Given two numbers $x_1$, $x_2$ and their respective binding numbers, $b_1$ and $b_2$, let's take their Pedersen Commitment to be $C(x_n, b_n)$ $\forall n=1,2$.
What is $C(x_1 * x_2, b_1 * b_2)$?
1 Answer
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Sort of related, we have the identity $$C(x_1*x_2,-b_1*b_2)=x_1C(x_2,b_2)-b_2C(x_1,b_1)=x_2C(x_1,b_1)-b_1C(x_2,b_2)$$ (note the similarity to the Diffie-Hellman identity) but in general we cannot compute a Pedersen commitment of the product of two numbers from their Pedersen commitments without knowledge of the hidden values.
