Catalogued Assumptions

The Lattice Assumption Zoo currently catalogues 25 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

• LIP-based Assumptions
• Lattice Isomorphism Problem (LIP)
• LPN-based Assumptions
• Learning Parity with Noise (LPN) standard
• LWE-based Assumptions
• Learning with Errors (LWE) standard
• Learning with Rounding (LWR) implied
• LWE with Distributional Constraints
• Hollow LWE implied
• Sparse Matrix LWE implied
• LWE with External Information
• $$\ell$$-succinct LWE
• LWE with Hints
• Hint-LWE implied
• $$k$$-LWE implied
• Leaky LWE implied
• NTRU-based Assumptions
• NTRU
• SIS-based Assumptions
• Approximate SIS implied
• Short Integer Solution (SIS) standard
• SIS with External Information
• Basis-Augmented SIS (BASIS)
• $$h$$-BASIS
• $$\ell$$-succinct SIS
• SIS with Hints
• Generalised ISIS$$_f$$ (GenISIS$$_f$$)
• H-ISIS
• ISIS$$_f$$
• k-M-ISIS
• Knowledge k-M-ISIS broken
• $$k$$-SIS implied
• One-More-ISIS (OM-ISIS)
• Randomised One-More-ISIS (rOM-ISIS)
• Twin k-M-ISIS