Lattice Assumption Zoo
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 facilitates keeping track of novel assumptions (e.g., by following our RSS-Feed) to encourage reusing established assumptions rather than introducing new, ad-hoc ones.
- 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.
📣 Latest News
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🚧 Under Construction
Please note that this wiki does not cover all lattice-based assumptions yet. A list of assumptions that we are aware of and plan to add to the zoo, can be found here. 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Spotted a missing link or an outdated result?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.