# 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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### Frobenius Map on BN Curve sextic twist?

I'm new to cryptography and I am working on R-ate Pairings on a BN Curve: $y^2=x^3+b$ with $b$=5 with its M-type twist: $y^2=x^3+b\beta$, and $\beta^2 = -2$. The base finite field characteristic ...
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### BN-Curves for 256-bit symmetric security

I'm just studying the purpose of BN-Curves and I am interested in a setting for a 256-Bit security. So could you tell or link me to any information about this? are BN-Curves efficient for this ...
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### How can I plot graphs of CP-ABE scheme using charm crypto?

Can I use charm crypto tool to run it over my datasets for CPABE scheme and plot graphs using its Benchmarking tool ? Or, how can I use Charm Crypto tool with CPABE toolkit ?
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### Proof of a key agreement protocol based on bilinear pairings

I'm currently trying to understand a proof of a protocol of the paper of Liqun Chen and Caroline Kudla entitled "Identity Based Authenticated Key Agreement Protocols from Pairings". You can find a ...
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### Pairing - Is it possible to map two $r$-torsion points to a $r^2$-torsion point?

Let $E(\mathbb F_{q^k})$ be an elliptic curve on finite field $\mathbb F_{q^k}$, where $\mathbb F_{q^k}$ is an extension of $\mathbb F_q$ with $k>1$. Let $e: G_1 \times G_2 \rightarrow G_t$ be a ...
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### Order of target group in pairing

Let $N=pq$, where $p$ and $q$ are prime numbers, and order of $G_1$ and $G_2$ is equal to $p$. Suppose that $e(G_1, G_2)=G_t$ is a pairing of composite order. I know that, usually the order of target ...
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### Order of target group in bilinear pairing

Consider a bilinear pairing $e:G_1×G_2→G_T$, and $p^2q^2$ be the order of $G_1$ and $G_2$, where $p$ and $q$ are prime integers. Suppose that $g_1$ and $g_2$ are generators of $G_1$ and $G_2$ ...
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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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### 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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### Multiplication vs exponentiation in pairing based cryptography

$$P\in G_1$$$$Q\in G_1$$ $$a,b \in Z_q$$ $G_1$ isadditive cyclic group of prime order $q$ $$e(P^{a+b},Q)------(1)$$ $$e(aP+bP,Q)----(2)$$ (1) and (2) will give the same pairing result ...
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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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### Can I use computational diffie hellman problem in the following scheme?

Suppose $$X=mnrP , Y=\frac{1}{n}Q, R=e(P,Q)^m$$ $X,Y,P,Q$ are randomly chosen from $G_1$.And only $X,Y$ is given in public. $m,n,r$ are randomly chosen from $Z_q$. Anybody who knows $(1/r)$ can ...
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### Table of Curve Paramters

I'm studying Elliptic Cruve Cryptograhpy. When I do a search on Google of ECC, I find some pdf where I see these curve's paramters: $q, h, r, exp1, exp2$. What are these parameters ? Are there tables (...
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### How is it decided if $G_1$ and $G_2$ are two “additive” or “multiplicative” cyclic groups?

According to wiki's definition of Bilinear pairing… Let $G_1$ and $G_2$ be two additive cyclic groups of prime order $q$, and $G_T$ another cyclic group of order $q$ written multiplicatively. A ...
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### Choice of bilinear group for implementation of BLS signature with NIWI proof?

I am trying to sign the multiple (millions of) different readings but the receiver should not be able to link multiple signed readings together (unlinkability) or with the identity of the signer (...
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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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### Do I need to prove this?

I am using ABE scheme that has already proven under BDHE assumption. Here is the scheme https://eprint.iacr.org/2008/290.pdf In the key generation algorithm, I want to tie the user secret key ...
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### Why the group order has to be prime for pairing-based cryptography [duplicate]

I'm trying to get into pairing-based cryptography and I don't see why the group order of the group G in the pairing function e:G*G-> G_t has to be a prime number. I don't find an argument why ...
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### Sextic twist maps to q Eigenspace of Frobenius

Let $E(p)$ be a Barretto-Naehrig elliptic curve with r-torsion and embedding degree 12 and $E'$ a sextic twist with homomorphism $\psi$. How to show, that $E'$ has a unique r-torsion group $\psi$ ...
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### Are the values of Tate and Ate pairing the same?

Assume we have a Baretto Naehrig curve over $GF(p)$ and a field extension $GF(p^{12})$ given by a minimum polynomial. Let $G \in GF(p)$ and $Q \in GF(p^{12})$ from the trace 0 subgroup. Do then the ...
### In bilinear pairings, is it possible to let someone be only able to decrypt ciphertexts in $G_1$ but not able to decrypt the ciphertexts in $G$?
For example, in Don Boneh et al.'s paper "Evaluating 2-DNF Formulas on Ciphertexts", they gave an encryption system that the cihpertext can be in either $G$ (when only additional homomorphic ...