Fast scalar multiplication of degenerate divisors for hyperelliptic curve cryptosystems

2021 ◽  
Vol 404 ◽  
pp. 126239
Author(s):  
Zhi Hu ◽  
Dongdai Lin ◽  
Chang-An Zhao
Keyword(s):  
Hyperelliptic Curve ◽  
Scalar Multiplication

Implementation of an Elliptic Curve Scalar Multiplication Method Using Division Polynomials

2014 ◽  
Vol E97.A (1) ◽  
pp. 300-302 ◽  
Author(s):  
Naoki KANAYAMA ◽  
Yang LIU ◽  
Eiji OKAMOTO ◽  
Kazutaka SAITO ◽  
Tadanori TERUYA ◽  
...  
Keyword(s):  
Elliptic Curve ◽  
Scalar Multiplication ◽  
Division Polynomials ◽  
Elliptic Curve Scalar Multiplication

scholarly journals Dynamic Łukasiewicz logic and its application to immune system

2021 ◽  
Author(s):  
Antonio Di Nola ◽  
Revaz Grigolia ◽  
Nunu Mitskevich ◽  
Gaetano Vitale
Keyword(s):  
Immune System ◽  
Scalar Multiplication ◽  
Kripke Semantics ◽  
Łukasiewicz Logic ◽  
Lukasiewicz Logic ◽  
Regular Algebras

AbstractIt is introduced an immune dynamic n-valued Łukasiewicz logic $$ID{\L }_n$$ I D Ł n on the base of n-valued Łukasiewicz logic $${\L }_n$$ Ł n and corresponding to it immune dynamic $$MV_n$$ M V n -algebra ($$IDL_n$$ I D L n -algebra), $$1< n < \omega $$ 1 < n < ω , which are algebraic counterparts of the logic, that in turn represent two-sorted algebras $$(\mathcal {M}, \mathcal {R}, \Diamond )$$ ( M , R , ◊ ) that combine the varieties of $$MV_n$$ M V n -algebras $$\mathcal {M} = (M, \oplus , \odot , \sim , 0,1)$$ M = ( M , ⊕ , ⊙ , ∼ , 0 , 1 ) and regular algebras $$\mathcal {R} = (R,\cup , ;, ^*)$$ R = ( R , ∪ , ; , ∗ ) into a single finitely axiomatized variety resembling R-module with “scalar” multiplication $$\Diamond $$ ◊ . Kripke semantics is developed for immune dynamic Łukasiewicz logic $$ID{\L }_n$$ I D Ł n with application in immune system.

scholarly journals On Multi-Scalar Multiplication Algorithms for Register-Constrained Environments

Electronics ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 605
Author(s):  
Da-Zhi Sun ◽  
Ji-Dong Zhong ◽  
Hong-De Zhang ◽  
Xiang-Yu Guo
Keyword(s):  
Electronic Devices ◽  
Additive Group ◽  
Fixed Number ◽  
Scalar Multiplication ◽  
Computation Cost ◽  
Public Key Cryptosystems ◽  
Adaptive Window ◽  
Computation Efficiency ◽  
Window Method ◽  
Constrained Environments

A basic but expensive operation in the implementations of several famous public-key cryptosystems is the computation of the multi-scalar multiplication in a certain finite additive group defined by an elliptic curve. We propose an adaptive window method for the multi-scalar multiplication, which aims to balance the computation cost and the memory cost under register-constrained environments. That is, our method can maximize the computation efficiency of multi-scalar multiplication according to any small, fixed number of registers provided by electronic devices. We further demonstrate that our method is efficient when five registers are available. Our method is further studied in detail in the case where it is combined with the non-adjacent form (NAF) representation and the joint sparse form (JSF) representation. One efficiency result is that our method with the proposed improved NAF n-bit representation on average requires 209n/432 point additions. To the best of our knowledge, this efficiency result is optimal compared with those of similar methods using five registers. Unlike the previous window methods, which store all possible values in the window, our method stores those with comparatively high probabilities to reduce the number of required registers.

Improved authentication and computation of medical data transmission in the secure IoT using hyperelliptic curve cryptography

2021 ◽  
Author(s):  
B. Prasanalakshmi ◽  
K. Murugan ◽  
Karthik Srinivasan ◽  
S. Shridevi ◽  
Shermin Shamsudheen ◽  
...  
Keyword(s):  
Data Transmission ◽  
Hyperelliptic Curve ◽  
Medical Data ◽  
Hyperelliptic Curve Cryptography

scholarly journals THE HYPERELLIPTIC THETA MAP AND OSCULATING PROJECTIONS

2020 ◽  
pp. 1-23
Author(s):  
MICHELE BOLOGNESI ◽  
NÉSTOR FERNÁNDEZ VARGAS
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Hyperelliptic Curve ◽  
Geometric Description ◽  
Birational Model ◽  
Rank 2 ◽  
Semistable Vector Bundles ◽  
Ramification Locus

Abstract Let C be a hyperelliptic curve of genus $g \geq 3$ . In this paper, we give a new geometric description of the theta map for moduli spaces of rank 2 semistable vector bundles on C with trivial determinant. In order to do this, we describe a fibration of (a birational model of) the moduli space, whose fibers are GIT quotients $(\mathbb {P}^1)^{2g}//\text {PGL(2)}$ . Then, we identify the restriction of the theta map to these GIT quotients with some explicit degree 2 osculating projection. As a corollary of this construction, we obtain a birational inclusion of a fibration in Kummer $(g-1)$ -varieties over $\mathbb {P}^g$ inside the ramification locus of the theta map.

scholarly journals Two algebraic deformations of a K3 surface

1981 ◽  
Vol 82 ◽  
pp. 1-26
Author(s):  
Daniel Comenetz
Keyword(s):  
Hyperelliptic Curve ◽  
Double Cover ◽  
Rational Curves ◽  
K3 Surface ◽  
Quartic Surface ◽  
Quadric Cone ◽  
Birational Model ◽  
Affine Line ◽  
Characteristic 2 ◽  
General Member

Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3.

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