Add music

content/about/setup.md

@@ -1,42 +1,48 @@
 +++
-title = "setup"
+title = "Setup"
 +++
 
-# setup
+# Setup
 
 List of software and services I use and endorse, mostly FOSS.
 
-## desktop
+## Desktop
 
 - [**Arch Linux**](https://archlinux.org/) OS with rolling releases.
-- [**Home manager**](https://github.com/nix-community/home-manager) Dotfile manager.
-- [**Firefox**](https://www.mozilla.org/firefox) Browser.
-- [**Evolution**](https://wiki.gnome.org/Apps/Evolution) Email + calendar client.
+- [**Home manager** (MIT)](https://github.com/nix-community/home-manager) Dotfile manager.
+- [**Firefox** (MPL-2.0)](https://www.mozilla.org/firefox) Browser.
+- [**Thunderbird** (MPL-2.0)](https://www.thunderbird.net) Email + calendar client.
 
-## development
+## Development
 
-- [**Neovim**](https://neovim.io/) Text editor.
+- [**Neovim** (Apache-2.0/Vim)](https://neovim.io/) Text editor.
 
-## server
+## Server
 
-- [**NixOS**](https://nixos.org/) Declarative and reproducible operating system.
-- [**Hugo**](https://gohugo.io/) Static site generator that powers this site.
-- [**Gitea**](https://gitea.io) Self-hosted git.
+- [**NixOS** (MIT)](https://nixos.org/) Declarative and reproducible operating system.
+- [**Hugo** (Apache-2.0)](https://gohugo.io/) Static site generator that powers this site.
+- [**Gitea** (MIT)](https://gitea.io/) Self-hosted git.
 
-## mobile
+## Mobile
 
-- [**DAVx5**](https://www.davx5.com/) CalDAV and CardDAV sync for Android.
-- [**Shuttle**](https://www.shuttlemusicplayer.com/) Music player.
-- [**Gadgetbridge**](https://gadgetbridge.org/) Smartwatch client.
-- [**K-9 Mail**](https://k9mail.app/) Mail client.
-- [**Feeder**](https://f-droid.org/packages/com.nononsenseapps.feeder/) RSS aggregator.
+- [**DAVx5** (GPL-3.0)](https://www.davx5.com/) CalDAV and CardDAV sync for Android.
+- [**Gadgetbridge** (AGPL-3.0)](https://gadgetbridge.org/) Smartwatch client.
+- [**K-9 Mail** (Apache-2.0)](https://k9mail.app/) Mail client.
+- [**Feeder** (GPL-3.0)](https://f-droid.org/packages/com.nononsenseapps.feeder/) RSS aggregator.
 
-## services
+## Music
 
-- [**ProtonMail**](https://protonmail.com/) Encrypted email.
-- [**Signal**](https://signal.org/) Encrypted chat.
+- [**Navidrome** (GPL-3.0)](https://navidrome.com) Self-hosted Subsonic-compatible streaming server.
+- [**Sublime Music** (GPL-3.0)](https://sublimemusic.app) GTK Subsonic-compatible music client.
+- [**Subtracks** (GPL-3.0)](https://github.com/austinried/subtracks) Android Subsonic-compatible music client.
+
+## Services
+
+- [**SourceHut** (AGPL-3.0)](https://sourcehut.org) Git, mailing list, IRC bouncer, etc. hosting.
 - [**Element**](https://element.io/) Federated chat provider.
+- [**ProtonMail** (Proprietary)](https://protonmail.com/) Encrypted email.
+- [**Signal** (GPL-3.0/AGPL-3.0)](https://signal.org/) Encrypted chat.
 
-## games
+## Games
 
 Mostly from Steam.

content/posts/2022-02-07-cybergrabs-ctf-unbreakable/index.md

@@ -32,22 +32,30 @@ first, but there are some important differences to note:
 - We're not given the public keys $e_1$ and $e_2$, but they are related through
     $x$.
 
-[Rabin]: https://en.wikipedia.org/wiki/Rabin_cryptosystem
-
 ## Finding $e_1$ and $e_2$
 
 We know that $e_1$ and $e_2$ are related through $x$, which is some even number
 greater than 2, but we're not given any of their real values. We're also given
 through an oddly-named `functor` function that:
 
-$$
-\begin{aligned}
-  1 + e_1 + e_1^2 + \cdots + e_1^x &= 1 + e_2 + e_2^2 \\\
-  \frac{1 - e_1^x}{1 - e_1} &= 1 + e_2 + e_2^2
-\end{aligned}
-$$
+$$ 1 + e_1 + e_1^2 + \cdots + e_1^x = 1 + e_2 + e_2^2 $$
 
-Interestingly enough, since $e_1$ and $e_2$ are primes, that means
+Taking the entire equation $\mod e_1$ gives us:
+
+$$\begin{aligned}
+1 &\equiv 1 + e_2 + e_2^2 \mod e_1 \\\
+0 &\equiv e_2 + e_2^2 \\\
+0 &\equiv e_2(1 + e_2)
+\end{aligned}$$
+
+This means there are two possibilities: either $e_1 = e_2$ or $e_1$ is even
+(since we know $e_2$ is a prime). The first case isn't possible, because with $x
+\> 2$, the geometric series equation would not be satisfied. So it must be true
+that $\boxed{e_1 = 2}$, the only even prime.
+
+Applying geometric series expansion, $1 + e_2 + e_2^2 = 2^x - 1$.
 
 I'd like to thank @10, @sahuang, and @thebishop in the Project Sekai discord for
-their help throughout this challenge.
+doing a lot of the heavy-lifting to solve this challenge.
+
+[Rabin]: https://en.wikipedia.org/wiki/Rabin_cryptosystem