystalline solid in three-dimensional space.
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