How Pedersen Commitments Work

In Monero, Pedersen Commitments are a core component to hide transaction amounts while still allowing for cryptographic verification that no coins are created or destroyed in a transaction.

A Pedersen Commitment to a value v (the amount) with a random blinding factor r is:

C = v ⋅ H + r ⋅ G

C: The commitment

G, H: Generator points on the elliptic curve (with H unrelated to G)

v: The amount (hidden)

r: A random blinding factor (also hidden)

This commitment is:

Hiding: You can’t determine v from C without knowing r

Binding: You can't change v later without altering the commitment