# 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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### Where can I find references to the theory behind PBC library?

I don't know if this is the right place to ask this type of question. Anyway, I'm using PBC library for a project, but I'm a very newbie for what concerns pairing based cryptography. Then I ask some ...
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### what is the non_residue value of BN462

I found an algorithm to find the frobenius coeffs here. Here, the non_residue of BLS12-381 is -1, And non_residue of BLS12-377 is written -5. How can I find this value? And what is the non_residue ...
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### Can I convert $F_{q^{12}}$ to $F_q$?

I seeing a paper about Elliptic curve based proxy re-encryption. And I want to implement this through BLS12-381 Curve. However, When looking at the documentation for paring or the library, the value ...
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### What is different between G1×G1→GT and G1×G2→GT in the bilinear pairing?

It is an implementation of the bls12-381 algorithm known as pairing-friendly, at GitHub. Looking at this, the pairing parameters are $G_1$ and $G_2$, $G_1$ is the point of $F_q$, $G_2$ is the point of ...
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### How to estimate the computation overhead of ECDSA?

I am using ECDSA as a digital signature scheme. Using Charm, I got the timing for the multiplication, exponentiation, and pairing operations; they take 0.005, 9, and 4.4 ms respectively. I want to ...
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### Fixed variable in Groth16

In the paper On the Size of Pairing-based Non-interactive Arguments by Jens Groth, it is always referred in the equations to satisfy that $a_0 = 1$ and the others $a_1, ..., a_m \in \mathbb{F}$. I am ...
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### Bilinear pairings with groups of safe prime order

I am looking for a curve with a bilinear pairing of safe prime order. I.e. a bilinear map $G \times G \rightarrow G_T$ where $|G| = p$, $p = 2q +1$, and $p,q$ are both prime. Is it feasible to find ...
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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 ...
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### What to learn in order to understand Weil Divisors

My current role as a software developer is leading into areas of research in elliptic-curve-cryptography that keeps bringing me back to bilinear pairings. This includes BLS Signatures, CL Signatures ...
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### Group Signatures with VLR Revocation Check

I was reading the paper by Boneh et al. Link. The scheme describes what is called a Verifier Local Revocation Technique. The Scheme assumes that a Revocation List [RL] allows each verifier to check ...
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### Accumulation of elements with a bilinear (pairing-based) accumulator

My question concerns accumulation of new elements in bilinear (pairing-based) accumulators. Suppose you have a pairing $e:\mathbb{G}_1\times \mathbb{G}_2 \longrightarrow \mathbb{G}_T$ with ...
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### Calculation of the order of the cosets used in defining the Tate Pairing

I'm working through Pairings for Beginners by Craig Costello, and am trying to understand the preamble to the Tate pairing. (See p. 70 ff., section 5.2 of of the PDF.). I'm having trouble following a ...
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### Pairing-free group based encryption scheme

Can someone explain what is a pairing-free group ? There is encryption schemes, for example 1, that qualify there proposed construction as pairing-free group. However, they use bilinear group in the ...
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### What's the difference between symmetric and asymmetic multilinear map?

In pairing-based cryptography, we have 3 types, namely Type-I, where $\mathbb{G}_1 = \mathbb{G}_2$, and in Type-II and Type-III we have that $\mathbb{G}_1 \neq \mathbb{G}_2$, however in Type-II we ...
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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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### Do Weil, Tate, and Ate pairings exist on all elliptic curves?

I don't know much about the math behind elliptic curves. Do Weil, Tate and Ate pairings exist on all elliptic curves? If the answer is negative, then what pairings do MNT, BN and SS curves have? ...
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### What does the number 256 in pairing curve BN256 indicate?

There are many pairing based elliptic curves like MNT curves, BN curves, SS curves etc., When we say BN256 curve, what does the number 256 indicate? Is it some group order or number of bits required ...
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### Is there a concept of embedding degree for non-pairing based elliptic curves?

From this post, I learned the concept of embedding degree. Intuitively, if embedding degree of an elliptic curve $E(F_p)$ is $k$, it means there is a way to transform points in $E(F_p)$ to $F_{p^k}$. ...
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### Does this equation hold in a bilinear map?

I would like to verify whether or not the following equation holds: $e(a,c)^{c1\cdot c2\cdot c3}e(b,c)^{c1\cdot c2\cdot c4}==e(a,c)^{c2\cdot c3}e(b,c)^{c1^2\cdot c2\cdot c4}$ for appropriately ...
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### If curve bn256/bls12 support the isomorphism from $G_2$ to $G_1$?

Is bn256 or bls12 a type-2 pairing-friendly curve? As Dan Boneh said here While in many pairing instantiations this ψ exists naturally, in some instantiations it does not. However I can not find ...
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### Are there any NIST curves with pairings?

NIST FIPS.186-4 has standardized 5 ECC curves on field 𝔽𝑝 (P-192, P-224, P-256, P-384, P-521) and 10 elliptic curves on binary fields. None of them seem to have pairings. Are there any standard ...
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