MOSS Season 2 continues next week.

🎙️ Benjamin Wesolowski (CNRS & ENS Lyon, France)

Talk title: Random walks in number-theoretic cryptology

🗓️ Thursday, 7 May 2026 • 🕓 4:00 PM CEST • Online

Abstract: Cryptography met number theory in 1976, when Diffie and Hellman achieved what had long been considered impossible: a protocol for two people to exchange secret information on a public channel, even if they had never met before to establish some kind of password, a pre-shared key. Diffie and Hellman designed the protocol such that a spy attempting to find the secret would need to solve a presumably hard computational problem: the discrete logarithm problem in the multiplicative group of a finite field.

Since then, number theory has consistently met the challenges of cryptography, offering a variety of difficult algorithmic problems and powerful tools for their analysis. In this talk, we will explore this “mathematical cryptology”, with a focus on euclidean lattices (designed to resist against quantum computers), the use of random walks, and how spectral methods in number theory apply to cryptology.

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#Mathematics #NumberTheory #Cryptography #Lattices #PostQuantum #MOSS #EMS

📌 April-26:

The official bets are in: #Lattices vs #X25519 the #cryptographers 📈 #polymarket is open.

👉 My money would be on team @djb and @matthew_d_green

Any new #postquantum hard assumption will fail before #quantumcomputers deliver.

If @filippo pq apocalyptic timeframe is correct, only expensive, well understood, hash tree based signatures like #SPHINCS will save our ass (again).

https://github.com/FiloSottile/ecc-vs-lattices-long-bet

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