Schoenmakers’ Algorithm for Triple Scalar Multiplication
Efficient Scalar Multiplication by Isogeny Decompositions
... 6 Conclusion We have described a family of elliptic curve dened over a prime eld of large characteristic for which the multiplicationby 3 map, can be decomposed into the product of 2 isogenies. Explicit formulas indicate ...
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Faster implementation of scalar multiplication on Koblitz curves
... τNAF scalar multiplication ...the scalar multiplication operation for fixed, ran- dom and multiple ...point scalar multiplication in less than 10 5 clock cy- cles among all ...
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A Note on Scalar Multiplication Using Division Polynomials
... Net algorithm to compute scalar multiplication have three main ...the scalar. Hence this algorithm can resist side channel ...this algorithm should be improved compared to that ...
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Regular Ternary Algorithm for Scalar Multiplication on Elliptic Curves over Finite Fields of Characteristic Three
... ternary algorithm for scalar multiplication on elliptic curves over finite fields of characteristic ...a scalar to be multiplied. The cost per bit of this algorithm is lower than that ...
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Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians
... (GLS) multiplication, as well as higher-dimensional and higher-genus constructions—is to produce a short basis of a certain integer lattice involving the eigenvalues of the ...decomposed scalar ...
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High Performance Methods of Elliptic Curve Scalar Multiplication
... curve scalar multiplication using bi- nary, N AF , M OF and DRM algorithm require 23 , 21 , 25 and 24 respectively with respect to the number of operations, while the proposed algorithm/ ...
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New Fault Attack on Elliptic Curve Scalar Multiplication
... All these attacks (in contrast to ours) can be applied if only X -coordinate of the output point is available for analysis. 4 Fault Model Any fault attack depends on the specic implementation of target algorithm ...
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Scalar Multiplication on Koblitz Curves using Double Bases
... 5. V. S. Dimitrov, G. A. Jullien, and W. C. Miller. An algorithm for modular expo- nentiation. Information Processing Letters, 66(3):155–159, 1998. 6. R. P. Gallant, J. L. Lambert, and S. A. Vanstone. Faster Point ...
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Analysis of Multibase Scalar Point Multiplication Scheme in ECC
... springer algorithm for addition of points on elliptic curve is combined with multibase concept and set generation given in “on-the-fly multi-base recoding for ecc scalar multiplication without ...
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Four-Dimensional Gallant-Lambert-Vanstone Scalar Multiplication
... of scalar multiplication over prime fields is particularly difficult on modern multicore ...double-and-add algorithm from left to ...separate scalar multiplication with k i ...each ...
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Direct Exponent and Scalar Multiplication Classes of an MDS Matrix
... 2 Direct Exponent MDS Matrix Class In this section, we define a direct exponent MDS Matrix Class. We find out the number of MDS matrices in this class. We also have an example of direct exponent MDS Matrix Class in case ...
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GPU and ASIC Acceleration of Elliptic Curve Scalar Point Multiplication
... field multiplication algorithm be implemented using NVIDIA’s PTX low-level virtual machine language for several ...proposed algorithm, such as add-with- carry, and ...
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Using Random Digit Representation for Elliptic Curve Scalar Multiplication
... randomized algorithm will fail if it doesn’t provide a sufficiently large number of possible local internal states and transitions from that state, which will make these algorithms vulnerable to collision ...
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Optimizing scalar multiplication for koblitz curves using hybrid FPGAs
... a scalar multiple on a Koblitz curve the ability to calculate finite field inverses is a ...per scalar multi- ...inversion algorithm was used to perform field inversions, which is an algorithm ...
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Randomizing scalar multiplication using exact covering systems of congruences
... a 512-bit scalar multiplication. Regarding differential attacks, the built-in randomization of our algorithm may not necessitate such a large random factor r. The extra cost implied by integer ...
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Optimizing double-base elliptic-curve single-scalar multiplication
... The worst-case and average-case chain lengths produced by this double-base algorithm are difficult to analyze mathematically. However, the average chain length for all n’s can be estimated with high confidence as ...
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ACCELERATING THE SCALAR MULTIPLICATION ON GENUS 2 HYPERELLIPTIC CURVE CRYPTOSYSTEMS
... extended-Euclidean Algorithm for computing greatest common ...Euclidean algorithm has high computational cost and is hard to implement in ...for scalar multiplication on the Jacobian of low ...
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Fast and Regular Algorithms for Scalar Multiplication over Elliptic Curves
... the scalar multiplication which multiplies some point on an elliptic curve by some (usually secret) ...the scalar multiplication algorithm to be regular, namely to have an operation ...
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Scalar Multiplication on Koblitz Curves using $\tau^2-$NAF
... accelerating scalar multiplication for hardware designs [2–5, 7, ...the scalar was proposed to achieve fast scalar multiplication, which does point squaring instead of point ...τ−NAF ...
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Symmetric Digit Sets for Elliptic Curve Scalar Multiplication without Precomputation
... perform scalar multiplication on two classes of ordinary elliptic curves, namely E : y 2 = x 3 + Ax in prime charac- teristic p ≡ 1 mod 4, and E : y 2 = x 3 + B in prime characteristic p ≡ 1 mod ...the ...
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