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How to defeat Ed25519 and EdDSA using faults
The Latest News from Research at Kudelski Security
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Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,851 posts.
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Double encryption: Analyzing the NSA/GCHQ arguments against hybrids
In 2019, Google and Cloudflare ran an experiment where they upgraded HTTPS for many "real users’ connections" to use post-quantum encryption. They then reported statistics on how affordable this was. Google had also run a similar experiment in 2016: "While it's still very early days for quantum computers, we're…
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Hamilton-Jacobi-Bellman Equation: Reinforcement Learning and Diffusion Models
Why the HJB is Bellman's equation in continuous time, why continuous time matters, and how to solve the resulting control problem with neural policy iteration.
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To approximate 52! by hand, compute 54! and divide by 3000
Some time ago I gave a talk in which I showed that something unexpected happened with a deck of playing cards. I had some volunteers try it, and while they did so I talked about just how many orderings there are for 52 cards. I computed (an approximation to) $52!$ (52 factorial) by hand. It's not so hard - you just…
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MIT mathematicians solve age-old spaghetti mystery
Researchers have long have puzzled over why it’s so hard to break a piece of dry spaghetti into only two pieces. A new MIT study follows up on the musings of physicist Richard Feynman, showing how and why it can be done.
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Path Tracing 3D Fractals
In some ways path tracing is one of the simplest and most intuitive ways to do ray tracing.
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Gaussian Processes from Scratch (2019)
This post explores some concepts behind Gaussian processes, such as stochastic processes and the kernel function. We will build up deeper understanding of Gaussian process regression by implementing them from scratch using Python and NumPy.
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A brief introduction to the beauty of Information Theory
Lambdaclass's blog about distributed systems, machine learning, compilers, operating systems, security and cryptography.
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The algebra and calculus of algebraic data types
Just as algebra is fundamental to the whole of mathematics, algebraic data types (ADTs) are fundamental to many common functional programming languages. They’re the primitives upon which all of our richer data structures are built, including everything from sets, maps, and queues, to bloom filters and neural networks .
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A mathematical formalization of dimensional analysis (2012)
Mathematicians study a variety of different mathematical structures, but perhaps the structures that are most commonly associated with mathematics are the number systems, such as the integers $late…
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An unwinnable seed of Slay the Spire
Overview In this post, I will describe a collaborative effort that proved that unwinnable Slay the Spire seeds exist. This project is joint work with gamerpuppy and ForgottenArbiter and is based on the several attempts that have been made to prove unwinnability for seeds in Slay the Spire.
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Signals, the push-pull based algorithm
We have been using Signals in production for years via several modern front-end frameworks like Solid, Vue, and others, but few of us are able to explain how they work internally. I wanted to dig into it, especially diving deep into the push-pull based algorithm, the core mechanism behind their reactivity.
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Basic skeletal animation with geometric algebra
Klein - Realtime Projective Geometric Algebra
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A ternary plot of citrus geneology
Interactive ternary chart of citrus ancestry
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Calculus on Computational Graphs: Backpropagation (2015)
Backpropagation is the key algorithm that makes training deep models computationally tractable. For modern neural networks, it can make training with gradient descent as much as ten million times faster, relative to a naive implementation. That’s the difference between a model taking a week to train and taking 200,000…
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A Pretty Good Mathematical Model of Perfectionism
I struggle with perfectionism. Well, not so much “struggle with” — I’m f*cking great at it. It comes naturally. There are some upsides, but perfectionism is also associated …
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Ten Years of Purely Functional Data Structures (2008)
In 1998, I published a book called Purely Functional Data Structures . Ten years later, the book is still selling well. (Every time I get ...
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Neural ODE's: Understanding how they model data
In this blogpost I explore how ODE’s can be used to solve data modelling problems. I take a deep dive into the data modelling problem at hand and present ODE...
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Why numbering should start at zero (1982)
To denote the subsequence of natural numbers 2, 3, ..., 12 without the pernicious three dots, four conventions are open to us
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How to assign partial credit on an exam of true-false questions?
Note: the following is a record of some whimsical mathematical thoughts and computations I had after doing some grading. It is likely that the sort of problems discussed here are in fact well studi…
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A railroad simulation using discrete event simulation
In our previous post, we introduced how to utilize Discrete Event Simulation (DES) in PicoLisp. Now, let's explore another application: a railroad model…
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