I spent a lot of time doodling in middle school in lieu of whatever it is middle schoolers are supposed to be doing. Somewhere between the Cool S’s and Penrose triangles I stumbled upon a neat way to fill up graph paper by repeatedly combining and copying squares. I suspected there was more to the doodle but wasn’t quite sure how to analyze it. Deciding to delegate to a future version of me that knows more math, I put it up on the wall behind my desk where it has followed me from high school to college to the present day.

Anyway, after a series of accidents I am now the prophesized future version of me that knows a bit more math. Due to its petal-like blooming structure and timeless presence scotch taped to my wall I’ll be referring to the fractal affectionately as “the wallflower,” although further down we’ll see it’s closely related to some well-known fractals.

source: HN

The idea is simple: apart from regular numbers (like 4, 3.14 or 43942), you can also input ranges (like 4~6, 3.1~3.2 or 40000~45000). The character between the two extremes of the range is a tilde (~), a little wave symbol. You can find it on most keyboards, but for convenience, I also included it in the keypad above. The range notation says the following to the calculator: I am not sure about the exact number here, but I am 95% sure it’s somewhere in this range.

source: L

Two colliding blocks compute pi, here we dig into the physics to explain why.

The original paper by Gregory Galperin: https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf

Adam Brown’s paper on the analogy with Grover’s Algorithm: https://arxiv.org/pdf/1912.02207

In 1993, Intel released the high-performance Pentium processor, the start of the long-running Pentium line. I’ve been examining the Pentium’s circuitry in detail and I came across a circuit to multiply by three, a complex circuit with thousands of transistors. Why does the Pentium have a circuit to multiply specifically by three? Why is it so complicated? In this article, I examine this multiplier—which I’ll call the ×3 circuit—and explain its purpose and how it is implemented.

A calculator should show you the result of the mathematical expression you entered. That’s much, much harder than it sounds.

source: HN

Oftentimes in your “intro to proofs” class or your first “discrete math” class or something similar, you’ll be shown problems of the form “prove that for is a multiple of for every ”… But where do these problems come from? And have you ever stopped to think how magical this is? If I gave you some random polynomial in and asked you if it always output multiples of , the answer would almost always be “no”! So if you really needed to come up with an example of this phenomenon, how would you do it? In this blog post, we give one approach!

source: HN

We resolve the moving sofa problem by showing that Gerver’s construction with 18 curve sections attains the maximum area.

source: trivium

In this post, we will look at how the security of the AES-GCM mode of operation can be completely compromised when a nonce is reused.

Today, the team declared victory. They’ve finally verified the true value of a number called BB(5), which quantifies just how busy that fifth beaver is. They obtained the result — 47,176,870 — using a piece of software called the Coq proof assistant, which certifies that mathematical proofs are free of errors.

source: HN

Every time a block is broken in Minecraft versions Beta 1.8 through 1.12.2, the precise coordinates of the dropped item can reveal another player’s location. “Randar” is an exploit for Minecraft which uses LLL lattice reduction to crack the internal state of an incorrectly reused java.util.Random in the Minecraft server, then works backwards from that to locate other players currently loaded into the world.

source: HN

Now, by trade I’m a software engineer and a trainee scientist - I’ve never designed a book before. However, I’m no stranger to graphic design, having done a variety of things before now. But a book is a new proposition with different challenges. There was a lot of work ahead. But where to begin?

source: Dfly

Here, we’re looking at two main things: the calibration of a forecast — that is, whether events that we said would happen 30 percent of the time actually happened about 30 percent of the time — and how our forecast compared with an unskilled estimate that relies solely on historical averages. We can answer those questions using calibration plots and skill scores, respectively.

Go 1.20.2 fixed a small vulnerability in the crypto/elliptic package. The impact was minor, to the point that I don’t think any application was impacted, but the issue was interesting to look at as a near-miss, and to learn from.

source: L

The p-adic numbers are bizarre alternative number systems that are extremely useful in number theory. They arise by changing our notion of what it means for a number to be large. As a real number, 1 billion is huge. But as a 10-adic number, it is tiny!

https://en.wikipedia.org/wiki/P-adic_number

Veritasium: https://www.youtube.com/watch?v=tRaq4aYPzCc

The JPEG algorithm is rather complex and in this video, we break down the core parts of the algorithm, specifically color spaces, YCbCr, chroma subsampling, the discrete cosine transform, quantization, and lossless encoding. The majority of the focus is on the mathematical and signal processing insights that lead to advancements in image compression and the big themes in compression as a whole that we can take away from it.

A new kind of computer architecture that’s more elegant than 1s and 0s, being based directly on Mathematics.

If you’ve done any 3D programming, you’ve likely encountered the zoo of techniques and representations used when working with 3D rotations. Some of them are better than others, depending on the situation.

source: HN

Pernosco accepts uploaded rr recordings from customers and replays them with binary instrumentation to build a database of all program execution, to power an amazing debugging experience. Our infrastructure is Intel-based AWS instances. Some customers upload recordings made on AMD (Zen) machines; for these recordings to replay correctly on Intel machines, instruction execution needs to produce bit-identical results. This is almost always true, but I recently discovered that the approximate arithmetic instructions RSQRTSS, RCPSS and friends do not produce identical results on Zen vs Intel. Fortunately, since Pernosco replays with binary instrumentation, we can insert code to emulate the AMD behavior of these instructions. I just needed to figure out a good way to implement that emulation.

source: HN

Bit strings, error correcting, and coloring the corners of higher dimensional cubes.

The @CryptoHack__ account was pinged today by ENOENT, with a CTF-like challenge found in the wild: Source tweet. Here’s a write-up covering how given a partially redacted PEM, the whole private key can be recovered. The Twitter user, SAXX, shared a partially redacted private RSA key in a tweet about a penetration test where they had recovered a private key. Precisely, a screenshot of a PEM was shared online with 31 of 51 total lines of the file redacted. As ENOENT correctly identified, the redaction they had offered wasn’t sufficient, and from the shared screenshot, it was possible to totally recover the private key.

source: L