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Four-Dimensional Gallant-Lambert-Vanstone Scalar Multiplication
[chapter]

2012
*
Lecture Notes in Computer Science
*

The GLV method of

doi:10.1007/978-3-642-34961-4_43
fatcat:xevrjchidrc63dof2tw4aa4jde
*Gallant*,*Lambert*and*Vanstone*(CRYPTO 2001) computes any*multiple*kP of a point P of prime order n lying on an elliptic curve with a low-degree endomorphism Φ (called GLV curve) over ... We show in this work how to merge the two approaches in order to get, for twists of any GLV curve over F p 2 , a*four*-*dimensional*decomposition together with fast endomorphisms Φ, Ψ over F p 2 acting on ... Introduction The*Gallant*-*Lambert*-*Vanstone*(GLV) method is a generic approach to speed up the computation of*scalar**multiplication*on some elliptic curves defined over fields of large prime characteristic ...##
###
Four-Dimensional Gallant–Lambert–Vanstone Scalar Multiplication

2013
*
Journal of Cryptology
*

The GLV method of

doi:10.1007/s00145-012-9144-3
fatcat:v6z6u3oktvbopnaql2va65f6ky
*Gallant*,*Lambert*and*Vanstone*(CRYPTO 2001) computes any*multiple*kP of a point P of prime order n lying on an elliptic curve with a low-degree endomorphism Φ (called GLV curve) over ... We show in this work how to merge the two approaches in order to get, for twists of any GLV curve over F p 2 , a*four*-*dimensional*decomposition together with fast endomorphisms Φ, Ψ over F p 2 acting on ... Introduction The*Gallant*-*Lambert*-*Vanstone*(GLV) method is a generic approach to speed up the computation of*scalar**multiplication*on some elliptic curves defined over fields of large prime characteristic ...##
###
Four-Dimensional Gallant-Lambert-Vanstone Scalar Multiplication
[article]

2011
*
arXiv
*
pre-print

The GLV method of

arXiv:1106.5149v4
fatcat:uekdpnpl5ngdhmd5dr7msri7ti
*Gallant*,*Lambert*and*Vanstone*(CRYPTO 2001) computes any*multiple*$kP$ of a point $P$ of prime order $n$ lying on an elliptic curve with a low-degree endomorphism $\Phi$ (called GLV curve ... We show in this work how to merge the two approaches in order to get, for twists of any GLV curve over $\mathbb{F}_{p^2}$, a*four*-*dimensional*decomposition together with fast endomorphisms $\Phi, \Psi$ ... We have shown how to generalize the*Gallant*-*Lambert*-*Vanstone**scalar**multiplication*method by combining it with the Galbraith-Lin-Scott ideas, to perform a proven almost fourfold speedup on GLV curves over ...##
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Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians
[article]

2013
*
arXiv
*
pre-print

The first step in elliptic curve

arXiv:1310.5250v1
fatcat:rbtyzwrvgncbdaxdlpjeopsvaq
*scalar**multiplication*algorithms based on*scalar*decompositions using efficient endomorphisms-including*Gallant*-*Lambert*-*Vanstone*(GLV) and Galbraith-Lin-Scott (GLS)*multiplication*... The shorter the basis vectors, the shorter the decomposed*scalar*coefficients, and the faster the resulting*scalar**multiplication*. ... A spectacular (and easy) example of this phenomemon is*scalar**multiplication*with endomorphism decompositions, originally proposed by*Gallant*,*Lambert*, and*Vanstone*[10] . ...##
###
Analysis of the Gallant-Lambert-Vanstone Method Based on Efficient Endomorphisms: Elliptic and Hyperelliptic Curves
[chapter]

2003
*
Lecture Notes in Computer Science
*

In this work we analyse the GLV method of

doi:10.1007/3-540-36492-7_3
fatcat:e3u6kspg5zechpqr333nnwobby
*Gallant*,*Lambert*and*Vanstone*(CRYPTO 2001) which uses a fast endomorphism Φ with minimal polynomial X 2 + rX + s to compute any*multiple*kP of a point P of order ... The first one is a straightforward generalisation of the*Gallant*-*Lambert*-*Vanstone*arguments, which involve only lattice theory, to a higher*dimensional*setting (namely d ≤ 2g instead of 2 in the case of ...*Gallant*,*Lambert*and*Vanstone*then claim without proof that in fact M ≤ k √ n, for some constant k. 1 We overcome this omission in the next section. ...##
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Fast ECDH Key Exchange Using Twisted Edwards Curves with an Efficiently Computable Endomorphism

2019
*
2019 International Workshop on Secure Internet of Things (SIOT)
*

Our software uses a special class of elliptic curves, namely twisted Edwards curves with an efficiently computable endomorphism similar to that of the socalled

doi:10.1109/siot48044.2019.9637091
fatcat:r33vqmchc5e2nb6mg7st2tehgu
*Gallant*-*Lambert*-*Vanstone*(GLV) curves. ... A variable-base*scalar**multiplication*on curves over the 159 and 207-bit field takes about 2.63 and 4.84 million clock cycles, respectively, on an MSP430F1611 processor. ...*Gallant*-*Lambert*-*Vanstone*(GLV) Curves At Crypto 2001,*Gallant*et al [13] presented an ingenious method to accelerate*scalar**multiplication*on elliptic curves equipped with an endomorphism φ whose characteristic ...##
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Implementing the 4-dimensional GLV method on GLS elliptic curves with j-invariant 0

2011
*
Designs, Codes and Cryptography
*

The

doi:10.1007/s10623-011-9558-1
fatcat:mr7vyfxvzfdcnfl6vhunrmj5ju
*Gallant*-*Lambert*-*Vanstone*(GLV) method is a very efcient technique for accelerating point*multiplication*on elliptic curves with eciently computable endomorphisms. Galbraith, Lin and Scott (J. ... We show how to get the 4-*dimensional*GLV decomposition with proper decomposed coecients, and thus reduce the number of doublings for point*multiplication*on these curves to only a quarter. ... Introduction The fundamental operation in elliptic curve cryptography is point*multiplication*. In 2001,*Gallant*,*Lambert*, and*Vanstone*[10] described a new method (a.k.a. ...##
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Efficient four-dimensional GLV curve with high security
[article]

2018
*
IACR Cryptology ePrint Archive
*

We apply Smith's construction [9] to generate

dblp:journals/iacr/BernardDM18
fatcat:kycgpb5vbnenhpgdlzx65v53ii
*four*-*dimensional*GLV curves with fast arithmetic in the group law as well as in the base eld. ... As Costello and Longa did in [5] for a 128-bit security level, we obtained an interesting curve for fast GLV*scalar**multiplication*, providing a high level of security (254 bits). ... Introduction In ,*Gallant*,*Lambert*and*Vanstone*introduce in [6] a new method named GLV 1 , to compute the*scalar**multiplication*on certain elliptic curves. ...##
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Efficient Implementations of Four-Dimensional GLV-GLS Scalar Multiplication on 8-Bit, 16-Bit, and 32-Bit Microcontrollers

2018
*
Applied Sciences
*

In this paper, we present the first constant-time implementations of

doi:10.3390/app8060900
fatcat:46julxtp4re2hk2potlxkgbahy
*four*-*dimensional**Gallant*-*Lambert*-*Vanstone*and Galbraith-Lin-Scott (GLV-GLS)*scalar**multiplication*using curve Ted127-glv4 on 8-bit AVR ... In Asiacrypt 2012, Longa and Sica introduced the*four*-*dimensional*GLV-GLS*scalar**multiplication*, and they reported the implementation results on Intel processors. ... Figure 1 . 1 The implementation hierarchy of*four*-*dimensional**Gallant*-*Lambert*-*Vanstone*and Galbraith-Lin-Scott (GLV-GLS)*scalar**multiplication*. ...##
###
Four-Dimensional GLV via the Weil Restriction
[chapter]

2013
*
Lecture Notes in Computer Science
*

The

doi:10.1007/978-3-642-42033-7_5
fatcat:jwogx3nulrdllclugfaizkejxa
*Gallant*-*Lambert*-*Vanstone*(GLV) algorithm uses efficiently computable endomorphisms to accelerate the computation of*scalar**multiplication*of points on an abelian variety. ... This leads to a*four*-*dimensional*GLV method on Freeman and Satoh's Jacobians and on two new families of elliptic curves defined over F p 2 . ... Secondly, in 2001,*Gallant*,*Lambert*and*Vanstone*[11] introduced a method which uses endomorphisms on the elliptic curve to decompose the*scalar**multiplication*in a 2-*dimensional*multi-*multiplication*...##
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Four $$\mathbb {Q}$$ : Four-Dimensional Decompositions on a $$\mathbb {Q}$$ -curve over the Mersenne Prime
[chapter]

2015
*
Lecture Notes in Computer Science
*

At the highest arithmetic level, cryptographic

doi:10.1007/978-3-662-48797-6_10
fatcat:klbaptuq3rhfrmd6ymc424tgmq
*scalar**multiplications*on FourQ can use a*four*-*dimensional**Gallant*-*Lambert*-*Vanstone*decomposition to minimize the total number of elliptic curve group operations ... We show that this powerful combination facilitates*scalar**multiplications*that are significantly faster than all prior works. ... It uses the endomorphisms ψ and φ to accelerate*scalar**multiplications*via*four*-*dimensional**Gallant*-*Lambert*-*Vanstone*(GLV)-style [22] decompositions. ...##
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Efficient and Secure Algorithms for GLV-Based Scalar Multiplication and Their Implementation on GLV-GLS Curves
[chapter]

2014
*
Lecture Notes in Computer Science
*

We propose efficient algorithms and formulas that improve the performance of sidechannel protected

doi:10.1007/978-3-319-04852-9_1
fatcat:mvber7wazrcihetm33kw6jrowy
*scalar**multiplication*exploiting the*Gallant*-*Lambert*-*Vanstone*(CRYPTO 2001) and Galbraith-Lin-Scott (EUROCRYPT ... Finally, we showcase the efficiency of the proposed techniques by implementing a state-of-the-art GLV-GLS curve in twisted Edwards form defined over F p 2 , which supports a*four**dimensional*decomposition ... The*Gallant*-*Lambert*-*Vanstone*(GLV) method computes the*scalar**multiplication*kP as k 1 P + k 2 φ(P ) [15] . ...##
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Lambda Coordinates for Binary Elliptic Curves
[chapter]

2013
*
Lecture Notes in Computer Science
*

a protected single-core

doi:10.1007/978-3-642-40349-1_18
fatcat:pcbkh2a4brd7deerbwlsvya4ve
*scalar**multiplication*in 114,800 cycles. ... As a result, we improve speed records for protected/unprotected single/multi-core software implementations of random-point elliptic curve*scalar**multiplication*at the 128-bit security level. ... This record was recently broken in [34, 35, 12] , where the authors merged the GLS (Galbraith, Lin and Scott) and GLV (*Gallant*,*Lambert*and*Vanstone*) methods to achieve a 4-*dimensional*decomposition of ...##
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Families of fast elliptic curves from Q-curves
[article]

2013
*
arXiv
*
pre-print

We construct new families of elliptic curves over _p^2 with efficiently computable endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the same way as

arXiv:1305.5400v1
fatcat:xmruklhivbdppfn22ocwm4nwsm
*Gallant*-*Lambert*-*Vanstone*... Our construction is based on reducing -curves-curves over quadratic number fields without complex*multiplication*, but with isogenies to their Galois conjugates-modulo inert primes. ... The classic*Gallant*-*Lambert*-*Vanstone*(GLV) construction [13] . ...##
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Families of Fast Elliptic Curves from ℚ-curves
[chapter]

2013
*
Lecture Notes in Computer Science
*

We construct new families of elliptic curves over F p 2 with efficiently computable endomorphisms, which can be used to accelerate elliptic curvebased cryptosystems in the same way as

doi:10.1007/978-3-642-42033-7_4
fatcat:7crodbpsjfej3ej2vjhtwwg4ei
*Gallant*-*Lambert*-*Vanstone*... Our construction is based on reducing Q-curves-curves over quadratic number fields without complex*multiplication*, but with isogenies to their Galois conjugates-modulo inert primes. ... The classic*Gallant*-*Lambert*-*Vanstone*(GLV) construction [13] . ...
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