# Questions tagged [pairings]

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

21 questions
1answer
2k views

### 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 ...
1answer
1k views

### Is pairing based cryptography ready for productive use?

I'm currently testing one among those many interesting cryptographic protocols based on bilinear maps. It's quite hard to understand the underlying fundamentals, especially since there are several ...
3answers
2k views

### When do we need composite order groups for bilinear maps and when prime order?

Why we need bilinear groups of composite order? What's the special security property of the composite order group in comparison with one of prime order? To put it in another way when do we need ...
1answer
707 views

### Discrete logs on elliptic curve with embedding degree 3 with the 'MOV' attack

The curve $E(\mathbb{F}_{47}):y^2=x^3+x+38$ has order $61$ and $61|47^3-1$ so the embedding degree of $E$ is $3$ and therefore the MOV attack, presumably using some sort of distortion map and a ...
3answers
8k views

### 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 ...
1answer
173 views

### the decryptNode function for leaf nodes in CP-ABE

Can someone please explain to me why decryptNode gives as result $e(g,g)^rq(0)$ for leaf nodes, I don't understand how they went from the second step to the third (here is the article: Ciphertext-...
1answer
3k views

### 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 ...
1answer
561 views

### 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 ...
1answer
406 views

### Why is a simple hash into $G_2$ for (certain) pairing based crypto not possible?

In the paper Pairings for Cryptographers we read about what the authors call a type 2 pairing in which we have a "pairing friendly curve $E$ over $\mathbb{F}_q$ with embedding degree $k>1$ and ...
1answer
950 views

1answer
522 views

### How to calculate mapping in bilinear

I am trying to read a paper in cryptography. In key generation phase, paper give a definition for bilinear like G and Gt be two cyclic groups of prime order p $e: G * G \to G_t$. be a map with the ...
2answers
190 views

### DDH and pairings are not contradictory in RingCT 2.0?

As I know DDH assumption and bilinear pairings are contradictory, but I see this in a paper, RingCT 2.0. How could this be ok? Linkable ring signature will be attacked by bilinear pairings.
0answers
34 views

### Prove that a signature scheme is RUF-NMA and not EUF-CMA

I am working on the following exercise: Now, assume the following signature scheme: $\operatorname{KeyGen} (1^k$) : On input of a security parameter $k$, choose a symmetric bilinear group with ...