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Powered Tate Pairing Computation
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2008 . In this paper, we introduce a powered Tate pairing on a supersingular elliptic curve that has the same shortened loop as the modified Tate pairing using the eta pairing approach by Barreto et al.
Bo Gyeong Kang, Je Hong Park
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Efficient Hardware for the Tate Pairing Calculation in Characteristic Three [PDF]
Lecture Notes in Computer Science, 2005 In this paper the benefits of implementation of the Tate pairing computation in dedicated hardware are discussed. The main observation lies in the fact that arithmetic architectures in the extension field GF(3^6m) are good candidates for parallelization,
T Kerins, Paulo S L M Barreto
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Faster computation of the Tate pairing [PDF]
Journal of Number Theory, 2009 International audienceText. This paper proposes new explicit formulas for the doubling and addition steps in Miller's algorithm to compute the Tate pairing on elliptic curves in Weierstrass and in Edwards form. For Edwards curves the formulas come from a
Lange, Tanja +15 more
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The yoga of the Cassels–Tate pairing [PDF]
LMS Journal of Computation and Mathematics, 2010 Cassels has described a pairing on the 2-Selmer group of an elliptic curve which shares some properties with the Cassels–Tate pairing. In this article, we prove that the two pairings are the same.
Michael Stoll +2 more
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Implementing the Tate Pairing [PDF]
, 2002 The Tate pairing has found several new applications in cryptography. This paper provides methods to quickly compute the Tate pairing, and hence enables efficient implementation of these cryptosystems.
Keith Harrison +5 more
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On binary quartics and the Cassels-Tate pairing
Research in Number Theory, 2022 We use the invariant theory of binary quartics to give a new formula for the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve. Unlike earlier methods, our formula does not require us to solve any conics.
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The Tate Pairing via Elliptic Nets [PDF]
, 2006 We derive a new algorithm for computing the Tate pairing on an elliptic curve over a finite field. The algorithm uses a generalisation of elliptic divisibility sequences known as elliptic nets, which are maps from Z^n to a ring that satisfy a certain ...
Katherine E. Stange +1 more
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Computing the Cassels-Tate Pairing for Jacobian Varieties of Genus Two Curves
, 2021 Let J be the Jacobian variety of a genus two curve defined over a number field K. The main focus of this thesis is on computing the Cassels-Tate pairing on the 2-Selmer group of J.
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The Cassels-Tate pairing on polarized abelian varieties [PDF]
The Annals of Mathematics, 1999 . Let (A, λ) be a principally polarized abelian variety defined over a global field k, and letX(A) be its Shafarevich–Tate group. LetX(A)nd denote the quotient ofX(A) by its maximal divisible subgroup.
Michael Stoll +3 more
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FPGA implementations of elliptic curve cryptography and Tate pairing over a binary field
Journal of Systems Architecture, 2008 Elliptic curve cryptography (ECC) and Tate pairing are two new types of public-key cryptographic schemes that become popular in recent years. ECC offers a smaller key size compared to traditional methods without sacrificing security level.
Dijiang Huang
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