Insertion

As described in the Cryptographic Specification, insertions to the accumulator are easily achieved via an elliptic curve point multiplication and addition.

To replace a value (originally $w_i$) at index \(i\) with $v_i$:

$C_{\mathsf{new}}=C+L\cdot (v_i-w_i)$

where $$\begin{gathered} L=\mathsf{commit}(L_i,\mathsf{srs}{ \\ }_{\mathsf{g}}1) \end{gathered}$$

If only insertions are allowed, $w_i$ is by definition the nothing-up-my-sleeve value.