Structured Reference String (SRS) ¶
Let \(e\) be a bilinear map pairing groups \(G, G_t\) of prime order \(p\). Assume \(g \in G\) is a generator, and \(D\) sets an upper bound on the polynomials degrees which we would like to support commitments to.
The structured reference string (SRS) consists of encodings in \(G\) of all powers of a random nonzero field element \(\tau \in F_p\). Here, \(\tau\) is an integer randomly selected from the range \(\{1, . . . , p−1\}\). The elements constituting the SRS are \((g, g^{\tau} , g^{\tau^2} , ... , g^{\tau^D})\).
It is noteworthy that the value \(\tau\) is toxic waste that must be discarded because it can be used to destroy binding and break the integrity of commitments.