Linear secret sharing schemes (LSSS) ⇔ MSP
Linear secret sharing schemes (LSSS) is equivalent to MSP.
Statement
Migrated verbatim from secret-sharing:
A secret sharing scheme is linear if the shares are linear functions of the secret and randomness. Equivalent to monotone span programs over .
Migrated verbatim from secret-sharing § Other results:
- LSSS is equivalent to monotone span programs, which characterize the class of access structures realizable by linear schemes — standard
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 2 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:
- Uncited equivalence; duplicates the ’# Other results’ bullet on line 65 (which carries the ’— standard’ folklore label).
- Neither ‘linear-secret-sharing-scheme’ nor ‘monotone-span-program’ has a page.
- Uncited, carries the ’— standard’ folklore label; duplicates line 57.
- Neither object has a page.
- The second clause (‘which characterize the class of access structures realizable by linear schemes’) is a separate characterization claim bundled in.