Pairings for Cryptographers

By Steven D. Galbraith, Kenneth G. Paterson, Nigel P. Smart. IACR Cryptology ePrint Archive, 2008

921 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Information Systems

View Paper: https://www.semanticscholar.org/paper/64adfdd87ab5afb0d03147c6671321f5e8c53174

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Information Systems

Citations in the corpus

Short Signatures Without Random Oracles and the SDH Assumption in Bilinear Groups (2008, background): “However there are several cases, called type 3 groups [22], where this homomorphism is degenerate.”
Identity-based key agreement protocols from pairings (2017, methodology): “We also assume that in all cases one uses pairing friendly fields [15], which makes our estimates slightly better than those presented in [14].”
Short Randomizable Signatures (2016, background): “Galbraith, Paterson, and Smart [GPS08] deﬁned three types of pairings: in type 1, G 1 = G 2 ; in type 2, G 1 (cid:54) = G 2 but there exists an eﬃcient homomorphism φ : G 2 → G 1 , while no eﬃcient one exists in the other direction; in type 3, G 1 (cid:54) = G 2 and no eﬃciently computable homomorph”
Multi-signatures in the plain public-Key model and a general forking lemma (2006, background): “…and 6 · 160 bits, which is what is needed, in this asymmetric-with-isomorphism setting, to provide the 1024-bit RSA level of security achieved by 160-bit EC groups [18]. pairing-based BSL [13] short signature scheme, but our gain in veriﬁcation time (by a factor of 12-40) more than compensates.”
jPBC: Java pairing based cryptography (2011, background): “Different curves give different settings with different properties, see [8] for a complete survey on the pairing for cryptography.”
A Taxonomy of Pairing-Friendly Elliptic Curves (2010, background): “We outline in Table 1 our own view of the matter, distilled from material taken from various authoritative sources, in particular [37] and [54].”
Structure-Preserving Signatures and Commitments to Group Elements (2010, background): “[51] distinguish between 3 types of bilinear-group generators.”
Efficient Protocols for Set Membership and Range Proofs (2008, methodology): “Using parameters from Galbraith, Paterson, and Smart [14], we estimate that the size of G1 is 256 bits, the size of GT is 3072 bits and the size of Zp is upper-bounded by 256 bits.”
Forward and Backward Private Searchable Encryption from Constrained Cryptographic Primitives (2017, methodology): “For the bilinear maps, we used a Type-3 pairing ( cf. [GPS06]) on Barreto-Naehrig curves [BN06].”
DP5: A Private Presence Service (2015, background): “The Decisional Diffie-Hellman problem is assumed to be hard in each of these groups (so that a “type 3” pairing [18], without an efficiently computable isomorphism from G2 to G1 or the reverse, is in use), as well as the Co-DHP (aka Co-CDH) [5] problem for G1 and G2.”
On the Size of Pairing-Based Non-interactive Arguments (2016, methodology): “Since pairing-friendly elliptic curves can be constructed such that the group element representations are smaller in G 1 than in G 2 [GPS08] we choose to assign A and C to the ﬁrst source group and B to the second source group for maximal eﬃciency.”
Additive Combinatorics and Discrete Logarithm Based Range Protocols (2010, neutral): “Let us assume that rlen(GT ) ≈ 12 · rlen(G1) ≈ 12 · rlen(Zp) [14].”