HIBE ⇒ IBE

HIBE implies IBE.

Statement

Migrated verbatim from hierarchical-identity-based-encryption § Hierarchical identity-based encryption:

A hierarchical identity-based encryption (HIBE) scheme extends IBE by organizing identities into a tree: an entity at depth $k$ holds an identity vector $\overrightarrow{id}=({id}_1,\dots ,{id}_k)$ where ${id}_1$ is the root domain and each subsequent component refines the identity. Any node can delegate a decryption key to any of its children without involvement of the root KGC. HIBE models real-world key delegation in organizations and DNS-style identity hierarchies.

Migrated verbatim from hierarchical-identity-based-encryption § Other results:

• HIBE strictly generalizes IBE: depth-1 hierarchies reduce to IBE (ignoring the $\mathsf{Delegate}$ algorithm)

Migrated verbatim from identity-based-encryption § Other results:

• IBE is generalized by HIBE, which adds a delegation algorithm allowing any identity to issue keys for its sub-identities

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.

This relation is stated on 3 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:

• Intro-paragraph claim: HIBE ‘extends’ IBE. No citation. Generalization direction is stated informally; the formal reduction (depth-1 HIBE = IBE) only appears in Other results line 79.
• No citation.
• ‘strictly generalizes’ additionally asserts a separation (IBE does not imply HIBE) which is neither cited nor stated as an open/known result.
• Mirror of the HIBE page line 79 bullet.