The Universal Accumulator paper mentions the following for updating non-membership witness upon member deletion.
Choose $r$ such that $a\hat x − rx ∈ Z$$2^l$
What is Z$2^l$ and how can we efficiently evaluate $r$?
I suppose we need to brute force search by guessing values of r, is there any room for optimization here? Perhaps by making an educated guess about the value of r.
Can it be that $a\hat x − rx$ can be construed as $a\hat x$ $mod x$? If yes, then we can find
$\hat a = a\hat x$ $modx$
$r = (a\hat x - \hat a)/x$
Am I right in assuming this?