No reduction from HE to CCA Security

A reduction of class unstated from HE to CCA Security would imply a contradiction.

Statement

Migrated verbatim from homomorphic-encryption § Security:

A homomorphic encryption scheme is IND-CPA secure if the standard PKE semantic security game is satisfied: no efficient adversary can distinguish $\mathsf{Enc}(\mathsf{pk},m_0)$ from $\mathsf{Enc}(\mathsf{pk},m_1)$ for any $m_0,m_1$. (CCA security is incompatible with homomorphism.)

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:

• Parenthetical claim ‘(CCA security is incompatible with homomorphism.)’ is a genuine barrier statement with no citation and no folklore label, violating the citation policy in CLAUDE.md.
• Imprecise: the incompatibility is with full IND-CCA2 and unrestricted homomorphism; HE can be IND-CCA1, and targeted/controlled-malleable CCA notions exist. Report only.