DLOG ⇒ PCS

DLOG implies PCS.

Statement

Migrated verbatim from polynomial-commitment:

A transparent polynomial commitment based on Pedersen commitments and a recursive inner-product argument. No trusted setup; no pairings needed.

• Proof size: $O(\log d)$
• Verification time: $O(d)$ (linear, but no pairing)
• Setup: Transparent
• Security: Discrete logarithm assumption

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:

• NO citation at all for this construction — content/References/‘BBB+18 - Bulletproofs Short Proofs for Confidential Transactions and More.md’ exists and is not cited.
• Hypotheses are split across prose and a bullet: ‘based on Pedersen commitments and a recursive inner-product argument’ (a construction path) plus ‘Security: Discrete logarithm assumption’.
• Composite in spirit: DLOG ⇒ Pedersen commitment ⇒ IPA-based PCS; the page states it as a single fact.