PCS ⇔ Vector commitments

PCS is equivalent to Vector commitments.

Statement

Migrated verbatim from polynomial-commitment § Other results:

• Polynomial commitments are equivalent to vector commitments with position-binding under certain reductions — 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.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• ‘under certain reductions’ is an untypeable hedge — the reduction class is exactly what the target model needs and the page refuses to name it.
• ‘vector commitment’ has no page (dangling object).
• Uncited, ’— standard’ label on a non-obvious equivalence.