$d$-th Composite Residuosity ⇒ HE

[[decisional-composite-residuosity#d-th-composite-residuosity|$d$-th Composite Residuosity]] implies HE.

Statement

Migrated verbatim from decisional-composite-residuosity § $d$-th Composite Residuosity:

Generalizes DCR to $d$-th powers modulo $n^{d+1}$. Gives homomorphism for messages modulo $n^d$.

Notes

source: folklore: the claim carried no citation on the page it was migrated from, and none was invented.

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:

• No citation (Damgard-Jurik missing).
• The relation between the d-th variant and base DCR (which implies which) is never stated.
• d-th-composite-residuosity has no page.