# 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 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 ...
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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, ...
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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-...
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### pairing teta function calculation

I am struggling with some pairing calculation techniques and i do not know how to approach them I would be glad if anyone can explain them in an easy way. For example i have these two formulas 1) ...
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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 ?
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### Are all MNT curves assumed to hold XDH?

For one of my projects, I need a pairing group which holds the External co-Diffie-Hellman assumption. I am trying to implement it using Charm crypto python modules which provides support for MNT ...
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### Security strength of JPBC Type A curve compared to SecP curve

I recently encountered some problems when learning about the JPBC library. Does the curve generated by (J)PBC using the method typeAcurvegenerator(160,512) and the ...
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### How do pairings behave on G2/twist points off the prime order subgroup?

$\newcommand{\F}{\mathbb{F}}$ Consider the ate pairing defined on a curve $G_1 = E(\F_q)$ and $G_2 = E'(\F_{q^r})$ where $E'$ is a twist of $E$ with the twisting isomorphism defined over $\F_{q^r}$. ...
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### Elliptic Curves for Pairings

how can is possible to know if an elliptic curve is suitable for protocols that adopt pairing? For example, in Certificateless Cryptography with pairing, is it possible to know if all elliptic curves ...
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### Is this an error in the Pinocchio Protocol paper

I am going through the Pinocchio protocol paper and I need 2 clarifications in the section Protocol 1 (Verifiable Computation from strong QAP). The part that explains the Verify process, which ...
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### How to apply lagrange interpolation on bilinear pairings?

I have seen in some places applications of Shamir secret sharing and lagrange interpolation mixed with bilinear pairings, however I fail to understand how this works. For instance, here I find the ...
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### Is there a bilinear map on a non abelian group or non cyclic group?

I've recently been studying a pairing map on cryptography. In usual definition, a pairing map is always defined on the cyclic group G. Is it possible to construct a bilinear map on a non-abelian group ...
In my question here Zero knowledge set membership protocol The suggested solution allows a prover to choose a commitment $C$. Then, A trusted third party ($T$) can validate if $C$ is valid or not. ...
Suppose $g$ is a pairing-friendly elliptic curve with subgroup generators $G_1$ and $G_2$. Suppose also that $M$ is the message I want to sign. Setup Compute $A = a \cdot G_1$ and $P = p \cdot G_2$, ...