Pairing-based cryptography uses bilinear maps to create a gap group that allows efficient constructions of certain primitives.

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Mapping points between elliptic curves and the integers

My primary question is: Is there an easy way to create a bijective mapping from points on an elliptic curve E (over a finite field) to the integers (desirably to $\mathbb{Z}^*_q$ where $q$ is the ...
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How to Mathematically Prove the Bilinear Pairing Properties [closed]

I am currently working on Bilinear Pairing.To start my work i need to find the mathematically prove of three properties of bilinear pairing. Let $ G_{1} $ and $ G_{T} $be a cyclic multiplicative ...
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Security of pairing-based cryptography over binary fields regarding new attacks

In the last week, the discrete logarithm problem was broken for the binary fields $\mathbb{F}_{2^{(14 \times 127)}}$ and $\mathbb{F}_{2^{(27 \times 73)}}$. Pairing-based cryptography using binary ...
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What is Identity-Based Encryption (IBE) and why is it “better”?

Most CS/Math undergrads run into the well-known RSA cryptosystem at some point. But about 10 years ago Boneh and Franklin introduced a practical Identity-Based Encryption system (IBE) that has ...
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Useful pairings for cryptography

I've recently looked a bit at pairing based cryptography and I was wondering what properties the groups involved should have in order to be useful for cryptographic purposes? Has anything more exact ...
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understanding pairing $e:G \times G \to G_T$ and ( Decision)BDH assumption

From DrLecter's comment, I know that DDH problem can be efficiently solved with this $$e(g^a,g^b)\stackrel{?}{=} e(g,g^z).$$ I have some trouble to understand this map $e:G \times G \to G_T$. Am I ...
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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 ...