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Under this formulation, the polynomial now encodes the vector, where <math>p(0)=x_0, p(1)=x_1, ...</math>. Let <math>p_0, p_1, ..., p_{n-1}</math> be the coefficients of <math>p</math>, such that <math display=inline>p(x)=\sum_{i=0}^{n-1} p_i x^i</math>. The commitment is calculated as
:<math>C=\sum_{i=0}^{n-1} p_i G t^i</math>
This is computed simply as a [[dot product]] between the predetermined values <math>G \cdot t^i</math> and the polynomial coefficients <math>p_i</math>. Since <math>\mathbb{G}_1</math> is an additive group with associativity and commutativity, <math>C</math> is equal to simply <math>G \cdot p(t)</math>, since all the additions and multiplications with <math>G</math> can be distributed out of the evaluation. Since the trapdoor value <math>t</math> is unknown, the commitment <math>C</math> is essentially the polynomial evaluated at a number known to no one, with the outcome obfuscated into an opaque element of <math>\mathbb{G}_1</math>.
====Reveal====
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