Challenge archive: SekaiCTF 2022 - FaILProof

Challenge: FaILProof
Event: SekaiCTF - 2022
Year: 2022
Category: Cryptography
Authors: deuterium
Mode: offline
Article: https://deut-erium.github.io/challenges/sekaictf-2022/failproof/
Text: https://deut-erium.github.io/challenges/sekaictf-2022/failproof/challenge.txt
JSON: https://deut-erium.github.io/challenges/sekaictf-2022/failproof/challenge.json

Original description:
I have designed a failproof encryption system with possibly arbitrarily small public keys. I will be as famous as Et Al one day, but only if I can somehow figure out a decryption mechanism...

Notes:
- The flag module is needed only to generate a new instance. Solve from the source and the two lines in output.txt; no server is needed.
- This fixed output was generated for the post with the unchanged original program and event flag. It is not a recording from the competition.
- This is a static archive. No live challenge service or runtime simulation is provided here.

Challenge files (primary):
- source.py (archived server source) (source.py; server-source)
  URL: https://deut-erium.github.io/assets/challenges/sekaictf-2022-failproof/source.py
  Bytes: 1151
  SHA-256: 998ba4502c33464f614ed76316aa20b1e118dbf637561225a4199f3b9252cc8c
  Upstream provenance: https://raw.githubusercontent.com/project-sekai-ctf/sekaictf-2022/383b16da68c438c5d516e6f00b2716210141f7a4/crypto/failproof/challenge/app/source.py
- Fixed instance (output.txt) (output.txt; fixed-instance)
  URL: https://deut-erium.github.io/assets/challenges/sekaictf-2022-failproof/output.txt
  Bytes: 1576
  SHA-256: 15632ae2a4ba1f1cc14a5c508c32617f07c4d6d16949ec30593840203fbb671c

Licenses (local copies):
- AGPL-3.0: https://deut-erium.github.io/assets/challenges/licenses/AGPL-3.0.txt
  Bytes: 34523
  SHA-256: 8486a10c4393cee1c25392769ddd3b2d6c242d6ec7928e1414efff7dfb2f07ef
  Upstream provenance: https://raw.githubusercontent.com/project-sekai-ctf/sekaictf-2022/383b16da68c438c5d516e6f00b2716210141f7a4/LICENSE
- CC BY-NC-SA 4.0: https://deut-erium.github.io/assets/challenges/licenses/CC-BY-NC-SA-4.0.txt
  Bytes: 19119
  SHA-256: 14d2138e3a8bd9448254f171b8e17130bf7104d2fd843ab0b924bd105fd00d5a
  Upstream provenance: https://raw.githubusercontent.com/project-sekai-ctf/sekaictf-2022/383b16da68c438c5d516e6f00b2716210141f7a4/LICENSE.content.md

SPOILERS - organizer files and solutions
Spoilers: organizer files and upstream source, archive, or solution links may reveal answers. Modified downloads are identified below.
Source: https://github.com/project-sekai-ctf/sekaictf-2022/blob/383b16da68c438c5d516e6f00b2716210141f7a4/crypto/failproof/README.md
Archive: https://github.com/project-sekai-ctf/sekaictf-2022/tree/383b16da68c438c5d516e6f00b2716210141f7a4/crypto/failproof
Solution: https://github.com/project-sekai-ctf/sekaictf-2022/tree/383b16da68c438c5d516e6f00b2716210141f7a4/crypto/failproof/solution