# Why pairing based crypto is suitable for some particular cryptographic primitives?

Why pairing based crypto is being widely used in some special crypto primitives as ID based crypto and variations of standard signatures? I mean taking as deep as possible what makes it suitable for that schemes while other schemes do not feet?

• What published literature have you looked at? Something like this should give you a good introduction. – mikeazo Aug 28 '12 at 14:23

Crypto based on cyclic groups is (at a very high level) about "hiding" things "in the exponent" and then manipulating those values as they live in the exponent. As an example, in a cyclic group $\langle g\rangle$, you can "hide" a random value $x$ as $g^x$.
Without a bilinear pairing, all you can really do "in the exponent" are linear/affine (degree-1) combinations of these hidden values. That is, given $g^{x_1}, \ldots, g^{x_n}$, you can obtain $g^{a_0 + a_1 x_1 + \cdots + a_n x_n}$ for known coefficients $a_i$.
• And taking this more deep what actually a bilinear pair is? I mean ok it's a mapping from two groups into another one. This mapping can be formulated as a non-linear function?What is this $e:GxG->G_1$ that all books describe?How i can more precisely formualte $e$? – curious Sep 24 '12 at 18:30
• Can you give me an example of a degree-2 combination? I.e given $g^{x_1}, \ldots ,g^{x_n}$ as a consequence of bilinearity i can have $g^{x_1 \ldots x_2}$ ? – curious Oct 26 '12 at 14:14