# What is the Bilinear-map accumulator disadvantage

Bilinear-map accumulator [1] is more efficient than the RSA accumulator [2] but do you know any disadvantage for the bilinear-map accumulator when compared to RSA accumulator?

• I've added related articles. [1] is the source for Bilinear-map accumulator and [2] is the performance comparison article. – kelalaka Feb 3 '20 at 21:55
• @kelalaka verification cost is o(1) or o(n) for rsa accumulator? I am confusing about that. – jhdm Apr 20 '20 at 7:12

2. A bilinear accumulator does not allow dynamic updates. If you have an accumulated digest $$A = g_1^{\prod\limits_{i=1}^N (s+d_i)}\;\;\; (s = \text{ the trapdoor})$$ and need to insert a new element $$d$$, you would need to update the accumulated digest to $$A^{s+d} = A^s*A^d$$. But in order to compute $$A^s$$ without the trapdoor, you would need to know the coefficients of the polynomial $$f(X):=\prod\limits_{i=1}^N (X+d_i)$$. You would then compute the coefficients of $$Xf(X)$$ and use those to compute $$A^s$$. Thus, inserting a single element has a run time of $$O(N)$$.