LWE-Based Assumptions

The Lattice Assumption Zoo currently catalogues 43 LWE-based assumptions; 26 of them are standard assumptions or implied by standard 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 ↗

  • Continuous LWE implied
  • Generalised-LWE
  • Integer Polynomial LWE
  • Variety LWE
• Structured LWE ↗

  • Decomposed LWE
  • Power Ring-LWE (P-RLWE)
  • Partial Vandermonde LWE (PV-LWE)
  • Secret-Power Ring-LWE (SP-RLWE)
  • Tensor LWE
• 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 ↗

  • $$\ell$$-succinct LWE
• 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

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