Here's a tool to calculate and visualize the nth roots of unity. I've taken the formula from Judson's Abstract Algebra, page 52 in the chapter on cyclic groups. Judson defines the nth roots of unity as the complex numbers \(z\) that satisfy the equation \(z^n=1\).

Further, Theorem 4.25 shows that for \(z^n=1\), the nth roots of unity are $$z=\operatorname{cis}\left(\frac{2k\pi}{n}\right)$$ for \(k=0,1,\dots,n-1\). That means for \(n\), there are \(n\) roots.

Here are some useful tricks for getting the best out of Echidna.

Echidna is a fuzzing tool for smart contracts written in Solidity. Solidity smart contracts primarily work on the Ethereum blockchain. Some smart contracts are responsible for managing large amounts of cryptocurrency. With Echidna you can evaluate the security of smart contracts.

Compared to code scanners and formal methods, Echidna is good at finding transactions that can trigger unintended behavior in smart contracts. Since Echidna is a coverage-guided fuzzer, it’s also good at finding ways to hit the entire code surface of a smart contract.

Compile static gdbserver for MIPS with Nix

I’ve tested the following instructions using GDB 15.2 and NixOS 24.11.

About gdbserver

When you run GDB to debug a process, two things happen:

1. GDB starts or attaches to a process that you want to debug.
2. GDB provides you a user interface so that you can control and inspect that process.

The GDB user interface itself typically runs on your own machine. You can start or attach to processes even outside of your own machine. GDB provides a program called gdbserver for this task. gdbserver manages process execution without providing a user interface itself. GDB then attaches to gdbserver over the network using a TCP socket.

These are some tricks that help me solve Hack The Box machines.

Here are interesting things I’ve come across when learning more about email topics

This article contains interesting things that I’ve come across while learning more about DNS.

Here are some snippets of code required to configure and run attic on macOS with nix-darwin, and use it as an optional cache.

Here are some keywords I’ve come across when studying computer networking topics.

Here are some keywords I’ve come across when studying information security topics.

Here are my notes on the useful parts of UML. Creating diagrams is an important part of technical documentation.

Here you can find useful Nix code snippets.

Alloy 6 introduces an easier way of expressing temporal logic. With temporal logic you can model possible state transitions and precisely define operations on data structures.

Here are some notes on how to download things from YouTube using yt-dlp (PyPI link).

This article outlines how I configure BorgBackup and borgmatic on my machines.