Meet "spinodoid" structures. You basically splash lots of waves in all sorts of random directions with random phases, and then you threshold the resulting mess.
These structures stem from the idea of a "spinodal decomposition" and the waves form a "Gaussian random field". The latter has been linked to/used for animal patterns (stripes etc), phase separation in chemistry/metallurgy, quantum mechanical random fields, up to cosmological structures...
But here I just use it to create stochastic lattice structures. Because my waves here have different orientations but the same frequency, they show up in a Fourier transform as a circle or sphere, which I think is just neat :)

Spinodoids are coming to Comodo very soon.

More on Spinodoids:
https://doi.org/10.1038/s41524-020-0341-6

Spinodal decomposition:
https://en.wikipedia.org/wiki/Spinodal_decomposition

Gaussian random fields:
https://en.wikipedia.org/wiki/Gaussian_random_field

#opensource #Julialang #GeometryProcessing #Lattices

Representing Type Lattices Compactly

https://bernsteinbear.com/blog/lattice-bitset/

#HackerNews #Representing #Type #Lattices #Compactly #TypeLattices #CompactData #Structures #HackerNews #TechBlog #LatticeBitset

More “L”s is better? Adding Lagrange's algorithm to the LLL lattice reduction produces vectors that are shorter without affecting much of the runtime.

Lenstra–Lenstra–Lovász-Lagrange is a mouthful, so thankfully the authors introduce this algorithm with the L4 name.

#Lattices #PQC #SVP
https://eprint.iacr.org/2024/1681

@philosophy
#infinite #math

nice take in 2 1/2 open acccess pages,

wrt #philosophers were well advised to not limiting the scope of their attention to #cardinal #numbers when referring to the #math #infinite. equally important [besides #ordering #structures and especially #ordinal #numbers] are e.g. #measures on #infinite #Booelan #lattices [#probability only a special case of these]

https://link.springer.com/article/10.1007/s10670-022-00643-6

Great highlight [1] by @QuantaMagazine on the work done [2] by Keegan Ryan and Nadia Heninger on improving the efficiency of the LLL algorithm using multiple techniques such as recursive structure and precision of numbers involved.
Featuring @[email protected]

[1]: https://www.quantamagazine.org/celebrated-cryptography-algorithm-gets-an-upgrade-20231214/
[2]: https://www.iacr.org/cryptodb/data/paper.php?pubkey=33301
#Lattices #cryptography #postquantum

Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems

https://openreview.net/forum?id=GaQBRQ4Prt

#lattice #lattices #convolutions

A. Berzati et al., "A Practical Template Attack on CRYSTALS-Dilithium"¹

This paper presents a new profiling side-channel attack on the signature scheme CRYSTALS-Dilithium, which has been selected by the NIST as the new primary standard for quantum-safe digital signatures. This algorithm has a constant-time implementation with consideration for side-channel resilience. However, it does not protect against attacks that exploit intermediate data leakage. We exploit such a leakage on a vector generated during the signing process and whose costly protection by masking is a matter of debate. We design a template attack that enables us to efficiently predict whether a given coefficient in one coordinate of this vector is zero or not. Once this value has been completely reconstructed, one can recover, using linear algebra methods, part of the secret key that is sufficient to produce universal forgeries. While our paper deeply discusses the theoretical attack path, it also demonstrates the validity of the assumption regarding the required leakage model, from practical experiments with the reference implementation on an ARM Cortex-M4.

#IACR #ResearchPapers #Dilithium #Lattices #PQCryptography #SideChannelAttacks #TemplateAttacks
__
¹ https://eprint.iacr.org/2023/050

J. Surin and S. Cohney, "A Gentle Tutorial for Lattice-Based Cryptanalysis"¹

The applicability of lattice reduction to a wide variety of cryptographic situations makes it an important part of the cryptanalyst's toolbox. Despite this, the construction of lattices and use of lattice reduction algorithms for cryptanalysis continue to be somewhat difficult to understand for beginners. This tutorial aims to be a gentle but detailed introduction to lattice-based cryptanalysis targeted towards the novice cryptanalyst with little to no background in lattices. We explain some popular attacks through a conceptual model that simplifies the various components of a lattice attack.

#IACR #ResearchPapers #Lattices #Tutorials
__
¹ https://eprint.iacr.org/2023/032