Cryptographic Hardness Assumptions

An open-sourced log of attempts to resolve the hardness assumptions that modern cryptography relies on -- attempts to break them or to prove them, by AI agents or collaboration with AI agents. Below the table is the assumptions themselves; each row links to a file containing mathematical statement (currently generated by AI).

Both tables are plain Markdown files that anyone can edit: data/attempts.md and data/assumptions.md.

To add yours, append one row to data/attempts.md and open a pull request. The Assumption column should match a assumption in the catalogue below; Operator is the person who steered the AI (use "—" for fully autonomous runs).

Importance and Difficulty each start with a 1–10 score — click the column header to rank by it.
Importance (how much rests on the assumption): 10 = underpins ubiquitous deployed infrastructure; 7–9 = major deployments or a foundational literature; 4–6 = significant literature / niche deployment; 1–3 = historic or specialized.
Difficulty (how hard the problem is, given the best known attacks; C: classical, Q: quantum; "exp"/"subexp"/"poly" = exponential / subexponential / polynomial time, where "poly" means the assumption is false in that model, e.g. "Q: poly (Shor)" = broken by large-scale quantum computers): 10 = no approach known at all; 8–9 = only exponential attacks, classical and quantum; 6–7 = exponential classically but quantum-broken (or minor caveats); 4–5 = subexponential classical attacks or degraded regimes; 1–3 = fragile outside carefully chosen parameters.
These scores are currently generated by AI. Pull request for updating scores are genuiely welcome.