# What does the $e$ operation mean in cryptography research papers?

I read a cryptography scheme that it include the following operation:

$$c= H(e(g_1,g_n)^t)$$ where H is a hash function. I need to know what the operation $$e$$ means.

• Actually, as far as I know, all articles have some explanation. Boneh et al's 2DNF explains very well. Evaluating 2-DNF Formulas on Ciphertexts. Where did you read? Sep 7, 2020 at 13:33

It's the pairing function. This bilinear map which takes as input an element from the set $$\mathbb{G}\times\hat{\mathbb{G}}$$ (in the common case, elliptic curves), and outputs a group element in $$\mathbb{G}_T$$, the target group.
In the symmetric case (Type 1), because $$e$$ is bilinear, you can deduce that $$e(g_1, g_n)^t= e(g, g)^{x_1x_nt}$$
with $$x_1,x_n$$ respectively the discrete logarithms of $$g_1, g_n$$ in base $$g$$.
• Could you please explain what exactly the bilinear map do in this computation if we suppose that e is a bilinear map $G$ X $G$ -> $G_T$ and $G , G_T$ are two cyclic groups of prime order p and g is a random generator for G Sep 7, 2020 at 13:42