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

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How to multiply two field elements generated by bilinear paring map? [on hold]

I wish to clarify how to multiply two field elements generated by bilinear paring map.Β The following is an example where I need to multiply e1 and e2. is it possible? If yes, then how? FieldElement ...
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Type of values that can be accumulated in bilinear map (multiplicative) accumulator reg.

Is there any restriction that the members to be accumulated in bilinear map (multiplicative) accumulator need to be relatively prime to P? Where P is the order of group.
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Is it an example of bilinear pairing?

Consider a bilinear pairing $e: G_1 \times G_2 \rightarrow G_T$. Let's assume, $G_1 = G_2 = G_T = (\mathbb{Z}_n,+)$, i.e. additive group of integer modulo $n$ and $e(x,y) = xy$ mod $n$. Isn't it an ...
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45 views

What is more efficient, pairing based cryptography or non pairing based cryptography? [closed]

As far as I know non pairing pairing based cryptography is less time consuming than pairing based because, pairing based uses complex operations. Are there any advantages of pairing based cryptography ...
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140 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 ...
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410 views

Blockwise Montgomery multiplication

I have to implement a 256*256 bit Montgomery multiplier for pairing computations. The straightforward approach is to use a bit-serial version, but I would like to utilize the built-in 64*64 bits ...
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75 views

Decryption of message in IBE without random oracle using bilinear pairig reg

I find the following IBE scheme from the videos posted and i don't understand the decryption algorithm, will any one please elaborate the 6th step scheme Setup($\lambda$) : $(\mathbb{G}, ...
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90 views

How to compute accumulated values in bilinear map accumulators

How to compute $ g^{1/(e_1+s)}$, where $g$ is the generator of group $\mathbb G$, and $e_1$ and $s$ are keys? I know only $s$ and $g^{e_1}$, not $e_1$. $\mathbb G$ has prime order for some prime $p$ ...
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127 views

security proof in pairing based cryptography

Let : $G_{0}$ and $G_{1}$ be two multiplicative cyclic groups of prime order $p$. $g$ is a generator of $G_{0}$ and $e$ is a bilinear map, $e : G0 Γ— G0 β†’ G1.$ $𝐢_{1} = 𝑔^{𝛽𝑠_{1}} $, $ 𝐢_{2} = ...
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Anyone familiar with domain of hash functions in bilinear pairing based system?

I need a clarification regarding domain of hash functions. I have defined a bilinear pairing based system as follows: Let G1 and G2 be cyclic multiplicative groups of prime order p generated by g1 ...
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Bilinear pairing arithmetic - cryptographic accumulators

For calculating accumulated values for set of elements chosen randomly from say $ { e_1 ,e_2,...e_n}\varepsilon X $ we use the formula $acc= g^{f(e,s)}$ where $ f(e,s)= (e_1+s)(e_2+s).....(e_n+s)$ ...
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Type 1 pairings and encoding function from $\mathbb G_T$ to $\mathbb G$

Let $e : \mathbb G \times \mathbb G \to \mathbb G_T$ be a Type 1 bilinear pairing. Is it possible to define an encoding function $E : \mathbb G_T \to \mathbb G$? If so, how could this encoding ...
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188 views

Given $g^a, g^b, g^c, g^{1/b}$, is it hard to distinguish $e(g, g)^{abc}$ from a random value?

where $g$ is a group element in bilinear group $\mathbb{G}$. I understand it is very similar to the conventional DBDH problem, but $g^{1/b}$ is also known, possibly making it easier? Does anyone know ...
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69 views

Bilinear pairing arithmetic

Is this $e(g^x,g^yH^z) = e(g^x,g^y)e(g^x,H^z)$ expression is true? where $ g$ is the generator and $ H \in G $
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59 views

Bilinear map + commitment

Let $\mathbb{G}_1,\mathbb{G}_2,\mathbb{G}_T$ be yclic group of the same order and $ e: \mathbb{G}_1 \times \mathbb{G}_2\rightarrow \mathbb{G}_T$, such that $u\in \mathbb{G}_1, g \in \mathbb{G}_2, ...
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security of pairing based cryptography

while going through some papers on cryptographic accumulators i find the following statement "several pairing-based accumulators have been proposed in the past. However, due to continuous and recent ...
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4k views

Simple example for CP-ABE (Ciphertext policy attribute-based encryption)

I'm currently working on Ciphertext Policy Attribute-Based Encryption (CP-ABE). So far I'm only using it with a basic understanding how it actually works. Now I want to understand it a bit better, but ...
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Are there any asymmetric composite order group bilinear pairings?

Are there any asymmetric composite order group bilinear pairings? Is there a drawback of asymmetric over symmetric bilinear pairings of composite order either in efficiency or in security ?
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104 views

Hardness of problem related to bilinear pairings

Let $e: \mathbb G_1 \times \mathbb G_1 \rightarrow \mathbb G_T$ be an efficient bilinear pairing. Note that the pairing is symmetric (i.e., Type 1). The problem is, given $g \in \mathbb G_1$ and ...
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Are Barreto-Naehrig Curves suitable for pairing-based cryptography?

If Barreto-Naehrig Curves are suitable for pairing-based cryptography, can I use the library available at Optimal ATE Pairing?
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Generating cyclic group for Ciphertext-Policy Attribute-Based Encryption [closed]

I am doing Project under the topic CP-ABE.I need to generate a symmetric bilinear group Go of prime order p and with generator g...Then how to choose random elements from Zp....kindly anyone help ...
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74 views

Hardness assumptions on composite order bilinear groups [closed]

I am not at all knowledgeable in elliptic curve cryptography. So, here lies a couple of questions that I failed to find answers for to my satisfaction. Is there any known Type-III bilinear pairing ...
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when do we need composite order groups for bilinear maps and when prime order?

Why we need bilinear groups of composite order? What's the special security property of the composite order group in comparison with one of prime order?To put it in another way when do we need ...
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why $e(g,g)^N=1$ in bilinear pairings holds?

I can't get the point of prime order bilinear pairings:$\mathbb{G}\times\mathbb{G}\rightarrow\mathbb{G}_T$,$g=$ generator of $\mathbb{G}$ , $N=p*q$, $p$ and $q$ primes and $e(g,g)^N=1$. why ...
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Group description in pairing based cryptography

Suppose we have a public key encryption scheme, in which public parameter contains $(p, G, G_t, e, g)$, where $p$ is prime number, $G$ is a (cyclic) group of prime order, $e:G \times G \mapsto G_t$. ...
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120 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 ...
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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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78 views

Symmetric vs non-symmetric pairing based crypto

I am trying to find a comparison of how different pairing-friendly elliptic curves perform (in terms of security) in real world applications; I am using PBC library, and it has type A curves and type ...
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Help in uderstanding NIZKPoK notation (and how to code it) needed

Hello fellow cryptographers I have a rather silly question for you; I am aware of how Schnorrs NIZKPoK / SoK works when someone must prove knowledge about DL: y = g^x; (and how to code it) RFC ...
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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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108 views

Generic group model: use of polynomials in the proof of the master theorem

I've been looking at the paper of Boneh, Boyen, Goh Hierarchical Identity Based Encryption with Constant Size Ciphertext which contains a general theorem (Theorem A.2) about the advantage of an ...
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56 views

Does the following linear equation hold in bilinear pairings:

Does the following hold in bilinear pairings: $$e(g^{a_1x_1}g^{a_2x_2},g^{c_1}g^{c_2})=e(g^{x_1+x_2},g^{a_1a_2(c_1+c_2)})$$
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Need: Fast bulk signature verification followed by fast non-interactive multisignature aggregation

Q: Is there an efficient way to batch-verify signatures (e.g. some may be incorrect) and then non-interactively aggregate the correct ones into a multisignature (they are of the same message) such ...
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112 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"). ...
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linear computations over bilinear pairings

Does this hold in asymetric bilinear pairings? $e(x_1,x_2)e(x_3,x_4) = e(x_1x_3,x_2x_4)$, where $x_1,x_3 \in \mathbb{G}_1$ and $x_2,x_4 \in \mathbb{G}_2$ for a bilinear pairing $e$
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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 ...
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pairing-based schemes

some authors claimed that computational performance of a pairing-fee scheme (based on scalar multiplication over an elliptic curve group) is about 1000% more efficient than a pairing based one I would ...
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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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110 views

Simplification of a pairing

The paper Expressive, Efficient, and Revocable Data Access Control for Multi-Authority Cloud Storage contains the following simplification: $$e(C_i,\text{GPK}_{uid})\cdot e(D_i, ...
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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) ...
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455 views

Smart Card Basics

I want to implement some of the basic encryption algorithms on smart card, could any body guide me how to program a smart card, which tools (hardware and software) I should have, and if these tools ...
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74 views

Pairing Field size as security parameter

I have read Pairings for cryptographers: It states that the groups $G_1$ and $G_2$ are groups of points on the curve and the group GT is a subgroup of the multiplicative group of a related finite ...
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in Bilinear pairings, what is the difference between Type 2 and Type 3?

in Bilinear pairings, what is the difference between Type 2 and Type 3? I understand in Type 2, there exists an efficiently computable homomorphic function $\phi : G_2 \rightarrow G_1$ , which is not ...
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Is pairing based cryptography ready for productive use?

I'm currently testing one among those many interesting cryptographic protocols based on bilinear maps. It's quite hard to understand the underlying fundamentals, especially since there are several ...
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Pairings in Identity-based encryption vs. Attribute-based encryption

The bilinear map in Identity-based encryption should satisfy $e(aP,bQ)=e(P,Q)^{a\cdot b}$ whereas Attribute-based encryption schemes use $e(P^a,Q^a)=e(P,Q)^{a\cdot b}$ with $a,b\in\mathbb{Z}_p$ and ...
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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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Weil pairing implementation - low level programming language

I'm just started to studying elliptic curve cryptosystems. My one month-goal is to write a simple signature system based on the Weil-pairing. Some parts of it can be written without deeper ...
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Sextic twist of BN pairing parameters vs security

I've previously asked questions on BN pairing parameters. Here's one more. In the BN construction, one is working in a subgroup of a curve over an extension field $\mathbf{F}_{p^{12}}$ for some ...
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Sextic twist optimization of BN pairing - cubic root extraction required?

I found the following paper really interesting: http://www.researchgate.net/publication/220378229_A_family_of_implementation-friendly_BN_elliptic_curves/file/79e4150b3a773beecd.pdf It allows ...
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Why is a simple hash into $G_2$ for (certain) pairing based crypto not possible?

In the paper Pairings for Cryptographers we read about what the authors call a type 2 pairing in which we have a "pairing friendly curve $E$ over $\mathbb{F}_q$ with embedding degree $k>1$ and ...