# 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. 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

I will list two disadvantages that come to mind.

1. A bilinear accumulator requires a public parameter which is linear in size, which means you need to have an upper bound on the number of data elements you would commit to the accumulator. The RSA accumulator requires a public parameter which is constant-sized.

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 $$O(N)$$.

• update cost in rsa dynamic accumulator is O(1). Am i right?
– jhdm
Apr 1 '20 at 9:21
• Yes, that is correct. Apr 13 '20 at 6:13
• if i cancel 5 certificate, so what is the corresponding verification cost. How can i calculate it
– jhdm
Apr 18 '20 at 14:41
• For example if i have five revoked certificate, what is the corresponding value of verification cost?
– jhdm
Apr 18 '20 at 14:49
• verification cost is also o(1) or o(n) for rsa accumulator?
– jhdm
Apr 19 '20 at 16:43