# 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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### Can cryptographically useful pairings only be used with elliptic curves?

As far as I understand one big advantage of ECC is that we can use pairings on the group of torsion points of the curve. I was wondering if it is possible to construct pairings from general finite ...
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### As a cryptographer, what are the things I should care about in my implementation of pairing functions?

As a beginner in cryptography, I do not know anything about different pairing types more than their names. So far, I know these names: Ate pairing, tate pairing, eta pairing, and r-ate pairing. I am ...
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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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### 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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### 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 ...
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### Pairings over elliptic curves on rings

Looking at this presentation, Boneh says that elliptic curves could be defined over $\mathbb{Z}/n\mathbb{Z}$ and not necessarily over a prime field $\mathbb{F}_p$ and hence we could define pairings ...
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### Prime extension field encoding ASN.1

ASN.1 encoding for elliptic curve cryptography is recommended by Certicom, as explained at a related question, covering curves over prime fields and binary extension fields. I'm looking for known ...
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### TypeA pairing, elliptic curves in pairing based cryptography

I am beginner to pairing-based cryptography. After downloading jpbc library, curve parameters files are seen as properties file. For example, for type A curve, following parameters are given. type a ...
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### Why does the new encryption scheme proposed by authors stop an adversary from guessing the subspace of the secret key?

In this paper, the authors construct an encryption scheme that is supposed to be resilient to tampering and leaking (as opposed to just leaking). Specifically this scheme: If you look at the ...
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### New Pairing Friendly Curves for SM9

A paper was presented at the INSCRYPT 2018 called: "Searching BN Curves for SM9" http://xxhb.fjnu.edu.cn/_upload/tpl/06/5d/1629/template1629/papers/88.pdf SM9 is a Chinese National Identity Based ...
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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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### Functional signatures with ECDSA Verifier

Functional signatures use some master key to create a functional signature key. The functional key can be used to sign messages, but only if the message is accepted by some predicate function. For ...
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### What pairings are used in PBC and charm-crypto with the proposed elliptic curves?

I'm implementing a pairing-based signature scheme using Charm Crypto and PBC, and I'm struggling to understand the relationship between the curves proposed for use with pairings and the pairings ...
192 views

### Frey-Rück Attack (FR-Reduction) - Tate Pairing

I am trying to understand the Frey-Rück attack and found different ways of a possible implementation. Since I am not yet very familiar with the Tate-Lichtenbaum pairing and the theory of divisors I ...
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### BLS signature choice of generator

Studying the bls signatures, I am wondering how in practice should we handle the parameter G. In many signatures scheme, the generator used is a well known constant, for example eddsa with ...
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### How to use maps in the Boneh Gentry Waters encryption scheme?

I am reading the source of pbc_bce library which implements the Boneh Gentry Waters broadcast encryption scheme. In this paper the authors use for their ...
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### Boneh/Franklin Identity based encryption with Tate pairing

Boneh/Franklin developed an identity based encryption scheme based on the Weil Pairing. This algorithm has also been standardised in IEEE P1363.3 . I know that this algorithm can also be implemented ...
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### For $e(g, d) = c$, can we compute $d$, given others

Given $$e(g, d) = c$$ where, $e$ is bilinear pairing function chosen by the user/attacker, the values of $g$ and $c$ are known $g, d ∈ \mathbb{G}_1$ , $c$ depends upon the $e$ can we somehow ...
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### BLS signatures in the G-valued Random Oracle Model

This paper on semi-generic algorithms considers "non-standard properties of the employed hash function". For BLS signatures whose main group is $G$, I'm curious what can be shown when the hash ...
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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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### 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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### Security of BLS under additional information on the secret key

Question A Is the BLS signature scheme still secure if an adversary in addition to the public key $pk = g_2 \, sk \in \mathbb{G}_2$ also obtains additional information on the private key $sk$, ...
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### The multi-linear maps are prone to zeroizing attack. Can anyone explain how the zeroizing attack breaks the computational assumptions?

I read that many cryptographic schemes based on multi-linear mapping are not secure because the zero testing procedure and zero encoding help an adversary to reveal the secrets and because of it, many ...
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### What should I change in my implementation to pass from a curve $y^2=x^3+1$ to $y^2=x^3+x$

I tried to change my implementation of pairing in curves $y^2 = x^3 + 1$ to use curves of the type $y^2 = x^3 + x$ but it didn't work. I thought the only thing I had to change in my code was the ...
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### Can the precompiles in Byzantium for pairings be used for implementation of BGLS verification?

BGLS  is an aggregate signature scheme by Boneh et al., that allows aggregation of BLS signatures on n different messages from n different signers. What I want to achieve is to verify such ...
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### Can someone give me an idea of active areas relating to pairing based cryptography, and what they involve?

Apologies if this isn't the place to ask this question. I'm an undergraduate math student and I've been reading about elliptic curves. I've learned about the Weil and Tate pairings as well as Miller's ...
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### Certificate Master Public Key with Pairing

I am currently working on CipherText Policy Attribute Based Encryption (CP-ABE) scheme. If we see the scheme, we can notice that the Authority may generate a Master Public Key and a Master Private Key(...
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### size of group points and parameters in pairing based cryptography

$$e:G_1\times G_1\rightarrow G_2$$ In symmetric pairing-based cryptography with groups$(G_1,G_2)$ of prime order $q$ and $a,b \in Z_q$Will the size of random generator $P$ from$G_1$ and $a$ be same?...
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### PBC library: group of composite order for pairing operation

How to generate composite order group using PBC library? With PBC library, element_init_G1(g,pairing) statement creates element $g$ for group of prime order. I want ...
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### What is the hardness in Decisional Linear Assumption (DLIN)?

I had understood what does the DLIN assumption means and here is a related question. But I fail to understand the 'real hardness' in this problem. I would be grateful if someone can help me to ...
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### DLOG in $\mathbb{F}_{p^n}^*$?

Assume that we are given an element $g\in \mathbb{F}_{p^n}^*$ and $g$ does not belong to any of the smaller subfields contained in $\mathbb{F}_{p^n}$. If the degree of $g$ is some number $q$, how much ...
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### A question about elliptic curves and finite fields in bilinear pairings

Based on what mentioned in the paper "Pairings For Cryptographers" http://www.sciencedirect.com/science/article/pii/S0166218X08000449 the two inputs of a pairing map are two members of two additive ...
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### Bilinear pairing

I am working on Efficient Construction of Pairings which are being realized by Miller's algorithm. In this algorithm the basic steps are point doubling and line function computation point addition ...
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### Why does computing g^a * g^{-a} with the PBC library result in zero?

My example code is as follows: /* * Example 1 * 1) Calculate g^a * 2) calculate g^{-a} * 3) multiply g^a * g^{-a} * */ Note: here ...
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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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### 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 ...
I know the basic definitions of bilinear groups. For example, there is a bilinear pairing that uses elliptic curves and has the following properties: For $G_1$, and $G_2$ are cyclic groups of prime ...