Questions tagged [pairings]

Pairing-based cryptography uses bilinear maps to create a gap group that allows efficient constructions of certain primitives.

52 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
4
votes
0answers
91 views

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 ...
4
votes
0answers
201 views

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 ...
3
votes
0answers
31 views

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 ...
3
votes
0answers
65 views

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 ...
3
votes
0answers
90 views

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 ...
3
votes
0answers
187 views

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 ...
3
votes
0answers
234 views

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 ...
3
votes
0answers
94 views

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 ...
2
votes
0answers
60 views

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 ...
2
votes
0answers
43 views

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 ...
2
votes
0answers
76 views

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 ...
2
votes
0answers
373 views

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 ...
2
votes
0answers
215 views

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 ...
2
votes
0answers
173 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 ...
2
votes
0answers
256 views

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 ...
2
votes
0answers
49 views

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 ...
2
votes
0answers
219 views

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 ...
2
votes
0answers
61 views

Construct points with the same discrete logarithm

Assume we have an elliptic curve $E$ with a Tate (or Ate,...) pairing $G_1 \times G_2 \mapsto G_T$ Now the task is to find $g_1, g_1' \in G_1$ and $g_2, g_2' \in G_2$ such that the discrete logarithm $...
2
votes
0answers
195 views

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 ...
2
votes
0answers
349 views

Type G Bilinear Pairings

I was reading PBC and its implementations for finding pairing parameters. I am particularly interested in implementing a BLS signature scheme with 20-byte (160-bit) signatures ("short signatures"). So,...
2
votes
0answers
206 views

Hardware Implementation of Pairing over BN curves

I am in the middle of FPGA based Hardware architecture design for the computation of Pairing (particularly R-ate Pairing) over BN curves. Where, the point addition, and point doubling should be ...
2
votes
0answers
142 views

Type 2 to Type 1 pairing transformation - why not considered?

How come that in various articles about pairings I never saw anybody mention that there is a possibility to turn Type 2 pairing into Type 1 by setting $e' : G_2 \times G_2 \rightarrow \mu, (P,Q) \...
2
votes
0answers
84 views

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 ...
2
votes
0answers
140 views

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 ...
1
vote
0answers
111 views

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 $\F_{q^r}$. ...
1
vote
0answers
104 views

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 $, ...
1
vote
0answers
15 views

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 ...
1
vote
0answers
54 views

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 ...
1
vote
0answers
38 views

Can the precompiles in Byzantium for pairings be used for implementation of BGLS verification?

BGLS [1] 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 ...
1
vote
0answers
53 views

Complexity lower bound in Uber-Assumption family

I try to wrap my head around calculating of complexity lower bound using Corollary 1 from The Uber-Assumption Family by X.Boyen (http://www.academia.edu/download/30698012/...
1
vote
0answers
43 views

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 ...
1
vote
0answers
94 views

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(...
1
vote
0answers
54 views

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?...
1
vote
0answers
313 views

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 ...
1
vote
0answers
159 views

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 ...
1
vote
0answers
107 views

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 ...
1
vote
0answers
248 views

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 ...
1
vote
0answers
236 views

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 ...
1
vote
0answers
142 views

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 ...
1
vote
1answer
976 views

Variant of the Decisional Bilinear Diffie Hellman problem

I am working on a cryptographic scheme and I need to rely on the following problem, which I have nicknamed the "Hybrid Decisional Bilinear Diffie Hellman (hDBDH)" problem: Let $e: \mathbb G_1 \...
0
votes
0answers
26 views

BN curves in Charm crypto library

I'm using Charm to implement a scheme and I know it has "SS512", "MNT159" and "prime192v1". I don't know if Charm includes BN curve? If it doesn't, how to implement it with Charm.
0
votes
0answers
27 views

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 ...
0
votes
0answers
44 views

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 ...
0
votes
0answers
19 views

What is the difference between these pairings classifications?

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 ...
0
votes
0answers
45 views

Prove that a given signature scheme is secure under random message attacks

This is a follow up to my previous question. Consider the following signature scheme: $\operatorname{KeyGen} (1^k$) : On input of a security parameter $k$, choose a symmetric bilinear group with $...
0
votes
0answers
37 views

Prove that a signature scheme is RUF-NMA and not EUF-CMA

I am working on the following exercise: Now, assume the following signature scheme: $\operatorname{KeyGen} (1^k$) : On input of a security parameter $k$, choose a symmetric bilinear group with ...
0
votes
1answer
87 views

How to change the following commitment scheme to Pedersen commitment?

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. ...
0
votes
0answers
15 views

Are compressed pairings used for Barreto-Naehrig curves in practice?

In 2009 Galbraith and Lin wrote the article "Computing Pairings Using x-Coordinates Only" https://link.springer.com/article/10.1007/s10623-008-9233-3, where they proposed to compute pairings on ...
0
votes
0answers
96 views

NIST ECC Curves without pairings

NIST FIPS.186-4 has standardized 5 ECC curves on field $\mathbb{F}_p$ (P-192, P-224, P-256, P-384, P-521) and 10 elliptic curves on binary fields. I need to use ECC curves without pairings for my ...
0
votes
0answers
82 views

Found weil pairing. Index Calculus method on the results of weil pairing

Consider Elliptic curve with p = 59, A = 1, B= 0, P = (25,30) and Q=(35,31). So I tried to solve this using MOV attack. The torsion point for them E[5] is R(-25,30i) where is sqroot -1 Chosen two ...