# 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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### Why use pairing to construct identity based encryption?

Identity Based Encryption is an asymmetric encryption scheme such that encryption uses the receiver's identity as the public key. Such a identity can be receiver's email address or some other string ...
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### Multiplicities of poles of a divisor of a rational function w.r.t. an elliptic curve

I am reading Sec 5.8.2 in the textbook Introduction to Mathematical Cryptology (Hoffstein, Pipher and Silverman), a precursor to introducing the structure of Weil pairing. It first defines a rational ...
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### A doubt in pairing based cryptography

I have seen authors taking $G_1=G_2=G_T=G$ to be the same group of prime order $q$. What I know is that for pairing of type $$e:G_1\times G_2\rightarrow G_T,$$ size of the element in the target group ...
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### Two different bilinear mappings in PBC

In pairings-based cryptography, are there any examples of systems where they use two different bilinear mappings. That is, they make use of both $e_1$ and $e_2$ where $e_1$ is a symmetric bilinear ...
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### 'NIZK arguments for quadratic arithmetic programs' of '[Groth16] On the Size of Pairing-based Non-interactive Arguments'

I wonder about the CRS of NIZK argument. I think [A]$_1$, [B]$_2$, [C]$_1$ is calculated using CRS. Instead of calculating A, B, C first and then calculating [A]$_1$, [C]$_1$, [B]$_2$. May I know if ...
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### How to get the generator of composite order group in JPBC?

I have read some code, the generator of the additive group of prime order is easy to get because every element in the group is a generator.So in JPBC I just need to randomly generate elements as ...
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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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### 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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### How to prove possession of a CL signature in zero-knowledge?

Assume that we have the following signature scheme CL Signature: Choose two cyclic groups $G = \langle g \rangle$ and $G_T = \langle g_T \rangle$ of order $q$, that have a pairing $e$. Uniformly and ...
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### How to prove in zero-knowledge that the attributes of Pointcheval Sanders signature is the opening of a commitment?

In anonymous credentials schemes, it is possible to anonymously prove knowledge of a signature. Proposals for anonymous credentials with attributes also include a method for proving statements about ...
1 vote
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### Can you use ECDSA on pairing-friendly curves?

I'm learning about Elliptic curve cryptography. If I understand right, ECDSA and other algorithms used in ECC are dependent on the curve chosen. So, before you want to use ECDSA, you first have to ...
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### Is BBS+ 1. a multi-messages signing protocol or 2. a group signature signed by a member of a group anonymously?

There's no doubt that the BBS Signature was born from this classic Short Group Signature paper in 2004. It's capable of Zero-knowledge. In the paper, section 5, it describes how a member of a group, ...
1 vote
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### Importance of supersingularity of elliptic curves

I'm struggling to understand the high-level idea of "Verifiable Delay Functions from Supersingular Isogenies and Pairings" (https://eprint.iacr.org/2019/166.pdf) by De Feo et al. I will ...
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### Current situation of bilinear pairing protocols

The bilinear pairings are considered as the key enabler for many novel cryptographic protocols, such as three-party one round DH, shorter signatures and certificateless (ID-based) crypto , which ...
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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-...
1 vote
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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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### Bilinear Map over group of unknown order

Is it possible to build a bilinear map where the underlying group is of unknown order? To maintain context, the original question appears below. As per poncho's excellent answer, my original idea is ...
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### What are the BLS12-381 settings?

I can't find the exact type and settings for the BLS12-381 curve. Is this type-3 in Symmetric XDH settings ?