Questions tagged [bilinear-pairing]

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48 views

pairings and clifford algebra connection

Pairing notation seems to suggest that bilinear pairings could be related to Clifford Algebra (ie: Geometric Algebra); and we only have an odd choice of notation that hides this fact. For example, if ...
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1answer
233 views

What is a function on a Line or a Curve?

I am reading up on Pairings using Elliptic curves & all the texts talk about functions on a Curve. I am finding it difficult to even figure out what they mean by "function on a curve" or ...
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20 views

Can I map a message M to a target group of bilinear pairs

Consider a bilinear pairing $e(G_1,G_2)=G_T$, let $G_1,G_2,G_T$ be multiplicative cyclic groups of order p. If I have a message $m$, can I map $m$ to $G_T$, and encrypt $m$ as $m \times G_T$?
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0answers
41 views

Multiplication of pairings vs. exponentiation of the group elements

Assume that we have a pairing as $e:G_1\times G_2\rightarrow G_T$. such that $g_1$ and $g_2$ are the generator of $G_1$ and $G_2$ respectively. In a protocol I have $A=\prod_{i=1}^n e(H(i),pk_i)$ ...
3
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1answer
81 views

Strong Diffie Hellman in bilinear groups

The $n$-strong Diffie Hellman assumption state that given the subset $\{g, g^s,\cdots,g^{s^n}\} \subseteq \mathbb{G}$ in a cyclic group $\mathbb{G}$ of prime order $p$, a PPT algorithm cannot output $...
4
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1answer
156 views

Elliptic curve bilinear pairing parameters for 80-bit security level

I am reading a paper based on elliptic curve bilinear pairing groups. The author has defined the size of private key, public key etc in terms of $|\mathbb{G}_1|, |\mathbb{G}_2|$ and $|\mathbb{G}_T|$. ...
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0answers
38 views

What's the difference between Optimal ate pairing and R-ate pairing?

I compare the algorithm description of Optimal ate pairing and R-ate pairing, it turns out to me that the formulas are the same. So I'm a little confused, what's the difference between them? or is it ...
3
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0answers
47 views

Decisional Diffie-Hellman Assumption on Pairing Friendly Curves

It is known that the Decision Diffie-Hellman (DDH) problem can be easily solved over groups on pairing friendly curves (that is: one can use pairing to tell if $g^x$ and $g^y$ and $g^z$ forms a DH ...
2
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0answers
78 views

Cryptographic invariant maps

In [BGK+18] in section 4, Boneh et al. write that: For any choice of ideal classes $\mathfrak{a}_1,\dots,\mathfrak{a}_n,\mathfrak{a}_1',\dots,\mathfrak{a}_n'$ in ${Cl}(\mathcal{O})$, the abelian ...
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98 views

The security level on BN254 and BLS381

Does BLS12-381 still provide 128bits security level? How about BN12-254? 112bits? Is there any references about the security level on pairing?
3
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1answer
264 views

Is this pairing-based signature scheme secure?

There are a number of signature schemes on small domains based on bilinear pairings which do not use random oracles. Examples are the Boneh-Boyen schemes and an interesting one from Okamoto which ...