# Questions tagged [pairings]

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

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### How to have a hash function that maps from a group element to a binary string of a certain size in charm-crypto?

I am facing a problem in programming with the charm-crypto library. The hash functions for pairing group elements in charm-crypto can only map from a string to a specific field: $\mathbb Z_r$, $G_1$ ...
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### Developments in ABE using Pairings

What are the recent developments in Attribute-Based Encryption (ABE) using Pairings assumptions? Is pairings the most viable assumption while designing ABE. What other assumptions are used for ABE ...
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### Multiplication of pairings vs. exponentiation of the group elements

Assume that we have a pairing as $e:G_1\times G_2\rightarrow G_T$. such that $g_1$ and $g_2$ are the generator of $G_1$ and $G_2$ respectively. In a protocol I have $A=\prod_{i=1}^n e(H(i),pk_i)$ ...
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### Exponentiation Problem of G2 in MNT curve

I made a simple python program in the Charm framework (https://github.com/JHUISI/charm): ...
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### issues understanding some basic points about identity based encryption

I've been trying to understand an article (https://ieeexplore.ieee.org/document/8538446) about using blockchain to overcome identity based encryption (ibe) drawbacks. My purpose is to be able to code ...
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### What's the difference between Optimal ate pairing and R-ate pairing?

I compare the algorithm description of Optimal ate pairing and R-ate pairing, it turns out to me that the formulas are the same. So I'm a little confused, what's the difference between them? or is it ...
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### Pairing-friendly curve whose group order is a safe prime

Are there any pairing-friendly curves whose group order is a safe prime? That is: the order of the group is $2q + 1$ for some prime number $q$. Or, is it impossible to have such groups?
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### Software implementation of symmetric and asymmetric bilinear pairings

I have recently read a paper about pairings, which only implemented asymmetric bilinear pairings and it mentiond that $\eta_{T}$ pairing is the most efficient algorithm for symmetric pairings. I ...
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### Chaining a smaller group inside the pairing friendly group

Let's say there is a bilinear pairing $G \times G \rightarrow G_t$ (e.g., for bn128), and let prime $q$ be the order of $G$. Is it possible to find a prime order group over integers such that its ...
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### Why do we use groups, rings and fields in cryptography?

I'm a student of Masters in Cyber Security. I have a habit to understand things from their first principles (at the very beginning). Kindly use any simple mathematical example to answer because I have ...
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### Sextic twist of BN pairing parameters vs security

I've previously asked questions on BN pairing parameters. Here's one more. In the BN construction, one is working in a subgroup of a curve over an extension field $\mathbf{F}_{p^{12}}$ for some ...
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### New Pairing Friendly Curves for SM9

A paper was presented at the INSCRYPT 2018 called: "Searching BN Curves for SM9 (Pay-Walled)" SM9 is a Chinese National Identity Based Cryptography Standard and was originally published using a 256-...
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### Understanding the groups used in bilinear Ate-pairing

The bilinear ate pairing $e:G_1\times G_2 \rightarrow G_T$ is defined over the following groups: \begin{equation} \begin{aligned} & G_1 = E(\mathbb{F}_p)[r] \cap Ker(\pi_p-), \\ & G_2 = E(...
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### Groth-Sahai Proof of multi-exponentiation

I want to create a NIZK proof of a multi-exponentiation via Groth-Sahai proofs. In the lectures of Jens Groth in a winter school of Bar-Ilan University, he shows a way to transform multi-...
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### Is the k-sum attack efficient in bilinear pairing variants?

From the k-sum definition, the objective is to solve something like: $\sum_{i=1}^n c_i = v_1$ where $v_1$ is known. If we use Elliptic Curve Points ($C_i$ and $G$) we can define a bilinear pairing ...
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### Can BLS aggregate signatures be merged?

In some non-interactive, pairing-friendly signature scheme, such as BLS12-381, is it possible to merge partially-overlapping aggregate signatures? For example, say you have two aggregate signatures, \$...
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### Pair-friendly elliptic curves vs non friendly

Group law operations on pair-friendly elliptic curves are slower than in non friendly elliptic curves, but how much slower? Can't seem to find a performance comparison between the two for a given ...