SIS-Based Assumptions

The Lattice Assumption Zoo currently catalogues 24 SIS-based assumptions; 8 of them are standard assumptions or implied by standard assumptions.

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 ↗

  • Decomposed SIS
  • Partial Vandermonde SIS (PV-SIS)
• SIS with External Information ↗

  • Basis-Augmented SIS (BASIS)
  • $$h$$-BASIS
  • $$\ell$$-succinct SIS
• SIS with Hints ↗

  • Algebraic One-More-MISIS (AOM-MISIS) implied
  • 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

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