Function secret sharing (FSS) ⇒ DPF

Function secret sharing (FSS) implies DPF.

Statement

Migrated verbatim from distributed-point-function:

DPFs are a special case of function secret sharing (FSS), introduced by Boyle, Gilboa, and Ishai — BGI15, BGI16. FSS generalizes DPFs to arbitrary function classes $\mathcal{F}$: one generates shares $(k_0,k_1)$ of any $f\in \mathcal{F}$, such that each key evaluates the function’s additive share, and each key hides $f$ individually.

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.

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

• ‘function-secret-sharing’ has no page or slug; FSS is defined only inside this Variations section despite being the more general object.
• Surface phrasing puts DPF first (‘DPFs are a special case of FSS’), so the implication direction is FSS ⇒ DPF — easy to get backwards.