The Weil Pairing, and Its Efficient Calculation
By Victor S. Miller. Journal of Cryptology, 2004
651 citations recorded by the source corpus.
Subfields: Artificial Intelligence, Geometry and Topology, Information Systems
View Paper: https://www.semanticscholar.org/paper/ec4c62fe581cd1ba4e6ba2ed165a148b745f1a4c
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In Artificial Intelligence
- Brent Waters
- Dan Boneh
- Xavier Boyen
- Allison Bishop
- David Mandell Freeman
- Craig Gentry
- Amit Sahai
- Alfred J. Menezes
In Geometry and Topology
- Brent Waters
- David Mandell Freeman
- Xavier Boyen
- Koray Karabina
- Dan Boneh
- Edlyn Teske
- Eu-Jin Goh
- Frederik Vercauteren
In Information Systems
- Brent Waters
- Xavier Boyen
- Dan Boneh
- Allison Bishop
- David Mandell Freeman
- Alfred J. Menezes
- Hovav Shacham
- Amit Sahai
Citations in the corpus
- A Taxonomy of Pairing-Friendly Elliptic Curves (2010, methodology): “The standard Miller algorithm for computing pairings [62] works by a double-and-add iteration on the bits of the prime subgroup order r.”
- Short Signatures from the Weil Pairing (2001, background): “(iv) Computable: for all R1, R2 ∈ E[p], the pairing e(R1, R2) can be computed in polynomial time [39].”
- Anonymous Hierarchical Identity-Based Encryption (Without Random Oracles) (2006, background): “Recall that a pairing is an efficiently computable [25], non-degenerate function, e : G×Ĝ → GT , with the bilinearity property that e(g, ĝ) = e(g, ĝ) .”
- Short Signatures Without Random Oracles and the SDH Assumption in Bilinear Groups (2008, methodology): “On algebraic curves in particular, these are very efficiently computable using an algorithm proposed in 1986 by Miller [34].”
- Direct chosen ciphertext security from identity-based techniques (2005, positive): “It also increases the decryption burden by an amount of work comparable to a pairing computation (the public test depends on the computation of a ratio of two pairings, which, in the case of the Weil and Tate pairings can be done almost as efficiently as a single pairing, by modifying Miller’s algor”
- Pairing-Based Cryptography at High Security Levels (2005, methodology): “According to Proposition 8 of [37] (see also [12]), the Weil pairing ê(P,Q) is given by the formula (−1)nP (Q) FQ(P ) , P 6= Q,”
- Faster Explicit Formulas for Computing Pairings over Ordinary Curves (2011, methodology): “Miller’s Algorithm [18,19] employs arithmetic in Fp12 during the accumulation steps (lines 3,5,11-12 in Algorithm 1) and at the final exponentiation (line 13 in the same algorithm).”
- Optimal Pairings (2010, methodology): “All fast algorithms to compute the Weil and Tate pairings on (hyper)elliptic curves are based on Miller’s algorithm [22], [23].”
- Evaluating 2-DNF Formulas on Ciphertexts (2005, background): “The modified Weil pairing on the curve [25, 22, 4, 26] gives a bilinear map e : G×G→ G1 with the required properties.”