# Prove I know only $a$ in $P=aG+bH+cQ$

Given a pedersen commitment $$P$$, is it possible to show that I only know $$a$$ in $$P=aG + bH + cQ$$ in zero knowledge

• Are you asking how to prove that you don't know $b, c$? Zero knowledge proofs generally can't prove lack-of-knowledge... – poncho Jun 12 at 14:45
• @poncho you can know b, c. But the proof should only prove that you know a – WeCanBeFriends Jun 12 at 15:20
• Given $P$ I can pick $a$ arbitrarily and then I ‘know’ some $a$ such that $P = [a]G + [b]H + [c]Q$, assuming $P$, $G$, $H$, and $Q$ all live in the same subgroup. (Of course, I can't find $b$ and $c$ without computing discrete logs here.) So, proving this is vacuous. What are you really trying to do? – Squeamish Ossifrage Jun 12 at 15:27