This comprehensive wiki catalogues average-case lattice assumptions so that cryptography-affine readers can quickly build an intuition for each assumption, understand the rationale behind its hardness, and explore its applications. Additionally, it serves as a centralised repository for essential literature related to novel assumptions, and provides a platform for publishing relevant cryptanalysis.

Furthermore, this resource is built with two additional goals in mind:

  • For designers: This website encourages reusing existing assumptions rather than introducing new, ad-hoc ones by simplifying the process of finding and understanding existing assumptions. It also makes tracking novel assumptions effortless via our RSS feed.
  • For cryptanalysts: This repository serves as an organised index of targets, simplifying the identification of compelling assumptions to analyse.

🧭 Explore the Lattice Assumption Graph

This interactive graph visualises the landscape of lattice-based assumptions, illustrating relationships such as reductions and generalizations. You can tailor the view to your needs – filtering by cryptographic primitive, historical timeline, or specific assumption variants.

📋 List of Catalogued Assumptions

If you prefer a list as a structured format, you can find a searchable index of all catalogued assumptions on the following page, or let chance decide where you start.

Catalogued Assumptions or discover a Random Assumption

📣 Latest News

Lattice Assumption Zoo Goes Live!

April 03, 2026

The gates are open: The Lattice Assumption Zoo (LAZ) is officially live and ready for visitors! Here’s a quick look...

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🚧 Under Construction

Please note that this wiki does not cover all lattice-based assumptions yet. We maintain a list of assumptions that will be added to the zoo. Of course, contributions of any kind are welcome!

✏️ Contribute

This wiki relies on the expertise of the cryptographic community. Anyone can contribute – whether it is adding a novel assumption, updating hardness estimates, providing further details, or linking a new construction.

Spotted a missing link or an outdated result? Propose a change on GitHub.