No reduction from IND-sHIBE-CPA Security (Selective) to IND-HIBE-CPA Security
A reduction of class unstated from IND-sHIBE-CPA Security (Selective) to IND-HIBE-CPA Security would imply a contradiction.
Statement
Migrated verbatim from hierarchical-identity-based-encryption:
In the selective variant, the adversary commits to the challenge identity before runs. The selective–adaptive separation is known to be strict for HIBE: there is no black-box complexity-leveraging argument that avoids an exponential loss in the depth .
Notes
source: folklore: the claim carried no citation on the page it was
migrated from, and none was invented.
Recorded during migration and not fixed — these are claims about the source text, not changes to it:
- NO CITATION and no folklore marker for a specific technical claim (‘the selective-adaptive separation is known to be STRICT for HIBE’). ‘is known to be’ asserts a published theorem while naming no paper.
- SUSPECTED MATH ERROR: it conflates two different statements — (a) selective and adaptive security are separated, and (b) complexity leveraging costs exponential-in-d. (b) is a statement about the cost of one particular technique, not a separation; (a) as stated (‘strict’) is much stronger than anything the sentence supports.
- Buried mid-page inside a security-definition subsection rather than in ’# Other results’.