Catalogued Assumptions
The Lattice Assumption Zoo currently catalogues 71 assumptions; couting… counting non-trivial variants.
Tags Explained
standard tags mark assumptions that can be reduced to long-standing, open problems and have undergone significant cryptanalytic effort.
implied tags mark assumptions with a reduction from a standard assumption that does not impose unusually strict conditions on parameter choices.
broken tags mark assumptions that have been compromised by known attacks.
List of Catalogued Assumptions
LWE-Based Assumptions ↗
- {0,1}-CRT-LWE implied
- Adaptive LWE
- Asymmetric LWE implied
- Circular LWE
- Equivocal LWE
- Evasive LWE
- Learning with Two Errors (LW2E) implied
- Learning with Alternating Moduli (LWAM) implied
- Learning with Errors (LWE) standard
- Learning with Rounding (LWR) implied
- qLWE implied
-
LWE over Exotic Domains ↗
-
LWE with Distributional Constraints ↗
- Augmented LWE implied
- Binary-Secret LWE implied
- Hollow LWE implied
- Learning with Errors with Output Dependencies (LWE-OD)
- Learning with Short and Sparse Errors (LWSSE)
- Non-Uniform LWE implied
- Sparse Matrix LWE implied
- Truncated LWE implied
-
LWE with External Information ↗
-
LWE with Leakage ↗
- Algebraic One-More-MLWE (AOM-MLWE) implied
- LWE with Error-Leakage implied
- Extended LWE implied
- First-Are-Errorless LWE (FAE-LWE) implied
- Fixed-Matrix Shifted LWE implied
- Hint-LWE implied
- $$k$$-LWE implied
- Known-Norm LWE implied
- Leaky LWE implied
- Learning with Physical Rounding (LWPR)
- Oracle MLWE
- Reused-A LWE implied
- Threshold LWE implied
- Yet-Another LWE implied
SIS-Based Assumptions ↗
- Approximate SIS implied
- Asymmetric SIS implied
- Evasive SIS
- Inhomogeneous Short and Sparse Integer Solution (ISSIS)
- SelfTargetMSIS implied
- Short Integer Solution (SIS) standard
- Split SIS implied
- $$t$$-M-ISIS implied
- Vanishing SIS
-
Structured SIS ↗
-
SIS with External Information ↗