NTRU ⇒ PKE

NTRU implies PKE.

Statement

Migrated verbatim from ntru § NTRU:

The NTRU assumption is a lattice-based hardness assumption over polynomial rings, introduced alongside the NTRU public-key cryptosystem — HPS98. The public key looks like a ratio $h=g\cdot f^{-1}\mathrm{mod}q$ of two short polynomials, and hardness asserts that recovering $f$ (or $g$) from $h$ alone is computationally infeasible.

Migrated verbatim from ntru § Related results:

• NTRU implies PKE — HPS98

Notes

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

This relation is stated on 2 pages; the statements above are all of them.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• Origin note (“introduced alongside the NTRU public-key cryptosystem”) that doubles as the NTRU ⇒ PKE claim restated at line 51.
• No security notion stated for the resulting PKE (the original NTRU scheme is not IND-CPA secure without padding).