Implementing the Tate Pairing

By Steven D. Galbraith, Keith A. Harrison, David Soldera. International Workshop on Ant Colony Optimization and Swarm Intelligence, 2002

588 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Geometry and Topology, Information Systems

View Paper: https://www.semanticscholar.org/paper/05c95ae28e83da76d4b98919274912d9708aae23

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Citations in the corpus

A One Round Protocol for Tripartite Diffie–Hellman (2000, background): “Of course, in that case, speed is of the essence and recent results show that it is possible to improve upon Miller’s algorithm by using numerous tricks (see [13] and [4]).”
Scalable Zero Knowledge Via Cycles of Elliptic Curves (2014, methodology): “In short, after breaking a pairing into its twomain parts, the Miller loop and the final exponentiation, and implementing both (using optimal pairings [110] and other methods [57,63,91]), they apply precomputation techniques to the verification key [27,53,95] and share subcomputations of the Miller ”
Multipurpose Identity-Based Signcryption (A Swiss Army Knife for Identity-Based Cryptography) (2003, methodology): “It is based on an elliptic-curve implementation of the BDH parameter generator G, which we describe following [2,14] as recently generalized in [6].”
Certificateless Public Key Cryptography (2003, unknown): “We refer to [2, 3, 6, 7, 9, 15, 17, 18] for a more comprehensive description of how these groups, pairings and other parameters should be selected in practice for efficiency and security.”
Public Key Encryption with Conjunctive Field Keyword Search (2004, methodology): “We can make the bilinear map using the Weil pairing or the Tate pairing [1, 5, 6 , 8]. In the pairings, the group G1 is a subgroup of the additive group of points of an elliptic curve.”
Improved Identity-Based Signcryption (2005, background): “From the de nitions of Ch1, CG1, Ch2 and CG2 above it is lear that Pr[Ch1 ^ CG1℄ = qs qs + qd 1 qs(q2 + qs) = 1 (qs + qd)(q2 + qs) and (11) Pr[Ch2 ^ CG2℄ = qd qs + qd 1 qd(q2 + qs) = 1 (qs + qd)(q2 + qs) : (12) Note that we are assuming a worst ase s enario here i.”
Identity-Based Encryption from the Weil Pairing (2001, methodology): “We note that both encryption and decryption in FullIdent can be made faster by using the Tate pairing on elliptic curves rather than the Weil pairing [ 19 , 1].”
Optimal Pairings (2010, background): “Since then a large number of papers [2], [3], [7], [13], [15]–[17], [20], [21], [26]–[29] have incrementally improved efficiency, interspersed with the occasional jumps caused by fundamentally new approaches.”
The Eta Pairing Revisited (2006, background): “A second useful property [12] is that can be replaced by any integer such that , i.e., .”
Efficient pairing computation on supersingular Abelian varieties (2007, methodology): “One very important property of the reduced pairing is the following [15].”
Identity based authenticated key agreement protocols from pairings (2003, background): “They are the Weil pairing [MOV93,Si94] and a modified version [Ve01,BF01], and the Tate pairing [FMR99, Ga01, GHSo02 ].”
Enhanced Privacy ID from Bilinear Pairing for Hardware Authentication and Attestation (2010, methodology): “We first review the description of an admissible bilinear map [5, 31 , 36] from the Tate pairing.”