Faster computation of the tate pairing

Author: dmoj

August undefined, 2024

WebAbstract. When performing a Tate pairing (or a derivative thereof) on an ordinary pairing-friendly elliptic curve, the computation can be looked at as having two stages, the Miller loop and the so-called ﬂnal exponentiation. As a result of good progress being made to reduce the Miller loop component of the algorithm (particularly with the discov- WebDownload BibTex. 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 …

Implementing the Tate pairing - HP Labs

WebThe Tate pairing on Edwards curves can be computed by using these functions in Miller’s algorithm. Computing the sum of two points or the double of a point and the … WebWe propose for the first time the computation of the Tate pairing on Jacobi intersection curves. For this, we use the geometric interpretation of the group law and the quadratic twist of Jacobi intersection curves to obtain a doubling step formula which is efficient but not competitive compared to the case of Weierstrass curves, Edwards curves and Jacobi … dehn\u0027s flowers and gifts

Faster computation of the Tate pairing - NASA/ADS

WebMiller’s algorithm to compute the Tate pairing. For Edwards curves the formulas come from a new way of seeing the arithmetic. We state the ﬁrst geometric interpretation of the … WebThis paper describes the design of a fast software library for the computation of the optimal ate pairing on a Barreto-Naehrig elliptic curve. Our library is able to compute the optimal ate pairing over a 254-bit prime field F p , in just 2.33 million of clock cycles on a single core of an Intel Core i7 2.8GHz processor, which implies that the ... WebIf the scalar a is a secret value the computation aP must not leak any information on ... a is a square in k and d is not a square in k then the denominators in the general addition formulas are never zero for any pair of ... Lange T, Naehrig M, Ritzenthaler C (2011) Faster computation of the Tate pairing. J Number Theory 131(5):842–857 ... fender blues jr tweed specs

Tate Pairing Computation on Jacobi’s Elliptic Curves

WebOur approach is generic, it is able to compute both Weil and Tate pairings on pairing-friendly Edwards curves of any embedding degree. Our analysis shows that the new algorithm is faster than the ... WebWe show how these faster formulas can be applied to Tate and ate pairing variants, thereby speeding up all practical suggestions for efficient pairing implementations over … fender blues deville tweed soundWebThe Tate pairing on Edwards curves can be computed by using these functions in Miller's algorithm. Computing the sum of two points or the double of a point and the coefficients … dehn\\u0027s flowers \\u0026 greenhouses inc

"WebIonica and Joux [23] use a diﬀerent map to a curve of degree 3 and compute the 4-th power of the Tate pairing. The latter poses no problem for usage in protocols as long as all … " - Faster computation of the tate pairing

Faster computation of the tate pairing

CiteSeerX — Fast computation of Tate pairing on general …

WebDec 2, 2011 · Fast Parallel Computation of Tate Pairing Abstract: In pairing-based cryptography, Miller's algorithm plays a key role in the calculation of pairing. Currently, … WebThis paper proposes new explicit formulas for the doubling and addition step in Miller's algorithm to compute the Tate pairing. For Edwards curves the formulas come from a …

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WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): For the Tate pairing implementation over hyperelliptic curves, there is a development by DuursmaLee and Barreto et al., and those computations are focused on degenerate divisors. As divisors are not degenerate form in general, it is necessary to find algorithms on general divisors … WebUsing the geometric interpretation of the group law, we obtain the Miller function for Tate pairing computation on twisted Edwards curves. Then we present the explicit formulae for pairing computation on twisted Edwards curves. Our formulae for the doubling step are a little faster than that proposed by Arène et al.

WebThis provides a framework for converting Tate-like pairing computation formulas and operation counts to their ate-like analogues. For BN curves [8], Akane, Nogami, and Morikawa showed in [1] that the ate pairing itself can be computed on the twisted curve. Our result covers more general curves but computes the ate pairing only up to a power ... WebJun 13, 2024 · If we generalise the optimal ate pairings, Miller’s loop has the lower bound of r 1/ϕk and ultimately helps in faster computation .The optimal Ate and twisted optimal Ate pairing are faster than or as fast as the Tate pairing in any conditions. Hence, Ate pairing is the fastest pairing we have as of now.

WebSep 1, 2010 · The authors examine faster computation of Tate pairing on elliptic curves by using some efficiently computable endomorphism. Focused on two typical types of elliptic curves with even embedding ... WebIn 2002, Barreto et al. and Galbraith et al. provided new algorithms for the fast computation of the Tate pairing in characteristic three. In this paper, we give a closed formula for the Tate pairing on the hyperelliptic curve y2 = xp - x + d in characteristic p. This result improves the implementations in [BKLS02], [GHS02] for the special case ...

WebAn Analysis of Affine Coordinates for Pairing Computation, , Pairing 2010, Yamanaka Hot Spring, Ishikawa, Japan, 2010-12-13 ... Video abstract for the paper Faster computation of the Tate pairing with Christophe …

WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): This paper proposes new explicit formulas for the doubling and addition step in Miller’s algorithm to compute the Tate pairing. For Edwards curves the formulas come from a new way of seeing the arithmetic. We state the first geometric interpretation of the group law on … fender bluetooth headphonesWebMiller’s algorithm is at the heart of all pairing-based cryptosystems since it is used in the computation of pairing such as that of Weil or Tate and their variants. Most of the optimizations of this algorithm involve elliptic curves of particular forms, or curves with even embedding degree, or having an equation of a special form. fender bluetooth amplifierWebJul 28, 2010 · 0:00 / 3:39 Faster Computation of the Tate Pairing JournalNumberTheory 1.25K subscribers Subscribe Like Share 2.1K views 12 years ago Christophe Arene, *Tanja Lange, Michael … dehnung biceps femorisWebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): This paper proposes new explicit formulas for the doubling and addition steps in Miller’s algorithm to … fender blues harmonica fender bluetooth スピーカーWebMay 1, 2011 · 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 … dehn\u0027s flowers saratoga nyWebFaster Computation of the Tate Pairing Christophe Arene, Tanja Lange, Michael Naehrig, and Christophe Ritzenthaler Abstract This paper proposes new explicit formulas for the … fender blues junior nos lacquered tweed